Finite Group Databasebeta

← #32166241

Subgroups — #32166241

Order 18176.

2598 conjugacy classes of subgroups.

The subgroup lattice has 1542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986551C211yesmaximal, characteristic, complemented
2C2×#117×D71C211yesmaximal, characteristic
3#22592059C211yesmaximal, characteristic, complemented
4#22592057C211yesmaximal, characteristic, complemented
5#22592052C211yesmaximal, characteristic, complemented
6#22592050C211yesmaximal, characteristic, complemented
7#22592037C211yesmaximal, characteristic, complemented
8#22592035C211yesmaximal, characteristic, complemented
9#22592030C211yesmaximal, characteristic, complemented
10#22592028C211yesmaximal, characteristic, complemented
11#22592018C211yesmaximal, characteristic, complemented
12#22592016C211yesmaximal, characteristic, complemented
13#22592010C211yesmaximal, characteristic, complemented
14#22592008C211yesmaximal, characteristic
15#22592005C211yesmaximal, characteristic
16#22592004C211yesmaximal, characteristic
17#22592003C211yesmaximal, characteristic
18#22591617C211yesmaximal, characteristic, complemented
19#22591617C211yesmaximal, characteristic, complemented
20#22591613C211yesmaximal, characteristic, complemented
21#22591611C211yesmaximal, characteristic, complemented
22#22590878C211yesmaximal, characteristic, complemented
23#22590874C211yesmaximal, characteristic, complemented
24#22590874C211yesmaximal, characteristic, complemented
25#22590870C211yesmaximal, characteristic, complemented
26#22590819C211yesmaximal, characteristic, complemented
27#22590819C211yesmaximal, characteristic, complemented
28#22590742C211yesmaximal, characteristic, complemented
29#22590720C211yesmaximal, characteristic
30C2×#17985846C211yesmaximal, characteristic
31C71×#2438C211yesmaximal, characteristic, complemented
32C23×C4×D71C2211yescharacteristic
33#17986551—28no—
34C2×#14556127C2211yescharacteristic, complemented
35C2×#14556126C2211yescharacteristic, complemented
36C2×#14556118C2211yescharacteristic, complemented
37C2×#14556118C2211yescharacteristic, complemented
38C2×#14556108C2211yescharacteristic
39C2×#14556107C2211yescharacteristic
40C2×#14556106C2211yescharacteristic
41C2×#14556106C2211yescharacteristic
42C2×#14556105C2211yescharacteristic
43C2×#14556105C2211yescharacteristic
44C2×#14556104C2211yescharacteristic
45C2×Q8×Dic71C2211yescharacteristic, complemented
46C2×#14556093C2211yescharacteristic, complemented
47C2×#14556093C2211yescharacteristic, complemented
48C2×#14556093C2211yescharacteristic, complemented
49C2×#14556087C2211yescharacteristic
50C2×#14556086C2211yescharacteristic
51C2×#14556086C2211yescharacteristic
52C2×#14556085C2211yescharacteristic
53C2×#14556085C2211yescharacteristic
54C2×#14556084C2211yescharacteristic
55C2×#14556084C2211yescharacteristic
56C2×#14556084C2211yescharacteristic
57C2×#14556084C2211yescharacteristic
58#117×D71—28no—
59C2×C4⋊C4×D71C2211yescharacteristic
60C2×C4⋊C4×D71C2211yescharacteristic
61C22×(C2×D71)⋊C4C2211yescharacteristic
62C22×(C2×D71)⋊C4C2211yescharacteristic
63C2×C22⋊C4×D71C2211yescharacteristic
64C2×C22⋊C4×D71C2211yescharacteristic
65C22×C4×Dic71C2211yescharacteristic
66C22×C4×Dic71C2211yescharacteristic
67C2×C42×D71C2211yescharacteristic
68C2×C42×D71C2211yescharacteristic
69#17985941C2211yescharacteristic, complemented
70#17985941C2211yescharacteristic, complemented
71#17985938C2211yescharacteristic, complemented
72#17985936C2211yescharacteristic
73#17985934C2211yescharacteristic
74#17985934C2211yescharacteristic
75#17985934C2211yescharacteristic
76#17985933C2211yescharacteristic, complemented
77#17985933C2211yescharacteristic, complemented
78#17985932C2211yescharacteristic, complemented
79#17985932C2211yescharacteristic, complemented
80#17985931C2211yescharacteristic, complemented
81#17985931C2211yescharacteristic, complemented
82#17985923C2211yescharacteristic
83#17985923C2211yescharacteristic
84#17985921C2211yescharacteristic
85#17985921C2211yescharacteristic
86#17985921C2211yescharacteristic
87#17985921C2211yescharacteristic
88#17985921C2211yescharacteristic
89#17985921C2211yescharacteristic
90#17985920C2211yescharacteristic, complemented
91#17985920C2211yescharacteristic, complemented
92#17985919C2211yescharacteristic, complemented
93#17985912C2211yescharacteristic
94#17985912C2211yescharacteristic
95#17985912C2211yescharacteristic
96#17985910C2211yescharacteristic
97#17985905C2211yescharacteristic, complemented
98#17985903C2211yescharacteristic, complemented
99#17985903C2211yescharacteristic, complemented
100#17985897C2211yescharacteristic, complemented
101#17985896C2211yescharacteristic, complemented
102#17985896C2211yescharacteristic, complemented
103#17985896C2211yescharacteristic, complemented
104#17985896C2211yescharacteristic, complemented
105#17985896C2211yescharacteristic, complemented
106#17985896C2211yescharacteristic, complemented
107#17985894C2211yescharacteristic, complemented
108#17985894C2211yescharacteristic, complemented
109#17985894C2211yescharacteristic, complemented
110#17985894C2211yescharacteristic, complemented
111#17985886C2211yescharacteristic, complemented
112#17985886C2211yescharacteristic, complemented
113#17985883C2211yescharacteristic, complemented
114#17985883C2211yescharacteristic, complemented
115#17985882C2211yescharacteristic, complemented
116#17985882C2211yescharacteristic, complemented
117#17985874C2211yescharacteristic
118#17985874C2211yescharacteristic
119#17985873C2211yescharacteristic
120#17985873C2211yescharacteristic
121#17985873C2211yescharacteristic
122#17985873C2211yescharacteristic
123#17985872C2211yescharacteristic
124#17985872C2211yescharacteristic
125#17985871C2211yescharacteristic
126#17985871C2211yescharacteristic
127#17985870C2211yescharacteristic
128#17985870C2211yescharacteristic
129#17985870C2211yescharacteristic
130#17985870C2211yescharacteristic
131#17985868C2211yescharacteristic, complemented
132#17985868C2211yescharacteristic, complemented
133#17985863C2211yescharacteristic, complemented
134#17985863C2211yescharacteristic, complemented
135#17985862C2211yescharacteristic
136#17985859C2211yescharacteristic
137#17985858C2211yescharacteristic
138#17985858C2211yescharacteristic
139#17985858C2211yescharacteristic
140#17985858C2211yescharacteristic
141#17985858C2211yescharacteristic
142#17985858C2211yescharacteristic
143#17985857C2211yescharacteristic
144#17985857C2211yescharacteristic
145#17985856C2211yescharacteristic
146#17985856C2211yescharacteristic
147#17985854C2211yescharacteristic
148#17985854C2211yescharacteristic
149C4⋊C4×Dic71C2211yescharacteristic, complemented
150C4⋊C4×Dic71C2211yescharacteristic, complemented
151C4⋊C4×Dic71C2211yescharacteristic, complemented
152C4⋊C4×Dic71C2211yescharacteristic, complemented
153C4⋊C4×Dic71C2211yescharacteristic, complemented
154C4⋊C4×Dic71C2211yescharacteristic, complemented
155#17985850C2211yescharacteristic, complemented
156#17985850C2211yescharacteristic, complemented
157#17985850C2211yescharacteristic, complemented
158#17985850C2211yescharacteristic, complemented
159#17985850C2211yescharacteristic, complemented
160#17985850C2211yescharacteristic, complemented
161#17985846C2211yescharacteristic
162#17985846C2211yescharacteristic
163#17985846C2211yescharacteristic
164#17985846C2211yescharacteristic
165#17985846C2211yescharacteristic
166#17985846C2211yescharacteristic
167#17985846C2211yescharacteristic
168#17985846C2211yescharacteristic
169#17985846C2211yescharacteristic
170#17985846C2211yescharacteristic
171#17985846C2211yescharacteristic
172#17985846C2211yescharacteristic
173C2×C71⋊#95C2211yescharacteristic
174C2×C22⋊Q8×C71C2211yescharacteristic
175C2×#117×C71C2211yescharacteristic
176#400×C71C2211yescharacteristic, complemented
177#398×C71C2211yescharacteristic, complemented
178#398×C71C2211yescharacteristic, complemented
179#395×C71C2211yescharacteristic, complemented
180#391×C71C2211yescharacteristic, complemented
181#389×C71C2211yescharacteristic, complemented
182#387×C71C2211yescharacteristic, complemented
183#387×C71C2211yescharacteristic, complemented
184#385×C71C2211yescharacteristic
185#385×C71C2211yescharacteristic
186#381×C71C2211yescharacteristic
187#380×C71C2211yescharacteristic
188C2×#95×C71C2211yescharacteristic
189C24×D71C2311yescharacteristic
190C22×Dic142C2311yescharacteristic
191C22×Dic142C2311yescharacteristic
192C22×Dic142C2311yescharacteristic
193C23×Dic71C2311yescharacteristic
194C23×Dic71C2311yescharacteristic
195C23×Dic71C2311yescharacteristic
196C22×C4×D71—24no—
197C22×C4×D71—24no—
198C22×C4×D71Q818yescomplemented
199C22×C4×D71C2311yescharacteristic
200C22×C4×D71C2311yescharacteristic
201C22×C4×D71C2311yescharacteristic
202C22×C4×D71C2311yescharacteristic
203C22×C4×D71C2311yescharacteristic
204C22×C4×D71C2311yescharacteristic
205C22×C4×D71C2311yescharacteristic
206C22×C4×D71C2311yescharacteristic
207#14556127—24no—
208#14556126—24no—
209#14556118—24no—
210#14556118—24no—
211#14556108—24no—
212#14556107—24no—
213#14556106—24no—
214#14556106—24no—
215#14556105—24no—
216#14556105—24no—
217#14556104—24no—
218Q8×Dic71—24no—
219#14556093—24no—
220#14556093—24no—
221#14556093—24no—
222#14556087—24no—
223#14556086—24no—
224#14556086—24no—
225#14556085—24no—
226#14556085—24no—
227#14556084—24no—
228#14556084—24no—
229#14556084—24no—
230#14556084D418yes—
231C2×C4⋊Dic71C2311yescharacteristic
232C2×C4⋊Dic71C2311yescharacteristic
233C2×C4⋊Dic71C2311yescharacteristic
234C2×C4⋊Dic71C2311yescharacteristic
235C2×C4⋊Dic71C2311yescharacteristic
236C2×C4⋊Dic71C2311yescharacteristic
237C2×C4⋊Dic71C2311yescharacteristic
238C2×C4⋊Dic71C2311yescharacteristic
239C2×C4⋊Dic71C2311yescharacteristic
240C2×C4⋊Dic71C2311yescharacteristic
241C2×C4⋊Dic71C2311yescharacteristic
242C2×Dic71⋊C4C2311yescharacteristic
243C2×Dic71⋊C4C2311yescharacteristic
244C2×Dic71⋊C4C2311yescharacteristic
245C2×Dic71⋊C4C2311yescharacteristic
246C2×Dic71⋊C4C2311yescharacteristic
247C2×Dic71⋊C4C2311yescharacteristic
248C2×Dic71⋊C4C2311yescharacteristic
249C2×Dic71⋊C4C2311yescharacteristic
250C2×Dic71⋊C4C2311yescharacteristic
251C2×Dic71⋊C4C2311yescharacteristic
252C2×Dic71⋊C4C2311yescharacteristic
253C2×Dic71⋊C4C2311yescharacteristic
254C2×Dic71⋊C4C2311yescharacteristic
255C2×Dic71⋊C4C2311yescharacteristic
256C2×Dic71⋊C4C2311yescharacteristic
257C2×Dic71⋊C4C2311yescharacteristic
258C2×Dic71⋊C4C2311yescharacteristic
259C2×Dic71⋊C4C2311yescharacteristic
260C2×Dic71⋊C4C2311yescharacteristic
261C2×Dic71⋊C4C2311yescharacteristic
262C2×Dic71⋊C4C2311yescharacteristic
263C2×Dic71⋊C4C2311yescharacteristic
264C2×Dic71⋊C4C2311yescharacteristic
265C2×Dic71⋊C4C2311yescharacteristic
266C2×Dic71⋊C4C2311yescharacteristic
267C2×Dic71⋊C4C2311yescharacteristic
268C4⋊C4×D71—24no—
269C4⋊C4×D71—24no—
270C2×C22⋊Dic71C2311yescharacteristic
271C2×C22⋊Dic71C2311yescharacteristic
272C2×C22⋊Dic71C2311yescharacteristic
273C2×C22⋊Dic71C2311yescharacteristic
274C2×(C2×D71)⋊C4—24no—
275C2×(C2×D71)⋊C4—24no—
276C2×(C2×D71)⋊C4C2311yescharacteristic
277C2×(C2×D71)⋊C4C2311yescharacteristic
278C2×(C2×D71)⋊C4C2311yescharacteristic
279C2×(C2×D71)⋊C4C2311yescharacteristic
280C2×(C2×D71)⋊C4C2311yescharacteristic
281C2×(C2×D71)⋊C4C2311yescharacteristic
282C2×(C2×D71)⋊C4C2311yescharacteristic
283C2×(C2×D71)⋊C4C2311yescharacteristic
284C2×(C2×D71)⋊C4C2311yescharacteristic
285C2×(C2×D71)⋊C4C2311yescharacteristic
286C2×(C2×D71)⋊C4C2311yescharacteristic
287C2×(C2×D71)⋊C4C2311yescharacteristic
288C2×(C2×D71)⋊C4C2311yescharacteristic
289C2×(C2×D71)⋊C4C2311yescharacteristic
290C2×(C2×D71)⋊C4C2311yescharacteristic
291C2×(C2×D71)⋊C4C2311yescharacteristic
292C2×(C2×D71)⋊C4C2311yescharacteristic
293C2×(C2×D71)⋊C4C2311yescharacteristic
294C2×(C2×D71)⋊C4C2311yescharacteristic
295C2×(C2×D71)⋊C4C2311yescharacteristic
296C22⋊C4×D71—24no—
297C22⋊C4×D71—24no—
298C2×C4×Dic71—24no—
299C2×C4×Dic71—24no—
300C2×C4×Dic71C2311yescharacteristic
301C2×C4×Dic71C2311yescharacteristic
302C2×C4×Dic71C2311yescharacteristic
303C2×C4×Dic71C2311yescharacteristic
304C2×C4×Dic71C2311yescharacteristic
305C2×C4×Dic71C2311yescharacteristic
306C2×C4×Dic71C2311yescharacteristic
307C2×C4×Dic71C2311yescharacteristic
308C2×C4×Dic71C2311yescharacteristic
309C2×C4×Dic71C2311yescharacteristic
310C2×C4×Dic71C2311yescharacteristic
311C2×C4×Dic71C2311yescharacteristic
312C2×C4×Dic71C2311yescharacteristic
313C2×C4×Dic71C2311yescharacteristic
314C2×C4×Dic71C2311yescharacteristic
315C2×C4×Dic71C2311yescharacteristic
316C2×C4×Dic71C2311yescharacteristic
317C2×C4×Dic71C2311yescharacteristic
318C42×D71—24no—
319C42×D71—24no—
320C71⋊#95C2311yescharacteristic
321C71⋊#95C2311yescharacteristic
322C71⋊#95C2311yescharacteristic
323C71⋊#95C2311yescharacteristic
324C71⋊#95C2311yescharacteristic
325C71⋊#95C2311yescharacteristic
326C71⋊#95C2311yescharacteristic
327C71⋊#95C2311yescharacteristic
328C71⋊#95C2311yescharacteristic
329C71⋊#95C2311yescharacteristic
330C71⋊#95C2311yescharacteristic
331C71⋊#95C2311yescharacteristic
332C71⋊#95C2311yescharacteristic
333C71⋊#95C2311yescharacteristic
334C71⋊#95C2311yescharacteristic
335C71⋊#95C2311yescharacteristic
336C71⋊#95C2311yescharacteristic
337C71⋊#95C2311yescharacteristic
338C71⋊#95C2311yescharacteristic
339C71⋊#95C2311yescharacteristic
340C71⋊#95C2311yescharacteristic
341C71⋊#95C2311yescharacteristic
342C71⋊#95C2311yescharacteristic
343C71⋊#95C2311yescharacteristic
344C71⋊#95C2311yescharacteristic
345C71⋊#95C2311yescharacteristic
346C22×Q8×C71C2311yescharacteristic
347C23×C4×C71C2311yescharacteristic
348C23×C4×C71C2311yescharacteristic
349C23×C4×C71C2311yescharacteristic
350C22⋊Q8×C71—24no—
351#117×C71—24no—
352C2×C4⋊C4×C71C2311yescharacteristic
353C2×C4⋊C4×C71C2311yescharacteristic
354C2×C4⋊C4×C71C2311yescharacteristic
355C2×C4⋊C4×C71C2311yescharacteristic
356C2×C4⋊C4×C71C2311yescharacteristic
357C2×C4⋊C4×C71C2311yescharacteristic
358C2×C4⋊C4×C71C2311yescharacteristic
359C2×C4⋊C4×C71C2311yescharacteristic
360C2×C4⋊C4×C71C2311yescharacteristic
361C2×C4⋊C4×C71C2311yescharacteristic
362C2×C4⋊C4×C71C2311yescharacteristic
363C2×C22⋊C4×C71C2311yescharacteristic
364C2×C22⋊C4×C71C2311yescharacteristic
365C2×C22⋊C4×C71C2311yescharacteristic
366C2×C22⋊C4×C71C2311yescharacteristic
367C2×C42×C71C2311yescharacteristic
368C2×C42×C71C2311yescharacteristic
369#95×C71C2311yescharacteristic
370#95×C71C2311yescharacteristic
371#95×C71C2311yescharacteristic
372#95×C71C2311yescharacteristic
373#95×C71C2311yescharacteristic
374#95×C71C2311yescharacteristic
375#95×C71C2311yescharacteristic
376#95×C71C2311yescharacteristic
377#95×C71C2311yescharacteristic
378#95×C71C2311yescharacteristic
379#95×C71C2311yescharacteristic
380#95×C71C2311yescharacteristic
381#95×C71C2311yescharacteristic
382#95×C71C2311yescharacteristic
383C23×D71—22no—
384C23×D71—22no—
385C23×D71—22no—
386C23×D71—22no—
387C23×D71—41no—
388C23×D71—41no—
389C23×D71C2×Q814yes—
390C23×D71C2411yescharacteristic
391C23×D71C2411yescharacteristic
392C2×Dic142—22no—
393C2×Dic142—22no—
394C2×Dic142—22no—
395C2×Dic142—22no—
396C2×Dic142—22no—
397C2×Dic142—22no—
398C2×Dic142—41no—
399C2×Dic142—41no—
400C2×Dic142—41no—
401C22×Dic71—22no—
402C22×Dic71—22no—
403C22×Dic71—22no—
404C22×Dic71—22no—
405C22×Dic71—41no—
406C22×Dic71—41no—
407C22×Dic71C2×D414yes—
408C22×Dic71C2×Q814yes—
409C22×Dic71#4114yes—
410C22×Dic71C2411yescharacteristic
411C22×Dic71C2411yescharacteristic
412C22×Dic71C2411yescharacteristic
413C22×Dic71C2411yescharacteristic
414C22×Dic71C2411yescharacteristic
415C22×Dic71C2411yescharacteristic
416C22×Dic71C2411yescharacteristic
417C22×Dic71C2411yescharacteristic
418C22×Dic71C2411yescharacteristic
419C22×Dic71C2411yescharacteristic
420C22×Dic71C2411yescharacteristic
421C22×Dic71C2411yescharacteristic
422C22×Dic71C2411yescharacteristic
423C22×Dic71C2411yescharacteristic
424C2×C4×D71—232no—
425C2×C4×D71—22no—
426C2×C4×D71—22no—
427C2×C4×D71—22no—
428C2×C4×D71—22no—
429C2×C4×D71—22no—
430C2×C4×D71—22no—
431C2×C4×D71—22no—
432C2×C4×D71—22no—
433C2×C4×D71—22no—
434C2×C4×D71—22no—
435C2×C4×D71—22no—
436C2×C4×D71—22no—
437C2×C4×D71—22no—
438C2×C4×D71—22no—
439C2×C4×D71—22no—
440C2×C4×D71—22no—
441C2×C4×D71—41no—
442C2×C4×D71—41no—
443C2×C4×D71—41no—
444C2×C4×D71—41no—
445C2×C4×D71C2×Q814yes—
446C2×C4×D71C2×Q814yes—
447C2×C4×D71C2×Q814yes—
448C2×C4×D71C2×Q814yes—
449C4⋊Dic71—22no—
450C4⋊Dic71—22no—
451C4⋊Dic71—22no—
452C4⋊Dic71—22no—
453C4⋊Dic71—22no—
454C4⋊Dic71—22no—
455C4⋊Dic71—22no—
456C4⋊Dic71—22no—
457C4⋊Dic71—41no—
458C4⋊Dic71—41no—
459C4⋊Dic71—41no—
460Dic71⋊C4—22no—
461Dic71⋊C4—22no—
462Dic71⋊C4—22no—
463Dic71⋊C4—22no—
464Dic71⋊C4—22no—
465Dic71⋊C4—22no—
466Dic71⋊C4—22no—
467Dic71⋊C4—22no—
468Dic71⋊C4—22no—
469Dic71⋊C4—22no—
470Dic71⋊C4—22no—
471Dic71⋊C4—22no—
472Dic71⋊C4—22no—
473Dic71⋊C4—22no—
474Dic71⋊C4—22no—
475Dic71⋊C4—22no—
476Dic71⋊C4—22no—
477Dic71⋊C4—22no—
478Dic71⋊C4—41no—
479Dic71⋊C4—41no—
480Dic71⋊C4—41no—
481Dic71⋊C4—41no—
482Dic71⋊C4—41no—
483Dic71⋊C4—41no—
484Dic71⋊C4C2×D414yes—
485Dic71⋊C4C2×D414yes—
486C22⋊Dic71—22no—
487C22⋊Dic71—22no—
488C22⋊Dic71—22no—
489C22⋊Dic71C2×D414yes—
490(C2×D71)⋊C4—22no—
491(C2×D71)⋊C4—22no—
492(C2×D71)⋊C4—22no—
493(C2×D71)⋊C4—22no—
494(C2×D71)⋊C4—22no—
495(C2×D71)⋊C4—22no—
496(C2×D71)⋊C4—22no—
497(C2×D71)⋊C4—22no—
498(C2×D71)⋊C4—22no—
499(C2×D71)⋊C4—22no—
500(C2×D71)⋊C4—22no—
501(C2×D71)⋊C4—22no—
502(C2×D71)⋊C4—22no—
503(C2×D71)⋊C4—22no—
504(C2×D71)⋊C4—41no—
505(C2×D71)⋊C4—41no—
506(C2×D71)⋊C4—41no—
507(C2×D71)⋊C4—41no—
508(C2×D71)⋊C4#4114yes—
509(C2×D71)⋊C4#4114yes—
510C4×Dic71—22no—
511C4×Dic71—22no—
512C4×Dic71—22no—
513C4×Dic71—22no—
514C4×Dic71—22no—
515C4×Dic71—22no—
516C4×Dic71—22no—
517C4×Dic71—22no—
518C4×Dic71—22no—
519C4×Dic71—22no—
520C4×Dic71—22no—
521C4×Dic71—22no—
522C4×Dic71—22no—
523C4×Dic71—22no—
524C4×Dic71—22no—
525C4×Dic71—22no—
526C4×Dic71C2×D414yes—
527C4×Dic71C2×D414yes—
528C24×C71C2411yescharacteristic
529C2×Q8×C71—22no—
530C2×Q8×C71—22no—
531C2×Q8×C71—41no—
532C22×C4×C71—22no—
533C22×C4×C71—22no—
534C22×C4×C71—22no—
535C22×C4×C71—22no—
536C22×C4×C71—22no—
537C22×C4×C71—22no—
538C22×C4×C71—41no—
539C22×C4×C71—41no—
540C22×C4×C71C2×Q814yes—
541C22×C4×C71C2411yescharacteristic
542C22×C4×C71C2411yescharacteristic
543C22×C4×C71C2411yescharacteristic
544C22×C4×C71C2411yescharacteristic
545C22×C4×C71C2411yescharacteristic
546C22×C4×C71C2411yescharacteristic
547C22×C4×C71C2411yescharacteristic
548C22×C4×C71C2411yescharacteristic
549C22×C4×C71C2411yescharacteristic
550C22×C4×C71C2411yescharacteristic
551C22×C4×C71C2411yescharacteristic
552C22×C4×C71C2411yescharacteristic
553C22×C4×C71C2411yescharacteristic
554C22×C4×C71C2411yescharacteristic
555C4⋊C4×C71—22no—
556C4⋊C4×C71—22no—
557C4⋊C4×C71—22no—
558C4⋊C4×C71—22no—
559C4⋊C4×C71—22no—
560C4⋊C4×C71—22no—
561C4⋊C4×C71—22no—
562C4⋊C4×C71—22no—
563C4⋊C4×C71—41no—
564C4⋊C4×C71—41no—
565C4⋊C4×C71—41no—
566C22⋊C4×C71—22no—
567C22⋊C4×C71—22no—
568C22⋊C4×C71—22no—
569C22⋊C4×C71C2×D414yes—
570C42×C71—22no—
571C42×C71—22no—
572C23×C71—21no—
573C23×C71—21no—
574C23×C71—21no—
575C23×C71—21no—
576C23×C71C22×D412yes—
577C23×C71C22×Q812yes—
578C23×C71C2×#4112yes—
579C23×C71C2511yescharacteristic
580C22×D71—21no—
581C22×D71—21no—
582C22×D71—21no—
583C22×D71—21no—
584C22×D71—28no—
585C22×D71—21no—
586C22×D71—21no—
587C22×D71—21no—
588C22×D71—21no—
589C22×D71—21no—
590C22×D71—21no—
591C22×D71—28no—
592C22×D71—44no—
593C22×D71—44no—
594C22×D71—44no—
595C22×D71—44no—
596C22×D71—44no—
597C22×D71C22×Q812yes—
598C22×D71C22×Q812yes—
599C22×D71C2×#4112yes—
600C22×D71C2×#4112yes—
601Q8×C71—44no—
602C2×C4×C71—28no—
603C2×C4×C71—21no—
604C2×C4×C71—21no—
605C2×C4×C71—21no—
606C2×C4×C71—21no—
607C2×C4×C71—21no—
608C2×C4×C71—21no—
609C2×C4×C71—21no—
610C2×C4×C71—21no—
611C2×C4×C71—21no—
612C2×C4×C71—21no—
613C2×C4×C71—21no—
614C2×C4×C71—21no—
615C2×C4×C71—21no—
616C2×C4×C71—21no—
617C2×C4×C71—21no—
618C2×C4×C71—21no—
619C2×C4×C71—21no—
620C2×C4×C71—21no—
621C2×C4×C71—21no—
622C2×C4×C71—21no—
623C2×C4×C71—21no—
624C2×C4×C71—21no—
625C2×C4×C71—21no—
626C2×C4×C71—21no—
627C2×C4×C71—21no—
628C2×C4×C71—21no—
629C2×C4×C71—21no—
630C2×C4×C71—21no—
631C2×C4×C71—21no—
632C2×C4×C71—21no—
633C2×C4×C71—21no—
634C2×C4×C71—21no—
635C2×C4×C71—21no—
636C2×C4×C71—21no—
637C2×C4×C71—21no—
638C2×C4×C71—21no—
639C2×C4×C71—44no—
640C2×C4×C71—44no—
641C2×C4×C71C22×D412yes—
642C2×C4×C71C22×D412yes—
643C2×C4×C71C22×Q812yes—
644C2×C4×C71C22×Q812yes—
645C2×C4×C71C2×#4112yes—
646C2×C4×C71C2×#4112yes—
647C2×Dic71—21no—
648C2×Dic71—21no—
649C2×Dic71—21no—
650C2×Dic71—21no—
651C2×Dic71—21no—
652C2×Dic71—21no—
653C2×Dic71—21no—
654C2×Dic71—21no—
655C2×Dic71—21no—
656C2×Dic71—21no—
657C2×Dic71—21no—
658C2×Dic71—21no—
659C2×Dic71—21no—
660C2×Dic71—21no—
661C2×Dic71—21no—
662C2×Dic71—21no—
663C2×Dic71—21no—
664C2×Dic71—21no—
665C2×Dic71—21no—
666C2×Dic71—21no—
667C2×Dic71—21no—
668C2×Dic71—21no—
669C2×Dic71—21no—
670C2×Dic71—21no—
671C2×Dic71—21no—
672C2×Dic71—21no—
673C2×Dic71—21no—
674C2×Dic71—21no—
675C2×Dic71—21no—
676C2×Dic71—21no—
677C2×Dic71—21no—
678C2×Dic71—21no—
679C2×Dic71—44no—
680C2×Dic71—44no—
681C2×Dic71C22⋊Q8116yescomplemented
682C2×Dic71C22×D412yes—
683C2×Dic71C22×D412yes—
684C2×Dic71C22×D412yes—
685C2×Dic71C22×D412yes—
686C2×Dic71C22×Q812yes—
687C2×Dic71C22×Q812yes—
688C2×Dic71C2×#4112yes—
689C2×Dic71C2×#4112yes—
690C2×Dic71C2×#4112yes—
691C2×Dic71C2×#4112yes—
692C4×D71—28no—
693C4×D71—28no—
694C4×D71—28no—
695C4×D71—28no—
696C4×D71—44no—
697C4×D71—44no—
698C4×D71—44no—
699C4×D71—44no—
700Dic142—44no—
701Dic142—44no—
702Dic142—44no—
703C22×C71—22no—
704C22×C71—22no—
705C22×C71—22no—
706C22×C71—22no—
707C22×C71—22no—
708C22×C71—22no—
709C22×C71C2×C22⋊Q814yes—
710C22×C71C23×D411yescharacteristic
711C22×C71C23×Q811yescharacteristic
712C22×C71C22×#4111yescharacteristic
713C22×C71C22×#4111yescharacteristic
714C22×C71C22×#4111yescharacteristic
715C22×C71#58511yescharacteristic
716C22×C71#58511yescharacteristic
717C2×D71—22no—
718C2×D71—22no—
719C2×D71—22no—
720C2×D71—22no—
721C2×D71—22no—
722C2×D71—22no—
723C2×D71—22no—
724C2×D71—22no—
725C2×D71—22no—
726C2×D71—416no—
727C2×D71—41no—
728C2×D71—41no—
729C2×D71—41no—
730C2×D71—41no—
731C2×D71#53314yescomplemented
732C4×C71—22no—
733C4×C71—22no—
734C4×C71—22no—
735C4×C71—22no—
736C4×C71—22no—
737C4×C71—22no—
738C4×C71—41no—
739C4×C71—41no—
740C4×C71—41no—
741C4×C71—41no—
742C4×C71—41no—
743C4×C71—41no—
744C4×C71—41no—
745C4×C71—41no—
746Dic71—22no—
747Dic71—22no—
748Dic71—22no—
749Dic71—22no—
750Dic71—41no—
751Dic71—41no—
752Dic71—41no—
753Dic71—41no—
754Dic71—41no—
755Dic71—41no—
756Dic71—41no—
757Dic71—41no—
758Dic71C2×C22⋊Q814yes—
759Dic71C2×C22⋊Q814yes—
760#34739—711nomaximal, Sylow
761C2×C71—24no—
762C2×C71C22×C22⋊Q811yescharacteristic
763C2×C71C2×#53311yescharacteristic
764C2×C71#345811yescharacteristic
765C2×C71D4×#4111yescharacteristic
766C2×C71D4×#4111yescharacteristic
767C2×C71#347511yescharacteristic
768C2×C71#347511yescharacteristic
769D71—24no—
770D71—42no—
771C2×#533—711no—
772C22×#117—711no—
773#2442—711no—
774#2442—711no—
775#2441—711no—
776#2441—711no—
777#2440—711no—
778#2440—711no—
779#2439—711no—
780#2439—711no—
781#2438—711no—
782#2438—711no—
783#2438—711no—
784#2438D7111yescharacteristic, complemented
785#2437—711no—
786#2437—711no—
787#2437—711no—
788#2437—711no—
789#2396—711no—
790#2396—711no—
791#2396—711no—
792#2396—711no—
793C4×C22⋊Q8—711no—
794C4×C22⋊Q8—711no—
795C4×C22⋊Q8—711no—
796C4×C22⋊Q8—711no—
797#2296—711no—
798#2296—711no—
799#2285—711no—
800#2280—711no—
801C2×C4×C22⋊C4—711no—
802C71#3473911yescharacteristic, complemented, Sylow
803C24×C4—711no—
804#533—1428no—
805C2×C4⋊Q8—711no—
806C2×C4⋊Q8—711no—
807C2×#125—711no—
808C2×#125—711no—
809C2×C22⋊Q8—711no—
810C2×C22⋊Q8—711no—
811C2×C22⋊Q8—711no—
812C2×C22⋊Q8—711no—
813C2×C22⋊Q8—711no—
814C2×C22⋊Q8—711no—
815C2×C22⋊Q8—711no—
816C2×C22⋊Q8C2×D7111yescharacteristic
817C2×C4×Q8—711no—
818C2×C4×Q8—711no—
819C2×C4×Q8—711no—
820C2×C4×Q8—711no—
821C2×#117—711no—
822C2×#117—711no—
823C2×#117—711no—
824C2×#117—711no—
825C2×#117—711no—
826C2×#117—711no—
827C2×#117—711no—
828C2×#117—711no—
829C2×#117—711no—
830C2×#117—1428no—
831C2×#117C2×D7111yescharacteristic
832C22×C4⋊C4—711no—
833C22×C4⋊C4—711no—
834C22×C22⋊C4—711no—
835C22×C22⋊C4—711no—
836C22×C22⋊C4—711no—
837C22×C22⋊C4—711no—
838C22×C42—711no—
839C22×C42—711no—
840C22×C42—711no—
841C22×C42—711no—
842#400—711no—
843#400—711no—
844#400—711no—
845#400C2×D7111yescharacteristic, complemented
846#399—711no—
847#399—711no—
848#399—711no—
849#399—711no—
850#398—711no—
851#398—711no—
852#398—711no—
853#398—711no—
854#398—711no—
855#398—711no—
856#398C2×D7111yescharacteristic, complemented
857#398C2×D7111yescharacteristic, complemented
858#396—711no—
859#396—711no—
860#396—711no—
861#396—711no—
862#396—711no—
863#396—711no—
864#396—711no—
865#396—711no—
866#395—711no—
867#395—711no—
868#395—711no—
869#395C2×D7111yescharacteristic, complemented
870#393—711no—
871#393—711no—
872#393—711no—
873#393—711no—
874#391—711no—
875#391—711no—
876#391—711no—
877#391C2×D7111yescharacteristic, complemented
878#389—711no—
879#389—711no—
880#389—711no—
881#389—711no—
882#389—711no—
883#389—711no—
884#389—711no—
885#389—711no—
886#389—711no—
887#389—711no—
888#389—711no—
889#389C2×D7111yescharacteristic, complemented
890#387—711no—
891#387—711no—
892#387—711no—
893#387—711no—
894#387—711no—
895#387—711no—
896#387C2×D7111yescharacteristic, complemented
897#387C2×D7111yescharacteristic, complemented
898#385—711no—
899#385—711no—
900#385—711no—
901#385—711no—
902#385—711no—
903#385—711no—
904#385—711no—
905#385—711no—
906#385—711no—
907#385—711no—
908#385—711no—
909#385—711no—
910#385—711no—
911#385—711no—
912#385C2×D7111yescharacteristic
913#385C2×D7111yescharacteristic
914#384—711no—
915#384—711no—
916#382—711no—
917#382—711no—
918#381—711no—
919#381C2×D7111yescharacteristic
920#380—711no—
921#380—711no—
922#380—711no—
923#380—711no—
924#380—711no—
925#380—711no—
926#380—711no—
927#380—711no—
928#380—711no—
929#380—711no—
930#380—711no—
931#380C2×D7111yescharacteristic
932#379—711no—
933#379—711no—
934C4×C4⋊C4—711no—
935C4×C4⋊C4—711no—
936C4×C4⋊C4—711no—
937C4×C4⋊C4—711no—
938C4×C4⋊C4—711no—
939C4×C4⋊C4—711no—
940C4×C4⋊C4—711no—
941C4×C4⋊C4—711no—
942C4×C4⋊C4—711no—
943C4×C4⋊C4—711no—
944C4×C4⋊C4—711no—
945C4×C4⋊C4—711no—
946C4×C22⋊C4—711no—
947C4×C22⋊C4—711no—
948C4×C22⋊C4—711no—
949C4×C22⋊C4—711no—
950C4×C22⋊C4—711no—
951C4×C22⋊C4—711no—
952C4×C22⋊C4—711no—
953C4×C22⋊C4—711no—
954C4×C22⋊C4—711no—
955C4×C22⋊C4—711no—
956C4×C22⋊C4—711no—
957C4×C22⋊C4—711no—
958C2×#95—711no—
959C2×#95C2×D7111yescharacteristic
960C25—711no—
961C22×Q8—711no—
962C22×Q8—711no—
963C22×Q8—711no—
964C22×Q8C22×D7111yescharacteristic
965C23×C4—711no—
966C23×C4—711no—
967C23×C4—711no—
968C23×C4—711no—
969C23×C4—711no—
970C23×C4—711no—
971C23×C4—711no—
972C23×C4—718no—
973C23×C4—711no—
974C23×C4—711no—
975C23×C4—711no—
976C23×C4—711no—
977C23×C4—1424no—
978C23×C4—1424no—
979C23×C4C22×D7111yescharacteristic
980C23×C4C22×D7111yescharacteristic
981C23×C4C22×D7111yescharacteristic
982C4⋊Q8—1424no—
983C4⋊Q8—1424no—
984#125—1424no—
985#125—1424no—
986C22⋊Q8—24no—
987C22⋊Q8—1424no—
988C22⋊Q8—1424no—
989C22⋊Q8—1424no—
990C22⋊Q8—1424no—
991C22⋊Q8—1424no—
992C22⋊Q8—1424no—
993C22⋊Q8—1424no—
994C4×Q8—1424no—
995C4×Q8—1424no—
996C4×Q8—1424no—
997C4×Q8—1424no—
998#117—24no—
999#117—718no—
1000#117—1424no—
1001#117—1424no—
1002#117—1424no—
1003#117—1424no—
1004#117—1424no—
1005#117—1424no—
1006#117—1424no—
1007#117—1424no—
1008C2×C4⋊C4—711no—
1009C2×C4⋊C4—711no—
1010C2×C4⋊C4—711no—
1011C2×C4⋊C4—711no—
1012C2×C4⋊C4—711no—
1013C2×C4⋊C4—711no—
1014C2×C4⋊C4—711no—
1015C2×C4⋊C4—711no—
1016C2×C4⋊C4—711no—
1017C2×C4⋊C4—711no—
1018C2×C4⋊C4—711no—
1019C2×C4⋊C4—711no—
1020C2×C4⋊C4—711no—
1021C2×C4⋊C4—711no—
1022C2×C4⋊C4—711no—
1023C2×C4⋊C4—711no—
1024C2×C4⋊C4—711no—
1025C2×C4⋊C4—711no—
1026C2×C4⋊C4—711no—
1027C2×C4⋊C4—711no—
1028C2×C4⋊C4—711no—
1029C2×C4⋊C4—711no—
1030C2×C4⋊C4—711no—
1031C2×C4⋊C4—711no—
1032C2×C4⋊C4—711no—
1033C2×C4⋊C4—711no—
1034C2×C4⋊C4—711no—
1035C2×C4⋊C4—711no—
1036C2×C4⋊C4—711no—
1037C2×C4⋊C4—711no—
1038C2×C4⋊C4—711no—
1039C2×C4⋊C4—711no—
1040C2×C4⋊C4—711no—
1041C2×C4⋊C4—711no—
1042C2×C4⋊C4—711no—
1043C2×C4⋊C4—711no—
1044C2×C4⋊C4—711no—
1045C2×C4⋊C4—1424no—
1046C2×C4⋊C4—1424no—
1047C2×C4⋊C4C22×D7111yescharacteristic
1048C2×C4⋊C4C22×D7111yescharacteristic
1049C2×C4⋊C4C22×D7111yescharacteristic
1050C2×C4⋊C4C22×D7111yescharacteristic
1051C2×C4⋊C4C22×D7111yescharacteristic
1052C2×C4⋊C4C22×D7111yescharacteristic
1053C2×C4⋊C4C22×D7111yescharacteristic
1054C2×C4⋊C4C22×D7111yescharacteristic
1055C2×C4⋊C4C22×D7111yescharacteristic
1056C2×C4⋊C4C22×D7111yescharacteristic
1057C2×C4⋊C4C22×D7111yescharacteristic
1058C2×C22⋊C4—711no—
1059C2×C22⋊C4—711no—
1060C2×C22⋊C4—711no—
1061C2×C22⋊C4—711no—
1062C2×C22⋊C4—711no—
1063C2×C22⋊C4—711no—
1064C2×C22⋊C4—711no—
1065C2×C22⋊C4—711no—
1066C2×C22⋊C4—711no—
1067C2×C22⋊C4—711no—
1068C2×C22⋊C4—711no—
1069C2×C22⋊C4—711no—
1070C2×C22⋊C4—711no—
1071C2×C22⋊C4—711no—
1072C2×C22⋊C4—711no—
1073C2×C22⋊C4—711no—
1074C2×C22⋊C4—711no—
1075C2×C22⋊C4—711no—
1076C2×C22⋊C4—711no—
1077C2×C22⋊C4—711no—
1078C2×C22⋊C4—711no—
1079C2×C22⋊C4—711no—
1080C2×C22⋊C4—711no—
1081C2×C22⋊C4—711no—
1082C2×C22⋊C4—1424no—
1083C2×C22⋊C4—1424no—
1084C2×C22⋊C4—1424no—
1085C2×C22⋊C4—1424no—
1086C2×C22⋊C4C22×D7111yescharacteristic
1087C2×C22⋊C4C22×D7111yescharacteristic
1088C2×C22⋊C4C22×D7111yescharacteristic
1089C2×C22⋊C4C22×D7111yescharacteristic
1090C2×C42—711no—
1091C2×C42—711no—
1092C2×C42—711no—
1093C2×C42—711no—
1094C2×C42—711no—
1095C2×C42—711no—
1096C2×C42—711no—
1097C2×C42—711no—
1098C2×C42—711no—
1099C2×C42—711no—
1100C2×C42—711no—
1101C2×C42—711no—
1102C2×C42—711no—
1103C2×C42—711no—
1104C2×C42—711no—
1105C2×C42—711no—
1106C2×C42—711no—
1107C2×C42—711no—
1108C2×C42—1424no—
1109C2×C42—1424no—
1110C2×C42—1424no—
1111C2×C42—1424no—
1112C2×C42C22×D7111yescharacteristic
1113C2×C42C22×D7111yescharacteristic
1114#95—711no—
1115#95—711no—
1116#95—711no—
1117#95—711no—
1118#95—711no—
1119#95—711no—
1120#95—711no—
1121#95—711no—
1122#95—711no—
1123#95—711no—
1124#95—711no—
1125#95—711no—
1126#95—711no—
1127#95—711no—
1128#95—711no—
1129#95—711no—
1130#95—711no—
1131#95—711no—
1132#95—711no—
1133#95—711no—
1134#95—711no—
1135#95—711no—
1136#95—711no—
1137#95—711no—
1138#95—711no—
1139#95—711no—
1140#95C22×D7111yescharacteristic
1141#95C22×D7111yescharacteristic
1142#95C22×D7111yescharacteristic
1143#95C22×D7111yescharacteristic
1144#95C22×D7111yescharacteristic
1145#95C22×D7111yescharacteristic
1146#95C22×D7111yescharacteristic
1147#95C22×D7111yescharacteristic
1148#95C22×D7111yescharacteristic
1149#95C22×D7111yescharacteristic
1150#95C22×D7111yescharacteristic
1151#95C22×D7111yescharacteristic
1152#95C22×D7111yescharacteristic
1153#95C22×D7111yescharacteristic
1154C24—2841no—
1155C24—2841no—
1156C24—714no—
1157C24—711no—
1158C24—711no—
1159C24—1422no—
1160C24—1422no—
1161C24—1422no—
1162C24—1422no—
1163C24C23×D7111yescharacteristic
1164C2×Q8—22no—
1165C2×Q8—22no—
1166C2×Q8—41no—
1167C2×Q8—2841no—
1168C2×Q8—2841no—
1169C2×Q8—2841no—
1170C2×Q8—1422no—
1171C2×Q8—1422no—
1172C2×Q8—1422no—
1173C2×Q8—1422no—
1174C2×Q8—1422no—
1175C2×Q8—1422no—
1176C22×C4—22no—
1177C22×C4—22no—
1178C22×C4—22no—
1179C22×C4—22no—
1180C22×C4—22no—
1181C22×C4—22no—
1182C22×C4—41no—
1183C22×C4—41no—
1184C22×C4—2841no—
1185C22×C4—2841no—
1186C22×C4—2841no—
1187C22×C4—2841no—
1188C22×C4—2841no—
1189C22×C4—2841no—
1190C22×C4—714no—
1191C22×C4—714no—
1192C22×C4—714no—
1193C22×C4—711no—
1194C22×C4—711no—
1195C22×C4—711no—
1196C22×C4—711no—
1197C22×C4—711no—
1198C22×C4—711no—
1199C22×C4—714no—
1200C22×C4—714no—
1201C22×C4—714no—
1202C22×C4—714no—
1203C22×C4—711no—
1204C22×C4—711no—
1205C22×C4—711no—
1206C22×C4—711no—
1207C22×C4—711no—
1208C22×C4—711no—
1209C22×C4—711no—
1210C22×C4—711no—
1211C22×C4—1422no—
1212C22×C4—1422no—
1213C22×C4—1422no—
1214C22×C4—1422no—
1215C22×C4—1422no—
1216C22×C4—1422no—
1217C22×C4—1422no—
1218C22×C4—1422no—
1219C22×C4—1422no—
1220C22×C4—1422no—
1221C22×C4—1422no—
1222C22×C4—1422no—
1223C22×C4—1422no—
1224C22×C4—1422no—
1225C22×C4—14232no—
1226C22×C4—1422no—
1227C22×C4—1422no—
1228C22×C4—1422no—
1229C22×C4—1422no—
1230C22×C4—1422no—
1231C22×C4—1422no—
1232C22×C4Q8×D7114yes—
1233C22×C4C23×D7111yescharacteristic
1234C22×C4C23×D7111yescharacteristic
1235C22×C4C23×D7111yescharacteristic
1236C22×C4C23×D7111yescharacteristic
1237C22×C4C23×D7111yescharacteristic
1238C22×C4C23×D7111yescharacteristic
1239C22×C4C23×D7111yescharacteristic
1240C22×C4C23×D7111yescharacteristic
1241C22×C4C23×D7111yescharacteristic
1242C22×C4C23×D7111yescharacteristic
1243C22×C4C23×D7111yescharacteristic
1244C22×C4C23×D7111yescharacteristic
1245C22×C4C23×D7111yescharacteristic
1246C22×C4C23×D7111yescharacteristic
1247C4⋊C4—22no—
1248C4⋊C4—22no—
1249C4⋊C4—22no—
1250C4⋊C4—22no—
1251C4⋊C4—22no—
1252C4⋊C4—22no—
1253C4⋊C4—22no—
1254C4⋊C4—22no—
1255C4⋊C4—41no—
1256C4⋊C4—41no—
1257C4⋊C4—41no—
1258C4⋊C4—2841no—
1259C4⋊C4—2841no—
1260C4⋊C4—2841no—
1261C4⋊C4—2841no—
1262C4⋊C4—2841no—
1263C4⋊C4—2841no—
1264C4⋊C4—2841no—
1265C4⋊C4—2841no—
1266C4⋊C4—2841no—
1267C4⋊C4—714no—
1268C4⋊C4—714no—
1269C4⋊C4—1422no—
1270C4⋊C4—1422no—
1271C4⋊C4—1422no—
1272C4⋊C4—1422no—
1273C4⋊C4—1422no—
1274C4⋊C4—1422no—
1275C4⋊C4—1422no—
1276C4⋊C4—1422no—
1277C4⋊C4—1422no—
1278C4⋊C4—1422no—
1279C4⋊C4—1422no—
1280C4⋊C4—1422no—
1281C4⋊C4—1422no—
1282C4⋊C4—1422no—
1283C4⋊C4—1422no—
1284C4⋊C4—1422no—
1285C4⋊C4—1422no—
1286C4⋊C4—1422no—
1287C4⋊C4—1422no—
1288C4⋊C4—1422no—
1289C4⋊C4—1422no—
1290C4⋊C4—1422no—
1291C4⋊C4—1422no—
1292C4⋊C4—1422no—
1293C4⋊C4—1422no—
1294C4⋊C4—1422no—
1295C22⋊C4—22no—
1296C22⋊C4—22no—
1297C22⋊C4—22no—
1298C22⋊C4—2841no—
1299C22⋊C4—2841no—
1300C22⋊C4—2841no—
1301C22⋊C4—2841no—
1302C22⋊C4—714no—
1303C22⋊C4—714no—
1304C22⋊C4—714no—
1305C22⋊C4—1422no—
1306C22⋊C4—1422no—
1307C22⋊C4—1422no—
1308C22⋊C4—1422no—
1309C22⋊C4—1422no—
1310C22⋊C4—1422no—
1311C22⋊C4—1422no—
1312C22⋊C4—1422no—
1313C22⋊C4—1422no—
1314C22⋊C4—1422no—
1315C22⋊C4—1422no—
1316C22⋊C4—1422no—
1317C22⋊C4—1422no—
1318C22⋊C4—1422no—
1319C22⋊C4—1422no—
1320C22⋊C4—1422no—
1321C22⋊C4—1422no—
1322C22⋊C4D4×D7114yes—
1323C42—22no—
1324C42—22no—
1325C42—714no—
1326C42—714no—
1327C42—1422no—
1328C42—1422no—
1329C42—1422no—
1330C42—1422no—
1331C42—1422no—
1332C42—1422no—
1333C42—1422no—
1334C42—1422no—
1335C42—1422no—
1336C42—1422no—
1337C42—1422no—
1338C42—1422no—
1339C42—1422no—
1340C42—1422no—
1341C42—1422no—
1342C42—1422no—
1343C23—21no—
1344C23—21no—
1345C23—21no—
1346C23—21no—
1347C23—2844no—
1348C23—2844no—
1349C23—2844no—
1350C23—2844no—
1351C23—2844no—
1352C23—712no—
1353C23—712no—
1354C23—712no—
1355C23—712no—
1356C23—1428no—
1357C23—1421no—
1358C23—1421no—
1359C23—1421no—
1360C23—1421no—
1361C23—1421no—
1362C23—1421no—
1363C23—1428no—
1364C23—1421no—
1365C23—1421no—
1366C23—1421no—
1367C23—1421no—
1368C23C2×D4×D7112yes—
1369C23C2×Q8×D7112yes—
1370C23#41×D7112yes—
1371C23C24×D7111yescharacteristic
1372Q8—44no—
1373Q8—2844no—
1374Q8—2844no—
1375Q8—2844no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—28no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—44no—
1414C2×C4—44no—
1415C2×C4—2844no—
1416C2×C4—2844no—
1417C2×C4—2844no—
1418C2×C4—2844no—
1419C2×C4—2844no—
1420C2×C4—2844no—
1421C2×C4—712no—
1422C2×C4—712no—
1423C2×C4—712no—
1424C2×C4—712no—
1425C2×C4—712no—
1426C2×C4—712no—
1427C2×C4—7116no—
1428C2×C4—712no—
1429C2×C4—712no—
1430C2×C4—712no—
1431C2×C4—712no—
1432C2×C4—1428no—
1433C2×C4—1428no—
1434C2×C4—1428no—
1435C2×C4—1428no—
1436C2×C4—1421no—
1437C2×C4—1421no—
1438C2×C4—1421no—
1439C2×C4—1421no—
1440C2×C4—1421no—
1441C2×C4—1421no—
1442C2×C4—1421no—
1443C2×C4—1421no—
1444C2×C4—1421no—
1445C2×C4—1421no—
1446C2×C4—1421no—
1447C2×C4—1421no—
1448C2×C4—1421no—
1449C2×C4—1421no—
1450C2×C4—1421no—
1451C2×C4—1421no—
1452C2×C4—1421no—
1453C2×C4—1421no—
1454C2×C4—1421no—
1455C2×C4—1421no—
1456C2×C4—1421no—
1457C2×C4—1421no—
1458C2×C4—1421no—
1459C2×C4—1421no—
1460C2×C4—1421no—
1461C2×C4—1421no—
1462C2×C4—1421no—
1463C2×C4—1421no—
1464C2×C4—1421no—
1465C2×C4—1421no—
1466C2×C4—1421no—
1467C2×C4—1421no—
1468C2×C4C2×D4×D7112yes—
1469C2×C4C2×D4×D7112yes—
1470C2×C4C2×Q8×D7112yes—
1471C2×C4C2×Q8×D7112yes—
1472C2×C4#41×D7112yes—
1473C2×C4#41×D7112yes—
1474C22—22no—
1475C22—22no—
1476C22—22no—
1477C22—22no—
1478C22—22no—
1479C22—22no—
1480C22—28416no—
1481C22—2841no—
1482C22—2841no—
1483C22—2841no—
1484C22—2841no—
1485C22—714no—
1486C22—1422no—
1487C22—1422no—
1488C22—1422no—
1489C22—1422no—
1490C22—1422no—
1491C22—1422no—
1492C22—1422no—
1493C22—1422no—
1494C22—1422no—
1495C22C22⋊Q8×D7114yes—
1496C22C22×D4×D7111yescharacteristic
1497C22C22×Q8×D7111yescharacteristic
1498C22C2×#41×D7111yescharacteristic
1499C22C2×#41×D7111yescharacteristic
1500C22C2×#41×D7111yescharacteristic
1501C22#1798683411yescharacteristic
1502C22#1798683611yescharacteristic
1503C4—22no—
1504C4—22no—
1505C4—22no—
1506C4—22no—
1507C4—22no—
1508C4—22no—
1509C4—41no—
1510C4—41no—
1511C4—41no—
1512C4—41no—
1513C4—41no—
1514C4—41no—
1515C4—41no—
1516C4—41no—
1517C4—2841no—
1518C4—2841no—
1519C4—2841no—
1520C4—2841no—
1521C4—2841no—
1522C4—2841no—
1523C4—2841no—
1524C4—2841no—
1525C4—714no—
1526C4—714no—
1527C4—1422no—
1528C4—1422no—
1529C4—1422no—
1530C4—1422no—
1531C2—24no—
1532C2—2842no—
1533C2—1424no—
1534C2C2×C22⋊Q8×D7111yescharacteristic
1535C2#533×D7111yescharacteristic
1536C2#2260174411yescharacteristic
1537C2#2260182411yescharacteristic
1538C2#2260182711yescharacteristic
1539C2#2260189511yescharacteristic
1540C2#2260190511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2438C2
prime radicalC24×D71C23
hypercenter#2438D71
hypocenterC71#34739
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2438

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#17986551C2semidirect
3. #22592059C2semidirect
4. #22592057C2semidirect
5. #22592052C2semidirect
6. #22592050C2semidirect
7. #22592037C2semidirect
8. #22592035C2semidirect
9. #22592030C2semidirect
10. #22592028C2semidirect
11. #22592018C2semidirect
12. #22592016C2semidirect
13. #22592010C2semidirect
18. #22591617C2semidirect
19. #22591617C2semidirect
20. #22591613C2semidirect
21. #22591611C2semidirect
22. #22590878C2semidirect
23. #22590874C2semidirect
24. #22590874C2semidirect
25. #22590870C2semidirect
26. #22590819C2semidirect
27. #22590819C2semidirect
28. #22590742C2semidirect
31. C71×#2438C2semidirect
34. C2×#14556127C22semidirect
35. C2×#14556126C22semidirect
36. C2×#14556118C22semidirect
37. C2×#14556118C22semidirect
45. C2×Q8×Dic71C22semidirect
46. C2×#14556093C22semidirect
47. C2×#14556093C22semidirect
48. C2×#14556093C22semidirect
69. #17985941C22semidirect
70. #17985941C22semidirect
71. #17985938C22semidirect
76. #17985933C22semidirect
77. #17985933C22semidirect
78. #17985932C22semidirect
79. #17985932C22semidirect
80. #17985931C22semidirect
81. #17985931C22semidirect
90. #17985920C22semidirect
91. #17985920C22semidirect
92. #17985919C22semidirect
97. #17985905C22semidirect
98. #17985903C22semidirect
99. #17985903C22semidirect
100. #17985897C22semidirect
101. #17985896C22semidirect
102. #17985896C22semidirect
103. #17985896C22semidirect
104. #17985896C22semidirect
105. #17985896C22semidirect
106. #17985896C22semidirect
107. #17985894C22semidirect
108. #17985894C22semidirect
109. #17985894C22semidirect
110. #17985894C22semidirect
111. #17985886C22semidirect
112. #17985886C22semidirect
113. #17985883C22semidirect
114. #17985883C22semidirect
115. #17985882C22semidirect
116. #17985882C22semidirect
131. #17985868C22semidirect
132. #17985868C22semidirect
133. #17985863C22semidirect
134. #17985863C22semidirect
149. C4⋊C4×Dic71C22semidirect
150. C4⋊C4×Dic71C22semidirect
151. C4⋊C4×Dic71C22semidirect
152. C4⋊C4×Dic71C22semidirect
153. C4⋊C4×Dic71C22semidirect
154. C4⋊C4×Dic71C22semidirect
155. #17985850C22semidirect
156. #17985850C22semidirect
157. #17985850C22semidirect
158. #17985850C22semidirect
159. #17985850C22semidirect
160. #17985850C22semidirect
176. #400×C71C22semidirect
177. #398×C71C22semidirect
178. #398×C71C22semidirect
179. #395×C71C22semidirect
180. #391×C71C22semidirect
181. #389×C71C22semidirect
182. #387×C71C22semidirect
183. #387×C71C22semidirect
198. C22×C4×D71Q8semidirect
681. C2×Dic71C22⋊Q8semidirect
731. C2×D71#533semidirect
784. #2438D71semidirect
802. C71#34739semidirect
845. #400C2×D71semidirect
856. #398C2×D71semidirect
857. #398C2×D71semidirect
869. #395C2×D71semidirect
877. #391C2×D71semidirect
889. #389C2×D71semidirect
896. #387C2×D71semidirect
897. #387C2×D71semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179865512
C2×#117×D712
#225920592
#225920572
#225920522
#225920502
#225920372
#225920352
#225920302
#225920282
#225920182
#225920162
#225920102
#225920082
#225920052
#225920042
#225920032
#225916172
#225916132
#225916112
#225908782
#225908742
#225908702
#225908192
#225907422
#225907202
C2×#179858462
C71×#24382
#3473971