Finite Group Databasebeta

← C2×#22602074 #32905798

Subgroups — C2×#22602074 #32905798

Order 18176.

8006 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602074C2132yesmaximal, direct product factor
2C2×#17986712C211yesmaximal, characteristic, complemented
3C2×#17986699C211yesmaximal, characteristic, complemented
4C2×#17986696C211yesmaximal, characteristic, complemented
5C2×#17986695C211yesmaximal, characteristic, complemented
6C2×#17986693C211yesmaximal, characteristic, complemented
7C2×#17986679C212yesmaximal, complemented
8C2×#17986673C212yesmaximal, complemented
9C2×#17986652C211yesmaximal, characteristic, complemented
10C2×#17986649C211yesmaximal, characteristic, complemented
11C2×#17986642C212yesmaximal, complemented
12C2×#17986638C212yesmaximal, complemented
13C2×#17986626C211yesmaximal, characteristic, complemented
14C2×#17986613C212yesmaximal, complemented
15C2×#17986599C212yesmaximal, complemented
16C2×#17986565C211yesmaximal, characteristic, complemented
17C2×#17986548C212yesmaximal, complemented
18C2×#17986527C212yesmaximal, complemented
19C2×#17986508C211yesmaximal, characteristic, complemented
20C2×#121×D71C211yesmaximal, characteristic, complemented
21C2×#17986479C211yesmaximal, characteristic, complemented
22C2×#17986471C211yesmaximal, characteristic, complemented
23C2×#117×D71C211yesmaximal, characteristic, complemented
24C2×#555×C71C211yesmaximal, characteristic, complemented
25C22×#11765866C2212yescomplemented
26C22×#11765865C2211yescharacteristic
27C22×#11765864C2212yescomplemented
28C22×D4×D71C2211yescharacteristic
29C22×D4×D71C2212yes—
30C23×C4×D71C2211yescharacteristic
31#17986712C22116yescomplemented
32#17986699C22116yescomplemented
33#17986696C22116yescomplemented
34#17986695C22116yescomplemented
35#17986693C22116yescomplemented
36#17986679C22132yescomplemented
37#17986673C22132yescomplemented
38#17986652C22116yescomplemented
39#17986649C22116yescomplemented
40#17986642C22132yescomplemented
41#17986638C22132yescomplemented
42#17986626C22116yescomplemented
43#17986613C22132yescomplemented
44#17986599C22132yescomplemented
45#17986565C22116yescomplemented
46#17986548C22132yescomplemented
47C2×#14556127C2211yescharacteristic, complemented
48C2×#14556126C2212yescomplemented
49C2×#14556124C2212yescomplemented
50#17986527C22132yescomplemented
51C2×#14556123C2212yescomplemented
52C2×#14556122C2212yescomplemented
53C2×#14556121C2212yescomplemented
54C2×#14556121C2212yescomplemented
55C2×#14556120C2211yescharacteristic, complemented
56C2×#14556119C2211yescharacteristic, complemented
57C2×#14556118C2212yescomplemented
58C2×#14556116C2212yescomplemented
59C2×#14556114C2212yescomplemented
60C2×#14556114C2212yescomplemented
61#17986508C22116yescomplemented
62C2×#14556113C2211yescharacteristic
63C2×#14556113C2212yescomplemented
64C2×#14556113C2212yescomplemented
65C2×#14556111C2212yescomplemented
66C2×#14556110C2211yescharacteristic
67C2×#14556110C2212yescomplemented
68C2×#14556110C2212yescomplemented
69C2×#14556110C2212yescomplemented
70C2×#14556109C2212yescomplemented
71C2×#14556109C2212yescomplemented
72C2×#14556106C2212yes—
73C2×#14556106C2211yescharacteristic, complemented
74C2×#14556105C2212yescomplemented
75C2×#14556105C2211yescharacteristic, complemented
76C2×#14556104C2212yes—
77C2×#14556104C2212yescomplemented
78C2×#14556103C2211yescharacteristic
79C2×#14556103C2211yescharacteristic, complemented
80C2×#14556102C2211yescharacteristic
81C2×#14556102C2211yescharacteristic, complemented
82C2×#14556101C2212yes—
83C2×#14556101C2212yescomplemented
84C2×#14556101C2212yescomplemented
85C2×#14556101C2212yescomplemented
86C2×#14556101C2211yescharacteristic, complemented
87C2×#14556100C2212yes—
88C2×#14556100C2212yescomplemented
89C2×#14556100C2211yescharacteristic, complemented
90C2×#14556099C2211yescharacteristic
91C2×#14556099C2212yescomplemented
92C2×#14556099C2211yescharacteristic, complemented
93#121×D71C22116yescomplemented
94C2×#14556098C2211yescharacteristic
95C2×#14556098C2212yes—
96C2×#14556096C2211yescharacteristic
97C2×#14556096C2212yes—
98#17986479C22116yescomplemented
99#17986471C22116yescomplemented
100C2×C4×Dic142C2212yescomplemented
101C2×C4×D284C2212yes—
102C2×C4×D284C2211yescharacteristic, complemented
103C2×C4×D284C2212yescomplemented
104C2×C4×D284C2211yescharacteristic, complemented
105C2×D4×Dic71C2211yescharacteristic, complemented
106C2×#14556090C2211yescharacteristic, complemented
107C2×C4×C22⋊D71C2212yescomplemented
108C2×C4×C22⋊D71C2212yescomplemented
109C2×C4×C22⋊D71C2211yescharacteristic, complemented
110C2×C4×C22⋊D71C2211yescharacteristic, complemented
111C2×(C22⋊D71)⋊C4C2212yes—
112C2×(C22⋊D71)⋊C4C2212yescomplemented
113C2×(C22⋊D71)⋊C4C2212yescomplemented
114C2×(C22⋊D71)⋊C4C2212yescomplemented
115C2×(C22⋊D71)⋊C4C2212yescomplemented
116C2×#14556087C2211yescharacteristic, complemented
117C2×#14556086C2211yescharacteristic
118C2×#14556086C2211yescharacteristic
119C2×#14556086C2211yescharacteristic, complemented
120C2×#14556085C2211yescharacteristic
121C2×#14556085C2212yes—
122C2×#14556085C2212yescomplemented
123C2×#14556084C2212yescomplemented
124#117×D71C22116yescomplemented
125C22×C4⋊Dic71C2211yescharacteristic, complemented
126C2×C4⋊C4×D71C2211yescharacteristic
127C2×C4⋊C4×D71C2211yescharacteristic, complemented
128C2×C4⋊C4×D71C2211yescharacteristic, complemented
129C2×C4⋊C4×D71C2211yescharacteristic, complemented
130C22×(C2×D71)⋊C4C2212yes—
131C2×C22⋊C4×D71C2212yes—
132C2×C22⋊C4×D71C2212yes—
133C2×C22⋊C4×D71C2212yes—
134C2×C42×D71C2212yescomplemented
135#555×C71C22116yescomplemented
136C2×C4⋊Q8×C71C2211yescharacteristic, complemented
137C2×#124×C71C2212yescomplemented
138C2×#124×C71C2212yescomplemented
139C2×#121×C71C2211yescharacteristic
140C2×#121×C71C2212yescomplemented
141C2×#121×C71C2211yescharacteristic, complemented
142C2×C4×D4×C71C2211yescharacteristic, complemented
143C2×C4×D4×C71C2211yescharacteristic, complemented
144C2×#117×C71C2211yescharacteristic, complemented
145C2×#117×C71C2211yescharacteristic, complemented
146C2×#117×C71C2212yescomplemented
147C24×D71C2311yescharacteristic
148C24×D71C2312yes—
149C2×#11765866—48no—
150C2×#11765866C23116yescomplemented
151C2×#11765865—28no—
152C2×#11765865C2318yes—
153C2×#11765864—48no—
154C2×#11765864C23116yescomplemented
155C22×Dic142C2311yescharacteristic
156C22×Dic142C2312yes—
157C22×D284C2312yes—
158C22×D284C2311yescharacteristic
159C22×D284C2311yescharacteristic
160C22×D284C2311yescharacteristic
161C22×D284C2312yes—
162C22×C22⋊D71C2312yes—
163C22×C22⋊D71C2312yes—
164C22×C22⋊D71C2311yescharacteristic
165C22×C22⋊D71C2311yescharacteristic
166C22×C22⋊D71C2311yescharacteristic
167C22×C22⋊D71C2312yes—
168C22×C22⋊D71C2312yes—
169C22×C22⋊D71C2312yes—
170C22×C22⋊D71C2311yescharacteristic
171C2×D4×D71—28no—
172C2×D4×D71—48no—
173C2×D4×D71C2318yes—
174C2×D4×D71C23116yes—
175C23×Dic71C2311yescharacteristic
176C23×Dic71C2312yes—
177C23×Dic71C2312yes—
178C22×C4×D71—28no—
179C22×C4×D71C2311yescharacteristic
180C22×C4×D71C2311yescharacteristic
181C22×C4×D71C2311yescharacteristic
182C22×C4×D71C2318yes—
183C22×C4×D71C2312yes—
184C22×C4×D71C2311yescharacteristic
185C22×C4×D71C2312yes—
186C22×C4×D71C2312yes—
187C22×C4×D71C2312yes—
188C22×C4×D71C2312yes—
189C22×C4×D71C2312yes—
190C22×C4×D71C2311yescharacteristic
191#14556127C2318yescomplemented
192#14556126C23116yescomplemented
193#14556124C23116yescomplemented
194#14556123C23116yescomplemented
195#14556122C23116yescomplemented
196#14556121C23116yescomplemented
197#14556121C23116yescomplemented
198#14556120C2318yescomplemented
199#14556119C2318yescomplemented
200#14556118C23116yescomplemented
201#14556116C23116yescomplemented
202#14556114C23116yescomplemented
203#14556114C23116yescomplemented
204#14556113C2318yes—
205#14556113C23116yescomplemented
206#14556113C23116yescomplemented
207#14556111C23116yescomplemented
208#14556110C2318yes—
209#14556110C23116yescomplemented
210#14556110C23116yescomplemented
211#14556110C23116yescomplemented
212#14556109C23116yescomplemented
213#14556109C23116yescomplemented
214#14556106C23116yes—
215#14556106C2318yescomplemented
216#14556105C2318yescomplemented
217#14556105C23116yescomplemented
218#14556104C23116yes—
219#14556104C23116yescomplemented
220#14556103C2318yes—
221#14556103C2318yescomplemented
222#14556102C2318yes—
223#14556102C2318yescomplemented
224#14556101C23116yes—
225#14556101C23116yescomplemented
226#14556101C23116yescomplemented
227#14556101C23116yescomplemented
228#14556101C2318yescomplemented
229#14556100C23116yes—
230#14556100C2318yescomplemented
231#14556100C23116yescomplemented
232#14556099C2318yes—
233#14556099C2318yescomplemented
234#14556099C23116yescomplemented
235#14556098C23116yes—
236#14556098C2318yes—
237#14556096C23116yes—
238#14556096C2318yes—
239C4×Dic142C23116yescomplemented
240C4×D284C23116yes—
241C4×D284C23116yescomplemented
242C4×D284C2318yescomplemented
243C4×D284C2318yescomplemented
244D4×Dic71C2318yescomplemented
245#14556090C2318yescomplemented
246C4×C22⋊D71C23116yescomplemented
247C4×C22⋊D71C23116yescomplemented
248C4×C22⋊D71C2318yescomplemented
249C4×C22⋊D71C2318yescomplemented
250(C22⋊D71)⋊C4C23116yes—
251(C22⋊D71)⋊C4C23116yescomplemented
252(C22⋊D71)⋊C4C23116yescomplemented
253(C22⋊D71)⋊C4C23116yescomplemented
254(C22⋊D71)⋊C4C23116yescomplemented
255#14556087C2318yescomplemented
256#14556086C2318yes—
257#14556086C2318yes—
258#14556086C2318yescomplemented
259#14556085C2318yes—
260#14556085C23116yes—
261#14556085C23116yescomplemented
262#14556084C23116yescomplemented
263C2×C4⋊Dic71C2311yescharacteristic
264C2×C4⋊Dic71C2311yescharacteristic
265C2×C4⋊Dic71C2311yescharacteristic
266C2×C4⋊Dic71C2312yes—
267C2×C4⋊Dic71C2312yes—
268C2×C4⋊Dic71C2311yescharacteristic
269C2×C4⋊Dic71C2318yescomplemented
270C2×Dic71⋊C4C2312yes—
271C2×Dic71⋊C4C2312yes—
272C2×Dic71⋊C4C2312yes—
273C2×Dic71⋊C4C2312yes—
274C2×Dic71⋊C4C2311yescharacteristic
275C2×Dic71⋊C4C2311yescharacteristic
276C2×Dic71⋊C4C2311yescharacteristic
277C2×Dic71⋊C4C2312yes—
278C2×Dic71⋊C4C2312yes—
279C2×Dic71⋊C4C2312yes—
280C2×Dic71⋊C4C2312yes—
281C2×Dic71⋊C4C2311yescharacteristic
282C4⋊C4×D71C2318yes—
283C4⋊C4×D71C2318yescomplemented
284C4⋊C4×D71C2318yescomplemented
285C4⋊C4×D71C2318yescomplemented
286C2×C22⋊Dic71C2312yes—
287C2×C22⋊Dic71C2312yes—
288C2×C22⋊Dic71C2312yes—
289C2×C22⋊Dic71C2312yes—
290C2×C22⋊Dic71C2311yescharacteristic
291C2×C22⋊Dic71C2311yescharacteristic
292C2×(C2×D71)⋊C4C23116yes—
293C2×(C2×D71)⋊C4C2312yes—
294C2×(C2×D71)⋊C4C2311yescharacteristic
295C2×(C2×D71)⋊C4C2312yes—
296C2×(C2×D71)⋊C4C2312yes—
297C2×(C2×D71)⋊C4C2312yes—
298C2×(C2×D71)⋊C4C2311yescharacteristic
299C2×(C2×D71)⋊C4C2312yes—
300C2×(C2×D71)⋊C4C2312yes—
301C2×(C2×D71)⋊C4C2312yes—
302C2×(C2×D71)⋊C4C2312yes—
303C2×(C2×D71)⋊C4C2311yescharacteristic
304C2×(C2×D71)⋊C4C2311yescharacteristic
305C2×(C2×D71)⋊C4C2311yescharacteristic
306C2×(C2×D71)⋊C4C2312yes—
307C2×(C2×D71)⋊C4C2311yescharacteristic
308C22⋊C4×D71C23116yes—
309C22⋊C4×D71C23116yes—
310C22⋊C4×D71C23116yes—
311C2×C4×Dic71C2312yes—
312C2×C4×Dic71C2312yes—
313C2×C4×Dic71C2312yes—
314C2×C4×Dic71C2311yescharacteristic
315C2×C4×Dic71C2312yes—
316C42×D71C23116yescomplemented
317C22×Q8×C71C2312yes—
318C22×D4×C71C2311yescharacteristic
319C22×D4×C71C2312yes—
320C22×D4×C71C2312yes—
321C22×D4×C71C2311yescharacteristic
322C23×C4×C71C2311yescharacteristic
323C23×C4×C71C2311yescharacteristic
324C23×C4×C71C2312yes—
325C4⋊Q8×C71C2318yescomplemented
326#124×C71C23116yescomplemented
327#124×C71C23116yescomplemented
328#121×C71C2318yes—
329#121×C71C2318yescomplemented
330#121×C71C23116yescomplemented
331C4×D4×C71C2318yescomplemented
332C4×D4×C71C2318yescomplemented
333#117×C71C23116yescomplemented
334#117×C71C2318yescomplemented
335#117×C71C2318yescomplemented
336C2×C4⋊C4×C71C2311yescharacteristic
337C2×C4⋊C4×C71C2311yescharacteristic
338C2×C4⋊C4×C71C2311yescharacteristic
339C2×C4⋊C4×C71C2311yescharacteristic
340C2×C4⋊C4×C71C2312yes—
341C2×C22⋊C4×C71C2312yes—
342C2×C22⋊C4×C71C2312yes—
343C2×C22⋊C4×C71C2312yes—
344C2×C22⋊C4×C71C2312yes—
345C2×C22⋊C4×C71C2312yes—
346C2×C22⋊C4×C71C2311yescharacteristic
347C2×C22⋊C4×C71C2311yescharacteristic
348C2×C42×C71C2312yes—
349C2×C42×C71C2312yes—
350C2×C42×C71C2311yescharacteristic
351C23×D71—24no—
352C23×D71—24no—
353C23×D71—28no—
354C23×D71—42no—
355C23×D71—44no—
356C23×D71—44no—
357C23×D71C2411yescharacteristic
358C23×D71C2412yes—
359C23×D71C2414yes—
360C23×D71C2411yescharacteristic
361C23×D71C2411yescharacteristic
362C23×D71C2418yes—
363#11765866—432no—
364#11765865—232no—
365#11765864—432no—
366C2×Dic142—24no—
367C2×Dic142—44no—
368C2×Dic142C2414yes—
369C2×Dic142C2418yes—
370C2×D284—24no—
371C2×D284—28no—
372C2×D284—24no—
373C2×D284—24no—
374C2×D284—44no—
375C2×D284C2418yes—
376C2×D284C2414yes—
377C2×D284C2414yes—
378C2×D284C2414yes—
379C2×D284C2418yes—
380C2×C22⋊D71—24no—
381C2×C22⋊D71—28no—
382C2×C22⋊D71—24no—
383C2×C22⋊D71—28no—
384C2×C22⋊D71—24no—
385C2×C22⋊D71—44no—
386C2×C22⋊D71—42no—
387C2×C22⋊D71—44no—
388C2×C22⋊D71—44no—
389C2×C22⋊D71C2418yes—
390C2×C22⋊D71C2418yes—
391C2×C22⋊D71C2414yes—
392C2×C22⋊D71C2414yes—
393C2×C22⋊D71C2414yes—
394C2×C22⋊D71C2418yes—
395C2×C22⋊D71C2418yes—
396C2×C22⋊D71C2418yes—
397C2×C22⋊D71C2414yes—
398D4×D71—232no—
399D4×D71—432no—
400C22×Dic71—24no—
401C22×Dic71—44no—
402C22×Dic71—44no—
403C22×Dic71C2412yes—
404C22×Dic71C2411yescharacteristic
405C22×Dic71C2414yes—
406C22×Dic71C2411yescharacteristic
407C22×Dic71C2412yes—
408C22×Dic71C2412yes—
409C22×Dic71C2411yescharacteristic
410C22×Dic71C2411yescharacteristic
411C22×Dic71C2418yes—
412C22×Dic71C2418yes—
413C22×Dic71C2411yescharacteristic
414C2×C4×D71—24no—
415C2×C4×D71—28no—
416C2×C4×D71—24no—
417C2×C4×D71—24no—
418C2×C4×D71—24no—
419C2×C4×D71—232no—
420C2×C4×D71—44no—
421C2×C4×D71—44no—
422C2×C4×D71—44no—
423C2×C4×D71—44no—
424C2×C4×D71—44no—
425C2×C4×D71#4118yescomplemented
426C2×C4×D71C2414yes—
427C2×C4×D71C2414yes—
428C2×C4×D71C2414yes—
429C2×C4×D71C2418yes—
430C2×C4×D71C2414yes—
431C2×C4×D71C2418yes—
432C2×C4×D71C2418yes—
433C2×C4×D71C2418yes—
434C2×C4×D71C2418yes—
435C2×C4×D71C2418yes—
436C2×C4×D71C2414yes—
437C4⋊Dic71C2414yes—
438C4⋊Dic71C2414yes—
439C4⋊Dic71C2414yes—
440C4⋊Dic71C2418yes—
441C4⋊Dic71C2418yes—
442C4⋊Dic71C2414yes—
443Dic71⋊C4C2418yes—
444Dic71⋊C4C2418yes—
445Dic71⋊C4C2418yes—
446Dic71⋊C4C2418yes—
447Dic71⋊C4C2414yes—
448Dic71⋊C4C2414yes—
449Dic71⋊C4C2414yes—
450Dic71⋊C4C2418yes—
451Dic71⋊C4C2418yes—
452Dic71⋊C4C2418yes—
453Dic71⋊C4C2418yes—
454Dic71⋊C4C2414yes—
455C22⋊Dic71C2418yes—
456C22⋊Dic71C2418yes—
457C22⋊Dic71C2418yes—
458C22⋊Dic71C2418yes—
459C22⋊Dic71C2414yes—
460C22⋊Dic71C2414yes—
461(C2×D71)⋊C4C2418yes—
462(C2×D71)⋊C4C2414yes—
463(C2×D71)⋊C4C2418yes—
464(C2×D71)⋊C4C2418yes—
465(C2×D71)⋊C4C2418yes—
466(C2×D71)⋊C4C2414yes—
467(C2×D71)⋊C4C2418yes—
468(C2×D71)⋊C4C2418yes—
469(C2×D71)⋊C4C2418yes—
470(C2×D71)⋊C4C2418yes—
471(C2×D71)⋊C4C2414yes—
472(C2×D71)⋊C4C2414yes—
473(C2×D71)⋊C4C2414yes—
474(C2×D71)⋊C4C2418yes—
475(C2×D71)⋊C4C2414yes—
476C4×Dic71C2418yes—
477C4×Dic71C2418yes—
478C4×Dic71C2418yes—
479C4×Dic71C2414yes—
480C4×Dic71C2418yes—
481C24×C71C2411yescharacteristic
482C24×C71C2411yescharacteristic
483C24×C71C2412yes—
484C2×Q8×C71—44no—
485C2×Q8×C71C2418yes—
486C2×D4×C71—24no—
487C2×D4×C71—44no—
488C2×D4×C71—44no—
489C2×D4×C71—42no—
490C2×D4×C71C2414yes—
491C2×D4×C71C2418yes—
492C2×D4×C71C2418yes—
493C2×D4×C71C2414yes—
494C22×C4×C71—24no—
495C22×C4×C71—24no—
496C22×C4×C71—44no—
497C22×C4×C71C2411yescharacteristic
498C22×C4×C71C2412yes—
499C22×C4×C71C2411yescharacteristic
500C22×C4×C71C2412yes—
501C22×C4×C71C2414yes—
502C22×C4×C71C2412yes—
503C22×C4×C71C2411yescharacteristic
504C22×C4×C71C2414yes—
505C22×C4×C71C2411yescharacteristic
506C22×C4×C71C2418yes—
507C22×C4×C71C2411yescharacteristic
508C4⋊C4×C71C2414yes—
509C4⋊C4×C71C2414yes—
510C4⋊C4×C71C2414yes—
511C4⋊C4×C71C2414yes—
512C4⋊C4×C71C2418yes—
513C22⋊C4×C71C2418yes—
514C22⋊C4×C71C2418yes—
515C22⋊C4×C71C2418yes—
516C22⋊C4×C71C2418yes—
517C22⋊C4×C71C2418yes—
518C22⋊C4×C71C2414yes—
519C22⋊C4×C71C2414yes—
520C42×C71C2418yes—
521C42×C71C2418yes—
522C42×C71C2414yes—
523C23×C71—22no—
524C23×C71—22no—
525C23×C71—24no—
526C23×C71—22no—
527C23×C71—24no—
528C23×C71—22no—
529C23×C71—24no—
530C23×C71—22no—
531C23×C71—22no—
532C23×C71C2512yes—
533C23×C71C2514yes—
534C23×C71C2512yes—
535C23×C71C2511yescharacteristic
536C22×D71—22no—
537C22×D71—22no—
538C22×D71—22no—
539C22×D71—22no—
540C22×D71—22no—
541C22×D71—24no—
542C22×D71—22no—
543C22×D71—24no—
544C22×D71—24no—
545C22×D71—22no—
546C22×D71—28no—
547C22×D71—28no—
548C22×D71—216no—
549C22×D71—44no—
550C22×D71—416no—
551C22×D71—48no—
552C22×D71—48no—
553C22×D71—816no—
554C22×D71C2×#4114yes—
555C22×D71H(5,𝔽2)14yes—
556C22×D71C2514yes—
557C22×D71C2512yes—
558C22×D71C2512yes—
559C22×D71C2512yes—
560Q8×C71—48no—
561D4×C71—28no—
562D4×C71—44no—
563D4×C71—48no—
564D4×C71—48no—
565C2×C4×C71—22no—
566C2×C4×C71—22no—
567C2×C4×C71—24no—
568C2×C4×C71—24no—
569C2×C4×C71—22no—
570C2×C4×C71—22no—
571C2×C4×C71—24no—
572C2×C4×C71—28no—
573C2×C4×C71—28no—
574C2×C4×C71—48no—
575C2×C4×C71C2×#4114yes—
576C2×C4×C71C2512yes—
577C2×C4×C71C2514yes—
578C2×C4×C71C2512yes—
579C2×C4×C71C2512yes—
580C2×C4×C71C2514yes—
581C2×C4×C71C2514yes—
582C2×C4×C71C2512yes—
583C2×C4×C71C2512yes—
584C22⋊D71—28no—
585C22⋊D71—216no—
586C22⋊D71—28no—
587C22⋊D71—216no—
588C22⋊D71—28no—
589C22⋊D71—48no—
590C22⋊D71—44no—
591C22⋊D71—48no—
592C22⋊D71—48no—
593C2×Dic71—22no—
594C2×Dic71—22no—
595C2×Dic71—24no—
596C2×Dic71—24no—
597C2×Dic71—22no—
598C2×Dic71—22no—
599C2×Dic71—24no—
600C2×Dic71—28no—
601C2×Dic71—48no—
602C2×Dic71—48no—
603C2×Dic71C2×#4114yes—
604C2×Dic71C2512yes—
605C2×Dic71C2514yes—
606C2×Dic71C2514yes—
607C2×Dic71C2512yes—
608C2×Dic71C2512yes—
609C2×Dic71C2514yes—
610C2×Dic71C2512yes—
611C2×Dic71C2512yes—
612D284—28no—
613D284—216no—
614D284—28no—
615D284—28no—
616D284—48no—
617C4×D71—28no—
618C4×D71—216no—
619C4×D71—28no—
620C4×D71—28no—
621C4×D71—28no—
622C4×D71—48no—
623C4×D71—48no—
624C4×D71—48no—
625C4×D71—48no—
626C4×D71—48no—
627C4×D71C2×#41116yescomplemented
628Dic142—28no—
629Dic142—48no—
630C22×C71—22no—
631C22×C71—22no—
632C22×C71—24no—
633C22×C71—22no—
634C22×C71—24no—
635C22×C71—22no—
636C22×C71—22no—
637C22×C71—24no—
638C22×C71—22no—
639C22×C71—44no—
640C22×C71—48no—
641C22×C71—44no—
642C22×C71C22×#4112yes—
643C22×C71C2×H(5,𝔽2)12yes—
644C22×C71#58512yes—
645C22×C71C2611yescharacteristic
646C2×D71—22no—
647C2×D71—22no—
648C2×D71—22no—
649C2×D71—22no—
650C2×D71—28no—
651C2×D71—28no—
652C2×D71—22no—
653C2×D71—24no—
654C2×D71—22no—
655C2×D71—24no—
656C2×D71—24no—
657C2×D71—22no—
658C2×D71—416no—
659C2×D71—44no—
660C2×D71—48no—
661C2×D71—816no—
662C2×D71C22×#4114yes—
663C2×D71C2×H(5,𝔽2)14yes—
664C4×C71—22no—
665C4×C71—22no—
666C4×C71—24no—
667C4×C71—24no—
668C4×C71—22no—
669C4×C71—24no—
670C4×C71—22no—
671C4×C71C22×#4114yes—
672Dic71—22no—
673Dic71—22no—
674Dic71—22no—
675Dic71—24no—
676Dic71—24no—
677Dic71—22no—
678Dic71—24no—
679Dic71C22×#4114yes—
680C2×#3494—711nomaximal, Sylow
681C2×C71—42no—
682C2×C71—44no—
683C2×C71—42no—
684C2×C71#349414yescomplemented
685C2×C71C23×#4111yescharacteristic
686C2×C71C22×H(5,𝔽2)11yescharacteristic
687C2×C71C2×#58511yescharacteristic
688D71—24no—
689D71—24no—
690D71—42no—
691D71—44no—
692#3494—7132no—
693C2×#555—711no—
694C2×#555D7111yescharacteristic, complemented
695C2×#553—711no—
696C2×#553—711no—
697C2×#553—711no—
698C2×#553—711no—
699C2×#551—712no—
700C2×#551—712no—
701C2×#547—711no—
702C2×#547—711no—
703C2×#546—712no—
704C2×#546—712no—
705C2×#544—711no—
706C2×#542—712no—
707C2×#540—712no—
708C2×#535—711no—
709C2×#532—712no—
710C2×#529—712no—
711C2×#525—711no—
712C22×#121—711no—
713C2×#520—711no—
714C2×#518—711no—
715C22×#117—711no—
716C71C2×#349411yescharacteristic, complemented, Sylow
717C22×#41—712no—
718C22×#41—712no—
719C22×#41—711no—
720C23×D4—712no—
721C23×D4—711no—
722C24×C4—711no—
723#555—7116no—
724#555C2×D71116yescomplemented
725#553—7116no—
726#553—7116no—
727#553—7116no—
728#553—7116no—
729#551—7132no—
730#551—7132no—
731#547—7116no—
732#547—7116no—
733#546—7132no—
734#546—7132no—
735#544—7116no—
736#542—7132no—
737#540—7132no—
738#535—7116no—
739#532—7132no—
740C2×C4⋊Q8—712no—
741C2×C4⋊Q8—711no—
742C2×C4⋊Q8C2×D7111yescharacteristic, complemented
743C2×#127—712no—
744#529—7132no—
745C2×#126—712no—
746C2×#126—712no—
747C2×#126—712no—
748C2×#126—712no—
749C2×#125—712no—
750C2×#125—711no—
751C2×#125—711no—
752C2×#124—712no—
753C2×#124—712no—
754C2×#124—712no—
755C2×#124C2×D7112yescomplemented
756C2×#124C2×D7112yescomplemented
757#525—7116no—
758C2×#123—712no—
759C2×#123—712no—
760C2×#123—712no—
761C2×#123—711no—
762C2×#123—712no—
763C2×#123—712no—
764C2×#123—711no—
765C2×#123—712no—
766C2×#123—712no—
767C2×#123—712no—
768C2×C22⋊Q8—712no—
769C2×C22⋊Q8—712no—
770C2×C22⋊Q8—711no—
771C2×C22⋊Q8—712no—
772C2×C22⋊Q8—711no—
773C2×C22⋊Q8—712no—
774C2×#121—712no—
775C2×#121—711no—
776C2×#121—711no—
777C2×#121—711no—
778C2×#121—712no—
779C2×#121—712no—
780C2×#121—711no—
781C2×#121—711no—
782C2×#121—7116no—
783C2×#121—711no—
784C2×#121—711no—
785C2×#121—712no—
786C2×#121—711no—
787C2×#121—712no—
788C2×#121—712no—
789C2×#121—712no—
790C2×#121C2×D7111yescharacteristic
791C2×#121C2×D7111yescharacteristic, complemented
792C2×#121C2×D7112yescomplemented
793C2×#120—711no—
794C2×#120—712no—
795C2×#120—711no—
796C2×#120—712no—
797#520—7116no—
798#518—7116no—
799C2×C4×Q8—712no—
800C2×C4×D4—711no—
801C2×C4×D4—712no—
802C2×C4×D4—711no—
803C2×C4×D4—711no—
804C2×C4×D4—712no—
805C2×C4×D4—711no—
806C2×C4×D4—712no—
807C2×C4×D4—712no—
808C2×C4×D4—712no—
809C2×C4×D4—712no—
810C2×C4×D4—712no—
811C2×C4×D4—711no—
812C2×C4×D4—712no—
813C2×C4×D4—711no—
814C2×C4×D4—712no—
815C2×C4×D4C2×D7111yescharacteristic, complemented
816C2×C4×D4C2×D7111yescharacteristic, complemented
817C2×#117—711no—
818C2×#117—7116no—
819C2×#117—711no—
820C2×#117—711no—
821C2×#117—711no—
822C2×#117—712no—
823C2×#117—712no—
824C2×#117—711no—
825C2×#117—712no—
826C2×#117C2×D7111yescharacteristic, complemented
827C2×#117C2×D7111yescharacteristic, complemented
828C2×#117C2×D7112yescomplemented
829C22×C4⋊C4—711no—
830C22×C4⋊C4—711no—
831C22×C4⋊C4—711no—
832C22×C4⋊C4—711no—
833C22×C4⋊C4—711no—
834C22×C22⋊C4—712no—
835C22×C22⋊C4—712no—
836C22×C22⋊C4—712no—
837C22×C22⋊C4—712no—
838C22×C42—712no—
839C25—712no—
840C25—711no—
841C2×#41—2848no—
842C2×#41—2848no—
843C2×#41—7116no—
844C2×#41—7116no—
845C2×#41—718no—
846C2×#41—1428no—
847C22×Q8—712no—
848C22×Q8—711no—
849C22×Q8C22×D7112yes—
850C22×D4—2848no—
851C22×D4—711no—
852C22×D4—712no—
853C22×D4—712no—
854C22×D4—712no—
855C22×D4—7116no—
856C22×D4—711no—
857C22×D4—712no—
858C22×D4—711no—
859C22×D4—711no—
860C22×D4—712no—
861C22×D4—718no—
862C22×D4—712no—
863C22×D4—711no—
864C22×D4—711no—
865C22×D4—711no—
866C22×D4—712no—
867C22×D4—1428no—
868C22×D4C22×D7111yescharacteristic
869C22×D4C22×D7111yescharacteristic
870C22×D4C22×D7112yes—
871C22×D4C22×D7112yes—
872C23×C4—712no—
873C23×C4—712no—
874C23×C4—712no—
875C23×C4—712no—
876C23×C4—712no—
877C23×C4—712no—
878C23×C4—712no—
879C23×C4—711no—
880C23×C4—711no—
881C23×C4—711no—
882C23×C4—712no—
883C23×C4—711no—
884C23×C4—711no—
885C23×C4—718no—
886C23×C4—711no—
887C23×C4—1428no—
888C23×C4C22×D7111yescharacteristic
889C23×C4C22×D7111yescharacteristic
890C23×C4C22×D7112yes—
891C4⋊Q8—7116no—
892C4⋊Q8—718no—
893C4⋊Q8C22×D7118yescomplemented
894#127—7116no—
895#126—7116no—
896#126—7116no—
897#126—7116no—
898#126—7116no—
899#125—7116no—
900#125—718no—
901#125—718no—
902#124—7116no—
903#124—7116no—
904#124—7116no—
905#124C22×D71116yescomplemented
906#124C22×D71116yescomplemented
907#123—7116no—
908#123—7116no—
909#123—7116no—
910#123—718no—
911#123—7116no—
912#123—7116no—
913#123—718no—
914#123—7116no—
915#123—7116no—
916#123—7116no—
917C22⋊Q8—7116no—
918C22⋊Q8—7116no—
919C22⋊Q8—718no—
920C22⋊Q8—7116no—
921C22⋊Q8—718no—
922C22⋊Q8—7116no—
923#121—7116no—
924#121—718no—
925#121—718no—
926#121—718no—
927#121—7116no—
928#121—7116no—
929#121—718no—
930#121—718no—
931#121—718no—
932#121—718no—
933#121—7116no—
934#121—718no—
935#121—7116no—
936#121—7116no—
937#121—7116no—
938#121C22×D7118yes—
939#121C22×D7118yescomplemented
940#121C22×D71116yescomplemented
941#120—718no—
942#120—7116no—
943#120—718no—
944#120—7116no—
945C4×Q8—7116no—
946C4×D4—718no—
947C4×D4—7116no—
948C4×D4—718no—
949C4×D4—718no—
950C4×D4—7116no—
951C4×D4—718no—
952C4×D4—7116no—
953C4×D4—7116no—
954C4×D4—7116no—
955C4×D4—7116no—
956C4×D4—7116no—
957C4×D4—718no—
958C4×D4—7116no—
959C4×D4—718no—
960C4×D4—7116no—
961C4×D4C22×D7118yescomplemented
962C4×D4C22×D7118yescomplemented
963#117—718no—
964#117—718no—
965#117—718no—
966#117—718no—
967#117—7116no—
968#117—7116no—
969#117—718no—
970#117—7116no—
971#117C22×D7118yescomplemented
972#117C22×D7118yescomplemented
973#117C22×D71116yescomplemented
974C2×C4⋊C4—711no—
975C2×C4⋊C4—711no—
976C2×C4⋊C4—711no—
977C2×C4⋊C4—712no—
978C2×C4⋊C4—712no—
979C2×C4⋊C4—712no—
980C2×C4⋊C4—712no—
981C2×C4⋊C4—712no—
982C2×C4⋊C4—718no—
983C2×C4⋊C4—711no—
984C2×C4⋊C4—711no—
985C2×C4⋊C4—711no—
986C2×C4⋊C4—712no—
987C2×C4⋊C4—712no—
988C2×C4⋊C4—712no—
989C2×C4⋊C4—712no—
990C2×C4⋊C4—712no—
991C2×C4⋊C4—711no—
992C2×C4⋊C4—711no—
993C2×C4⋊C4—718no—
994C2×C4⋊C4—718no—
995C2×C4⋊C4—718no—
996C2×C4⋊C4—718no—
997C2×C4⋊C4C22×D7111yescharacteristic
998C2×C4⋊C4C22×D7111yescharacteristic
999C2×C4⋊C4C22×D7111yescharacteristic
1000C2×C4⋊C4C22×D7111yescharacteristic
1001C2×C4⋊C4C22×D7112yes—
1002C2×C22⋊C4—712no—
1003C2×C22⋊C4—712no—
1004C2×C22⋊C4—712no—
1005C2×C22⋊C4—712no—
1006C2×C22⋊C4—711no—
1007C2×C22⋊C4—711no—
1008C2×C22⋊C4—712no—
1009C2×C22⋊C4—711no—
1010C2×C22⋊C4—711no—
1011C2×C22⋊C4—712no—
1012C2×C22⋊C4—712no—
1013C2×C22⋊C4—712no—
1014C2×C22⋊C4—712no—
1015C2×C22⋊C4—7116no—
1016C2×C22⋊C4—712no—
1017C2×C22⋊C4—712no—
1018C2×C22⋊C4—712no—
1019C2×C22⋊C4—711no—
1020C2×C22⋊C4—711no—
1021C2×C22⋊C4—711no—
1022C2×C22⋊C4—712no—
1023C2×C22⋊C4—711no—
1024C2×C22⋊C4—7116no—
1025C2×C22⋊C4—7116no—
1026C2×C22⋊C4—7116no—
1027C2×C22⋊C4C22×D7112yes—
1028C2×C22⋊C4C22×D7112yes—
1029C2×C22⋊C4C22×D7112yes—
1030C2×C22⋊C4C22×D7112yes—
1031C2×C22⋊C4C22×D7112yes—
1032C2×C22⋊C4C22×D7111yescharacteristic
1033C2×C22⋊C4C22×D7111yescharacteristic
1034C2×C42—712no—
1035C2×C42—712no—
1036C2×C42—712no—
1037C2×C42—712no—
1038C2×C42—711no—
1039C2×C42—7116no—
1040C2×C42C22×D7112yes—
1041C2×C42C22×D7111yescharacteristic
1042C2×C42C22×D7112yes—
1043C24—2842no—
1044C24—2844no—
1045C24—2844no—
1046C24—718no—
1047C24—714no—
1048C24—711no—
1049C24—711no—
1050C24—712no—
1051C24—711no—
1052C24—1424no—
1053C24—1424no—
1054C24—1428no—
1055C24C23×D7111yescharacteristic
1056C24C23×D7112yes—
1057C24C23×D7111yescharacteristic
1058#41—28432no—
1059#41—28432no—
1060#41—14232no—
1061C2×Q8—44no—
1062C2×Q8—2844no—
1063C2×Q8—718no—
1064C2×Q8—714no—
1065C2×Q8—1424no—
1066C2×Q8C23×D7118yes—
1067C2×D4—24no—
1068C2×D4—44no—
1069C2×D4—42no—
1070C2×D4—44no—
1071C2×D4—2844no—
1072C2×D4—28432no—
1073C2×D4—2844no—
1074C2×D4—2842no—
1075C2×D4—2844no—
1076C2×D4—2844no—
1077C2×D4—714no—
1078C2×D4—718no—
1079C2×D4—718no—
1080C2×D4—718no—
1081C2×D4—714no—
1082C2×D4—718no—
1083C2×D4—714no—
1084C2×D4—714no—
1085C2×D4—718no—
1086C2×D4—718no—
1087C2×D4—714no—
1088C2×D4—714no—
1089C2×D4—714no—
1090C2×D4—718no—
1091C2×D4—1428no—
1092C2×D4—1424no—
1093C2×D4—1424no—
1094C2×D4—14232no—
1095C2×D4—1428no—
1096C2×D4—1424no—
1097C2×D4—1428no—
1098C2×D4—1424no—
1099C2×D4—1424no—
1100C2×D4—1424no—
1101C2×D4C23×D7114yes—
1102C2×D4C23×D7114yes—
1103C2×D4C23×D7118yes—
1104C2×D4C23×D7118yes—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—44no—
1108C22×C4—2844no—
1109C22×C4—2844no—
1110C22×C4—2844no—
1111C22×C4—2844no—
1112C22×C4—2844no—
1113C22×C4—2844no—
1114C22×C4—2844no—
1115C22×C4—718no—
1116C22×C4—718no—
1117C22×C4—718no—
1118C22×C4—718no—
1119C22×C4—718no—
1120C22×C4—718no—
1121C22×C4—718no—
1122C22×C4—711no—
1123C22×C4—718no—
1124C22×C4—714no—
1125C22×C4—714no—
1126C22×C4—711no—
1127C22×C4—712no—
1128C22×C4—712no—
1129C22×C4—711no—
1130C22×C4—711no—
1131C22×C4—712no—
1132C22×C4—711no—
1133C22×C4—714no—
1134C22×C4—718no—
1135C22×C4—714no—
1136C22×C4—714no—
1137C22×C4—714no—
1138C22×C4—1424no—
1139C22×C4—14232no—
1140C22×C4—1424no—
1141C22×C4—1428no—
1142C22×C4—1424no—
1143C22×C4—1424no—
1144C22×C4—1424no—
1145C22×C4C23×D7114yes—
1146C22×C4C23×D7114yes—
1147C22×C4C23×D7111yescharacteristic
1148C22×C4C23×D7112yes—
1149C22×C4C23×D7112yes—
1150C22×C4C23×D7111yescharacteristic
1151C22×C4C23×D7111yescharacteristic
1152C22×C4C23×D7111yescharacteristic
1153C22×C4C23×D7112yes—
1154C22×C4C23×D7118yes—
1155C22×C4C23×D7111yescharacteristic
1156C4⋊C4—718no—
1157C4⋊C4—718no—
1158C4⋊C4—718no—
1159C4⋊C4—718no—
1160C4⋊C4—714no—
1161C4⋊C4—714no—
1162C4⋊C4—714no—
1163C4⋊C4—718no—
1164C4⋊C4—718no—
1165C4⋊C4—718no—
1166C4⋊C4—718no—
1167C4⋊C4—714no—
1168C4⋊C4—714no—
1169C4⋊C4—714no—
1170C4⋊C4—714no—
1171C4⋊C4—718no—
1172C4⋊C4—718no—
1173C4⋊C4—714no—
1174C4⋊C4C23×D7114yes—
1175C4⋊C4C23×D7114yes—
1176C4⋊C4C23×D7114yes—
1177C4⋊C4C23×D7114yes—
1178C4⋊C4C23×D7118yes—
1179C22⋊C4—718no—
1180C22⋊C4—718no—
1181C22⋊C4—718no—
1182C22⋊C4—718no—
1183C22⋊C4—714no—
1184C22⋊C4—714no—
1185C22⋊C4—718no—
1186C22⋊C4—714no—
1187C22⋊C4—714no—
1188C22⋊C4—718no—
1189C22⋊C4—718no—
1190C22⋊C4—718no—
1191C22⋊C4—718no—
1192C22⋊C4—718no—
1193C22⋊C4—718no—
1194C22⋊C4—718no—
1195C22⋊C4—714no—
1196C22⋊C4—714no—
1197C22⋊C4—714no—
1198C22⋊C4—718no—
1199C22⋊C4—714no—
1200C22⋊C4C23×D7118yes—
1201C22⋊C4C23×D7118yes—
1202C22⋊C4C23×D7118yes—
1203C22⋊C4C23×D7118yes—
1204C22⋊C4C23×D7118yes—
1205C22⋊C4C23×D7114yes—
1206C22⋊C4C23×D7114yes—
1207C42—718no—
1208C42—718no—
1209C42—718no—
1210C42—718no—
1211C42—714no—
1212C42C23×D7118yes—
1213C42C23×D7114yes—
1214C42C23×D7118yes—
1215C23—22no—
1216C23—22no—
1217C23—24no—
1218C23—22no—
1219C23—24no—
1220C23—22no—
1221C23—24no—
1222C23—22no—
1223C23—22no—
1224C23—2844no—
1225C23—2848no—
1226C23—2848no—
1227C23—28416no—
1228C23—56816no—
1229C23—714no—
1230C23—714no—
1231C23—712no—
1232C23—712no—
1233C23—714no—
1234C23—712no—
1235C23—1428no—
1236C23—1428no—
1237C23—14216no—
1238C23—1422no—
1239C23—1424no—
1240C23—1422no—
1241C23—1424no—
1242C23—1424no—
1243C23—1422no—
1244C23—1422no—
1245C23—1422no—
1246C23—1422no—
1247C23—1422no—
1248C23C24×D7112yes—
1249C23C24×D7114yes—
1250C23C24×D7112yes—
1251C23C24×D7111yescharacteristic
1252Q8—48no—
1253Q8—2848no—
1254Q8—1428no—
1255D4—28no—
1256D4—48no—
1257D4—48no—
1258D4—44no—
1259D4—2848no—
1260D4—2848no—
1261D4—2844no—
1262D4—2848no—
1263D4—2848no—
1264D4—14216no—
1265D4—1428no—
1266D4—1428no—
1267D4—14216no—
1268D4—1428no—
1269D4—14216no—
1270D4—1428no—
1271D4—1428no—
1272D4—1428no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—28no—
1281C2×C4—28no—
1282C2×C4—48no—
1283C2×C4—2848no—
1284C2×C4—2848no—
1285C2×C4—2848no—
1286C2×C4—2848no—
1287C2×C4—2848no—
1288C2×C4—2848no—
1289C2×C4—2848no—
1290C2×C4—714no—
1291C2×C4—712no—
1292C2×C4—7116no—
1293C2×C4—712no—
1294C2×C4—714no—
1295C2×C4—714no—
1296C2×C4—712no—
1297C2×C4—712no—
1298C2×C4—714no—
1299C2×C4—712no—
1300C2×C4—1428no—
1301C2×C4—1428no—
1302C2×C4—14216no—
1303C2×C4—1428no—
1304C2×C4—1422no—
1305C2×C4—1422no—
1306C2×C4—1424no—
1307C2×C4—1424no—
1308C2×C4—1422no—
1309C2×C4—1422no—
1310C2×C4—1424no—
1311C2×C4—1428no—
1312C2×C4—1428no—
1313C2×C4#41×D7114yes—
1314C2×C4C24×D7112yes—
1315C2×C4C24×D7114yes—
1316C2×C4C24×D7114yes—
1317C2×C4C24×D7112yes—
1318C2×C4C24×D7112yes—
1319C2×C4C24×D7112yes—
1320C2×C4C24×D7114yes—
1321C2×C4C24×D7112yes—
1322C22—22no—
1323C22—22no—
1324C22—24no—
1325C22—22no—
1326C22—24no—
1327C22—22no—
1328C22—24no—
1329C22—22no—
1330C22—22no—
1331C22—44no—
1332C22—48no—
1333C22—44no—
1334C22—28416no—
1335C22—2848no—
1336C22—2844no—
1337C22—56816no—
1338C22—714no—
1339C22—714no—
1340C22—1422no—
1341C22—1424no—
1342C22—1422no—
1343C22—1424no—
1344C22—1424no—
1345C22—1422no—
1346C22—1428no—
1347C22—1428no—
1348C22—1422no—
1349C22—1422no—
1350C22—1422no—
1351C22—1422no—
1352C22C2×#41×D7112yes—
1353C22H(5,𝔽2)×D7112yes—
1354C22#1798683512yes—
1355C22C25×D7111yescharacteristic
1356C4—22no—
1357C4—22no—
1358C4—24no—
1359C4—22no—
1360C4—24no—
1361C4—22no—
1362C4—24no—
1363C4—714no—
1364C4—1422no—
1365C4—1422no—
1366C4—1424no—
1367C4—1424no—
1368C4—1422no—
1369C4—1422no—
1370C4—1424no—
1371C4C2×#41×D7114yes—
1372C2—42no—
1373C2—44no—
1374C2—42no—
1375C2—2844no—
1376C2—2842no—
1377C2—1424no—
1378C2—1424no—
1379C2#2260207414yesdirect product factor
1380C2C22×#41×D7111yescharacteristic
1381C2C2×H(5,𝔽2)×D7111yescharacteristic
1382C2C2×#1798683511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#555×C71C2
socleC23×C71C25
hypercenterC2×#555D71
hypocenterC71C2×#3494
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #22602074C2direct (N × H)
2. C2×#17986712C2semidirect
3. C2×#17986699C2semidirect
4. C2×#17986696C2semidirect
5. C2×#17986695C2semidirect
6. C2×#17986693C2semidirect
7. C2×#17986679C2semidirect
8. C2×#17986673C2semidirect
9. C2×#17986652C2semidirect
10. C2×#17986649C2semidirect
11. C2×#17986642C2semidirect
12. C2×#17986638C2semidirect
13. C2×#17986626C2semidirect
14. C2×#17986613C2semidirect
15. C2×#17986599C2semidirect
16. C2×#17986565C2semidirect
17. C2×#17986548C2semidirect
18. C2×#17986527C2semidirect
19. C2×#17986508C2semidirect
20. C2×#121×D71C2semidirect
21. C2×#17986479C2semidirect
22. C2×#17986471C2semidirect
23. C2×#117×D71C2semidirect
24. C2×#555×C71C2semidirect
25. C22×#11765866C22semidirect
27. C22×#11765864C22semidirect
31. #17986712C22semidirect
32. #17986699C22semidirect
33. #17986696C22semidirect
34. #17986695C22semidirect
35. #17986693C22semidirect
36. #17986679C22semidirect
37. #17986673C22semidirect
38. #17986652C22semidirect
39. #17986649C22semidirect
40. #17986642C22semidirect
41. #17986638C22semidirect
42. #17986626C22semidirect
43. #17986613C22semidirect
44. #17986599C22semidirect
45. #17986565C22semidirect
46. #17986548C22semidirect
47. C2×#14556127C22semidirect
48. C2×#14556126C22semidirect
49. C2×#14556124C22semidirect
50. #17986527C22semidirect
51. C2×#14556123C22semidirect
52. C2×#14556122C22semidirect
53. C2×#14556121C22semidirect
54. C2×#14556121C22semidirect
55. C2×#14556120C22semidirect
56. C2×#14556119C22semidirect
57. C2×#14556118C22semidirect
58. C2×#14556116C22semidirect
59. C2×#14556114C22semidirect
60. C2×#14556114C22semidirect
61. #17986508C22semidirect
63. C2×#14556113C22semidirect
64. C2×#14556113C22semidirect
65. C2×#14556111C22semidirect
67. C2×#14556110C22semidirect
68. C2×#14556110C22semidirect
69. C2×#14556110C22semidirect
70. C2×#14556109C22semidirect
71. C2×#14556109C22semidirect
73. C2×#14556106C22semidirect
74. C2×#14556105C22semidirect
75. C2×#14556105C22semidirect
77. C2×#14556104C22semidirect
79. C2×#14556103C22semidirect
81. C2×#14556102C22semidirect
83. C2×#14556101C22semidirect
84. C2×#14556101C22semidirect
85. C2×#14556101C22semidirect
86. C2×#14556101C22semidirect
88. C2×#14556100C22semidirect
89. C2×#14556100C22semidirect
91. C2×#14556099C22semidirect
92. C2×#14556099C22semidirect
93. #121×D71C22semidirect
98. #17986479C22semidirect
99. #17986471C22semidirect
100. C2×C4×Dic142C22semidirect
102. C2×C4×D284C22semidirect
103. C2×C4×D284C22semidirect
104. C2×C4×D284C22semidirect
105. C2×D4×Dic71C22semidirect
106. C2×#14556090C22semidirect
107. C2×C4×C22⋊D71C22semidirect
108. C2×C4×C22⋊D71C22semidirect
109. C2×C4×C22⋊D71C22semidirect
110. C2×C4×C22⋊D71C22semidirect
112. C2×(C22⋊D71)⋊C4C22semidirect
113. C2×(C22⋊D71)⋊C4C22semidirect
114. C2×(C22⋊D71)⋊C4C22semidirect
115. C2×(C22⋊D71)⋊C4C22semidirect
116. C2×#14556087C22semidirect
119. C2×#14556086C22semidirect
122. C2×#14556085C22semidirect
123. C2×#14556084C22semidirect
124. #117×D71C22semidirect
125. C22×C4⋊Dic71C22semidirect
127. C2×C4⋊C4×D71C22semidirect
128. C2×C4⋊C4×D71C22semidirect
129. C2×C4⋊C4×D71C22semidirect
134. C2×C42×D71C22semidirect
135. #555×C71C22semidirect
136. C2×C4⋊Q8×C71C22semidirect
137. C2×#124×C71C22semidirect
138. C2×#124×C71C22semidirect
140. C2×#121×C71C22semidirect
141. C2×#121×C71C22semidirect
142. C2×C4×D4×C71C22semidirect
143. C2×C4×D4×C71C22semidirect
144. C2×#117×C71C22semidirect
145. C2×#117×C71C22semidirect
146. C2×#117×C71C22semidirect
150. C2×#11765866C23semidirect
154. C2×#11765864C23semidirect
191. #14556127C23semidirect
192. #14556126C23semidirect
193. #14556124C23semidirect
194. #14556123C23semidirect
195. #14556122C23semidirect
196. #14556121C23semidirect
197. #14556121C23semidirect
198. #14556120C23semidirect
199. #14556119C23semidirect
200. #14556118C23semidirect
201. #14556116C23semidirect
202. #14556114C23semidirect
203. #14556114C23semidirect
205. #14556113C23semidirect
206. #14556113C23semidirect
207. #14556111C23semidirect
209. #14556110C23semidirect
210. #14556110C23semidirect
211. #14556110C23semidirect
212. #14556109C23semidirect
213. #14556109C23semidirect
215. #14556106C23semidirect
216. #14556105C23semidirect
217. #14556105C23semidirect
219. #14556104C23semidirect
221. #14556103C23semidirect
223. #14556102C23semidirect
225. #14556101C23semidirect
226. #14556101C23semidirect
227. #14556101C23semidirect
228. #14556101C23semidirect
230. #14556100C23semidirect
231. #14556100C23semidirect
233. #14556099C23semidirect
234. #14556099C23semidirect
239. C4×Dic142C23semidirect
241. C4×D284C23semidirect
242. C4×D284C23semidirect
243. C4×D284C23semidirect
244. D4×Dic71C23semidirect
245. #14556090C23semidirect
246. C4×C22⋊D71C23semidirect
247. C4×C22⋊D71C23semidirect
248. C4×C22⋊D71C23semidirect
249. C4×C22⋊D71C23semidirect
251. (C22⋊D71)⋊C4C23semidirect
252. (C22⋊D71)⋊C4C23semidirect
253. (C22⋊D71)⋊C4C23semidirect
254. (C22⋊D71)⋊C4C23semidirect
255. #14556087C23semidirect
258. #14556086C23semidirect
261. #14556085C23semidirect
262. #14556084C23semidirect
269. C2×C4⋊Dic71C23semidirect
283. C4⋊C4×D71C23semidirect
284. C4⋊C4×D71C23semidirect
285. C4⋊C4×D71C23semidirect
316. C42×D71C23semidirect
325. C4⋊Q8×C71C23semidirect
326. #124×C71C23semidirect
327. #124×C71C23semidirect
329. #121×C71C23semidirect
330. #121×C71C23semidirect
331. C4×D4×C71C23semidirect
332. C4×D4×C71C23semidirect
333. #117×C71C23semidirect
334. #117×C71C23semidirect
335. #117×C71C23semidirect
425. C2×C4×D71#41semidirect
627. C4×D71C2×#41semidirect
684. C2×C71#3494semidirect
694. C2×#555D71semidirect
716. C71C2×#3494semidirect
724. #555C2×D71semidirect
742. C2×C4⋊Q8C2×D71semidirect
755. C2×#124C2×D71semidirect
756. C2×#124C2×D71semidirect
791. C2×#121C2×D71semidirect
792. C2×#121C2×D71semidirect
815. C2×C4×D4C2×D71semidirect
816. C2×C4×D4C2×D71semidirect
826. C2×#117C2×D71semidirect
827. C2×#117C2×D71semidirect
828. C2×#117C2×D71semidirect
893. C4⋊Q8C22×D71semidirect
905. #124C22×D71semidirect
906. #124C22×D71semidirect
939. #121C22×D71semidirect
940. #121C22×D71semidirect
961. C4×D4C22×D71semidirect
962. C4×D4C22×D71semidirect
971. #117C22×D71semidirect
972. #117C22×D71semidirect
973. #117C22×D71semidirect
1379. C2#22602074direct (N × H)

Maximal subgroups

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

subgroupindex
#226020742
C2×#179867122
C2×#179866992
C2×#179866962
C2×#179866952
C2×#179866932
C2×#179866792
C2×#179866732
C2×#179866522
C2×#179866492
C2×#179866422
C2×#179866382
C2×#179866262
C2×#179866132
C2×#179865992
C2×#179865652
C2×#179865482
C2×#179865272
C2×#179865082
C2×#121×D712
C2×#179864792
C2×#179864712
C2×#117×D712
C2×#555×C712
C2×#349471