Finite Group Databasebeta

← #13525507

Subgroups — #13525507

Order 1792.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2462C211yesmaximal, characteristic
2#11740479C211yesmaximal, characteristic
3Dic7×#125C211yesmaximal, characteristic
4#11739917C211yesmaximal, characteristic
5C4×Q8×Dic7C211yesmaximal, characteristic
6#11735237C211yesmaximal, characteristic
7#11735231C211yesmaximal, characteristic
8#11735186C211yesmaximal, characteristic
9#11735186C211yesmaximal, characteristic
10#11734637C211yesmaximal, characteristic
11#11734636C211yesmaximal, characteristic
12#11734616C211yesmaximal, characteristic
13#11734616C211yesmaximal, characteristic
14#11733535C211yesmaximal, characteristic
15#11733459C211yesmaximal, characteristic
16#11733412C211yesmaximal, characteristic
17#11733407C211yesmaximal, characteristic
18#11732554C211yesmaximal, characteristic
19#11732547C211yesmaximal, characteristic
20#11732546C211yesmaximal, characteristic
21#11732484C211yesmaximal, characteristic
22#11732473C211yesmaximal, characteristic
23#11732432C211yesmaximal, characteristic
24#11732388C211yesmaximal, characteristic
25#11732388C211yesmaximal, characteristic
26#11732388C211yesmaximal, characteristic
27#11732383C211yesmaximal, characteristic
28#11732383C211yesmaximal, characteristic
29#11732383C211yesmaximal, characteristic
30#11731145C211yesmaximal, characteristic
31C4×#6450C211yesmaximal, characteristic
32C2×C7×#125C2211yescharacteristic
33C2×C4×C7×Q8C2211yescharacteristic
34C2×Q8×Dic7C2211yescharacteristic
35C2×Q8×Dic7C2211yescharacteristic
36C2×#6452C2211yescharacteristic
37C2×#6452C2211yescharacteristic
38C2×#6452C2211yescharacteristic
39C2×#6451C2211yescharacteristic
40C2×#6450C2211yescharacteristic
41C2×#6450C2211yescharacteristic
42C2×#6450C2211yescharacteristic
43C2×#6450C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#398C2211yescharacteristic
46C7×#398C2211yescharacteristic
47C7×#395C2211yescharacteristic
48C7×#395C2211yescharacteristic
49C7×#389C2211yescharacteristic
50C7×#389C2211yescharacteristic
51C7×#387C2211yescharacteristic
52C7×#387C2211yescharacteristic
53C7×#387C2211yescharacteristic
54C7×#387C2211yescharacteristic
55C7×#387C2211yescharacteristic
56C7×#387C2211yescharacteristic
57C4×C7×C4⋊C4C2211yescharacteristic
58#90001C2211yescharacteristic
59#90001C2211yescharacteristic
60#89758C2211yescharacteristic
61#89758C2211yescharacteristic
62#89757C2211yescharacteristic
63#89757C2211yescharacteristic
64#89757C2211yescharacteristic
65#89756C2211yescharacteristic
66#89756C2211yescharacteristic
67#89756C2211yescharacteristic
68#89756C2211yescharacteristic
69#89756C2211yescharacteristic
70#89756C2211yescharacteristic
71#89755C2211yescharacteristic
72#89755C2211yescharacteristic
73#89755C2211yescharacteristic
74#89755C2211yescharacteristic
75#89754C2211yescharacteristic
76#89754C2211yescharacteristic
77#89753C2211yescharacteristic
78#89753C2211yescharacteristic
79#89753C2211yescharacteristic
80#89753C2211yescharacteristic
81#89753C2211yescharacteristic
82#89753C2211yescharacteristic
83#89753C2211yescharacteristic
84#89750C2211yescharacteristic
85#89750C2211yescharacteristic
86#89748C2211yescharacteristic
87C4⋊C4×Dic7C2211yescharacteristic
88C4⋊C4×Dic7C2211yescharacteristic
89C4⋊C4×Dic7C2211yescharacteristic
90C4⋊C4×Dic7C2211yescharacteristic
91C4⋊C4×Dic7C2211yescharacteristic
92C4⋊C4×Dic7C2211yescharacteristic
93C4⋊C4×Dic7C2211yescharacteristic
94C4⋊C4×Dic7C2211yescharacteristic
95C4⋊C4×Dic7C2211yescharacteristic
96C4⋊C4×Dic7C2211yescharacteristic
97C4⋊C4×Dic7C2211yescharacteristic
98C4⋊C4×Dic7C2211yescharacteristic
99C4⋊C4×Dic7C2211yescharacteristic
100C4⋊C4×Dic7C2211yescharacteristic
101C4⋊C4×Dic7C2211yescharacteristic
102C4⋊C4×Dic7C2211yescharacteristic
103#89746C2211yescharacteristic
104#89744C2211yescharacteristic
105#89744C2211yescharacteristic
106#89744C2211yescharacteristic
107#89744C2211yescharacteristic
108#89744C2211yescharacteristic
109#89744C2211yescharacteristic
110#89744C2211yescharacteristic
111#89744C2211yescharacteristic
112#89708C2211yescharacteristic
113C4×C4⋊Dic7C2211yescharacteristic
114C4×C4⋊Dic7C2211yescharacteristic
115C4×C4⋊Dic7C2211yescharacteristic
116#89705C2211yescharacteristic
117#89705C2211yescharacteristic
118#89705C2211yescharacteristic
119#89705C2211yescharacteristic
120#89705C2211yescharacteristic
121#89705C2211yescharacteristic
122C4×Dic7⋊C4C2211yescharacteristic
123C4×Dic7⋊C4C2211yescharacteristic
124C42×Dic7C2211yescharacteristic
125C42×Dic7C2211yescharacteristic
126C42×Dic7C2211yescharacteristic
127C42×Dic7C2211yescharacteristic
128C42×Dic7C2211yescharacteristic
129#89701C2211yescharacteristic
130#89700C2211yescharacteristic
131#89433C2211yescharacteristic
132#89433C2211yescharacteristic
133#89433C2211yescharacteristic
134#89433C2211yescharacteristic
135#89432C2211yescharacteristic
136#89432C2211yescharacteristic
137#89431C2211yescharacteristic
138#89431C2211yescharacteristic
139#89428C2211yescharacteristic
140#89428C2211yescharacteristic
141#89428C2211yescharacteristic
142#89428C2211yescharacteristic
143#89427C2211yescharacteristic
144#89427C2211yescharacteristic
145#89427C2211yescharacteristic
146#89427C2211yescharacteristic
147#89427C2211yescharacteristic
148#89426C2211yescharacteristic
149#89426C2211yescharacteristic
150#89426C2211yescharacteristic
151#89424C2211yescharacteristic
152#89424C2211yescharacteristic
153#89424C2211yescharacteristic
154#89422C2211yescharacteristic
155#89422C2211yescharacteristic
156#89422C2211yescharacteristic
157#89421C2211yescharacteristic
158#89421C2211yescharacteristic
159#89421C2211yescharacteristic
160#89421C2211yescharacteristic
161#89421C2211yescharacteristic
162#89421C2211yescharacteristic
163#89421C2211yescharacteristic
164#89421C2211yescharacteristic
165#89421C2211yescharacteristic
166#89421C2211yescharacteristic
167#89421C2211yescharacteristic
168#89421C2211yescharacteristic
169#89420C2211yescharacteristic
170#89420C2211yescharacteristic
171#89420C2211yescharacteristic
172#89420C2211yescharacteristic
173#89419C2211yescharacteristic
174#89419C2211yescharacteristic
175#89419C2211yescharacteristic
176#89419C2211yescharacteristic
177#89419C2211yescharacteristic
178#89419C2211yescharacteristic
179#89418C2211yescharacteristic
180#89418C2211yescharacteristic
181#89418C2211yescharacteristic
182#89418C2211yescharacteristic
183#89418C2211yescharacteristic
184#89418C2211yescharacteristic
185#89418C2211yescharacteristic
186#89418C2211yescharacteristic
187#34920—71nomaximal, Sylow
188C22×C7×Q8C2311yescharacteristic
189C22×Dic14C2311yescharacteristic
190C22×Dic14C2311yescharacteristic
191C22×Dic14C2311yescharacteristic
192C7×#125—24no—
193C4×C7×Q8—24no—
194C2×C7×C4⋊C4C2311yescharacteristic
195C2×C7×C4⋊C4C2311yescharacteristic
196C2×C7×C4⋊C4C2311yescharacteristic
197C2×C7×C4⋊C4C2311yescharacteristic
198C2×C7×C4⋊C4C2311yescharacteristic
199C2×C7×C4⋊C4C2311yescharacteristic
200C2×C7×C4⋊C4C2311yescharacteristic
201C2×C7×C4⋊C4C2311yescharacteristic
202C2×C7×C4⋊C4C2311yescharacteristic
203C2×C7×C4⋊C4C2311yescharacteristic
204C2×C7×C4⋊C4C2311yescharacteristic
205C2×C7×C4⋊C4C2311yescharacteristic
206C2×C7×C4⋊C4C2311yescharacteristic
207C2×C7×C4⋊C4C2311yescharacteristic
208C2×C7×C4⋊C4C2311yescharacteristic
209C2×C42×C7C2311yescharacteristic
210C2×C42×C7C2311yescharacteristic
211C2×C42×C7C2311yescharacteristic
212C2×C42×C7C2311yescharacteristic
213C2×C42×C7C2311yescharacteristic
214Q8×Dic7—24no—
215Q8×Dic7—24no—
216C2×C4⋊Dic7C2311yescharacteristic
217C2×C4⋊Dic7C2311yescharacteristic
218C2×C4⋊Dic7C2311yescharacteristic
219C2×C4⋊Dic7C2311yescharacteristic
220C2×C4⋊Dic7C2311yescharacteristic
221C2×C4⋊Dic7C2311yescharacteristic
222C2×C4⋊Dic7C2311yescharacteristic
223C2×C4⋊Dic7C2311yescharacteristic
224C2×C4⋊Dic7C2311yescharacteristic
225C2×C4⋊Dic7C2311yescharacteristic
226C2×C4⋊Dic7C2311yescharacteristic
227C2×C4⋊Dic7C2311yescharacteristic
228C2×C4⋊Dic7C2311yescharacteristic
229C2×C4⋊Dic7C2311yescharacteristic
230C2×C4⋊Dic7C2311yescharacteristic
231C2×Dic7⋊C4C2311yescharacteristic
232C2×Dic7⋊C4C2311yescharacteristic
233C2×Dic7⋊C4C2311yescharacteristic
234C2×Dic7⋊C4C2311yescharacteristic
235C2×Dic7⋊C4C2311yescharacteristic
236C2×Dic7⋊C4C2311yescharacteristic
237C2×Dic7⋊C4C2311yescharacteristic
238C2×Dic7⋊C4C2311yescharacteristic
239C2×Dic7⋊C4C2311yescharacteristic
240C2×Dic7⋊C4C2311yescharacteristic
241C2×Dic7⋊C4C2311yescharacteristic
242C2×Dic7⋊C4C2311yescharacteristic
243C2×Dic7⋊C4C2311yescharacteristic
244C2×Dic7⋊C4C2311yescharacteristic
245C2×Dic7⋊C4C2311yescharacteristic
246C2×Dic7⋊C4C2311yescharacteristic
247C2×Dic7⋊C4C2311yescharacteristic
248C2×Dic7⋊C4C2311yescharacteristic
249C2×Dic7⋊C4C2311yescharacteristic
250C2×Dic7⋊C4C2311yescharacteristic
251C2×Dic7⋊C4C2311yescharacteristic
252C2×Dic7⋊C4C2311yescharacteristic
253C2×Dic7⋊C4C2311yescharacteristic
254C2×Dic7⋊C4C2311yescharacteristic
255C2×Dic7⋊C4C2311yescharacteristic
256C2×Dic7⋊C4C2311yescharacteristic
257C2×C4×Dic7C2311yescharacteristic
258C2×C4×Dic7C2311yescharacteristic
259C2×C4×Dic7C2311yescharacteristic
260C2×C4×Dic7C2311yescharacteristic
261C2×C4×Dic7C2311yescharacteristic
262C2×C4×Dic7C2311yescharacteristic
263C2×C4×Dic7C2311yescharacteristic
264C2×C4×Dic7C2311yescharacteristic
265C2×C4×Dic7C2311yescharacteristic
266C2×C4×Dic7C2311yescharacteristic
267C2×C4×Dic7C2311yescharacteristic
268C2×C4×Dic7C2311yescharacteristic
269C2×C4×Dic7C2311yescharacteristic
270C2×C4×Dic7C2311yescharacteristic
271C2×C4×Dic7C2311yescharacteristic
272C2×C4×Dic7C2311yescharacteristic
273C2×C4×Dic7C2311yescharacteristic
274C2×C4×Dic7C2311yescharacteristic
275C2×C4×Dic7C2311yescharacteristic
276C2×C4×Dic7C2311yescharacteristic
277C2×C4×Dic7C2311yescharacteristic
278C2×C4×Dic7C2311yescharacteristic
279C2×C4×Dic7C2311yescharacteristic
280C2×C4×Dic7C2311yescharacteristic
281C2×C4×Dic7C2311yescharacteristic
282C2×C4×Dic7C2311yescharacteristic
283C2×C4×Dic7C2311yescharacteristic
284C2×C4×Dic7C2311yescharacteristic
285C2×C4×Dic7C2311yescharacteristic
286C2×C4×Dic7C2311yescharacteristic
287#6452—24no—
288#6452—24no—
289#6452—24no—
290#6451—24no—
291#6450—24no—
292#6450—24no—
293#6450—24no—
294#6450Q818yescomplemented
295C4×Dic14—24no—
296C7×#95C2311yescharacteristic
297C7×#95C2311yescharacteristic
298C7×#95C2311yescharacteristic
299C7×#95C2311yescharacteristic
300C7×#95C2311yescharacteristic
301C7×#95C2311yescharacteristic
302C7×#95C2311yescharacteristic
303C7×#95C2311yescharacteristic
304C7×#95C2311yescharacteristic
305C7×#95C2311yescharacteristic
306C7×#95C2311yescharacteristic
307C7×#95C2311yescharacteristic
308C7×#95C2311yescharacteristic
309C7×#95C2311yescharacteristic
310C7⋊#95C2311yescharacteristic
311C7⋊#95C2311yescharacteristic
312C7⋊#95C2311yescharacteristic
313C7⋊#95C2311yescharacteristic
314C7⋊#95C2311yescharacteristic
315C7⋊#95C2311yescharacteristic
316C7⋊#95C2311yescharacteristic
317C7⋊#95C2311yescharacteristic
318C7⋊#95C2311yescharacteristic
319C7⋊#95C2311yescharacteristic
320C7⋊#95C2311yescharacteristic
321C7⋊#95C2311yescharacteristic
322C7⋊#95C2311yescharacteristic
323C7⋊#95C2311yescharacteristic
324C7⋊#95C2311yescharacteristic
325C7⋊#95C2311yescharacteristic
326C7⋊#95C2311yescharacteristic
327C7⋊#95C2311yescharacteristic
328C7⋊#95C2311yescharacteristic
329C7⋊#95C2311yescharacteristic
330C7⋊#95C2311yescharacteristic
331C7⋊#95C2311yescharacteristic
332C7⋊#95C2311yescharacteristic
333C7⋊#95C2311yescharacteristic
334C7⋊#95C2311yescharacteristic
335C7⋊#95C2311yescharacteristic
336C7⋊#95C2311yescharacteristic
337C7⋊#95C2311yescharacteristic
338C7⋊#95C2311yescharacteristic
339C7⋊#95C2311yescharacteristic
340C7⋊#95C2311yescharacteristic
341C7⋊#95C2311yescharacteristic
342C7⋊#95C2311yescharacteristic
343C7⋊#95C2311yescharacteristic
344C7⋊#95C2311yescharacteristic
345C7⋊#95C2311yescharacteristic
346C7⋊#95C2311yescharacteristic
347C7⋊#95C2311yescharacteristic
348C7⋊#95C2311yescharacteristic
349C7⋊#95C2311yescharacteristic
350C7⋊#95C2311yescharacteristic
351C7⋊#95C2311yescharacteristic
352C7⋊#95C2311yescharacteristic
353C7⋊#95C2311yescharacteristic
354C7⋊#95C2311yescharacteristic
355C7⋊#95C2311yescharacteristic
356#2590—71no—
357#2590—71no—
358#2588—71no—
359#2588—71no—
360#2584—71no—
361#2581—71no—
362#2565—71no—
363#2550—71no—
364#2520—71no—
365#2520—71no—
366#2508—71no—
367#2506—71no—
368#2462—71no—
369#2462D711yescharacteristic
370#2453—71no—
371#2451—71no—
372#2402—71no—
373#2402—71no—
374#2399—71no—
375#2399—71no—
376C4×C4⋊Q8—71no—
377C4×#125—71no—
378C4×#125—71no—
379C4×#125—71no—
380C4×#125—71no—
381#2295—71no—
382#2295—71no—
383#2295—71no—
384#2295—71no—
385C42×Q8—71no—
386C42×Q8—71no—
387C2×C7×Q8—22no—
388C2×C7×Q8—22no—
389C2×C7×Q8—22no—
390C22×C4×C7C2411yescharacteristic
391C22×C4×C7C2411yescharacteristic
392C22×C4×C7C2411yescharacteristic
393C22×C4×C7C2411yescharacteristic
394C22×C4×C7C2411yescharacteristic
395C22×C4×C7C2411yescharacteristic
396C22×C4×C7C2411yescharacteristic
397C22×C4×C7C2411yescharacteristic
398C22×C4×C7C2411yescharacteristic
399C22×C4×C7C2411yescharacteristic
400C22×C4×C7C2411yescharacteristic
401C22×C4×C7C2411yescharacteristic
402C22×C4×C7C2411yescharacteristic
403C22×C4×C7C2411yescharacteristic
404C22×C4×C7C2411yescharacteristic
405C22×Dic7C2411yescharacteristic
406C22×Dic7C2411yescharacteristic
407C22×Dic7C2411yescharacteristic
408C22×Dic7C2411yescharacteristic
409C22×Dic7C2411yescharacteristic
410C22×Dic7C2411yescharacteristic
411C22×Dic7C2411yescharacteristic
412C22×Dic7C2411yescharacteristic
413C22×Dic7C2411yescharacteristic
414C22×Dic7C2411yescharacteristic
415C22×Dic7C2411yescharacteristic
416C22×Dic7C2411yescharacteristic
417C22×Dic7C2411yescharacteristic
418C22×Dic7C2411yescharacteristic
419C22×Dic7C2411yescharacteristic
420C22×Dic7C2411yescharacteristic
421C2×Dic14—22no—
422C2×Dic14—22no—
423C2×Dic14—22no—
424C2×Dic14—22no—
425C2×Dic14—22no—
426C2×Dic14—22no—
427C2×Dic14—41no—
428C2×Dic14—41no—
429C2×Dic14C2×Q814yes—
430C7×C4⋊C4—22no—
431C7×C4⋊C4—22no—
432C7×C4⋊C4—22no—
433C7×C4⋊C4—22no—
434C7×C4⋊C4—22no—
435C7×C4⋊C4—22no—
436C7×C4⋊C4—22no—
437C7×C4⋊C4—22no—
438C7×C4⋊C4—22no—
439C7×C4⋊C4—22no—
440C7×C4⋊C4—22no—
441C7×C4⋊C4—22no—
442C7×C4⋊C4—22no—
443C7×C4⋊C4C2×Q814yes—
444C7×C4⋊C4#4114yes—
445C42×C7—22no—
446C42×C7—22no—
447C42×C7—22no—
448C42×C7—22no—
449C42×C7—22no—
450C4⋊Dic7—22no—
451C4⋊Dic7—22no—
452C4⋊Dic7—22no—
453C4⋊Dic7—22no—
454C4⋊Dic7—22no—
455C4⋊Dic7—22no—
456C4⋊Dic7—22no—
457C4⋊Dic7—22no—
458C4⋊Dic7—22no—
459C4⋊Dic7—22no—
460C4⋊Dic7—22no—
461C4⋊Dic7—41no—
462C4⋊Dic7—41no—
463C4⋊Dic7—41no—
464C4⋊Dic7—41no—
465Dic7⋊C4—22no—
466Dic7⋊C4—22no—
467Dic7⋊C4—22no—
468Dic7⋊C4—22no—
469Dic7⋊C4—22no—
470Dic7⋊C4—22no—
471Dic7⋊C4—22no—
472Dic7⋊C4—22no—
473Dic7⋊C4—22no—
474Dic7⋊C4—22no—
475Dic7⋊C4—22no—
476Dic7⋊C4—22no—
477Dic7⋊C4—22no—
478Dic7⋊C4—22no—
479Dic7⋊C4—22no—
480Dic7⋊C4—22no—
481Dic7⋊C4—22no—
482Dic7⋊C4—22no—
483Dic7⋊C4—22no—
484Dic7⋊C4—41no—
485Dic7⋊C4—41no—
486Dic7⋊C4—41no—
487Dic7⋊C4—41no—
488Dic7⋊C4C2×Q814yes—
489Dic7⋊C4C2×Q814yes—
490Dic7⋊C4#4114yes—
491C4×Dic7—22no—
492C4×Dic7—22no—
493C4×Dic7—22no—
494C4×Dic7—22no—
495C4×Dic7—22no—
496C4×Dic7—22no—
497C4×Dic7—22no—
498C4×Dic7—22no—
499C4×Dic7—22no—
500C4×Dic7—22no—
501C4×Dic7—22no—
502C4×Dic7—22no—
503C4×Dic7—22no—
504C4×Dic7—22no—
505C4×Dic7—22no—
506C4×Dic7—22no—
507C4×Dic7—22no—
508C4×Dic7—22no—
509C4×Dic7—22no—
510C4×Dic7—22no—
511C4×Dic7—41no—
512C4×Dic7—41no—
513C4×Dic7—41no—
514C4×Dic7—41no—
515C4×Dic7—41no—
516C4×Dic7C2×Q814yes—
517C4×Dic7C2×Q814yes—
518C4×Dic7C2×Q814yes—
519C4×Dic7#4114yes—
520C4×Dic7#4114yes—
521C2×C4⋊Q8—71no—
522C2×#125—71no—
523C2×#125—71no—
524C2×#125—71no—
525C2×#125C2×D711yescharacteristic
526C2×C4×Q8—71no—
527C2×C4×Q8—71no—
528C2×C4×Q8—71no—
529C2×C4×Q8—71no—
530C2×C4×Q8—71no—
531C2×C4×Q8—71no—
532C2×C4×Q8—71no—
533C2×C4×Q8C2×D711yescharacteristic
534#400—71no—
535#400—71no—
536#400—71no—
537#400—71no—
538#400—71no—
539#400—71no—
540#400—71no—
541#400—71no—
542#398—71no—
543#398—71no—
544#398—71no—
545#398—71no—
546#398—71no—
547#398—71no—
548#398—71no—
549#398—71no—
550#398—71no—
551#398—71no—
552#398—71no—
553#398—71no—
554#398—71no—
555#398—71no—
556#398C2×D711yescharacteristic
557#398C2×D711yescharacteristic
558#395—71no—
559#395—71no—
560#395—71no—
561#395—71no—
562#395—71no—
563#395—71no—
564#395C2×D711yescharacteristic
565#395C2×D711yescharacteristic
566#391—71no—
567#391—71no—
568#391—71no—
569#391—71no—
570#391—71no—
571#391—71no—
572#391—71no—
573#391—71no—
574#391—71no—
575#391—71no—
576#389—71no—
577#389—71no—
578#389—71no—
579#389—71no—
580#389—71no—
581#389—71no—
582#389—71no—
583#389—71no—
584#389—71no—
585#389—71no—
586#389—71no—
587#389—71no—
588#389—71no—
589#389—71no—
590#389—71no—
591#389—71no—
592#389—71no—
593#389—71no—
594#389C2×D711yescharacteristic
595#389C2×D711yescharacteristic
596#387—71no—
597#387—71no—
598#387—71no—
599#387—71no—
600#387—71no—
601#387—71no—
602#387—71no—
603#387—71no—
604#387—71no—
605#387—71no—
606#387—71no—
607#387—71no—
608#387—71no—
609#387—71no—
610#387—71no—
611#387—71no—
612#387—71no—
613#387—71no—
614#387—71no—
615#387—71no—
616#387—71no—
617#387—71no—
618#387—71no—
619#387—71no—
620#387—71no—
621#387—71no—
622#387C2×D711yescharacteristic
623#387C2×D711yescharacteristic
624#387C2×D711yescharacteristic
625#387C2×D711yescharacteristic
626#387C2×D711yescharacteristic
627#387C2×D711yescharacteristic
628#384—71no—
629#382—71no—
630#382—71no—
631#382—71no—
632#382—71no—
633C4×C4⋊C4—71no—
634C4×C4⋊C4—71no—
635C4×C4⋊C4—71no—
636C4×C4⋊C4—71no—
637C4×C4⋊C4—71no—
638C4×C4⋊C4—71no—
639C4×C4⋊C4—71no—
640C4×C4⋊C4—71no—
641C4×C4⋊C4—71no—
642C4×C4⋊C4—71no—
643C4×C4⋊C4—71no—
644C4×C4⋊C4—71no—
645C4×C4⋊C4—71no—
646C4×C4⋊C4—71no—
647C4×C4⋊C4—71no—
648C4×C4⋊C4—71no—
649C4×C4⋊C4—71no—
650C4×C4⋊C4—71no—
651C4×C4⋊C4—71no—
652C4×C4⋊C4—71no—
653C4×C4⋊C4—71no—
654C4×C4⋊C4—71no—
655C4×C4⋊C4—71no—
656C4×C4⋊C4—71no—
657C4×C4⋊C4—71no—
658C4×C4⋊C4—71no—
659C4×C4⋊C4—71no—
660C4×C4⋊C4—71no—
661C4×C4⋊C4—71no—
662C4×C4⋊C4—71no—
663C4×C4⋊C4—71no—
664C4×C4⋊C4—71no—
665C4×C4⋊C4—71no—
666C4×C4⋊C4C2×D711yescharacteristic
667#376—71no—
668#376—71no—
669#376—71no—
670#376—71no—
671C43—71no—
672C43—71no—
673C43—71no—
674C43—71no—
675C43—71no—
676C23×C7C2511yescharacteristic
677C7×Q8—28no—
678C2×C4×C7—21no—
679C2×C4×C7—21no—
680C2×C4×C7—21no—
681C2×C4×C7—21no—
682C2×C4×C7—21no—
683C2×C4×C7—21no—
684C2×C4×C7—21no—
685C2×C4×C7—21no—
686C2×C4×C7—21no—
687C2×C4×C7—21no—
688C2×C4×C7—21no—
689C2×C4×C7—21no—
690C2×C4×C7—21no—
691C2×C4×C7—21no—
692C2×C4×C7—21no—
693C2×C4×C7—21no—
694C2×C4×C7—21no—
695C2×C4×C7—21no—
696C2×C4×C7—21no—
697C2×C4×C7—21no—
698C2×C4×C7—21no—
699C2×C4×C7—21no—
700C2×C4×C7—21no—
701C2×C4×C7—21no—
702C2×C4×C7—21no—
703C2×C4×C7—21no—
704C2×C4×C7—21no—
705C2×C4×C7—21no—
706C2×C4×C7—21no—
707C2×C4×C7—21no—
708C2×C4×C7—21no—
709C2×C4×C7—21no—
710C2×C4×C7—21no—
711C2×C4×C7—21no—
712C2×C4×C7—21no—
713C2×C4×C7—21no—
714C2×C4×C7C22×Q812yes—
715C2×C4×C7C22×Q812yes—
716C2×C4×C7C22×Q812yes—
717C2×C4×C7C2×#4112yes—
718C2×C4×C7C2×#4112yes—
719C2×C4×C7C2×#4112yes—
720C2×C4×C7C2×#4112yes—
721C2×C4×C7C2×#4112yes—
722C2×C4×C7C2×#4112yes—
723C2×Dic7—21no—
724C2×Dic7—21no—
725C2×Dic7—21no—
726C2×Dic7—21no—
727C2×Dic7—21no—
728C2×Dic7—21no—
729C2×Dic7—21no—
730C2×Dic7—21no—
731C2×Dic7—21no—
732C2×Dic7—21no—
733C2×Dic7—21no—
734C2×Dic7—21no—
735C2×Dic7—21no—
736C2×Dic7—21no—
737C2×Dic7—21no—
738C2×Dic7—21no—
739C2×Dic7—21no—
740C2×Dic7—21no—
741C2×Dic7—21no—
742C2×Dic7—21no—
743C2×Dic7—21no—
744C2×Dic7—21no—
745C2×Dic7—21no—
746C2×Dic7—21no—
747C2×Dic7—21no—
748C2×Dic7—21no—
749C2×Dic7—21no—
750C2×Dic7—21no—
751C2×Dic7—21no—
752C2×Dic7—21no—
753C2×Dic7—21no—
754C2×Dic7—21no—
755C2×Dic7—21no—
756C2×Dic7—21no—
757C2×Dic7—21no—
758C2×Dic7—21no—
759C2×Dic7—21no—
760C2×Dic7C22×Q812yes—
761C2×Dic7C22×Q812yes—
762C2×Dic7C22×Q812yes—
763C2×Dic7C22×Q812yes—
764C2×Dic7C2×#4112yes—
765C2×Dic7C2×#4112yes—
766C2×Dic7C2×#4112yes—
767C2×Dic7C2×#4112yes—
768C2×Dic7C2×#4112yes—
769C2×Dic7C2×#4112yes—
770C2×Dic72−1+412yes—
771Dic14—28no—
772Dic14—44no—
773Dic14—44no—
774C22×Q8—71no—
775C22×Q8—71no—
776C22×Q8—71no—
777C22×Q8C22×D711yescharacteristic
778C4⋊Q8—144no—
779#125—24no—
780#125—144no—
781#125—144no—
782#125—144no—
783C4×Q8—24no—
784C4×Q8—78no—
785C4×Q8—144no—
786C4×Q8—144no—
787C4×Q8—144no—
788C4×Q8—144no—
789C4×Q8—144no—
790C4×Q8—144no—
791C2×C4⋊C4—71no—
792C2×C4⋊C4—71no—
793C2×C4⋊C4—71no—
794C2×C4⋊C4—71no—
795C2×C4⋊C4—71no—
796C2×C4⋊C4—71no—
797C2×C4⋊C4—71no—
798C2×C4⋊C4—71no—
799C2×C4⋊C4—71no—
800C2×C4⋊C4—71no—
801C2×C4⋊C4—71no—
802C2×C4⋊C4—71no—
803C2×C4⋊C4—71no—
804C2×C4⋊C4—71no—
805C2×C4⋊C4—71no—
806C2×C4⋊C4—71no—
807C2×C4⋊C4—71no—
808C2×C4⋊C4—71no—
809C2×C4⋊C4—71no—
810C2×C4⋊C4—71no—
811C2×C4⋊C4—71no—
812C2×C4⋊C4—71no—
813C2×C4⋊C4—71no—
814C2×C4⋊C4—71no—
815C2×C4⋊C4—71no—
816C2×C4⋊C4—71no—
817C2×C4⋊C4—71no—
818C2×C4⋊C4—71no—
819C2×C4⋊C4—71no—
820C2×C4⋊C4—71no—
821C2×C4⋊C4—71no—
822C2×C4⋊C4—71no—
823C2×C4⋊C4—71no—
824C2×C4⋊C4—71no—
825C2×C4⋊C4—71no—
826C2×C4⋊C4—71no—
827C2×C4⋊C4—71no—
828C2×C4⋊C4—71no—
829C2×C4⋊C4—71no—
830C2×C4⋊C4—71no—
831C2×C4⋊C4—71no—
832C2×C4⋊C4C22×D711yescharacteristic
833C2×C4⋊C4C22×D711yescharacteristic
834C2×C4⋊C4C22×D711yescharacteristic
835C2×C4⋊C4C22×D711yescharacteristic
836C2×C4⋊C4C22×D711yescharacteristic
837C2×C4⋊C4C22×D711yescharacteristic
838C2×C4⋊C4C22×D711yescharacteristic
839C2×C4⋊C4C22×D711yescharacteristic
840C2×C4⋊C4C22×D711yescharacteristic
841C2×C4⋊C4C22×D711yescharacteristic
842C2×C4⋊C4C22×D711yescharacteristic
843C2×C4⋊C4C22×D711yescharacteristic
844C2×C4⋊C4C22×D711yescharacteristic
845C2×C4⋊C4C22×D711yescharacteristic
846C2×C4⋊C4C22×D711yescharacteristic
847C2×C42—71no—
848C2×C42—71no—
849C2×C42—71no—
850C2×C42—71no—
851C2×C42—71no—
852C2×C42—71no—
853C2×C42—71no—
854C2×C42—71no—
855C2×C42—71no—
856C2×C42—71no—
857C2×C42—71no—
858C2×C42—71no—
859C2×C42—71no—
860C2×C42—71no—
861C2×C42—71no—
862C2×C42—71no—
863C2×C42—71no—
864C2×C42—71no—
865C2×C42—71no—
866C2×C42—71no—
867C2×C42—71no—
868C2×C42—71no—
869C2×C42—71no—
870C2×C42—71no—
871C2×C42—71no—
872C2×C42—71no—
873C2×C42—71no—
874C2×C42—71no—
875C2×C42—71no—
876C2×C42—71no—
877C2×C42C22×D711yescharacteristic
878C2×C42C22×D711yescharacteristic
879C2×C42C22×D711yescharacteristic
880C2×C42C22×D711yescharacteristic
881C2×C42C22×D711yescharacteristic
882#95—71no—
883#95—71no—
884#95—71no—
885#95—71no—
886#95—71no—
887#95—71no—
888#95—71no—
889#95—71no—
890#95—71no—
891#95—71no—
892#95—71no—
893#95—71no—
894#95—71no—
895#95—71no—
896#95—71no—
897#95—71no—
898#95—71no—
899#95—71no—
900#95—71no—
901#95—71no—
902#95—71no—
903#95—71no—
904#95—71no—
905#95—71no—
906#95—71no—
907#95—71no—
908#95—71no—
909#95—71no—
910#95—71no—
911#95—71no—
912#95—71no—
913#95—71no—
914#95—71no—
915#95—71no—
916#95—71no—
917#95—71no—
918#95—71no—
919#95—71no—
920#95—71no—
921#95—71no—
922#95—71no—
923#95—71no—
924#95—71no—
925#95—71no—
926#95—71no—
927#95—71no—
928#95C22×D711yescharacteristic
929#95C22×D711yescharacteristic
930#95C22×D711yescharacteristic
931#95C22×D711yescharacteristic
932#95C22×D711yescharacteristic
933#95C22×D711yescharacteristic
934#95C22×D711yescharacteristic
935#95C22×D711yescharacteristic
936#95C22×D711yescharacteristic
937#95C22×D711yescharacteristic
938#95C22×D711yescharacteristic
939#95C22×D711yescharacteristic
940#95C22×D711yescharacteristic
941#95C22×D711yescharacteristic
942C22×C7C23×Q811yescharacteristic
943C22×C7C22×#4111yescharacteristic
944C22×C7C22×#4111yescharacteristic
945C22×C7C22×#4111yescharacteristic
946C22×C7C22×#4111yescharacteristic
947C22×C7C2×2−1+411yescharacteristic
948C22×C7#58511yescharacteristic
949C4×C7—22no—
950C4×C7—22no—
951C4×C7—22no—
952C4×C7—22no—
953C4×C7—22no—
954C4×C7—22no—
955C4×C7—22no—
956C4×C7—22no—
957C4×C7—22no—
958C4×C7—41no—
959C4×C7—41no—
960C4×C7—41no—
961C4×C7—41no—
962C4×C7—41no—
963C4×C7—41no—
964Dic7—22no—
965Dic7—22no—
966Dic7—22no—
967Dic7—22no—
968Dic7—22no—
969Dic7—41no—
970Dic7—41no—
971Dic7—41no—
972Dic7—41no—
973Dic7—41no—
974Dic7—41no—
975Dic7—41no—
976Dic7—41no—
977Dic7—41no—
978Dic7#53314yes—
979Dic7#55714yes—
980C2×Q8—22no—
981C2×Q8—22no—
982C2×Q8—22no—
983C2×Q8—74no—
984C2×Q8—142no—
985C2×Q8—142no—
986C2×Q8—142no—
987C2×Q8—142no—
988C2×Q8—142no—
989C2×Q8—142no—
990C2×Q8—281no—
991C2×Q8—281no—
992C22×C4—71no—
993C22×C4—71no—
994C22×C4—71no—
995C22×C4—71no—
996C22×C4—71no—
997C22×C4—71no—
998C22×C4—71no—
999C22×C4—71no—
1000C22×C4—71no—
1001C22×C4—71no—
1002C22×C4—71no—
1003C22×C4—71no—
1004C22×C4—71no—
1005C22×C4—71no—
1006C22×C4—71no—
1007C22×C4—71no—
1008C22×C4C23×D711yescharacteristic
1009C22×C4C23×D711yescharacteristic
1010C22×C4C23×D711yescharacteristic
1011C22×C4C23×D711yescharacteristic
1012C22×C4C23×D711yescharacteristic
1013C22×C4C23×D711yescharacteristic
1014C22×C4C23×D711yescharacteristic
1015C22×C4C23×D711yescharacteristic
1016C22×C4C23×D711yescharacteristic
1017C22×C4C23×D711yescharacteristic
1018C22×C4C23×D711yescharacteristic
1019C22×C4C23×D711yescharacteristic
1020C22×C4C23×D711yescharacteristic
1021C22×C4C23×D711yescharacteristic
1022C22×C4C23×D711yescharacteristic
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—22no—
1030C4⋊C4—22no—
1031C4⋊C4—22no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—74no—
1037C4⋊C4—74no—
1038C4⋊C4—74no—
1039C4⋊C4—142no—
1040C4⋊C4—142no—
1041C4⋊C4—142no—
1042C4⋊C4—142no—
1043C4⋊C4—142no—
1044C4⋊C4—142no—
1045C4⋊C4—142no—
1046C4⋊C4—142no—
1047C4⋊C4—142no—
1048C4⋊C4—142no—
1049C4⋊C4—142no—
1050C4⋊C4—142no—
1051C4⋊C4—142no—
1052C4⋊C4—142no—
1053C4⋊C4—142no—
1054C4⋊C4—142no—
1055C4⋊C4—142no—
1056C4⋊C4—142no—
1057C4⋊C4—142no—
1058C4⋊C4—142no—
1059C4⋊C4—142no—
1060C4⋊C4—142no—
1061C4⋊C4—142no—
1062C4⋊C4—142no—
1063C4⋊C4—142no—
1064C4⋊C4—142no—
1065C4⋊C4—142no—
1066C4⋊C4—142no—
1067C4⋊C4—142no—
1068C4⋊C4—142no—
1069C4⋊C4—281no—
1070C4⋊C4—281no—
1071C4⋊C4—281no—
1072C4⋊C4—281no—
1073C4⋊C4—281no—
1074C4⋊C4—281no—
1075C4⋊C4—281no—
1076C4⋊C4—281no—
1077C4⋊C4#115914yes—
1078C4⋊C4Q8×D714yes—
1079C42—22no—
1080C42—22no—
1081C42—22no—
1082C42—22no—
1083C42—22no—
1084C42—74no—
1085C42—74no—
1086C42—74no—
1087C42—74no—
1088C42—74no—
1089C42—142no—
1090C42—142no—
1091C42—142no—
1092C42—142no—
1093C42—142no—
1094C42—142no—
1095C42—142no—
1096C42—142no—
1097C42—142no—
1098C42—142no—
1099C42—142no—
1100C42—142no—
1101C42—142no—
1102C42—142no—
1103C42—142no—
1104C42—142no—
1105C42—142no—
1106C42—142no—
1107C42—142no—
1108C42—142no—
1109C42—281no—
1110C42—281no—
1111C42—281no—
1112C42—281no—
1113C42—281no—
1114C2×C7C2×#53311yescharacteristic
1115C2×C7#344411yescharacteristic
1116C2×C7#346111yescharacteristic
1117C2×C7#347511yescharacteristic
1118C2×C7C2×#55711yescharacteristic
1119C2×C7Q8×#4111yescharacteristic
1120C2×C7#348211yescharacteristic
1121C23C24×D711yescharacteristic
1122Q8—28no—
1123Q8—148no—
1124Q8—284no—
1125Q8—284no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—72no—
1163C2×C4—72no—
1164C2×C4—72no—
1165C2×C4—72no—
1166C2×C4—72no—
1167C2×C4—72no—
1168C2×C4—72no—
1169C2×C4—72no—
1170C2×C4—72no—
1171C2×C4—72no—
1172C2×C4—72no—
1173C2×C4—141no—
1174C2×C4—141no—
1175C2×C4—141no—
1176C2×C4—141no—
1177C2×C4—141no—
1178C2×C4—141no—
1179C2×C4—141no—
1180C2×C4—141no—
1181C2×C4—141no—
1182C2×C4—141no—
1183C2×C4—141no—
1184C2×C4—141no—
1185C2×C4—141no—
1186C2×C4—141no—
1187C2×C4—141no—
1188C2×C4—141no—
1189C2×C4—141no—
1190C2×C4—141no—
1191C2×C4—141no—
1192C2×C4—141no—
1193C2×C4—141no—
1194C2×C4—141no—
1195C2×C4—141no—
1196C2×C4—141no—
1197C2×C4—141no—
1198C2×C4—141no—
1199C2×C4—141no—
1200C2×C4—141no—
1201C2×C4—141no—
1202C2×C4—141no—
1203C2×C4—141no—
1204C2×C4—141no—
1205C2×C4—141no—
1206C2×C4—141no—
1207C2×C4—141no—
1208C2×C4—141no—
1209C2×C4—141no—
1210C2×C4C2×#115912yes—
1211C2×C4C2×#115912yes—
1212C2×C4C2×#115912yes—
1213C2×C4C2×Q8×D712yes—
1214C2×C4C2×Q8×D712yes—
1215C2×C4C2×Q8×D712yes—
1216C2×C4D7×#4112yes—
1217C2×C4D7×#4112yes—
1218C2×C4D7×#4112yes—
1219C7#3492011yescharacteristic, complemented, Sylow
1220C22C22×#115911yescharacteristic
1221C22C22×Q8×D711yescharacteristic
1222C22C2×D7×#4111yescharacteristic
1223C22C2×D7×#4111yescharacteristic
1224C22C2×D7×#4111yescharacteristic
1225C22D7×2−1+411yescharacteristic
1226C22#9062011yescharacteristic
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—22no—
1232C4—22no—
1233C4—22no—
1234C4—22no—
1235C4—22no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—74no—
1243C4—74no—
1244C4—142no—
1245C4—142no—
1246C4—142no—
1247C4—142no—
1248C4—142no—
1249C4—281no—
1250C4—281no—
1251C4—281no—
1252C4—281no—
1253C4—281no—
1254C4—281no—
1255C4—281no—
1256C4—281no—
1257C4—281no—
1258C2#1174308611yescharacteristic
1259C2D7×#53311yescharacteristic
1260C2#1174356411yescharacteristic
1261C2#1174374411yescharacteristic
1262C2Q8×#115911yescharacteristic
1263C2#1174389511yescharacteristic
1264C2D7×#55711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, prime radical, cosocleC23×C7C25
FittingC7×#2462C2
hypercenter#2462D7
hypocenterC7#34920
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2462

Complements

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

NH ≅ G/Ntype
294. #6450Q8semidirect
1219. C7#34920semidirect

Maximal subgroups

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

subgroupindex
C7×#24622
#117404792
Dic7×#1252
#117399172
C4×Q8×Dic72
#117352372
#117352312
#117351862
#117346372
#117346362
#117346162
#117335352
#117334592
#117334122
#117334072
#117325542
#117325472
#117325462
#117324842
#117324732
#117324322
#117323882
#117323832
#117311452
C4×#64502
#349207