Finite Group Databasebeta

← #13520793

Subgroups — #13520793

Order 1792.

1536 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×#2402C211yesmaximal, characteristic, complemented
2#11735678C211yesmaximal, characteristic
3#11735675C211yesmaximal, characteristic, complemented
4#11735675C211yesmaximal, characteristic, complemented
5#11735674C211yesmaximal, characteristic, complemented
6#11735671C211yesmaximal, characteristic
7#11735667C211yesmaximal, characteristic
8#11735665C211yesmaximal, characteristic
9#11735655C211yesmaximal, characteristic, complemented
10#11735289C211yesmaximal, characteristic, complemented
11#11735286C211yesmaximal, characteristic, complemented
12#11735284C211yesmaximal, characteristic
13#11735280C211yesmaximal, characteristic, complemented
14#11735278C211yesmaximal, characteristic
15#11735270C211yesmaximal, characteristic
16#11735269C211yesmaximal, characteristic
17#11735268C211yesmaximal, characteristic, complemented
18#11731224C211yesmaximal, characteristic
19#11731223C211yesmaximal, characteristic
20#11731223C211yesmaximal, characteristic
21#11731115C211yesmaximal, characteristic, complemented
22#11731115C211yesmaximal, characteristic, complemented
23#11731114C211yesmaximal, characteristic, complemented
24C4×#6453C211yesmaximal, characteristic, complemented
25C4×#6452C211yesmaximal, characteristic, complemented
26C4×#6461C211yesmaximal, characteristic
27C4×#6461C211yesmaximal, characteristic
28#11731065C211yesmaximal, characteristic
29C4×#6450C211yesmaximal, characteristic, complemented
30#11730865C211yesmaximal, characteristic
31#11730829C211yesmaximal, characteristic, complemented
32C2×#6461C2211yescharacteristic
33C2×#6461C2211yescharacteristic
34C2×#6453C2211yescharacteristic
35C2×#6452C2211yescharacteristic
36C2×#6450C2211yescharacteristic
37C2×#6450C2211yescharacteristic
38C2×#6435C2211yescharacteristic
39C2×C4×Dic14C2211yescharacteristic
40C2×C4×Dic14C2211yescharacteristic
41C7×#400C2211yescharacteristic
42C7×#400C2211yescharacteristic
43C7×#400C2211yescharacteristic
44C7×#400C2211yescharacteristic
45C7×#398C2211yescharacteristic
46C7×#398C2211yescharacteristic
47C7×#398C2211yescharacteristic
48C7×#398C2211yescharacteristic
49C4×C7×C4⋊C4C2211yescharacteristic
50C4×C7×C4⋊C4C2211yescharacteristic
51C4×C7×C4⋊C4C2211yescharacteristic
52C4×C7×C4⋊C4C2211yescharacteristic
53C4×C7×C4⋊C4C2211yescharacteristic
54C4×C7×C4⋊C4C2211yescharacteristic
55C7×#376C2211yescharacteristic
56#89766C2211yescharacteristic
57#89766C2211yescharacteristic
58#89766C2211yescharacteristic
59#89765C2211yescharacteristic
60#89764C2211yescharacteristic
61#89764C2211yescharacteristic
62#89762C2211yescharacteristic
63#89762C2211yescharacteristic
64#89762C2211yescharacteristic
65#89762C2211yescharacteristic
66#89758C2211yescharacteristic
67#89757C2211yescharacteristic
68#89756C2211yescharacteristic
69#89756C2211yescharacteristic
70#89756C2211yescharacteristic
71#89756C2211yescharacteristic
72#89755C2211yescharacteristic
73#89755C2211yescharacteristic
74#89754C2211yescharacteristic
75#89754C2211yescharacteristic
76#89754C2211yescharacteristic
77#89753C2211yescharacteristic
78#89753C2211yescharacteristic
79#89753C2211yescharacteristic
80#89752C2211yescharacteristic
81#89752C2211yescharacteristic
82#89752C2211yescharacteristic
83#89752C2211yescharacteristic
84#89751C2211yescharacteristic
85#89751C2211yescharacteristic
86#89751C2211yescharacteristic
87#89751C2211yescharacteristic
88#89750C2211yescharacteristic
89#89750C2211yescharacteristic
90#89750C2211yescharacteristic
91#89750C2211yescharacteristic
92#89750C2211yescharacteristic
93#89749C2211yescharacteristic
94C4⋊C4×Dic7C2211yescharacteristic
95C4⋊C4×Dic7C2211yescharacteristic
96#89745C2211yescharacteristic
97#89744C2211yescharacteristic
98C4×(C2×D7)⋊C4C2211yescharacteristic
99C4×(C2×D7)⋊C4C2211yescharacteristic
100C4×(C2×D7)⋊C4C2211yescharacteristic
101C4×(C2×D7)⋊C4C2211yescharacteristic
102C4×(C2×D7)⋊C4C2211yescharacteristic
103C4×(C2×D7)⋊C4C2211yescharacteristic
104C4×C4⋊Dic7C2211yescharacteristic
105C4×C4⋊Dic7C2211yescharacteristic
106C4×C4⋊Dic7C2211yescharacteristic
107C4×C4⋊Dic7C2211yescharacteristic
108#89704C2211yescharacteristic
109#89704C2211yescharacteristic
110C4×Dic7⋊C4C2211yescharacteristic
111C4×Dic7⋊C4C2211yescharacteristic
112C4×Dic7⋊C4C2211yescharacteristic
113C4×Dic7⋊C4C2211yescharacteristic
114C4×Dic7⋊C4C2211yescharacteristic
115C4×Dic7⋊C4C2211yescharacteristic
116C4×Dic7⋊C4C2211yescharacteristic
117C4×Dic7⋊C4C2211yescharacteristic
118C4×Dic7⋊C4C2211yescharacteristic
119C4×Dic7⋊C4C2211yescharacteristic
120C42×Dic7C2211yescharacteristic
121C42×Dic7C2211yescharacteristic
122C42×Dic7C2211yescharacteristic
123#89448C2211yescharacteristic
124#89448C2211yescharacteristic
125#89448C2211yescharacteristic
126#89447C2211yescharacteristic
127#89447C2211yescharacteristic
128#89447C2211yescharacteristic
129#89447C2211yescharacteristic
130#89446C2211yescharacteristic
131#89445C2211yescharacteristic
132#89445C2211yescharacteristic
133#89442C2211yescharacteristic
134#89442C2211yescharacteristic
135#89442C2211yescharacteristic
136#89442C2211yescharacteristic
137#89441C2211yescharacteristic
138#89441C2211yescharacteristic
139C7⋊#401C2211yescharacteristic
140C7⋊#401C2211yescharacteristic
141#89432C2211yescharacteristic
142#89431C2211yescharacteristic
143#89431C2211yescharacteristic
144#89430C2211yescharacteristic
145#89430C2211yescharacteristic
146#89430C2211yescharacteristic
147#89430C2211yescharacteristic
148#89430C2211yescharacteristic
149#89430C2211yescharacteristic
150#89430C2211yescharacteristic
151#89430C2211yescharacteristic
152#89430C2211yescharacteristic
153#89429C2211yescharacteristic
154#89429C2211yescharacteristic
155#89429C2211yescharacteristic
156#89429C2211yescharacteristic
157#89429C2211yescharacteristic
158#89429C2211yescharacteristic
159#89428C2211yescharacteristic
160#89428C2211yescharacteristic
161#89427C2211yescharacteristic
162#89427C2211yescharacteristic
163#89427C2211yescharacteristic
164#89427C2211yescharacteristic
165#89427C2211yescharacteristic
166#89427C2211yescharacteristic
167#89426C2211yescharacteristic
168#89426C2211yescharacteristic
169#89426C2211yescharacteristic
170#89426C2211yescharacteristic
171#89426C2211yescharacteristic
172#89426C2211yescharacteristic
173#89425C2211yescharacteristic
174#89424C2211yescharacteristic
175#89423C2211yescharacteristic
176#89423C2211yescharacteristic
177#89422C2211yescharacteristic
178#89421C2211yescharacteristic
179#89421C2211yescharacteristic
180#89421C2211yescharacteristic
181#89421C2211yescharacteristic
182#89419C2211yescharacteristic
183#89419C2211yescharacteristic
184#89419C2211yescharacteristic
185#89418C2211yescharacteristic
186#89418C2211yescharacteristic
187#34604—71nomaximal, Sylow
188C22×C4×D7C2311yescharacteristic
189C22×Dic14C2311yescharacteristic
190C22×Dic14C2311yescharacteristic
191C2×C7×C4⋊C4C2311yescharacteristic
192C2×C7×C4⋊C4C2311yescharacteristic
193C2×C7×C4⋊C4C2311yescharacteristic
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×C42×C7C2311yescharacteristic
204C2×C42×C7C2311yescharacteristic
205C2×C42×C7C2311yescharacteristic
206C2×C42×C7C2311yescharacteristic
207C2×C42×C7C2311yescharacteristic
208C2×C42×C7C2311yescharacteristic
209C2×C42×C7C2311yescharacteristic
210C2×(C2×D7)⋊C4C2311yescharacteristic
211C2×(C2×D7)⋊C4C2311yescharacteristic
212C2×(C2×D7)⋊C4C2311yescharacteristic
213C2×(C2×D7)⋊C4C2311yescharacteristic
214C2×(C2×D7)⋊C4C2311yescharacteristic
215C2×(C2×D7)⋊C4C2311yescharacteristic
216C2×(C2×D7)⋊C4C2311yescharacteristic
217C2×(C2×D7)⋊C4C2311yescharacteristic
218C2×(C2×D7)⋊C4C2311yescharacteristic
219C2×(C2×D7)⋊C4C2311yescharacteristic
220C2×(C2×D7)⋊C4C2311yescharacteristic
221C2×(C2×D7)⋊C4C2311yescharacteristic
222C2×(C2×D7)⋊C4C2311yescharacteristic
223C2×(C2×D7)⋊C4C2311yescharacteristic
224C2×C4⋊Dic7C2311yescharacteristic
225C2×C4⋊Dic7C2311yescharacteristic
226C2×C4⋊Dic7C2311yescharacteristic
227C2×C4⋊Dic7C2311yescharacteristic
228C2×C4⋊Dic7C2311yescharacteristic
229C2×C4⋊Dic7C2311yescharacteristic
230C2×C4⋊Dic7C2311yescharacteristic
231C2×C4⋊Dic7C2311yescharacteristic
232C2×C4⋊Dic7C2311yescharacteristic
233C2×C4⋊Dic7C2311yescharacteristic
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×Dic7⋊C4C2311yescharacteristic
258C2×Dic7⋊C4C2311yescharacteristic
259C2×Dic7⋊C4C2311yescharacteristic
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
279#6461—24no—
280#6461—24no—
281#6453—24no—
282#6452—24no—
283#6450—24no—
284#6450—24no—
285#6435—24no—
286C4×Dic14—24no—
287C4×Dic14—24no—
288C7×#95C2311yescharacteristic
289C7×#95C2311yescharacteristic
290C7×#95C2311yescharacteristic
291C7×#95C2311yescharacteristic
292C7×#95C2311yescharacteristic
293C7×#95C2311yescharacteristic
294C7×#95C2311yescharacteristic
295C7×#95C2311yescharacteristic
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
352#2666—71no—
353#2666—71no—
354#2664—71no—
355#2664—71no—
356#2655—71no—
357#2655—71no—
358#2655—71no—
359#2655—71no—
360#2654—71no—
361#2654—71no—
362#2650—71no—
363#2650—71no—
364#2637—71no—
365#2637—71no—
366#2634—71no—
367#2634—71no—
368#2402—71no—
369#2402—71no—
370#2402D711yescharacteristic, complemented
371#2401—71no—
372#2401—71no—
373#2399—71no—
374#2396—71no—
375#2396—71no—
376C4×#125—71no—
377C4×#125—71no—
378C4×#126—71no—
379C4×#126—71no—
380#2298—71no—
381#2295—71no—
382C42×Q8—71no—
383C23×D7C2411yescharacteristic
384C22×C4×C7C2411yescharacteristic
385C22×C4×C7C2411yescharacteristic
386C22×C4×C7C2411yescharacteristic
387C22×C4×C7C2411yescharacteristic
388C22×C4×C7C2411yescharacteristic
389C22×C4×C7C2411yescharacteristic
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×Dic7C2411yescharacteristic
400C22×Dic7C2411yescharacteristic
401C22×Dic7C2411yescharacteristic
402C22×Dic7C2411yescharacteristic
403C22×Dic7C2411yescharacteristic
404C22×Dic7C2411yescharacteristic
405C22×Dic7C2411yescharacteristic
406C22×Dic7C2411yescharacteristic
407C22×Dic7C2411yescharacteristic
408C22×Dic7C2411yescharacteristic
409C22×Dic7C2411yescharacteristic
410C22×Dic7C2411yescharacteristic
411C22×Dic7C2411yescharacteristic
412C22×Dic7C2411yescharacteristic
413C22×Dic7C2411yescharacteristic
414C2×C4×D7—22no—
415C2×C4×D7—22no—
416C2×C4×D7—22no—
417C2×Dic14—22no—
418C2×Dic14—22no—
419C2×Dic14—22no—
420C2×Dic14—22no—
421C2×Dic14—41no—
422C2×Dic14—41no—
423C7×C4⋊C4—22no—
424C7×C4⋊C4—22no—
425C7×C4⋊C4—22no—
426C7×C4⋊C4—22no—
427C7×C4⋊C4—22no—
428C7×C4⋊C4—22no—
429C7×C4⋊C4—41no—
430C7×C4⋊C4—41no—
431C7×C4⋊C4—41no—
432C7×C4⋊C4—41no—
433C7×C4⋊C4—41no—
434C7×C4⋊C4—41no—
435C42×C7—22no—
436C42×C7—22no—
437C42×C7—22no—
438C42×C7—22no—
439C42×C7—22no—
440C42×C7—22no—
441C42×C7—22no—
442(C2×D7)⋊C4—22no—
443(C2×D7)⋊C4—22no—
444(C2×D7)⋊C4—22no—
445(C2×D7)⋊C4—22no—
446(C2×D7)⋊C4—22no—
447(C2×D7)⋊C4—22no—
448(C2×D7)⋊C4—22no—
449(C2×D7)⋊C4—22no—
450(C2×D7)⋊C4—41no—
451(C2×D7)⋊C4—41no—
452(C2×D7)⋊C4—41no—
453(C2×D7)⋊C4—41no—
454(C2×D7)⋊C4—41no—
455(C2×D7)⋊C4—41no—
456C4⋊Dic7—22no—
457C4⋊Dic7—22no—
458C4⋊Dic7—22no—
459C4⋊Dic7—22no—
460C4⋊Dic7—22no—
461C4⋊Dic7—22no—
462C4⋊Dic7—22no—
463C4⋊Dic7—22no—
464C4⋊Dic7—41no—
465C4⋊Dic7—41no—
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⋊C4—41no—
489Dic7⋊C4—41no—
490Dic7⋊C4—41no—
491Dic7⋊C4—41no—
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—41no—
503C4×Dic7—41no—
504C4×Dic7—41no—
505C4×Dic7—41no—
506C4×Dic7—41no—
507C4×Dic7—41no—
508C4×Dic7#4114yes—
509C4×Dic7#4114yes—
510C4×Dic7#4114yes—
511C2×#126—71no—
512C2×#126—71no—
513C2×#125—71no—
514C2×#125—71no—
515C2×C4×Q8—71no—
516C2×C4×Q8—71no—
517C2×C4×Q8—71no—
518C2×C4×Q8—71no—
519C2×#117—71no—
520#401—71no—
521#401—71no—
522#400—71no—
523#400—71no—
524#400—71no—
525#400—71no—
526#400—71no—
527#400—71no—
528#400—71no—
529#400—71no—
530#400—71no—
531#400—71no—
532#400—71no—
533#400—71no—
534#400—71no—
535#400—71no—
536#400—71no—
537#400—71no—
538#400C2×D711yescharacteristic
539#400C2×D711yescharacteristic
540#400C2×D711yescharacteristic
541#400C2×D711yescharacteristic
542#399—71no—
543#399—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#398—71no—
557#398—71no—
558#398—71no—
559#398—71no—
560#398C2×D711yescharacteristic
561#398C2×D711yescharacteristic
562#398C2×D711yescharacteristic
563#398C2×D711yescharacteristic
564#397—71no—
565#397—71no—
566#397—71no—
567#397—71no—
568#397—71no—
569#397—71no—
570#396—71no—
571#396—71no—
572#396—71no—
573#396—71no—
574#396—71no—
575#396—71no—
576#395—71no—
577#395—71no—
578#395—71no—
579#395—71no—
580#395—71no—
581#395—71no—
582#393—71no—
583#393—71no—
584#391—71no—
585#391—71no—
586#389—71no—
587#389—71no—
588#389—71no—
589#389—71no—
590#389—71no—
591#389—71no—
592#388—71no—
593#388—71no—
594#388—71no—
595#388—71no—
596#388—71no—
597#388—71no—
598#388—71no—
599#388—71no—
600#388—71no—
601#388—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#387—71no—
623#387—71no—
624#383—71no—
625#383—71no—
626#382—71no—
627#382—71no—
628C4×C4⋊C4—71no—
629C4×C4⋊C4—71no—
630C4×C4⋊C4—71no—
631C4×C4⋊C4—71no—
632C4×C4⋊C4—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⋊C4C2×D711yescharacteristic
649C4×C4⋊C4C2×D711yescharacteristic
650C4×C4⋊C4C2×D711yescharacteristic
651C4×C4⋊C4C2×D711yescharacteristic
652C4×C4⋊C4C2×D711yescharacteristic
653C4×C4⋊C4C2×D711yescharacteristic
654C4×C22⋊C4—71no—
655C4×C22⋊C4—71no—
656C4×C22⋊C4—71no—
657C4×C22⋊C4—71no—
658C4×C22⋊C4—71no—
659C4×C22⋊C4—71no—
660#376—71no—
661#376—71no—
662#376C2×D711yescharacteristic
663C43—71no—
664C43—71no—
665C43—71no—
666C23×C7C2511yescharacteristic
667C22×D7—21no—
668C22×D7—21no—
669C22×D7—21no—
670C22×D7—21no—
671C22×D7—21no—
672C22×D7—21no—
673C22×D7—21no—
674C2×C4×C7—21no—
675C2×C4×C7—21no—
676C2×C4×C7—21no—
677C2×C4×C7—21no—
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×C7C2×#4112yes—
715C2×C4×C7C2×#4112yes—
716C2×C4×C7C2×#4112yes—
717C2×C4×C72−1+412yes—
718C2×C4×C72−1+412yes—
719C2×Dic7—21no—
720C2×Dic7—21no—
721C2×Dic7—21no—
722C2×Dic7—21no—
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×Dic7C2×#4112yes—
759C2×Dic7C2×#4112yes—
760C2×Dic7C2×#4112yes—
761C2×Dic7C2×#4112yes—
762C2×Dic7C2×#4112yes—
763C2×Dic7C2×#4112yes—
764C4×D7—44no—
765Dic14—28no—
766Dic14—44no—
767C22×Q8—71no—
768C22×Q8—71no—
769C23×C4—71no—
770#126—144no—
771#126—144no—
772#125—144no—
773#125—144no—
774C4×Q8—144no—
775C4×Q8—144no—
776C4×Q8—144no—
777C4×Q8—144no—
778#117—144no—
779C2×C4⋊C4—71no—
780C2×C4⋊C4—71no—
781C2×C4⋊C4—71no—
782C2×C4⋊C4—71no—
783C2×C4⋊C4—71no—
784C2×C4⋊C4—71no—
785C2×C4⋊C4—71no—
786C2×C4⋊C4—71no—
787C2×C4⋊C4—71no—
788C2×C4⋊C4—71no—
789C2×C4⋊C4—71no—
790C2×C4⋊C4—71no—
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⋊C4C22×D711yescharacteristic
816C2×C4⋊C4C22×D711yescharacteristic
817C2×C4⋊C4C22×D711yescharacteristic
818C2×C4⋊C4C22×D711yescharacteristic
819C2×C4⋊C4C22×D711yescharacteristic
820C2×C4⋊C4C22×D711yescharacteristic
821C2×C4⋊C4C22×D711yescharacteristic
822C2×C4⋊C4C22×D711yescharacteristic
823C2×C4⋊C4C22×D711yescharacteristic
824C2×C4⋊C4C22×D711yescharacteristic
825C2×C4⋊C4C22×D711yescharacteristic
826C2×C4⋊C4C22×D711yescharacteristic
827C2×C22⋊C4—71no—
828C2×C22⋊C4—71no—
829C2×C22⋊C4—71no—
830C2×C22⋊C4—71no—
831C2×C22⋊C4—71no—
832C2×C22⋊C4—71no—
833C2×C22⋊C4—71no—
834C2×C22⋊C4—71no—
835C2×C22⋊C4—71no—
836C2×C22⋊C4—71no—
837C2×C22⋊C4—71no—
838C2×C22⋊C4—71no—
839C2×C22⋊C4—71no—
840C2×C22⋊C4—71no—
841C2×C42—71no—
842C2×C42—71no—
843C2×C42—71no—
844C2×C42—71no—
845C2×C42—71no—
846C2×C42—71no—
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×C42C22×D711yescharacteristic
861C2×C42C22×D711yescharacteristic
862C2×C42C22×D711yescharacteristic
863C2×C42C22×D711yescharacteristic
864C2×C42C22×D711yescharacteristic
865C2×C42C22×D711yescharacteristic
866C2×C42C22×D711yescharacteristic
867#95—71no—
868#95—71no—
869#95—71no—
870#95—71no—
871#95—71no—
872#95—71no—
873#95—71no—
874#95—71no—
875#95—71no—
876#95—71no—
877#95—71no—
878#95—71no—
879#95—71no—
880#95—71no—
881#95—71no—
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#95C22×D711yescharacteristic
916#95C22×D711yescharacteristic
917#95C22×D711yescharacteristic
918#95C22×D711yescharacteristic
919#95C22×D711yescharacteristic
920#95C22×D711yescharacteristic
921#95C22×D711yescharacteristic
922#95C22×D711yescharacteristic
923#95C22×D711yescharacteristic
924#95C22×D711yescharacteristic
925#95C22×D711yescharacteristic
926#95C22×D711yescharacteristic
927#95C22×D711yescharacteristic
928#95C22×D711yescharacteristic
929#95C22×D711yescharacteristic
930#95C22×D711yescharacteristic
931C22×C7C22×#4111yescharacteristic
932C22×C7C22×#4111yescharacteristic
933C22×C7C22×#4111yescharacteristic
934C22×C7C2×2−1+411yescharacteristic
935C22×C7C2×2−1+411yescharacteristic
936C22×C7#58511yescharacteristic
937C22×C7#58511yescharacteristic
938C2×D7—41no—
939C2×D7—41no—
940C2×D7—41no—
941C2×D7—41no—
942C2×D7—41no—
943C2×D7—41no—
944C2×D7—41no—
945C4×C7—22no—
946C4×C7—22no—
947C4×C7—41no—
948C4×C7—41no—
949C4×C7—41no—
950C4×C7—41no—
951C4×C7—41no—
952C4×C7—41no—
953C4×C7—41no—
954C4×C7—41no—
955C4×C7—41no—
956C4×C7—41no—
957C4×C7—41no—
958C4×C7—41no—
959C4×C7#54114yes—
960Dic7—22no—
961Dic7—22no—
962Dic7—22no—
963Dic7—22no—
964Dic7—22no—
965Dic7—22no—
966Dic7—41no—
967Dic7—41no—
968Dic7—41no—
969Dic7—41no—
970Dic7—41no—
971Dic7—41no—
972Dic7—41no—
973Dic7—41no—
974Dic7—41no—
975C24—71no—
976C2×Q8—142no—
977C2×Q8—142no—
978C2×Q8—142no—
979C2×Q8—142no—
980C2×Q8—281no—
981C2×Q8—281no—
982C22×C4—71no—
983C22×C4—71no—
984C22×C4—71no—
985C22×C4—71no—
986C22×C4—71no—
987C22×C4—71no—
988C22×C4—71no—
989C22×C4—71no—
990C22×C4—71no—
991C22×C4—71no—
992C22×C4—71no—
993C22×C4—71no—
994C22×C4—71no—
995C22×C4—71no—
996C22×C4—71no—
997C22×C4—142no—
998C22×C4—142no—
999C22×C4—142no—
1000C22×C4C23×D711yescharacteristic
1001C22×C4C23×D711yescharacteristic
1002C22×C4C23×D711yescharacteristic
1003C22×C4C23×D711yescharacteristic
1004C22×C4C23×D711yescharacteristic
1005C22×C4C23×D711yescharacteristic
1006C22×C4C23×D711yescharacteristic
1007C22×C4C23×D711yescharacteristic
1008C22×C4C23×D711yescharacteristic
1009C22×C4C23×D711yescharacteristic
1010C22×C4C23×D711yescharacteristic
1011C22×C4C23×D711yescharacteristic
1012C22×C4C23×D711yescharacteristic
1013C22×C4C23×D711yescharacteristic
1014C22×C4C23×D711yescharacteristic
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
1020C4⋊C4—22no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—142no—
1028C4⋊C4—142no—
1029C4⋊C4—142no—
1030C4⋊C4—142no—
1031C4⋊C4—142no—
1032C4⋊C4—142no—
1033C4⋊C4—142no—
1034C4⋊C4—142no—
1035C4⋊C4—142no—
1036C4⋊C4—142no—
1037C4⋊C4—142no—
1038C4⋊C4—142no—
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—281no—
1054C4⋊C4—281no—
1055C4⋊C4—281no—
1056C4⋊C4—281no—
1057C4⋊C4—281no—
1058C4⋊C4—281no—
1059C4⋊C4—281no—
1060C4⋊C4—281no—
1061C4⋊C4—281no—
1062C4⋊C4—281no—
1063C22⋊C4—142no—
1064C22⋊C4—142no—
1065C22⋊C4—142no—
1066C22⋊C4—142no—
1067C22⋊C4—142no—
1068C22⋊C4—142no—
1069C22⋊C4—142no—
1070C22⋊C4—142no—
1071C22⋊C4—281no—
1072C22⋊C4—281no—
1073C22⋊C4—281no—
1074C22⋊C4—281no—
1075C22⋊C4—281no—
1076C22⋊C4—281no—
1077C42—22no—
1078C42—22no—
1079C42—22no—
1080C42—22no—
1081C42—22no—
1082C42—22no—
1083C42—22no—
1084C42—74no—
1085C42—74no—
1086C42—74no—
1087C42—142no—
1088C42—142no—
1089C42—142no—
1090C42—142no—
1091C42—142no—
1092C42—142no—
1093C42—142no—
1094C42—142no—
1095C42—142no—
1096C42—142no—
1097C42—281no—
1098C42—281no—
1099C42—281no—
1100C42—281no—
1101C42—281no—
1102C42—281no—
1103C2×C7#344411yescharacteristic
1104C2×C7C2×#54111yescharacteristic
1105C2×C7#345511yescharacteristic
1106C2×C7#346111yescharacteristic
1107C2×C7#346111yescharacteristic
1108C2×C7#346111yescharacteristic
1109C2×C7#346111yescharacteristic
1110D7—81no—
1111C23—141no—
1112C23—141no—
1113C23—141no—
1114C23—141no—
1115C23—141no—
1116C23—141no—
1117C23—141no—
1118C23C24×D711yescharacteristic
1119Q8—148no—
1120Q8—284no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
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—72no—
1162C2×C4—72no—
1163C2×C4—72no—
1164C2×C4—72no—
1165C2×C4—72no—
1166C2×C4—72no—
1167C2×C4—141no—
1168C2×C4—141no—
1169C2×C4—141no—
1170C2×C4—141no—
1171C2×C4—141no—
1172C2×C4—141no—
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—284no—
1207C2×C4#655112yes—
1208C2×C4D7×#4112yes—
1209C2×C4D7×#4112yes—
1210C2×C4D7×#4112yes—
1211C2×C4#655412yes—
1212C7#3460411yescharacteristic, complemented, Sylow
1213C22—281no—
1214C22—281no—
1215C22—281no—
1216C22—281no—
1217C22—281no—
1218C22—281no—
1219C22—281no—
1220C22C2×#655111yescharacteristic
1221C22C2×D7×#4111yescharacteristic
1222C22C2×D7×#4111yescharacteristic
1223C22C2×D7×#4111yescharacteristic
1224C22C2×#655411yescharacteristic
1225C22#9061611yescharacteristic
1226C22#9061611yescharacteristic
1227C4—22no—
1228C4—22no—
1229C4—41no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—142no—
1242C4—142no—
1243C4—142no—
1244C4—142no—
1245C4—142no—
1246C4—142no—
1247C4—281no—
1248C4—281no—
1249C4—281no—
1250C4—281no—
1251C4—281no—
1252C4—281no—
1253C4—281no—
1254C4—281no—
1255C4—281no—
1256C4#9038714yes—
1257C2—561no—
1258C2C2×#9038711yescharacteristic
1259C2#1174318711yescharacteristic
1260C2#1174318811yescharacteristic
1261C2#1174321411yescharacteristic
1262C2#1174321711yescharacteristic
1263C2#1174334311yescharacteristic
1264C2#1174334311yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutator, socle, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC7×#2402C2
prime radicalC23×D7C24
hypercenter#2402D7
hypocenterC7#34604
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #2402

Complements

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

NH ≅ G/Ntype
1. C7×#2402C2semidirect
3. #11735675C2semidirect
4. #11735675C2semidirect
5. #11735674C2semidirect
9. #11735655C2semidirect
10. #11735289C2semidirect
11. #11735286C2semidirect
13. #11735280C2semidirect
17. #11735268C2semidirect
21. #11731115C2semidirect
22. #11731115C2semidirect
23. #11731114C2semidirect
24. C4×#6453C2semidirect
25. C4×#6452C2semidirect
29. C4×#6450C2semidirect
31. #11730829C2semidirect
370. #2402D7semidirect
1212. C7#34604semidirect

Maximal subgroups

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

subgroupindex
C7×#24022
#117356782
#117356752
#117356742
#117356712
#117356672
#117356652
#117356552
#117352892
#117352862
#117352842
#117352802
#117352782
#117352702
#117352692
#117352682
#117312242
#117312232
#117311152
#117311142
C4×#64532
C4×#64522
C4×#64612
#117310652
C4×#64502
#117308652
#117308292
#346047