Finite Group Databasebeta

← #13520779

Subgroups — #13520779

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×#2655C211yesmaximal, characteristic, complemented
2#11735863C211yesmaximal, characteristic, complemented
3#11735854C211yesmaximal, characteristic
4#11735681C211yesmaximal, characteristic, complemented
5#11735678C211yesmaximal, characteristic
6#11735673C211yesmaximal, characteristic, complemented
7#11735667C211yesmaximal, characteristic
8#11735578C211yesmaximal, characteristic, complemented
9#11735578C211yesmaximal, characteristic, complemented
10#11735577C211yesmaximal, characteristic
11#11735575C211yesmaximal, characteristic
12#11735277C211yesmaximal, characteristic
13#11735269C211yesmaximal, characteristic
14#11735268C211yesmaximal, characteristic, complemented
15#11735186C211yesmaximal, characteristic, complemented
16#11735185C211yesmaximal, characteristic, complemented
17#11735184C211yesmaximal, characteristic
18#11733553C211yesmaximal, characteristic
19#11733411C211yesmaximal, characteristic, complemented
20#11732828C211yesmaximal, characteristic
21#11732823C211yesmaximal, characteristic
22#11732591C211yesmaximal, characteristic, complemented
23#11732586C211yesmaximal, characteristic, complemented
24#11732580C211yesmaximal, characteristic, complemented
25#11732388C211yesmaximal, characteristic, complemented
26#11732387C211yesmaximal, characteristic
27#11732387C211yesmaximal, characteristic
28#11732384C211yesmaximal, characteristic
29#11732383C211yesmaximal, characteristic, complemented
30#11731190C211yesmaximal, characteristic
31C4×#6450C211yesmaximal, characteristic, complemented
32C2×#6461C2211yescharacteristic
33C2×#6461C2211yescharacteristic
34C2×#6455C2211yescharacteristic
35C2×#6453C2211yescharacteristic
36C2×#6452C2211yescharacteristic
37C2×#6450C2211yescharacteristic
38C2×#6450C2211yescharacteristic
39C2×#6450C2211yescharacteristic
40C2×C4×Dic14C2211yescharacteristic
41C7×#401C2211yescharacteristic
42C7×#400C2211yescharacteristic
43C7×#400C2211yescharacteristic
44C7×#400C2211yescharacteristic
45C7×#400C2211yescharacteristic
46C7×#398C2211yescharacteristic
47C7×#398C2211yescharacteristic
48C7×#398C2211yescharacteristic
49C7×#389C2211yescharacteristic
50C7×#387C2211yescharacteristic
51C7×#387C2211yescharacteristic
52C7×#387C2211yescharacteristic
53C7×#387C2211yescharacteristic
54C7×#387C2211yescharacteristic
55C4×C7×C4⋊C4C2211yescharacteristic
56#89766C2211yescharacteristic
57#89766C2211yescharacteristic
58#89766C2211yescharacteristic
59#89765C2211yescharacteristic
60#89764C2211yescharacteristic
61#89764C2211yescharacteristic
62#89762C2211yescharacteristic
63#89762C2211yescharacteristic
64#89762C2211yescharacteristic
65#89758C2211yescharacteristic
66#89756C2211yescharacteristic
67#89756C2211yescharacteristic
68#89756C2211yescharacteristic
69#89756C2211yescharacteristic
70#89755C2211yescharacteristic
71#89754C2211yescharacteristic
72#89753C2211yescharacteristic
73#89753C2211yescharacteristic
74#89752C2211yescharacteristic
75#89752C2211yescharacteristic
76#89752C2211yescharacteristic
77#89751C2211yescharacteristic
78#89751C2211yescharacteristic
79#89751C2211yescharacteristic
80#89751C2211yescharacteristic
81#89750C2211yescharacteristic
82#89750C2211yescharacteristic
83#89749C2211yescharacteristic
84C4⋊C4×Dic7C2211yescharacteristic
85C4⋊C4×Dic7C2211yescharacteristic
86C4⋊C4×Dic7C2211yescharacteristic
87C4⋊C4×Dic7C2211yescharacteristic
88C4⋊C4×Dic7C2211yescharacteristic
89C4⋊C4×Dic7C2211yescharacteristic
90C4⋊C4×Dic7C2211yescharacteristic
91C4⋊C4×Dic7C2211yescharacteristic
92C4⋊C4×Dic7C2211yescharacteristic
93C4⋊C4×Dic7C2211yescharacteristic
94#89744C2211yescharacteristic
95#89744C2211yescharacteristic
96#89712C2211yescharacteristic
97#89712C2211yescharacteristic
98#89712C2211yescharacteristic
99#89705C2211yescharacteristic
100#89705C2211yescharacteristic
101C4×Dic7⋊C4C2211yescharacteristic
102C4×Dic7⋊C4C2211yescharacteristic
103C42×Dic7C2211yescharacteristic
104C42×Dic7C2211yescharacteristic
105C42×Dic7C2211yescharacteristic
106#89700C2211yescharacteristic
107#89448C2211yescharacteristic
108#89448C2211yescharacteristic
109#89448C2211yescharacteristic
110#89447C2211yescharacteristic
111#89447C2211yescharacteristic
112#89447C2211yescharacteristic
113#89447C2211yescharacteristic
114#89446C2211yescharacteristic
115#89445C2211yescharacteristic
116#89445C2211yescharacteristic
117#89442C2211yescharacteristic
118#89442C2211yescharacteristic
119#89442C2211yescharacteristic
120#89441C2211yescharacteristic
121#89438C2211yescharacteristic
122#89438C2211yescharacteristic
123#89438C2211yescharacteristic
124#89438C2211yescharacteristic
125#89438C2211yescharacteristic
126#89438C2211yescharacteristic
127C7⋊#401C2211yescharacteristic
128#89433C2211yescharacteristic
129#89432C2211yescharacteristic
130#89432C2211yescharacteristic
131#89432C2211yescharacteristic
132#89432C2211yescharacteristic
133#89432C2211yescharacteristic
134#89431C2211yescharacteristic
135#89431C2211yescharacteristic
136#89430C2211yescharacteristic
137#89430C2211yescharacteristic
138#89430C2211yescharacteristic
139#89430C2211yescharacteristic
140#89430C2211yescharacteristic
141#89430C2211yescharacteristic
142#89430C2211yescharacteristic
143#89429C2211yescharacteristic
144#89429C2211yescharacteristic
145#89429C2211yescharacteristic
146#89429C2211yescharacteristic
147#89429C2211yescharacteristic
148#89429C2211yescharacteristic
149#89429C2211yescharacteristic
150#89429C2211yescharacteristic
151#89428C2211yescharacteristic
152#89428C2211yescharacteristic
153#89427C2211yescharacteristic
154#89427C2211yescharacteristic
155#89427C2211yescharacteristic
156#89426C2211yescharacteristic
157#89426C2211yescharacteristic
158#89425C2211yescharacteristic
159#89425C2211yescharacteristic
160#89425C2211yescharacteristic
161#89425C2211yescharacteristic
162#89425C2211yescharacteristic
163#89424C2211yescharacteristic
164#89423C2211yescharacteristic
165#89423C2211yescharacteristic
166#89422C2211yescharacteristic
167#89421C2211yescharacteristic
168#89421C2211yescharacteristic
169#89421C2211yescharacteristic
170#89421C2211yescharacteristic
171#89421C2211yescharacteristic
172#89421C2211yescharacteristic
173#89421C2211yescharacteristic
174#89421C2211yescharacteristic
175#89421C2211yescharacteristic
176#89421C2211yescharacteristic
177#89421C2211yescharacteristic
178#89421C2211yescharacteristic
179#89421C2211yescharacteristic
180#89420C2211yescharacteristic
181#89420C2211yescharacteristic
182#89420C2211yescharacteristic
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×(C2×D7)⋊C4C2311yescharacteristic
207C2×(C2×D7)⋊C4C2311yescharacteristic
208C2×(C2×D7)⋊C4C2311yescharacteristic
209C2×(C2×D7)⋊C4C2311yescharacteristic
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×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×Dic7⋊C4C2311yescharacteristic
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×C4×Dic7C2311yescharacteristic
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
279#6461—24no—
280#6461—24no—
281#6455—24no—
282#6453—24no—
283#6452—24no—
284#6450—24no—
285#6450—24no—
286#6450—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#2655D711yescharacteristic, complemented
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#2402—71no—
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—22no—
430C7×C4⋊C4—22no—
431C7×C4⋊C4—41no—
432C7×C4⋊C4—41no—
433C7×C4⋊C4—41no—
434C7×C4⋊C4—41no—
435C42×C7—22no—
436C42×C7—41no—
437C42×C7—41no—
438(C2×D7)⋊C4—22no—
439(C2×D7)⋊C4—22no—
440(C2×D7)⋊C4—22no—
441(C2×D7)⋊C4—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—41no—
447(C2×D7)⋊C4—41no—
448(C2×D7)⋊C4—41no—
449(C2×D7)⋊C4—41no—
450(C2×D7)⋊C4—41no—
451(C2×D7)⋊C4—41no—
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—41no—
461C4⋊Dic7—41no—
462Dic7⋊C4—22no—
463Dic7⋊C4—22no—
464Dic7⋊C4—22no—
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—41no—
479Dic7⋊C4—41no—
480Dic7⋊C4—41no—
481Dic7⋊C4—41no—
482Dic7⋊C4—41no—
483Dic7⋊C4—41no—
484Dic7⋊C4—41no—
485Dic7⋊C4—41no—
486Dic7⋊C4—41no—
487Dic7⋊C4—41no—
488C4×Dic7—22no—
489C4×Dic7—22no—
490C4×Dic7—22no—
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—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#401C2×D711yescharacteristic
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#398—71no—
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#389C2×D711yescharacteristic
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#387C2×D711yescharacteristic
620#387C2×D711yescharacteristic
621#387C2×D711yescharacteristic
622#387C2×D711yescharacteristic
623#387C2×D711yescharacteristic
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⋊C4—71no—
649C4×C4⋊C4—71no—
650C4×C4⋊C4—71no—
651C4×C4⋊C4—71no—
652C4×C4⋊C4—71no—
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#376—71no—
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×C7—21no—
715C2×C4×C7—21no—
716C2×C4×C7C2×#4112yes—
717C2×C4×C7C2×#4112yes—
718C2×C4×C7C2×#4112yes—
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×Dic7C2×#4112yes—
757C2×Dic7C2×#4112yes—
758C2×Dic7C2×#4112yes—
759C2×Dic7C2×#4112yes—
760C2×Dic7C2×#4112yes—
761C2×Dic7C2×#4112yes—
762C2×Dic72−1+412yes—
763C2×Dic72−1+412yes—
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×C42—71no—
861C2×C42—71no—
862C2×C42—71no—
863C2×C42—71no—
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#95C22×D711yescharacteristic
912#95C22×D711yescharacteristic
913#95C22×D711yescharacteristic
914#95C22×D711yescharacteristic
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—22no—
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—41no—
960Dic7—22no—
961Dic7—22no—
962Dic7—22no—
963Dic7—22no—
964Dic7—22no—
965Dic7—41no—
966Dic7—41no—
967Dic7—41no—
968Dic7—41no—
969Dic7—41no—
970Dic7—41no—
971Dic7—41no—
972Dic7—41no—
973Dic7—41no—
974Dic7#54114yes—
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—22no—
1022C4⋊C4—22no—
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—281no—
1052C4⋊C4—281no—
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—41no—
1079C42—41no—
1080C42—74no—
1081C42—74no—
1082C42—74no—
1083C42—142no—
1084C42—142no—
1085C42—142no—
1086C42—142no—
1087C42—142no—
1088C42—142no—
1089C42—142no—
1090C42—142no—
1091C42—142no—
1092C42—142no—
1093C42—142no—
1094C42—142no—
1095C42—142no—
1096C42—142no—
1097C42—142no—
1098C42—142no—
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—21no—
1162C2×C4—21no—
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—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—141no—
1207C2×C4—141no—
1208C2×C4—284no—
1209C2×C4D7×#4112yes—
1210C2×C4D7×#4112yes—
1211C2×C4D7×#4112yes—
1212C7#3460411yescharacteristic, complemented, Sylow
1213C22—281no—
1214C22—281no—
1215C22—281no—
1216C22—281no—
1217C22—281no—
1218C22—281no—
1219C22—281no—
1220C22C2×D7×#4111yescharacteristic
1221C22C2×D7×#4111yescharacteristic
1222C22C2×D7×#4111yescharacteristic
1223C22#9061811yescharacteristic
1224C22D7×2−1+411yescharacteristic
1225C22D7×2−1+411yescharacteristic
1226C22#9062011yescharacteristic
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—74no—
1243C4—142no—
1244C4—142no—
1245C4—142no—
1246C4—142no—
1247C4—142no—
1248C4—281no—
1249C4—281no—
1250C4—281no—
1251C4—281no—
1252C4—281no—
1253C4—281no—
1254C4—281no—
1255C4—281no—
1256C4—281no—
1257C2—561no—
1258C2#1174318711yescharacteristic
1259C2#1174349711yescharacteristic
1260C2#1174349711yescharacteristic
1261C2#1174356411yescharacteristic
1262C2#1174356411yescharacteristic
1263C2D7×#54111yescharacteristic
1264C2#1174359111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2655C2
prime radicalC23×D7C24
hypercenter#2655D7
hypocenterC7#34604
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2655

Complements

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

NH ≅ G/Ntype
1. C7×#2655C2semidirect
2. #11735863C2semidirect
4. #11735681C2semidirect
6. #11735673C2semidirect
8. #11735578C2semidirect
9. #11735578C2semidirect
14. #11735268C2semidirect
15. #11735186C2semidirect
16. #11735185C2semidirect
19. #11733411C2semidirect
22. #11732591C2semidirect
23. #11732586C2semidirect
24. #11732580C2semidirect
25. #11732388C2semidirect
29. #11732383C2semidirect
31. C4×#6450C2semidirect
359. #2655D7semidirect
1212. C7#34604semidirect

Maximal subgroups

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

subgroupindex
C7×#26552
#117358632
#117358542
#117356812
#117356782
#117356732
#117356672
#117355782
#117355772
#117355752
#117352772
#117352692
#117352682
#117351862
#117351852
#117351842
#117335532
#117334112
#117328282
#117328232
#117325912
#117325862
#117325802
#117323882
#117323872
#117323842
#117323832
#117311902
C4×#64502
#346047