Finite Group Databasebeta

← #13568209

Subgroups — #13568209

Order 1792.

1518 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2313C211yesmaximal, characteristic, complemented
2#11739643C211yesmaximal, characteristic, complemented
3#11739615C211yesmaximal, characteristic, complemented
4#11732883C211yesmaximal, characteristic, complemented
5#11732826C211yesmaximal, characteristic, complemented
6#11732812C211yesmaximal, characteristic, complemented
7#11732776C211yesmaximal, characteristic, complemented
8#11732738C211yesmaximal, characteristic, complemented
9#11732737C211yesmaximal, characteristic, complemented
10#11732722C211yesmaximal, characteristic, complemented
11#11732718C211yesmaximal, characteristic, complemented
12#11732702C211yesmaximal, characteristic, complemented
13#11732680C211yesmaximal, characteristic, complemented
14#11732664C211yesmaximal, characteristic, complemented
15#11732610C211yesmaximal, characteristic, complemented
16#11732599C211yesmaximal, characteristic, complemented
17#11732581C211yesmaximal, characteristic, complemented
18#11732555C211yesmaximal, characteristic, complemented
19#11732456C211yesmaximal, characteristic, complemented
20#11731587C211yesmaximal, characteristic, complemented
21#11731558C211yesmaximal, characteristic, complemented
22#11731555C211yesmaximal, characteristic, complemented
23#11731554C211yesmaximal, characteristic
24#11731421C211yesmaximal, characteristic, complemented
25#11731419C211yesmaximal, characteristic, complemented
26#11731415C211yesmaximal, characteristic, complemented
27#11731414C211yesmaximal, characteristic
28#11731053C211yesmaximal, characteristic
29#11730939C211yesmaximal, characteristic, complemented
30#11730896C211yesmaximal, characteristic, complemented
31#11730884C211yesmaximal, characteristic, complemented
32C22×C7×C4⋊C4C2211yescharacteristic
33C2×#6492C2211yescharacteristic
34C2×#6492C2211yescharacteristic
35C2×C4×C22⋊D7C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C2×#6457C2211yescharacteristic
38C2×#6452C2211yescharacteristic
39C2×#6435C2211yescharacteristic
40C2×#6433C2211yescharacteristic
41C7×#387C2211yescharacteristic
42C7×#387C2211yescharacteristic
43C7×#387C2211yescharacteristic
44C7×#387C2211yescharacteristic
45C7×#387C2211yescharacteristic
46C7×#387C2211yescharacteristic
47C7×#387C2211yescharacteristic
48C7×#387C2211yescharacteristic
49C7×#381C2211yescharacteristic
50C7×#381C2211yescharacteristic
51C7×#380C2211yescharacteristic
52C7×#380C2211yescharacteristic
53C4×C7×C22⋊C4C2211yescharacteristic
54C4×C7×C22⋊C4C2211yescharacteristic
55#89985C2211yescharacteristic
56#89985C2211yescharacteristic
57#89985C2211yescharacteristic
58#89984C2211yescharacteristic
59#89983C2211yescharacteristic
60#89982C2211yescharacteristic
61#89982C2211yescharacteristic
62#89982C2211yescharacteristic
63#89766C2211yescharacteristic
64#89766C2211yescharacteristic
65#89766C2211yescharacteristic
66#89766C2211yescharacteristic
67#89766C2211yescharacteristic
68#89766C2211yescharacteristic
69#89765C2211yescharacteristic
70#89764C2211yescharacteristic
71#89762C2211yescharacteristic
72#89762C2211yescharacteristic
73#89762C2211yescharacteristic
74#89762C2211yescharacteristic
75#89761C2211yescharacteristic
76#89761C2211yescharacteristic
77#89756C2211yescharacteristic
78#89756C2211yescharacteristic
79#89756C2211yescharacteristic
80#89756C2211yescharacteristic
81#89756C2211yescharacteristic
82#89756C2211yescharacteristic
83#89754C2211yescharacteristic
84#89753C2211yescharacteristic
85#89753C2211yescharacteristic
86#89752C2211yescharacteristic
87#89750C2211yescharacteristic
88#89750C2211yescharacteristic
89#89744C2211yescharacteristic
90#89744C2211yescharacteristic
91#89744C2211yescharacteristic
92#89744C2211yescharacteristic
93#89733C2211yescharacteristic
94#89733C2211yescharacteristic
95#89732C2211yescharacteristic
96#89729C2211yescharacteristic
97#89729C2211yescharacteristic
98#89729C2211yescharacteristic
99#89728C2211yescharacteristic
100#89725C2211yescharacteristic
101#89721C2211yescharacteristic
102#89721C2211yescharacteristic
103#89720C2211yescharacteristic
104#89720C2211yescharacteristic
105#89717C2211yescharacteristic
106#89716C2211yescharacteristic
107#89716C2211yescharacteristic
108#89716C2211yescharacteristic
109#89712C2211yescharacteristic
110#89712C2211yescharacteristic
111#89712C2211yescharacteristic
112#89711C2211yescharacteristic
113C4×(C2×D7)⋊C4C2211yescharacteristic
114C4×(C2×D7)⋊C4C2211yescharacteristic
115#89707C2211yescharacteristic
116#89705C2211yescharacteristic
117C4×Dic7⋊C4C2211yescharacteristic
118C4×Dic7⋊C4C2211yescharacteristic
119C42×Dic7C2211yescharacteristic
120#89700C2211yescharacteristic
121#89700C2211yescharacteristic
122#89700C2211yescharacteristic
123#89448C2211yescharacteristic
124#89448C2211yescharacteristic
125#89447C2211yescharacteristic
126#89447C2211yescharacteristic
127#89447C2211yescharacteristic
128#89447C2211yescharacteristic
129#89447C2211yescharacteristic
130#89447C2211yescharacteristic
131#89446C2211yescharacteristic
132#89446C2211yescharacteristic
133#89444C2211yescharacteristic
134#89444C2211yescharacteristic
135#89444C2211yescharacteristic
136#89442C2211yescharacteristic
137#89442C2211yescharacteristic
138#89442C2211yescharacteristic
139#89442C2211yescharacteristic
140#89442C2211yescharacteristic
141#89442C2211yescharacteristic
142#89441C2211yescharacteristic
143#89441C2211yescharacteristic
144#89441C2211yescharacteristic
145#89440C2211yescharacteristic
146#89440C2211yescharacteristic
147#89440C2211yescharacteristic
148#89440C2211yescharacteristic
149#89439C2211yescharacteristic
150#89437C2211yescharacteristic
151#89432C2211yescharacteristic
152#89432C2211yescharacteristic
153#89432C2211yescharacteristic
154#89431C2211yescharacteristic
155#89430C2211yescharacteristic
156#89430C2211yescharacteristic
157#89430C2211yescharacteristic
158#89430C2211yescharacteristic
159#89429C2211yescharacteristic
160#89429C2211yescharacteristic
161#89429C2211yescharacteristic
162#89427C2211yescharacteristic
163#89427C2211yescharacteristic
164#89427C2211yescharacteristic
165#89426C2211yescharacteristic
166#89426C2211yescharacteristic
167#89426C2211yescharacteristic
168#89426C2211yescharacteristic
169#89425C2211yescharacteristic
170#89425C2211yescharacteristic
171#89425C2211yescharacteristic
172#89424C2211yescharacteristic
173#89424C2211yescharacteristic
174#89424C2211yescharacteristic
175#89424C2211yescharacteristic
176#89424C2211yescharacteristic
177#89423C2211yescharacteristic
178#89422C2211yescharacteristic
179#89422C2211yescharacteristic
180#89419C2211yescharacteristic
181#89419C2211yescharacteristic
182#89419C2211yescharacteristic
183#89419C2211yescharacteristic
184#89419C2211yescharacteristic
185#89419C2211yescharacteristic
186#89419C2211yescharacteristic
187#36994—71nomaximal, Sylow
188C23×C4×C7C2311yescharacteristic
189C23×C4×C7C2311yescharacteristic
190C23×C4×C7C2311yescharacteristic
191C22×C22⋊D7C2311yescharacteristic
192C22×C22⋊D7C2311yescharacteristic
193C22×D28C2311yescharacteristic
194C22×C4×D7C2311yescharacteristic
195C22×C4×D7C2311yescharacteristic
196C2×C7×C4⋊C4—24no—
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×C22⋊C4C2311yescharacteristic
206C2×C7×C22⋊C4C2311yescharacteristic
207C2×C7×C22⋊C4C2311yescharacteristic
208C2×C7×C22⋊C4C2311yescharacteristic
209C2×C42×C7C2311yescharacteristic
210C2×C42×C7C2311yescharacteristic
211C2×C42×C7C2311yescharacteristic
212C2×C42×C7C2311yescharacteristic
213C2×C22⋊Dic7C2311yescharacteristic
214C2×C22⋊Dic7C2311yescharacteristic
215C2×C22⋊Dic7C2311yescharacteristic
216C2×C22⋊Dic7C2311yescharacteristic
217C2×C22⋊Dic7C2311yescharacteristic
218C2×C22⋊Dic7C2311yescharacteristic
219#6492—24no—
220#6492—42no—
221C4×C22⋊D7—24no—
222C2×(C2×D7)⋊C4C2311yescharacteristic
223C2×(C2×D7)⋊C4C2311yescharacteristic
224C2×(C2×D7)⋊C4C2311yescharacteristic
225C2×(C2×D7)⋊C4C2311yescharacteristic
226C2×(C2×D7)⋊C4C2311yescharacteristic
227C2×(C2×D7)⋊C4C2311yescharacteristic
228C2×(C2×D7)⋊C4C2311yescharacteristic
229C2×(C2×D7)⋊C4C2311yescharacteristic
230C2×(C2×D7)⋊C4C2311yescharacteristic
231C2×(C2×D7)⋊C4C2311yescharacteristic
232C2×(C2×D7)⋊C4C2311yescharacteristic
233C2×(C2×D7)⋊C4C2311yescharacteristic
234C2×(C2×D7)⋊C4C2311yescharacteristic
235C2×(C2×D7)⋊C4C2311yescharacteristic
236C2×(C2×D7)⋊C4C2311yescharacteristic
237C2×(C2×D7)⋊C4C2311yescharacteristic
238C2×(C2×D7)⋊C4C2311yescharacteristic
239C2×(C2×D7)⋊C4C2311yescharacteristic
240C2×(C2×D7)⋊C4C2311yescharacteristic
241C2×(C2×D7)⋊C4C2311yescharacteristic
242C2×(C2×D7)⋊C4C2311yescharacteristic
243C2×(C2×D7)⋊C4C2311yescharacteristic
244C2×(C2×D7)⋊C4C2311yescharacteristic
245C2×(C2×D7)⋊C4C2311yescharacteristic
246#6489—42no—
247C2×C4⋊Dic7C2311yescharacteristic
248C2×C4⋊Dic7C2311yescharacteristic
249C2×C4⋊Dic7C2311yescharacteristic
250C2×C4⋊Dic7C2311yescharacteristic
251C2×C4⋊Dic7C2311yescharacteristic
252C2×C4⋊Dic7C2311yescharacteristic
253C2×C4⋊Dic7C2311yescharacteristic
254C2×C4⋊Dic7C2311yescharacteristic
255C2×C4⋊Dic7C2311yescharacteristic
256C2×C4⋊Dic7C2311yescharacteristic
257C2×C4⋊Dic7C2311yescharacteristic
258C2×Dic7⋊C4C2311yescharacteristic
259C2×Dic7⋊C4C2311yescharacteristic
260C2×Dic7⋊C4C2311yescharacteristic
261C2×Dic7⋊C4C2311yescharacteristic
262C2×Dic7⋊C4C2311yescharacteristic
263C2×Dic7⋊C4C2311yescharacteristic
264C2×Dic7⋊C4C2311yescharacteristic
265C2×Dic7⋊C4C2311yescharacteristic
266C2×Dic7⋊C4C2311yescharacteristic
267C2×Dic7⋊C4C2311yescharacteristic
268C2×Dic7⋊C4C2311yescharacteristic
269C2×Dic7⋊C4C2311yescharacteristic
270C2×Dic7⋊C4C2311yescharacteristic
271C2×Dic7⋊C4C2311yescharacteristic
272C2×Dic7⋊C4C2311yescharacteristic
273C2×Dic7⋊C4C2311yescharacteristic
274C2×Dic7⋊C4C2311yescharacteristic
275C2×Dic7⋊C4C2311yescharacteristic
276C2×Dic7⋊C4C2311yescharacteristic
277C2×Dic7⋊C4C2311yescharacteristic
278C2×Dic7⋊C4C2311yescharacteristic
279C2×Dic7⋊C4C2311yescharacteristic
280C2×Dic7⋊C4C2311yescharacteristic
281C2×Dic7⋊C4C2311yescharacteristic
282C2×Dic7⋊C4C2311yescharacteristic
283C2×Dic7⋊C4C2311yescharacteristic
284C2×C4×Dic7C2311yescharacteristic
285C2×C4×Dic7C2311yescharacteristic
286C2×C4×Dic7C2311yescharacteristic
287C2×C4×Dic7C2311yescharacteristic
288C2×C4×Dic7C2311yescharacteristic
289C2×C4×Dic7C2311yescharacteristic
290C2×C4×Dic7C2311yescharacteristic
291C2×C4×Dic7C2311yescharacteristic
292C2×C4×Dic7C2311yescharacteristic
293C2×C4×Dic7C2311yescharacteristic
294#6457—42no—
295#6452—42no—
296#6435—42no—
297#6433—42no—
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#2865—71no—
353#2864—71no—
354#2802—71no—
355#2800—71no—
356#2793—71no—
357#2790—71no—
358#2777—71no—
359#2772—71no—
360#2771—71no—
361#2761—71no—
362#2752—71no—
363#2750—71no—
364#2740—71no—
365#2738—71no—
366#2719—71no—
367#2707—71no—
368#2707—71no—
369#2706—71no—
370#2652—71no—
371#2649—71no—
372#2602—71no—
373#2590—71no—
374#2579—71no—
375#2577—71no—
376#2475—71no—
377#2470—71no—
378#2441—71no—
379#2413—71no—
380#2335—71no—
381#2313D711yescharacteristic, complemented
382#2293—71no—
383C24×C7C2411yescharacteristic
384C23×D7C2411yescharacteristic
385C23×D7C2411yescharacteristic
386C22×C4×C7—22no—
387C22×C4×C7—22no—
388C22×C4×C7—41no—
389C22×C4×C7—41no—
390C22×C4×C7—41no—
391C22×C4×C7—41no—
392C22×C4×C7—41no—
393C22×C4×C7—41no—
394C22×C4×C7#4114yes—
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×C4×C7C2411yescharacteristic
406C22×C4×C7C2411yescharacteristic
407C22×C4×C7C2411yescharacteristic
408C22×C4×C7C2411yescharacteristic
409C2×C22⋊D7—22no—
410C2×C22⋊D7—22no—
411C2×C22⋊D7—22no—
412C2×C22⋊D7—41no—
413C2×C22⋊D7—41no—
414C2×C22⋊D7—41no—
415C22×Dic7C2411yescharacteristic
416C22×Dic7C2411yescharacteristic
417C22×Dic7C2411yescharacteristic
418C22×Dic7C2411yescharacteristic
419C22×Dic7C2411yescharacteristic
420C22×Dic7C2411yescharacteristic
421C22×Dic7C2411yescharacteristic
422C22×Dic7C2411yescharacteristic
423C22×Dic7C2411yescharacteristic
424C22×Dic7C2411yescharacteristic
425C22×Dic7C2411yescharacteristic
426C22×Dic7C2411yescharacteristic
427C22×Dic7C2411yescharacteristic
428C22×Dic7C2411yescharacteristic
429C2×D28—41no—
430C2×D28—41no—
431C2×D28—41no—
432C2×C4×D7—22no—
433C2×C4×D7—41no—
434C2×C4×D7—41no—
435C2×C4×D7—41no—
436C2×C4×D7—41no—
437C2×C4×D7—41no—
438C7×C4⋊C4—22no—
439C7×C4⋊C4—22no—
440C7×C4⋊C4—22no—
441C7×C4⋊C4—22no—
442C7×C4⋊C4—41no—
443C7×C4⋊C4—41no—
444C7×C4⋊C4—41no—
445C7×C4⋊C4—41no—
446C7×C22⋊C4—41no—
447C7×C22⋊C4—41no—
448C7×C22⋊C4—41no—
449C7×C22⋊C4—41no—
450C42×C7—41no—
451C42×C7—41no—
452C42×C7—41no—
453C42×C7—41no—
454C22⋊Dic7—22no—
455C22⋊Dic7—22no—
456C22⋊Dic7—22no—
457C22⋊Dic7—41no—
458C22⋊Dic7—41no—
459C22⋊Dic7—41no—
460(C2×D7)⋊C4—22no—
461(C2×D7)⋊C4—22no—
462(C2×D7)⋊C4—22no—
463(C2×D7)⋊C4—22no—
464(C2×D7)⋊C4—22no—
465(C2×D7)⋊C4—22no—
466(C2×D7)⋊C4—41no—
467(C2×D7)⋊C4—41no—
468(C2×D7)⋊C4—41no—
469(C2×D7)⋊C4—41no—
470(C2×D7)⋊C4—41no—
471(C2×D7)⋊C4—41no—
472(C2×D7)⋊C4—41no—
473(C2×D7)⋊C4—41no—
474(C2×D7)⋊C4—41no—
475(C2×D7)⋊C4—41no—
476(C2×D7)⋊C4—41no—
477(C2×D7)⋊C4—41no—
478(C2×D7)⋊C4—41no—
479(C2×D7)⋊C4—41no—
480(C2×D7)⋊C4—41no—
481(C2×D7)⋊C4—41no—
482(C2×D7)⋊C4—41no—
483(C2×D7)⋊C4—41no—
484C4⋊Dic7—22no—
485C4⋊Dic7—22no—
486C4⋊Dic7—41no—
487C4⋊Dic7—41no—
488C4⋊Dic7—41no—
489C4⋊Dic7—41no—
490C4⋊Dic7—41no—
491C4⋊Dic7—41no—
492C4⋊Dic7—41no—
493C4⋊Dic7—41no—
494C4⋊Dic7—41no—
495Dic7⋊C4—22no—
496Dic7⋊C4—22no—
497Dic7⋊C4—22no—
498Dic7⋊C4—22no—
499Dic7⋊C4—22no—
500Dic7⋊C4—22no—
501Dic7⋊C4—22no—
502Dic7⋊C4—22no—
503Dic7⋊C4—41no—
504Dic7⋊C4—41no—
505Dic7⋊C4—41no—
506Dic7⋊C4—41no—
507Dic7⋊C4—41no—
508Dic7⋊C4—41no—
509Dic7⋊C4—41no—
510Dic7⋊C4—41no—
511Dic7⋊C4—41no—
512Dic7⋊C4—41no—
513Dic7⋊C4—41no—
514Dic7⋊C4—41no—
515Dic7⋊C4—41no—
516Dic7⋊C4—41no—
517Dic7⋊C4—41no—
518Dic7⋊C4—41no—
519Dic7⋊C4—41no—
520Dic7⋊C4—41no—
521C4×Dic7—22no—
522C4×Dic7—22no—
523C4×Dic7—22no—
524C4×Dic7—41no—
525C4×Dic7—41no—
526C4×Dic7—41no—
527C4×Dic7—41no—
528C4×Dic7—41no—
529C4×Dic7—41no—
530C4×Dic7—41no—
531C2×#125—71no—
532C2×#125—71no—
533C2×#123—71no—
534C2×#123—71no—
535C2×#123—71no—
536C2×C4×D4—71no—
537C2×#117—71no—
538C2×#117—71no—
539C22×C4⋊C4C2×D711yescharacteristic
540#400—71no—
541#400—71no—
542#400—71no—
543#400—71no—
544#400—71no—
545#400—71no—
546#400—71no—
547#400—71no—
548#400—71no—
549#399—71no—
550#399—71no—
551#399—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#398—71no—
562#397—71no—
563#397—71no—
564#397—71no—
565#397—71no—
566#397—71no—
567#397—71no—
568#397—71no—
569#397—71no—
570#397—71no—
571#397—71no—
572#396—71no—
573#396—71no—
574#396—71no—
575#396—71no—
576#396—71no—
577#396—71no—
578#396—71no—
579#396—71no—
580#396—71no—
581#396—71no—
582#394—71no—
583#394—71no—
584#394—71no—
585#394—71no—
586#394—71no—
587#392—71no—
588#390—71no—
589#390—71no—
590#390—71no—
591#390—71no—
592#389—71no—
593#389—71no—
594#389—71no—
595#389—71no—
596#389—71no—
597#389—71no—
598#389—71no—
599#389—71no—
600#389—71no—
601#389—71no—
602#389—71no—
603#389—71no—
604#389—71no—
605#389—71no—
606#388—71no—
607#388—71no—
608#388—71no—
609#388—71no—
610#388—71no—
611#388—71no—
612#388—71no—
613#388—71no—
614#388—71no—
615#388—71no—
616#388—71no—
617#388—71no—
618#388—71no—
619#388—71no—
620#388—71no—
621#388—71no—
622#388—71no—
623#388—71no—
624#388—71no—
625#388—71no—
626#387—71no—
627#387—71no—
628#387—71no—
629#387—71no—
630#387—71no—
631#387—71no—
632#387—71no—
633#387—71no—
634#387—71no—
635#387—71no—
636#387—71no—
637#387—71no—
638#387—71no—
639#387—71no—
640#387—71no—
641#387—71no—
642#387—71no—
643#387—71no—
644#387—71no—
645#387—71no—
646#387C2×D711yescharacteristic
647#387C2×D711yescharacteristic
648#387C2×D711yescharacteristic
649#387C2×D711yescharacteristic
650#387C2×D711yescharacteristic
651#387C2×D711yescharacteristic
652#387C2×D711yescharacteristic
653#387C2×D711yescharacteristic
654#386—71no—
655#386—71no—
656#386—71no—
657#386—71no—
658#386—71no—
659#385—71no—
660#385—71no—
661#385—71no—
662#385—71no—
663#385—71no—
664#385—71no—
665#385—71no—
666#385—71no—
667#385—71no—
668#384—71no—
669#383—71no—
670#382—71no—
671#382—71no—
672#381—71no—
673#381C2×D711yescharacteristic
674#381C2×D711yescharacteristic
675#380—71no—
676#380—71no—
677#380C2×D711yescharacteristic
678#380C2×D711yescharacteristic
679C4×C4⋊C4—71no—
680C4×C4⋊C4—71no—
681C4×C22⋊C4—71no—
682C4×C22⋊C4—71no—
683C4×C22⋊C4C2×D711yescharacteristic
684C4×C22⋊C4C2×D711yescharacteristic
685C43—71no—
686C23×C7—21no—
687C23×C7—21no—
688C23×C7—21no—
689C23×C7—21no—
690C23×C7—21no—
691C23×C7—21no—
692C23×C7C2×#4112yes—
693C23×C7C2511yescharacteristic
694C22×D7—21no—
695C22×D7—21no—
696C22×D7—21no—
697C22×D7—21no—
698C22×D7—21no—
699C22×D7—21no—
700C22×D7—21no—
701C22×D7—21no—
702C22×D7—21no—
703C22×D7—21no—
704C22×D7—21no—
705C22×D7—21no—
706C22×D7—21no—
707C22×D7—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×C7—21no—
717C2×C4×C7—21no—
718C2×C4×C7—21no—
719C2×C4×C7—21no—
720C2×C4×C7—21no—
721C2×C4×C7—21no—
722C2×C4×C7—21no—
723C2×C4×C7—21no—
724C2×C4×C7—21no—
725C2×C4×C7—21no—
726C2×C4×C7—21no—
727C2×C4×C7—21no—
728C2×C4×C7—21no—
729C2×C4×C7—21no—
730C2×C4×C7—21no—
731C2×C4×C7—21no—
732C2×C4×C7—21no—
733C2×C4×C7—21no—
734C2×C4×C7—21no—
735C2×C4×C7—21no—
736C2×C4×C7—21no—
737C2×C4×C7—21no—
738C2×C4×C7—21no—
739C2×C4×C7—21no—
740C2×C4×C7—21no—
741C2×C4×C7—21no—
742C2×C4×C7—21no—
743C2×C4×C7—21no—
744C2×C4×C7—21no—
745C2×C4×C7—21no—
746C2×C4×C7—21no—
747C2×C4×C7—21no—
748C2×C4×C7—44no—
749C2×C4×C7—44no—
750C2×C4×C7—82no—
751C2×C4×C7C2×#4112yes—
752C2×C4×C7C2×#4112yes—
753C22⋊D7—44no—
754C22⋊D7—82no—
755C2×Dic7—21no—
756C2×Dic7—21no—
757C2×Dic7—21no—
758C2×Dic7—21no—
759C2×Dic7—21no—
760C2×Dic7—21no—
761C2×Dic7—21no—
762C2×Dic7—21no—
763C2×Dic7—21no—
764C2×Dic7—21no—
765C2×Dic7—21no—
766C2×Dic7—21no—
767C2×Dic7—21no—
768C2×Dic7—21no—
769C2×Dic7—21no—
770C2×Dic7—21no—
771C2×Dic7—21no—
772C2×Dic7—21no—
773C2×Dic7—21no—
774C2×Dic7—21no—
775C2×Dic7—21no—
776C2×Dic7—21no—
777C2×Dic7—21no—
778C2×Dic7—21no—
779C2×Dic7—21no—
780C2×Dic7—21no—
781C2×Dic7—21no—
782C2×Dic7—21no—
783C2×Dic7—21no—
784C2×Dic7—21no—
785C2×Dic7—21no—
786C2×Dic7—21no—
787C2×Dic7—21no—
788C2×Dic7—21no—
789C2×Dic7—21no—
790C2×Dic7—21no—
791C2×Dic7—21no—
792C2×Dic7—21no—
793C2×Dic7—21no—
794C2×Dic7—21no—
795C2×Dic7H(5,𝔽2)12yes—
796C2×Dic72−1+412yes—
797D28—82no—
798C4×D7—44no—
799C4×D7—82no—
800C22×D4—71no—
801C22×D4—71no—
802C22×D4—71no—
803C23×C4—71no—
804C23×C4—71no—
805C23×C4C22×D711yescharacteristic
806C23×C4C22×D711yescharacteristic
807C23×C4C22×D711yescharacteristic
808#125—282no—
809#125—282no—
810#123—144no—
811#123—282no—
812#123—282no—
813C4×D4—144no—
814#117—282no—
815#117—282no—
816C2×C4⋊C4—24no—
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⋊C4—71no—
833C2×C4⋊C4—71no—
834C2×C4⋊C4—71no—
835C2×C4⋊C4—71no—
836C2×C4⋊C4—71no—
837C2×C4⋊C4—71no—
838C2×C4⋊C4—71no—
839C2×C4⋊C4—71no—
840C2×C4⋊C4—71no—
841C2×C4⋊C4—71no—
842C2×C4⋊C4—71no—
843C2×C4⋊C4—71no—
844C2×C4⋊C4—71no—
845C2×C4⋊C4—71no—
846C2×C4⋊C4—71no—
847C2×C4⋊C4—71no—
848C2×C4⋊C4—71no—
849C2×C4⋊C4—71no—
850C2×C4⋊C4—71no—
851C2×C4⋊C4—71no—
852C2×C4⋊C4—71no—
853C2×C4⋊C4—71no—
854C2×C4⋊C4C22×D711yescharacteristic
855C2×C4⋊C4C22×D711yescharacteristic
856C2×C4⋊C4C22×D711yescharacteristic
857C2×C4⋊C4C22×D711yescharacteristic
858C2×C4⋊C4C22×D711yescharacteristic
859C2×C4⋊C4C22×D711yescharacteristic
860C2×C4⋊C4C22×D711yescharacteristic
861C2×C4⋊C4C22×D711yescharacteristic
862C2×C22⋊C4—71no—
863C2×C22⋊C4—71no—
864C2×C22⋊C4—71no—
865C2×C22⋊C4—71no—
866C2×C22⋊C4—71no—
867C2×C22⋊C4—71no—
868C2×C22⋊C4—71no—
869C2×C22⋊C4—71no—
870C2×C22⋊C4—71no—
871C2×C22⋊C4—71no—
872C2×C22⋊C4—71no—
873C2×C22⋊C4—71no—
874C2×C22⋊C4—71no—
875C2×C22⋊C4—71no—
876C2×C22⋊C4—71no—
877C2×C22⋊C4—71no—
878C2×C22⋊C4—71no—
879C2×C22⋊C4—71no—
880C2×C22⋊C4—71no—
881C2×C22⋊C4—71no—
882C2×C22⋊C4—71no—
883C2×C22⋊C4—71no—
884C2×C22⋊C4—71no—
885C2×C22⋊C4—71no—
886C2×C22⋊C4—71no—
887C2×C22⋊C4—71no—
888C2×C22⋊C4—71no—
889C2×C22⋊C4—71no—
890C2×C22⋊C4—71no—
891C2×C22⋊C4—71no—
892C2×C22⋊C4C22×D711yescharacteristic
893C2×C22⋊C4C22×D711yescharacteristic
894C2×C22⋊C4C22×D711yescharacteristic
895C2×C22⋊C4C22×D711yescharacteristic
896C2×C42—71no—
897C2×C42—71no—
898C2×C42—71no—
899C2×C42—71no—
900C2×C42—71no—
901C2×C42—71no—
902C2×C42—71no—
903C2×C42—71no—
904C2×C42—71no—
905C2×C42—71no—
906C2×C42C22×D711yescharacteristic
907C2×C42C22×D711yescharacteristic
908C2×C42C22×D711yescharacteristic
909C2×C42C22×D711yescharacteristic
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#95—71no—
929#95—71no—
930#95—71no—
931#95—71no—
932#95—71no—
933#95—71no—
934#95—71no—
935#95—71no—
936#95—71no—
937#95—71no—
938#95—71no—
939#95—71no—
940#95—71no—
941#95—71no—
942#95—71no—
943#95—71no—
944#95—71no—
945#95—71no—
946#95—71no—
947#95—71no—
948#95C22×D711yescharacteristic
949#95C22×D711yescharacteristic
950#95C22×D711yescharacteristic
951#95C22×D711yescharacteristic
952#95C22×D711yescharacteristic
953#95C22×D711yescharacteristic
954#95C22×D711yescharacteristic
955#95C22×D711yescharacteristic
956#95C22×D711yescharacteristic
957#95C22×D711yescharacteristic
958#95C22×D711yescharacteristic
959#95C22×D711yescharacteristic
960#95C22×D711yescharacteristic
961#95C22×D711yescharacteristic
962#95C22×D711yescharacteristic
963#95C22×D711yescharacteristic
964C22×C7—22no—
965C22×C7—22no—
966C22×C7—22no—
967C22×C7—41no—
968C22×C7—41no—
969C22×C7—41no—
970C22×C7—41no—
971C22×C7C22×#4111yescharacteristic
972C22×C7C2×H(5,𝔽2)11yescharacteristic
973C22×C7C2×2−1+411yescharacteristic
974C22×C7#58511yescharacteristic
975C22×C7#58511yescharacteristic
976C22×C7#58511yescharacteristic
977C22×C7#58511yescharacteristic
978C2×D7—41no—
979C2×D7—41no—
980C2×D7—41no—
981C2×D7—41no—
982C2×D7—41no—
983C2×D7—41no—
984C2×D7—41no—
985C2×D7—41no—
986C2×D7—41no—
987C2×D7—41no—
988C2×D7—41no—
989C2×D7—41no—
990C2×D7—41no—
991C2×D7—41no—
992C4×C7—22no—
993C4×C7—22no—
994C4×C7—41no—
995C4×C7—41no—
996C4×C7—41no—
997C4×C7—41no—
998C4×C7—41no—
999C4×C7—41no—
1000C4×C7—41no—
1001C4×C7—41no—
1002C4×C7—41no—
1003C4×C7—41no—
1004C4×C7—41no—
1005C4×C7—41no—
1006Dic7—22no—
1007Dic7—22no—
1008Dic7—41no—
1009Dic7—41no—
1010Dic7—41no—
1011Dic7—41no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7—41no—
1020C24—71no—
1021C24—71no—
1022C24C23×D711yescharacteristic
1023C2×D4—142no—
1024C2×D4—142no—
1025C2×D4—142no—
1026C2×D4—281no—
1027C2×D4—281no—
1028C2×D4—281no—
1029C2×D4—281no—
1030C2×D4—281no—
1031C2×D4—281no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—41no—
1035C22×C4—41no—
1036C22×C4—41no—
1037C22×C4—41no—
1038C22×C4—41no—
1039C22×C4—41no—
1040C22×C4—71no—
1041C22×C4—71no—
1042C22×C4—71no—
1043C22×C4—71no—
1044C22×C4—71no—
1045C22×C4—71no—
1046C22×C4—71no—
1047C22×C4—71no—
1048C22×C4—71no—
1049C22×C4—71no—
1050C22×C4—71no—
1051C22×C4—71no—
1052C22×C4—71no—
1053C22×C4—71no—
1054C22×C4—142no—
1055C22×C4—281no—
1056C22×C4—281no—
1057C22×C4—281no—
1058C22×C4—281no—
1059C22×C4—281no—
1060C22×C4#115714yes—
1061C22×C4C23×D711yescharacteristic
1062C22×C4C23×D711yescharacteristic
1063C22×C4C23×D711yescharacteristic
1064C22×C4C23×D711yescharacteristic
1065C22×C4C23×D711yescharacteristic
1066C22×C4C23×D711yescharacteristic
1067C22×C4C23×D711yescharacteristic
1068C22×C4C23×D711yescharacteristic
1069C22×C4C23×D711yescharacteristic
1070C22×C4C23×D711yescharacteristic
1071C22×C4C23×D711yescharacteristic
1072C22×C4C23×D711yescharacteristic
1073C22×C4C23×D711yescharacteristic
1074C22×C4C23×D711yescharacteristic
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—22no—
1078C4⋊C4—22no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—142no—
1084C4⋊C4—142no—
1085C4⋊C4—142no—
1086C4⋊C4—142no—
1087C4⋊C4—142no—
1088C4⋊C4—142no—
1089C4⋊C4—142no—
1090C4⋊C4—142no—
1091C4⋊C4—142no—
1092C4⋊C4—142no—
1093C4⋊C4—281no—
1094C4⋊C4—281no—
1095C4⋊C4—281no—
1096C4⋊C4—281no—
1097C4⋊C4—281no—
1098C4⋊C4—281no—
1099C4⋊C4—281no—
1100C4⋊C4—281no—
1101C4⋊C4—281no—
1102C4⋊C4—281no—
1103C4⋊C4—281no—
1104C4⋊C4—281no—
1105C4⋊C4—281no—
1106C4⋊C4—281no—
1107C4⋊C4—281no—
1108C4⋊C4—281no—
1109C4⋊C4—281no—
1110C4⋊C4—281no—
1111C4⋊C4—281no—
1112C4⋊C4—281no—
1113C4⋊C4—281no—
1114C4⋊C4—281no—
1115C4⋊C4—281no—
1116C4⋊C4—281no—
1117C4⋊C4—281no—
1118C4⋊C4—281no—
1119C4⋊C4—281no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—142no—
1125C22⋊C4—142no—
1126C22⋊C4—142no—
1127C22⋊C4—142no—
1128C22⋊C4—142no—
1129C22⋊C4—142no—
1130C22⋊C4—142no—
1131C22⋊C4—142no—
1132C22⋊C4—142no—
1133C22⋊C4—281no—
1134C22⋊C4—281no—
1135C22⋊C4—281no—
1136C22⋊C4—281no—
1137C22⋊C4—281no—
1138C22⋊C4—281no—
1139C22⋊C4—281no—
1140C22⋊C4—281no—
1141C22⋊C4—281no—
1142C22⋊C4—281no—
1143C22⋊C4—281no—
1144C22⋊C4—281no—
1145C22⋊C4—281no—
1146C22⋊C4—281no—
1147C22⋊C4—281no—
1148C22⋊C4—281no—
1149C22⋊C4—281no—
1150C22⋊C4—281no—
1151C22⋊C4—281no—
1152C22⋊C4—281no—
1153C22⋊C4—281no—
1154C42—41no—
1155C42—41no—
1156C42—41no—
1157C42—41no—
1158C42—142no—
1159C42—142no—
1160C42—142no—
1161C42—281no—
1162C42—281no—
1163C42—281no—
1164C42—281no—
1165C42—281no—
1166C42—281no—
1167C42—281no—
1168C2×C7—42no—
1169C2×C7#345511yescharacteristic
1170C2×C7#349511yescharacteristic
1171C2×C7#350511yescharacteristic
1172C2×C7#355711yescharacteristic
1173C2×C7#355911yescharacteristic
1174C2×C7#356211yescharacteristic
1175C2×C7#356711yescharacteristic
1176D7—81no—
1177D7—81no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—141no—
1185C23—141no—
1186C23—141no—
1187C23—141no—
1188C23—141no—
1189C23—141no—
1190C23—141no—
1191C23—141no—
1192C23—141no—
1193C23—141no—
1194C23—141no—
1195C23—141no—
1196C23—141no—
1197C23—141no—
1198C23C2×#115712yes—
1199C23C24×D711yescharacteristic
1200D4—284no—
1201D4—562no—
1202D4—562no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—44no—
1244C2×C4—44no—
1245C2×C4—72no—
1246C2×C4—72no—
1247C2×C4—82no—
1248C2×C4—141no—
1249C2×C4—141no—
1250C2×C4—141no—
1251C2×C4—141no—
1252C2×C4—141no—
1253C2×C4—141no—
1254C2×C4—141no—
1255C2×C4—141no—
1256C2×C4—141no—
1257C2×C4—141no—
1258C2×C4—141no—
1259C2×C4—141no—
1260C2×C4—141no—
1261C2×C4—141no—
1262C2×C4—141no—
1263C2×C4—141no—
1264C2×C4—141no—
1265C2×C4—141no—
1266C2×C4—141no—
1267C2×C4—141no—
1268C2×C4—141no—
1269C2×C4—141no—
1270C2×C4—141no—
1271C2×C4—141no—
1272C2×C4—141no—
1273C2×C4—141no—
1274C2×C4—141no—
1275C2×C4—141no—
1276C2×C4—141no—
1277C2×C4—141no—
1278C2×C4—141no—
1279C2×C4—141no—
1280C2×C4—141no—
1281C2×C4—141no—
1282C2×C4—141no—
1283C2×C4—141no—
1284C2×C4—141no—
1285C2×C4—141no—
1286C2×C4—141no—
1287C2×C4—141no—
1288C2×C4—284no—
1289C2×C4—562no—
1290C2×C4C2×#115712yes—
1291C2×C4C2×#115712yes—
1292C7#3699411yescharacteristic, complemented, Sylow
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—281no—
1301C22—281no—
1302C22—281no—
1303C22—281no—
1304C22—281no—
1305C22—281no—
1306C22—281no—
1307C22—281no—
1308C22—281no—
1309C22—281no—
1310C22—281no—
1311C22—281no—
1312C22—281no—
1313C22—281no—
1314C22C22×#115711yescharacteristic
1315C22#9061611yescharacteristic
1316C22#9061611yescharacteristic
1317C22D7×H(5,𝔽2)11yescharacteristic
1318C22#9061811yescharacteristic
1319C22D7×2−1+411yescharacteristic
1320C22#9062011yescharacteristic
1321C4—22no—
1322C4—22no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—142no—
1336C4—142no—
1337C4—281no—
1338C4—281no—
1339C4—281no—
1340C4—281no—
1341C4—281no—
1342C4—281no—
1343C4—281no—
1344C4—281no—
1345C4—281no—
1346C4—281no—
1347C4—281no—
1348C4—281no—
1349C2—42no—
1350C2—561no—
1351C2—561no—
1352C2#1174280611yescharacteristic
1353C2#1174292911yescharacteristic
1354C2#1174295011yescharacteristic
1355C2#1174350911yescharacteristic
1356C2#1174351211yescharacteristic
1357C2#1174351911yescharacteristic
1358C2#1174353211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2313C2
prime radical#89732C22
hypercenter#2313D7
hypocenterC7#36994
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2313

Complements

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

NH ≅ G/Ntype
1. C7×#2313C2semidirect
2. #11739643C2semidirect
3. #11739615C2semidirect
4. #11732883C2semidirect
5. #11732826C2semidirect
6. #11732812C2semidirect
7. #11732776C2semidirect
8. #11732738C2semidirect
9. #11732737C2semidirect
10. #11732722C2semidirect
11. #11732718C2semidirect
12. #11732702C2semidirect
13. #11732680C2semidirect
14. #11732664C2semidirect
15. #11732610C2semidirect
16. #11732599C2semidirect
17. #11732581C2semidirect
18. #11732555C2semidirect
19. #11732456C2semidirect
20. #11731587C2semidirect
21. #11731558C2semidirect
22. #11731555C2semidirect
24. #11731421C2semidirect
25. #11731419C2semidirect
26. #11731415C2semidirect
29. #11730939C2semidirect
30. #11730896C2semidirect
31. #11730884C2semidirect
381. #2313D7semidirect
1292. C7#36994semidirect

Maximal subgroups

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

subgroupindex
C7×#23132
#117396432
#117396152
#117328832
#117328262
#117328122
#117327762
#117327382
#117327372
#117327222
#117327182
#117327022
#117326802
#117326642
#117326102
#117325992
#117325812
#117325552
#117324562
#117315872
#117315582
#117315552
#117315542
#117314212
#117314192
#117314152
#117314142
#117310532
#117309392
#117308962
#117308842
#369947