Finite Group Databasebeta

← #13525154

Subgroups — #13525154

Order 1792.

1768 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2596C211yesmaximal, characteristic, complemented
2#11735604C211yesmaximal, characteristic, complemented
3#11735581C211yesmaximal, characteristic, complemented
4#11735577C211yesmaximal, characteristic, complemented
5#11735575C211yesmaximal, characteristic, complemented
6#11735467C211yesmaximal, characteristic
7#11735463C211yesmaximal, characteristic, complemented
8#11734938C211yesmaximal, characteristic
9#11734906C211yesmaximal, characteristic, complemented
10#11733466C211yesmaximal, characteristic, complemented
11#11733412C211yesmaximal, characteristic, complemented
12#11733070C211yesmaximal, characteristic, complemented
13#11733064C211yesmaximal, characteristic
14#11733038C211yesmaximal, characteristic
15#11733018C211yesmaximal, characteristic, complemented
16#11732968C211yesmaximal, characteristic, complemented
17#11732900C211yesmaximal, characteristic, complemented
18#11732899C211yesmaximal, characteristic
19#11732899C211yesmaximal, characteristic
20#11732896C211yesmaximal, characteristic, complemented
21#11732895C211yesmaximal, characteristic
22#11732535C211yesmaximal, characteristic, complemented
23#11732522C211yesmaximal, characteristic, complemented
24#11732499C211yesmaximal, characteristic, complemented
25#11732387C211yesmaximal, characteristic, complemented
26#11732384C211yesmaximal, characteristic, complemented
27#11732383C211yesmaximal, characteristic, complemented
28#11731185C211yesmaximal, characteristic, complemented
29#11731183C211yesmaximal, characteristic, complemented
30C4×#6450C211yesmaximal, characteristic, complemented
31C4×#6450C211yesmaximal, characteristic, complemented
32C2×#6461C2211yescharacteristic
33C2×#6455C2211yescharacteristic
34C2×#6451C2211yescharacteristic
35C2×#6450C2211yescharacteristic
36C2×#6450C2211yescharacteristic
37C2×#6450C2211yescharacteristic
38C2×#6450C2211yescharacteristic
39C2×#6450C2211yescharacteristic
40C2×#6448C2211yescharacteristic
41C2×#6448C2211yescharacteristic
42C2×(C22⋊D7)⋊C4C2211yescharacteristic
43C2×#6442C2211yescharacteristic
44C2×#6440C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46C2×C4×Dic14C2211yescharacteristic
47C7×#400C2211yescharacteristic
48C7×#400C2211yescharacteristic
49C7×#399C2211yescharacteristic
50C7×#397C2211yescharacteristic
51C7×#389C2211yescharacteristic
52C7×#388C2211yescharacteristic
53C7×#388C2211yescharacteristic
54C7×#388C2211yescharacteristic
55C7×#388C2211yescharacteristic
56C7×#388C2211yescharacteristic
57C7×#387C2211yescharacteristic
58C7×#387C2211yescharacteristic
59C7×#387C2211yescharacteristic
60C4×C7×C4⋊C4C2211yescharacteristic
61C4×C7×C4⋊C4C2211yescharacteristic
62#89766C2211yescharacteristic
63#89765C2211yescharacteristic
64#89764C2211yescharacteristic
65#89762C2211yescharacteristic
66#89762C2211yescharacteristic
67#89762C2211yescharacteristic
68#89762C2211yescharacteristic
69#89754C2211yescharacteristic
70#89754C2211yescharacteristic
71#89753C2211yescharacteristic
72#89753C2211yescharacteristic
73#89752C2211yescharacteristic
74#89752C2211yescharacteristic
75#89751C2211yescharacteristic
76#89750C2211yescharacteristic
77#89750C2211yescharacteristic
78#89748C2211yescharacteristic
79C4⋊C4×Dic7C2211yescharacteristic
80C4⋊C4×Dic7C2211yescharacteristic
81C4⋊C4×Dic7C2211yescharacteristic
82C4⋊C4×Dic7C2211yescharacteristic
83C4⋊C4×Dic7C2211yescharacteristic
84C4⋊C4×Dic7C2211yescharacteristic
85C4⋊C4×Dic7C2211yescharacteristic
86#89744C2211yescharacteristic
87#89744C2211yescharacteristic
88#89744C2211yescharacteristic
89#89744C2211yescharacteristic
90#89729C2211yescharacteristic
91#89729C2211yescharacteristic
92#89729C2211yescharacteristic
93#89729C2211yescharacteristic
94#89724C2211yescharacteristic
95#89724C2211yescharacteristic
96#89723C2211yescharacteristic
97#89723C2211yescharacteristic
98#89720C2211yescharacteristic
99#89720C2211yescharacteristic
100#89720C2211yescharacteristic
101#89719C2211yescharacteristic
102#89717C2211yescharacteristic
103#89717C2211yescharacteristic
104#89717C2211yescharacteristic
105#89717C2211yescharacteristic
106#89716C2211yescharacteristic
107#89716C2211yescharacteristic
108C22⋊C4×Dic7C2211yescharacteristic
109C22⋊C4×Dic7C2211yescharacteristic
110C22⋊C4×Dic7C2211yescharacteristic
111C22⋊C4×Dic7C2211yescharacteristic
112C22⋊C4×Dic7C2211yescharacteristic
113#89712C2211yescharacteristic
114#89712C2211yescharacteristic
115#89712C2211yescharacteristic
116#89712C2211yescharacteristic
117#89712C2211yescharacteristic
118#89705C2211yescharacteristic
119#89705C2211yescharacteristic
120#89705C2211yescharacteristic
121C4×Dic7⋊C4C2211yescharacteristic
122C4×Dic7⋊C4C2211yescharacteristic
123C4×Dic7⋊C4C2211yescharacteristic
124C4×Dic7⋊C4C2211yescharacteristic
125C42×Dic7C2211yescharacteristic
126C42×Dic7C2211yescharacteristic
127C42×Dic7C2211yescharacteristic
128C42×Dic7C2211yescharacteristic
129C42×Dic7C2211yescharacteristic
130#89700C2211yescharacteristic
131#89448C2211yescharacteristic
132#89448C2211yescharacteristic
133#89447C2211yescharacteristic
134#89446C2211yescharacteristic
135#89445C2211yescharacteristic
136#89442C2211yescharacteristic
137#89442C2211yescharacteristic
138#89441C2211yescharacteristic
139#89441C2211yescharacteristic
140#89438C2211yescharacteristic
141#89438C2211yescharacteristic
142#89438C2211yescharacteristic
143#89438C2211yescharacteristic
144#89438C2211yescharacteristic
145C7⋊#401C2211yescharacteristic
146C7⋊#401C2211yescharacteristic
147#89432C2211yescharacteristic
148#89432C2211yescharacteristic
149#89431C2211yescharacteristic
150#89430C2211yescharacteristic
151#89429C2211yescharacteristic
152#89429C2211yescharacteristic
153#89428C2211yescharacteristic
154#89427C2211yescharacteristic
155#89427C2211yescharacteristic
156#89426C2211yescharacteristic
157#89426C2211yescharacteristic
158#89425C2211yescharacteristic
159#89425C2211yescharacteristic
160#89424C2211yescharacteristic
161#89424C2211yescharacteristic
162#89423C2211yescharacteristic
163#89423C2211yescharacteristic
164#89422C2211yescharacteristic
165#89422C2211yescharacteristic
166#89421C2211yescharacteristic
167#89421C2211yescharacteristic
168#89421C2211yescharacteristic
169#89421C2211yescharacteristic
170#89421C2211yescharacteristic
171#89421C2211yescharacteristic
172#89421C2211yescharacteristic
173#89421C2211yescharacteristic
174#89421C2211yescharacteristic
175#89421C2211yescharacteristic
176#89421C2211yescharacteristic
177#89420C2211yescharacteristic
178#89420C2211yescharacteristic
179#89419C2211yescharacteristic
180#89419C2211yescharacteristic
181#89418C2211yescharacteristic
182#89418C2211yescharacteristic
183#89418C2211yescharacteristic
184#89418C2211yescharacteristic
185#89418C2211yescharacteristic
186#89418C2211yescharacteristic
187#34902—71nomaximal, Sylow
188C22×C22⋊D7C2311yescharacteristic
189C23×Dic7C2311yescharacteristic
190C22×C4×D7C2311yescharacteristic
191C22×Dic14C2311yescharacteristic
192C22×Dic14C2311yescharacteristic
193C22×Dic14C2311yescharacteristic
194C2×C7×C4⋊C4C2311yescharacteristic
195C2×C7×C4⋊C4C2311yescharacteristic
196C2×C7×C4⋊C4C2311yescharacteristic
197C2×C7×C4⋊C4C2311yescharacteristic
198C2×C7×C4⋊C4C2311yescharacteristic
199C2×C7×C4⋊C4C2311yescharacteristic
200C2×C7×C4⋊C4C2311yescharacteristic
201C2×C7×C4⋊C4C2311yescharacteristic
202C2×C7×C4⋊C4C2311yescharacteristic
203C2×C7×C22⋊C4C2311yescharacteristic
204C2×C7×C22⋊C4C2311yescharacteristic
205C2×C7×C22⋊C4C2311yescharacteristic
206C2×C7×C22⋊C4C2311yescharacteristic
207C2×C7×C22⋊C4C2311yescharacteristic
208C2×C7×C22⋊C4C2311yescharacteristic
209C2×C7×C22⋊C4C2311yescharacteristic
210C2×C42×C7C2311yescharacteristic
211C2×C42×C7C2311yescharacteristic
212C2×C42×C7C2311yescharacteristic
213C2×C42×C7C2311yescharacteristic
214C2×C42×C7C2311yescharacteristic
215C2×C22⋊Dic7C2311yescharacteristic
216C2×C22⋊Dic7C2311yescharacteristic
217C2×C22⋊Dic7C2311yescharacteristic
218C2×C22⋊Dic7C2311yescharacteristic
219C2×C22⋊Dic7C2311yescharacteristic
220C2×C22⋊Dic7C2311yescharacteristic
221C2×(C2×D7)⋊C4C2311yescharacteristic
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×C4⋊Dic7C2311yescharacteristic
235C2×C4⋊Dic7C2311yescharacteristic
236C2×C4⋊Dic7C2311yescharacteristic
237C2×C4⋊Dic7C2311yescharacteristic
238C2×C4⋊Dic7C2311yescharacteristic
239C2×C4⋊Dic7C2311yescharacteristic
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×Dic7⋊C4C2311yescharacteristic
261C2×Dic7⋊C4C2311yescharacteristic
262C2×Dic7⋊C4C2311yescharacteristic
263C2×C4×Dic7C2311yescharacteristic
264C2×C4×Dic7C2311yescharacteristic
265C2×C4×Dic7C2311yescharacteristic
266C2×C4×Dic7C2311yescharacteristic
267C2×C4×Dic7C2311yescharacteristic
268C2×C4×Dic7C2311yescharacteristic
269C2×C4×Dic7C2311yescharacteristic
270C2×C4×Dic7C2311yescharacteristic
271C2×C4×Dic7C2311yescharacteristic
272C2×C4×Dic7C2311yescharacteristic
273C2×C4×Dic7C2311yescharacteristic
274C2×C4×Dic7C2311yescharacteristic
275C2×C4×Dic7C2311yescharacteristic
276C2×C4×Dic7C2311yescharacteristic
277C2×C4×Dic7C2311yescharacteristic
278C2×C4×Dic7C2311yescharacteristic
279C2×C4×Dic7C2311yescharacteristic
280C2×C4×Dic7C2311yescharacteristic
281C2×C4×Dic7C2311yescharacteristic
282C2×C4×Dic7C2311yescharacteristic
283C2×C4×Dic7C2311yescharacteristic
284C2×C4×Dic7C2311yescharacteristic
285C2×C4×Dic7C2311yescharacteristic
286C2×C4×Dic7C2311yescharacteristic
287C2×C4×Dic7C2311yescharacteristic
288C2×C4×Dic7C2311yescharacteristic
289C2×C4×Dic7C2311yescharacteristic
290C2×C4×Dic7C2311yescharacteristic
291#6461—24no—
292#6455—24no—
293#6451—24no—
294#6450—24no—
295#6450—24no—
296#6450—24no—
297#6450—24no—
298#6450—24no—
299#6448—24no—
300#6448—24no—
301(C22⋊D7)⋊C4—24no—
302#6442—24no—
303#6440—24no—
304C4×Dic14—24no—
305C4×Dic14—24no—
306C7×#95C2311yescharacteristic
307C7×#95C2311yescharacteristic
308C7×#95C2311yescharacteristic
309C7×#95C2311yescharacteristic
310C7×#95C2311yescharacteristic
311C7×#95C2311yescharacteristic
312C7×#95C2311yescharacteristic
313C7×#95C2311yescharacteristic
314C7×#95C2311yescharacteristic
315C7×#95C2311yescharacteristic
316C7×#95C2311yescharacteristic
317C7×#95C2311yescharacteristic
318C7×#95C2311yescharacteristic
319C7×#95C2311yescharacteristic
320C7⋊#95C2311yescharacteristic
321C7⋊#95C2311yescharacteristic
322C7⋊#95C2311yescharacteristic
323C7⋊#95C2311yescharacteristic
324C7⋊#95C2311yescharacteristic
325C7⋊#95C2311yescharacteristic
326C7⋊#95C2311yescharacteristic
327C7⋊#95C2311yescharacteristic
328C7⋊#95C2311yescharacteristic
329C7⋊#95C2311yescharacteristic
330C7⋊#95C2311yescharacteristic
331C7⋊#95C2311yescharacteristic
332C7⋊#95C2311yescharacteristic
333C7⋊#95C2311yescharacteristic
334C7⋊#95C2311yescharacteristic
335C7⋊#95C2311yescharacteristic
336C7⋊#95C2311yescharacteristic
337C7⋊#95C2311yescharacteristic
338C7⋊#95C2311yescharacteristic
339C7⋊#95C2311yescharacteristic
340C7⋊#95C2311yescharacteristic
341C7⋊#95C2311yescharacteristic
342C7⋊#95C2311yescharacteristic
343C7⋊#95C2311yescharacteristic
344C7⋊#95C2311yescharacteristic
345C7⋊#95C2311yescharacteristic
346C7⋊#95C2311yescharacteristic
347C7⋊#95C2311yescharacteristic
348C7⋊#95C2311yescharacteristic
349C7⋊#95C2311yescharacteristic
350C7⋊#95C2311yescharacteristic
351C7⋊#95C2311yescharacteristic
352C7⋊#95C2311yescharacteristic
353C7⋊#95C2311yescharacteristic
354C7⋊#95C2311yescharacteristic
355C7⋊#95C2311yescharacteristic
356C7⋊#95C2311yescharacteristic
357C7⋊#95C2311yescharacteristic
358#2596—71no—
359#2596D711yescharacteristic, complemented
360#2594—71no—
361#2594—71no—
362#2592—71no—
363#2581—71no—
364#2570—71no—
365#2545—71no—
366#2525—71no—
367#2525—71no—
368#2514—71no—
369#2512—71no—
370#2469—71no—
371#2469—71no—
372#2448—71no—
373#2446—71no—
374#2401—71no—
375#2401—71no—
376#2396—71no—
377#2396—71no—
378C4×C4⋊Q8—71no—
379C4×#126—71no—
380C4×#126—71no—
381C4×#124—71no—
382C4×#124—71no—
383#2298—71no—
384#2298—71no—
385#2295—71no—
386#2293—71no—
387C42×Q8—71no—
388C42×Q8—71no—
389C24×C7C2411yescharacteristic
390C23×D7C2411yescharacteristic
391C22×C4×C7C2411yescharacteristic
392C22×C4×C7C2411yescharacteristic
393C22×C4×C7C2411yescharacteristic
394C22×C4×C7C2411yescharacteristic
395C22×C4×C7C2411yescharacteristic
396C22×C4×C7C2411yescharacteristic
397C22×C4×C7C2411yescharacteristic
398C22×C4×C7C2411yescharacteristic
399C22×C4×C7C2411yescharacteristic
400C22×C4×C7C2411yescharacteristic
401C22×C4×C7C2411yescharacteristic
402C22×C4×C7C2411yescharacteristic
403C22×C4×C7C2411yescharacteristic
404C22×C4×C7C2411yescharacteristic
405C2×C22⋊D7—22no—
406C2×C22⋊D7—22no—
407C2×C22⋊D7—22no—
408C22×Dic7—22no—
409C22×Dic7—22no—
410C22×Dic7—22no—
411C22×Dic7C2411yescharacteristic
412C22×Dic7C2411yescharacteristic
413C22×Dic7C2411yescharacteristic
414C22×Dic7C2411yescharacteristic
415C22×Dic7C2411yescharacteristic
416C22×Dic7C2411yescharacteristic
417C22×Dic7C2411yescharacteristic
418C22×Dic7C2411yescharacteristic
419C22×Dic7C2411yescharacteristic
420C22×Dic7C2411yescharacteristic
421C22×Dic7C2411yescharacteristic
422C22×Dic7C2411yescharacteristic
423C22×Dic7C2411yescharacteristic
424C22×Dic7C2411yescharacteristic
425C22×Dic7C2411yescharacteristic
426C2×C4×D7—22no—
427C2×C4×D7—22no—
428C2×C4×D7—22no—
429C2×Dic14—22no—
430C2×Dic14—22no—
431C2×Dic14—22no—
432C2×Dic14—22no—
433C2×Dic14—22no—
434C2×Dic14—22no—
435C2×Dic14—22no—
436C2×Dic14—22no—
437C2×Dic14#4114yes—
438C7×C4⋊C4—22no—
439C7×C4⋊C4—22no—
440C7×C4⋊C4—22no—
441C7×C4⋊C4—22no—
442C7×C4⋊C4—22no—
443C7×C4⋊C4—22no—
444C7×C4⋊C4—22no—
445C7×C4⋊C4—22no—
446C7×C4⋊C4—41no—
447C7×C22⋊C4—22no—
448C7×C22⋊C4—22no—
449C7×C22⋊C4—22no—
450C7×C22⋊C4—22no—
451C7×C22⋊C4—22no—
452C7×C22⋊C4—41no—
453C7×C22⋊C4—41no—
454C42×C7—22no—
455C42×C7—22no—
456C42×C7—41no—
457C42×C7—41no—
458C42×C7—41no—
459C22⋊Dic7—22no—
460C22⋊Dic7—22no—
461C22⋊Dic7—22no—
462C22⋊Dic7—22no—
463C22⋊Dic7—22no—
464C22⋊Dic7—41no—
465(C2×D7)⋊C4—22no—
466(C2×D7)⋊C4—22no—
467(C2×D7)⋊C4—22no—
468(C2×D7)⋊C4—22no—
469(C2×D7)⋊C4—22no—
470(C2×D7)⋊C4—22no—
471(C2×D7)⋊C4—22no—
472(C2×D7)⋊C4—22no—
473(C2×D7)⋊C4—22no—
474(C2×D7)⋊C4—22no—
475(C2×D7)⋊C4—41no—
476(C2×D7)⋊C4—41no—
477(C2×D7)⋊C4—41no—
478C4⋊Dic7—22no—
479C4⋊Dic7—22no—
480C4⋊Dic7—22no—
481C4⋊Dic7—22no—
482C4⋊Dic7—22no—
483C4⋊Dic7—22no—
484Dic7⋊C4—22no—
485Dic7⋊C4—22no—
486Dic7⋊C4—22no—
487Dic7⋊C4—22no—
488Dic7⋊C4—22no—
489Dic7⋊C4—22no—
490Dic7⋊C4—22no—
491Dic7⋊C4—22no—
492Dic7⋊C4—22no—
493Dic7⋊C4—22no—
494Dic7⋊C4—22no—
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#4114yes—
507C4×Dic7—22no—
508C4×Dic7—22no—
509C4×Dic7—22no—
510C4×Dic7—22no—
511C4×Dic7—22no—
512C4×Dic7—22no—
513C4×Dic7—22no—
514C4×Dic7—22no—
515C4×Dic7—22no—
516C4×Dic7—22no—
517C4×Dic7—22no—
518C4×Dic7—22no—
519C4×Dic7—22no—
520C4×Dic7—22no—
521C4×Dic7—22no—
522C4×Dic7—22no—
523C4×Dic7—22no—
524C4×Dic7—22no—
525C4×Dic7—22no—
526C4×Dic7—22no—
527C4×Dic7—22no—
528C4×Dic7—22no—
529C4×Dic7—22no—
530C4×Dic7—41no—
531C4×Dic7—41no—
532C4×Dic7#4114yes—
533C4×Dic7#4114yes—
534C4×Dic7#4114yes—
535C2×C4⋊Q8—71no—
536C2×#126—71no—
537C2×#126—71no—
538C2×#124—71no—
539C2×#124—71no—
540C2×C4×Q8—71no—
541C2×C4×Q8—71no—
542C2×C4×Q8—71no—
543C2×C4×Q8—71no—
544C2×C4×Q8—71no—
545C2×C4×Q8—71no—
546C2×C4×Q8—71no—
547C2×C4×D4—71no—
548C2×#117—71no—
549C2×#117—71no—
550#401—71no—
551#401—71no—
552#400—71no—
553#400—71no—
554#400—71no—
555#400—71no—
556#400—71no—
557#400—71no—
558#400C2×D711yescharacteristic
559#400C2×D711yescharacteristic
560#399—71no—
561#399C2×D711yescharacteristic
562#398—71no—
563#398—71no—
564#398—71no—
565#398—71no—
566#397—71no—
567#397—71no—
568#397—71no—
569#397—71no—
570#397—71no—
571#397C2×D711yescharacteristic
572#396—71no—
573#396—71no—
574#396—71no—
575#396—71no—
576#396—71no—
577#396—71no—
578#395—71no—
579#395—71no—
580#393—71no—
581#393—71no—
582#391—71no—
583#391—71no—
584#391—71no—
585#391—71no—
586#391—71no—
587#391—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#389C2×D711yescharacteristic
600#388—71no—
601#388—71no—
602#388—71no—
603#388—71no—
604#388—71no—
605#388—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#388C2×D711yescharacteristic
622#388C2×D711yescharacteristic
623#388C2×D711yescharacteristic
624#388C2×D711yescharacteristic
625#388C2×D711yescharacteristic
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#387C2×D711yescharacteristic
642#387C2×D711yescharacteristic
643#387C2×D711yescharacteristic
644#384—71no—
645#383—71no—
646#383—71no—
647#382—71no—
648#382—71no—
649C4×C4⋊C4—71no—
650C4×C4⋊C4—71no—
651C4×C4⋊C4—71no—
652C4×C4⋊C4—71no—
653C4×C4⋊C4—71no—
654C4×C4⋊C4—71no—
655C4×C4⋊C4—71no—
656C4×C4⋊C4—71no—
657C4×C4⋊C4—71no—
658C4×C4⋊C4—71no—
659C4×C4⋊C4—71no—
660C4×C4⋊C4—71no—
661C4×C4⋊C4—71no—
662C4×C4⋊C4—71no—
663C4×C4⋊C4—71no—
664C4×C4⋊C4—71no—
665C4×C4⋊C4—71no—
666C4×C4⋊C4—71no—
667C4×C4⋊C4—71no—
668C4×C4⋊C4—71no—
669C4×C4⋊C4—71no—
670C4×C4⋊C4—71no—
671C4×C4⋊C4C2×D711yescharacteristic
672C4×C4⋊C4C2×D711yescharacteristic
673C4×C22⋊C4—71no—
674C4×C22⋊C4—71no—
675C4×C22⋊C4—71no—
676C4×C22⋊C4—71no—
677C4×C22⋊C4—71no—
678C4×C22⋊C4—71no—
679C4×C22⋊C4—71no—
680C4×C22⋊C4—71no—
681C4×C22⋊C4—71no—
682C4×C22⋊C4—71no—
683#376—71no—
684#376—71no—
685C43—71no—
686C43—71no—
687C43—71no—
688C43—71no—
689C43—71no—
690C23×C7—21no—
691C23×C7—21no—
692C23×C7—21no—
693C23×C7—21no—
694C23×C7—21no—
695C23×C7—21no—
696C23×C7—21no—
697C23×C7C2511yescharacteristic
698C22×D7—21no—
699C22×D7—21no—
700C22×D7—21no—
701C22×D7—21no—
702C22×D7—21no—
703C22×D7—21no—
704C22×D7—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×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×C7C2×#4112yes—
743C2×C4×C7C2×#4112yes—
744C2×C4×C7C2×#4112yes—
745C2×C4×C7C2×#4112yes—
746C2×C4×C7C2×#4112yes—
747C22⋊D7—44no—
748C2×Dic7—21no—
749C2×Dic7—21no—
750C2×Dic7—21no—
751C2×Dic7—21no—
752C2×Dic7—21no—
753C2×Dic7—21no—
754C2×Dic7—21no—
755C2×Dic7—21no—
756C2×Dic7—21no—
757C2×Dic7—21no—
758C2×Dic7—21no—
759C2×Dic7—21no—
760C2×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—44no—
783C2×Dic7C2×#4112yes—
784C2×Dic7C2×#4112yes—
785C2×Dic7C2×#4112yes—
786C2×Dic7C2×#4112yes—
787C2×Dic7C2×#4112yes—
788C2×Dic7C2×#4112yes—
789C2×Dic7C2×#4112yes—
790C2×Dic7C2×#4112yes—
791C2×Dic7C2×#4112yes—
792C2×Dic7C2×#4112yes—
793C2×Dic72−1+412yes—
794C4×D7—44no—
795Dic14—28no—
796Dic14—28no—
797Dic14—44no—
798C22×Q8—71no—
799C22×Q8—71no—
800C22×Q8—71no—
801C22×D4—71no—
802C23×C4—71no—
803C23×C4—71no—
804C4⋊Q8—144no—
805#126—144no—
806#126—144no—
807#124—144no—
808#124—144no—
809C4×Q8—144no—
810C4×Q8—144no—
811C4×Q8—144no—
812C4×Q8—144no—
813C4×Q8—144no—
814C4×Q8—144no—
815C4×Q8—144no—
816C4×D4—144no—
817#117—144no—
818#117—144no—
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⋊C4C22×D711yescharacteristic
849C2×C4⋊C4C22×D711yescharacteristic
850C2×C4⋊C4C22×D711yescharacteristic
851C2×C4⋊C4C22×D711yescharacteristic
852C2×C4⋊C4C22×D711yescharacteristic
853C2×C4⋊C4C22×D711yescharacteristic
854C2×C4⋊C4C22×D711yescharacteristic
855C2×C4⋊C4C22×D711yescharacteristic
856C2×C4⋊C4C22×D711yescharacteristic
857C2×C22⋊C4—71no—
858C2×C22⋊C4—71no—
859C2×C22⋊C4—71no—
860C2×C22⋊C4—71no—
861C2×C22⋊C4—71no—
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⋊C4C22×D711yescharacteristic
877C2×C22⋊C4C22×D711yescharacteristic
878C2×C22⋊C4C22×D711yescharacteristic
879C2×C22⋊C4C22×D711yescharacteristic
880C2×C22⋊C4C22×D711yescharacteristic
881C2×C22⋊C4C22×D711yescharacteristic
882C2×C22⋊C4C22×D711yescharacteristic
883C2×C42—71no—
884C2×C42—71no—
885C2×C42—71no—
886C2×C42—71no—
887C2×C42—71no—
888C2×C42—71no—
889C2×C42—71no—
890C2×C42—71no—
891C2×C42—71no—
892C2×C42—71no—
893C2×C42—71no—
894C2×C42—71no—
895C2×C42—71no—
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×C42—71no—
907C2×C42—71no—
908C2×C42—71no—
909C2×C42—71no—
910C2×C42—71no—
911C2×C42C22×D711yescharacteristic
912C2×C42C22×D711yescharacteristic
913C2×C42C22×D711yescharacteristic
914C2×C42C22×D711yescharacteristic
915C2×C42C22×D711yescharacteristic
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#95—71no—
949#95—71no—
950#95—71no—
951#95—71no—
952#95—71no—
953#95—71no—
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
964#95C22×D711yescharacteristic
965#95C22×D711yescharacteristic
966#95C22×D711yescharacteristic
967#95C22×D711yescharacteristic
968C22×C7—41no—
969C22×C7—41no—
970C22×C7—41no—
971C22×C7—41no—
972C22×C7—41no—
973C22×C7—41no—
974C22×C7—41no—
975C22×C7C22×#4111yescharacteristic
976C22×C7C22×#4111yescharacteristic
977C22×C7C22×#4111yescharacteristic
978C22×C7C22×#4111yescharacteristic
979C22×C7C22×#4111yescharacteristic
980C22×C7C2×2−1+411yescharacteristic
981C22×C7#58511yescharacteristic
982C2×D7—41no—
983C2×D7—41no—
984C2×D7—41no—
985C2×D7—41no—
986C2×D7—41no—
987C2×D7—41no—
988C2×D7—41no—
989C4×C7—22no—
990C4×C7—22no—
991C4×C7—22no—
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—
1003Dic7—22no—
1004Dic7—22no—
1005Dic7—22no—
1006Dic7—22no—
1007Dic7—22no—
1008Dic7—41no—
1009Dic7—41no—
1010Dic7—41no—
1011Dic7—41no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7#52914yes—
1017Dic7#55614yes—
1018C24—71no—
1019C24C23×D711yescharacteristic
1020C2×Q8—74no—
1021C2×Q8—142no—
1022C2×Q8—142no—
1023C2×Q8—142no—
1024C2×Q8—142no—
1025C2×Q8—142no—
1026C2×Q8—142no—
1027C2×Q8—142no—
1028C2×Q8—142no—
1029C2×D4—142no—
1030C2×D4—142no—
1031C2×D4—142no—
1032C22×C4—71no—
1033C22×C4—71no—
1034C22×C4—71no—
1035C22×C4—71no—
1036C22×C4—71no—
1037C22×C4—71no—
1038C22×C4—71no—
1039C22×C4—71no—
1040C22×C4—71no—
1041C22×C4—71no—
1042C22×C4—71no—
1043C22×C4—71no—
1044C22×C4—71no—
1045C22×C4—71no—
1046C22×C4—71no—
1047C22×C4—142no—
1048C22×C4—142no—
1049C22×C4—142no—
1050C22×C4—142no—
1051C22×C4—142no—
1052C22×C4—142no—
1053C22×C4C23×D711yescharacteristic
1054C22×C4C23×D711yescharacteristic
1055C22×C4C23×D711yescharacteristic
1056C22×C4C23×D711yescharacteristic
1057C22×C4C23×D711yescharacteristic
1058C22×C4C23×D711yescharacteristic
1059C22×C4C23×D711yescharacteristic
1060C22×C4C23×D711yescharacteristic
1061C22×C4C23×D711yescharacteristic
1062C22×C4C23×D711yescharacteristic
1063C22×C4C23×D711yescharacteristic
1064C22×C4C23×D711yescharacteristic
1065C22×C4C23×D711yescharacteristic
1066C22×C4C23×D711yescharacteristic
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—22no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—41no—
1076C4⋊C4—74no—
1077C4⋊C4—142no—
1078C4⋊C4—142no—
1079C4⋊C4—142no—
1080C4⋊C4—142no—
1081C4⋊C4—142no—
1082C4⋊C4—142no—
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—142no—
1094C4⋊C4—142no—
1095C4⋊C4—142no—
1096C4⋊C4—142no—
1097C4⋊C4—142no—
1098C4⋊C4—142no—
1099C4⋊C4—142no—
1100C4⋊C4—142no—
1101C4⋊C4—142no—
1102C4⋊C4—281no—
1103C4⋊C4—281no—
1104C4⋊C4—281no—
1105C22⋊C4—22no—
1106C22⋊C4—22no—
1107C22⋊C4—22no—
1108C22⋊C4—22no—
1109C22⋊C4—22no—
1110C22⋊C4—41no—
1111C22⋊C4—41no—
1112C22⋊C4—142no—
1113C22⋊C4—142no—
1114C22⋊C4—142no—
1115C22⋊C4—142no—
1116C22⋊C4—142no—
1117C22⋊C4—142no—
1118C22⋊C4—142no—
1119C22⋊C4—142no—
1120C22⋊C4—142no—
1121C22⋊C4—142no—
1122C22⋊C4—142no—
1123C22⋊C4—142no—
1124C22⋊C4—142no—
1125C22⋊C4—142no—
1126C22⋊C4—142no—
1127C22⋊C4—281no—
1128C22⋊C4—281no—
1129C22⋊C4—281no—
1130C22⋊C4—281no—
1131C42—22no—
1132C42—22no—
1133C42—41no—
1134C42—41no—
1135C42—41no—
1136C42—74no—
1137C42—74no—
1138C42—74no—
1139C42—142no—
1140C42—142no—
1141C42—142no—
1142C42—142no—
1143C42—142no—
1144C42—142no—
1145C42—142no—
1146C42—142no—
1147C42—142no—
1148C42—142no—
1149C42—142no—
1150C42—142no—
1151C42—142no—
1152C42—142no—
1153C42—142no—
1154C42—142no—
1155C42—142no—
1156C42—142no—
1157C42—142no—
1158C42—142no—
1159C42—142no—
1160C42—142no—
1161C42—142no—
1162C42—281no—
1163C42—281no—
1164C2×C7—81no—
1165C2×C7C2×#52911yescharacteristic
1166C2×C7#344411yescharacteristic
1167C2×C7#346111yescharacteristic
1168C2×C7C2×#55611yescharacteristic
1169C2×C7#348011yescharacteristic
1170C2×C7#348011yescharacteristic
1171C2×C7#348211yescharacteristic
1172D7—81no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—141no—
1181C23—141no—
1182C23—141no—
1183C23—141no—
1184C23—141no—
1185C23—141no—
1186C23—141no—
1187C23C24×D711yescharacteristic
1188Q8—148no—
1189Q8—148no—
1190Q8—284no—
1191D4—284no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
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—72no—
1230C2×C4—72no—
1231C2×C4—72no—
1232C2×C4—72no—
1233C2×C4—72no—
1234C2×C4—72no—
1235C2×C4—72no—
1236C2×C4—72no—
1237C2×C4—72no—
1238C2×C4—72no—
1239C2×C4—72no—
1240C2×C4—141no—
1241C2×C4—141no—
1242C2×C4—141no—
1243C2×C4—141no—
1244C2×C4—141no—
1245C2×C4—141no—
1246C2×C4—141no—
1247C2×C4—141no—
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—284no—
1275C2×C4—284no—
1276C2×C4D7×#4112yes—
1277C2×C4D7×#4112yes—
1278C2×C4D7×#4112yes—
1279C2×C4D7×#4112yes—
1280C2×C4D7×#4112yes—
1281C7#3490211yescharacteristic, complemented, Sylow
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—281no—
1290C22—281no—
1291C22—281no—
1292C22—281no—
1293C22—281no—
1294C22—281no—
1295C22—281no—
1296C22C2×D7×#4111yescharacteristic
1297C22C2×D7×#4111yescharacteristic
1298C22C2×D7×#4111yescharacteristic
1299C22C2×D7×#4111yescharacteristic
1300C22C2×D7×#4111yescharacteristic
1301C22#9061811yescharacteristic
1302C22D7×2−1+411yescharacteristic
1303C4—22no—
1304C4—22no—
1305C4—22no—
1306C4—22no—
1307C4—22no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—74no—
1318C4—74no—
1319C4—142no—
1320C4—142no—
1321C4—142no—
1322C4—142no—
1323C4—142no—
1324C4—281no—
1325C4—281no—
1326C4—281no—
1327C4—281no—
1328C4—281no—
1329C4—281no—
1330C4—281no—
1331C4—281no—
1332C2—81no—
1333C2—561no—
1334C2#1174318711yescharacteristic
1335C2D7×#52911yescharacteristic
1336C2#1174349711yescharacteristic
1337C2#1174389611yescharacteristic
1338C2#1174394311yescharacteristic
1339C2D7×#55611yescharacteristic
1340C2#1174411711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2596C2
prime radicalC22×C22⋊D7C23
hypercenter#2596D7
hypocenterC7#34902
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2596

Complements

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

NH ≅ G/Ntype
1. C7×#2596C2semidirect
2. #11735604C2semidirect
3. #11735581C2semidirect
4. #11735577C2semidirect
5. #11735575C2semidirect
7. #11735463C2semidirect
9. #11734906C2semidirect
10. #11733466C2semidirect
11. #11733412C2semidirect
12. #11733070C2semidirect
15. #11733018C2semidirect
16. #11732968C2semidirect
17. #11732900C2semidirect
20. #11732896C2semidirect
22. #11732535C2semidirect
23. #11732522C2semidirect
24. #11732499C2semidirect
25. #11732387C2semidirect
26. #11732384C2semidirect
27. #11732383C2semidirect
28. #11731185C2semidirect
29. #11731183C2semidirect
30. C4×#6450C2semidirect
31. C4×#6450C2semidirect
359. #2596D7semidirect
1281. C7#34902semidirect

Maximal subgroups

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

subgroupindex
C7×#25962
#117356042
#117355812
#117355772
#117355752
#117354672
#117354632
#117349382
#117349062
#117334662
#117334122
#117330702
#117330642
#117330382
#117330182
#117329682
#117329002
#117328992
#117328962
#117328952
#117325352
#117325222
#117324992
#117323872
#117323842
#117323832
#117311852
#117311832
C4×#64502
#349027