Finite Group Databasebeta

← #13568196

Subgroups — #13568196

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×#2750C211yesmaximal, characteristic, complemented
2#11735754C211yesmaximal, characteristic, complemented
3#11735730C211yesmaximal, characteristic, complemented
4#11735690C211yesmaximal, characteristic, complemented
5#11735670C211yesmaximal, characteristic, complemented
6#11735642C211yesmaximal, characteristic, complemented
7#11735587C211yesmaximal, characteristic, complemented
8#11735064C211yesmaximal, characteristic, complemented
9#11734996C211yesmaximal, characteristic, complemented
10#11734819C211yesmaximal, characteristic, complemented
11#11734734C211yesmaximal, characteristic, complemented
12#11734472C211yesmaximal, characteristic, complemented
13#11734411C211yesmaximal, characteristic
14#11733267C211yesmaximal, characteristic, complemented
15#11733247C211yesmaximal, characteristic, complemented
16#11733160C211yesmaximal, characteristic, complemented
17#11732895C211yesmaximal, characteristic, complemented
18#11732737C211yesmaximal, characteristic, complemented
19#11732705C211yesmaximal, characteristic, complemented
20#11732290C211yesmaximal, characteristic
21#11732263C211yesmaximal, characteristic
22#11732136C211yesmaximal, characteristic, complemented
23#11732115C211yesmaximal, characteristic, complemented
24#11732020C211yesmaximal, characteristic, complemented
25#11732007C211yesmaximal, characteristic, complemented
26#11731930C211yesmaximal, characteristic, complemented
27#11731883C211yesmaximal, characteristic, complemented
28#11731555C211yesmaximal, characteristic, complemented
29#11731499C211yesmaximal, characteristic, complemented
30#11731415C211yesmaximal, characteristic, complemented
31#11731392C211yesmaximal, characteristic, complemented
32C2×#6498C2211yescharacteristic
33C2×#6498C2211yescharacteristic
34C2×#6492C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C2×#6455C2211yescharacteristic
37C2×#6452C2211yescharacteristic
38C2×#6452C2211yescharacteristic
39C2×(C22⋊D7)⋊C4C2211yescharacteristic
40C2×#6440C2211yescharacteristic
41C7×#400C2211yescharacteristic
42C7×#400C2211yescharacteristic
43C7×#400C2211yescharacteristic
44C7×#397C2211yescharacteristic
45C7×#396C2211yescharacteristic
46C7×#394C2211yescharacteristic
47C7×#388C2211yescharacteristic
48C7×#388C2211yescharacteristic
49C7×#387C2211yescharacteristic
50C7×#386C2211yescharacteristic
51C7×#386C2211yescharacteristic
52C7×#385C2211yescharacteristic
53C7×#385C2211yescharacteristic
54C7×#381C2211yescharacteristic
55C7×#380C2211yescharacteristic
56#89995C2211yescharacteristic
57#89993C2211yescharacteristic
58#89985C2211yescharacteristic
59#89983C2211yescharacteristic
60#89982C2211yescharacteristic
61#89982C2211yescharacteristic
62#89982C2211yescharacteristic
63C4×C22⋊Dic7C2211yescharacteristic
64#89766C2211yescharacteristic
65#89766C2211yescharacteristic
66#89765C2211yescharacteristic
67#89765C2211yescharacteristic
68#89764C2211yescharacteristic
69#89761C2211yescharacteristic
70#89757C2211yescharacteristic
71#89756C2211yescharacteristic
72#89756C2211yescharacteristic
73#89754C2211yescharacteristic
74#89753C2211yescharacteristic
75#89753C2211yescharacteristic
76#89752C2211yescharacteristic
77#89750C2211yescharacteristic
78#89750C2211yescharacteristic
79#89750C2211yescharacteristic
80#89750C2211yescharacteristic
81#89748C2211yescharacteristic
82#89745C2211yescharacteristic
83#89745C2211yescharacteristic
84#89744C2211yescharacteristic
85#89744C2211yescharacteristic
86#89744C2211yescharacteristic
87#89744C2211yescharacteristic
88#89744C2211yescharacteristic
89#89733C2211yescharacteristic
90#89733C2211yescharacteristic
91#89733C2211yescharacteristic
92#89731C2211yescharacteristic
93#89730C2211yescharacteristic
94#89729C2211yescharacteristic
95#89729C2211yescharacteristic
96#89729C2211yescharacteristic
97#89728C2211yescharacteristic
98#89724C2211yescharacteristic
99#89724C2211yescharacteristic
100#89724C2211yescharacteristic
101#89723C2211yescharacteristic
102#89723C2211yescharacteristic
103#89723C2211yescharacteristic
104#89723C2211yescharacteristic
105#89721C2211yescharacteristic
106#89721C2211yescharacteristic
107#89720C2211yescharacteristic
108#89720C2211yescharacteristic
109#89720C2211yescharacteristic
110#89720C2211yescharacteristic
111#89720C2211yescharacteristic
112#89718C2211yescharacteristic
113#89717C2211yescharacteristic
114#89717C2211yescharacteristic
115#89717C2211yescharacteristic
116#89717C2211yescharacteristic
117#89717C2211yescharacteristic
118#89716C2211yescharacteristic
119#89716C2211yescharacteristic
120#89716C2211yescharacteristic
121#89715C2211yescharacteristic
122#89714C2211yescharacteristic
123#89714C2211yescharacteristic
124#89714C2211yescharacteristic
125C22⋊C4×Dic7C2211yescharacteristic
126C22⋊C4×Dic7C2211yescharacteristic
127#89712C2211yescharacteristic
128#89705C2211yescharacteristic
129#89705C2211yescharacteristic
130C42×Dic7C2211yescharacteristic
131#89448C2211yescharacteristic
132#89448C2211yescharacteristic
133#89447C2211yescharacteristic
134#89447C2211yescharacteristic
135#89446C2211yescharacteristic
136#89446C2211yescharacteristic
137#89441C2211yescharacteristic
138#89441C2211yescharacteristic
139#89441C2211yescharacteristic
140#89441C2211yescharacteristic
141#89441C2211yescharacteristic
142#89440C2211yescharacteristic
143#89440C2211yescharacteristic
144#89438C2211yescharacteristic
145#89432C2211yescharacteristic
146#89432C2211yescharacteristic
147#89431C2211yescharacteristic
148#89430C2211yescharacteristic
149#89430C2211yescharacteristic
150#89429C2211yescharacteristic
151#89429C2211yescharacteristic
152#89429C2211yescharacteristic
153#89429C2211yescharacteristic
154#89429C2211yescharacteristic
155#89429C2211yescharacteristic
156#89429C2211yescharacteristic
157#89427C2211yescharacteristic
158#89427C2211yescharacteristic
159#89427C2211yescharacteristic
160#89426C2211yescharacteristic
161#89426C2211yescharacteristic
162#89426C2211yescharacteristic
163#89426C2211yescharacteristic
164#89426C2211yescharacteristic
165#89426C2211yescharacteristic
166#89425C2211yescharacteristic
167#89425C2211yescharacteristic
168#89425C2211yescharacteristic
169#89425C2211yescharacteristic
170#89425C2211yescharacteristic
171#89425C2211yescharacteristic
172#89425C2211yescharacteristic
173#89424C2211yescharacteristic
174#89424C2211yescharacteristic
175#89424C2211yescharacteristic
176#89423C2211yescharacteristic
177#89422C2211yescharacteristic
178#89422C2211yescharacteristic
179#89421C2211yescharacteristic
180#89421C2211yescharacteristic
181#89419C2211yescharacteristic
182#89419C2211yescharacteristic
183#89419C2211yescharacteristic
184#89419C2211yescharacteristic
185#89419C2211yescharacteristic
186#89419C2211yescharacteristic
187#36994—71nomaximal, Sylow
188C22×C7×D4C2311yescharacteristic
189C23×C4×C7C2311yescharacteristic
190C23×C4×C7C2311yescharacteristic
191C22×C22⋊D7C2311yescharacteristic
192C22×C22⋊D7C2311yescharacteristic
193C23×Dic7C2311yescharacteristic
194C23×Dic7C2311yescharacteristic
195C22×C4×D7C2311yescharacteristic
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×C7×C22⋊C4C2311yescharacteristic
211C2×C7×C22⋊C4C2311yescharacteristic
212C2×C7×C22⋊C4C2311yescharacteristic
213C2×C42×C7C2311yescharacteristic
214C2×C22⋊Dic7C2311yescharacteristic
215C2×C22⋊Dic7C2311yescharacteristic
216C2×C22⋊Dic7C2311yescharacteristic
217C2×C22⋊Dic7C2311yescharacteristic
218C2×C22⋊Dic7C2311yescharacteristic
219C2×C22⋊Dic7C2311yescharacteristic
220C2×C22⋊Dic7C2311yescharacteristic
221C2×C22⋊Dic7C2311yescharacteristic
222C2×C22⋊Dic7C2311yescharacteristic
223C2×C22⋊Dic7C2311yescharacteristic
224C2×C22⋊Dic7C2311yescharacteristic
225C2×C22⋊Dic7C2311yescharacteristic
226#6498—24no—
227#6498—42no—
228#6492—42no—
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×C4⋊Dic7—24no—
242C2×C4⋊Dic7C2311yescharacteristic
243C2×C4⋊Dic7C2311yescharacteristic
244C2×C4⋊Dic7C2311yescharacteristic
245C2×C4⋊Dic7C2311yescharacteristic
246C2×C4⋊Dic7C2311yescharacteristic
247C2×C4⋊Dic7C2311yescharacteristic
248C2×C4⋊Dic7C2311yescharacteristic
249C2×C4⋊Dic7C2311yescharacteristic
250C2×C4⋊Dic7C2311yescharacteristic
251C2×C4⋊Dic7C2311yescharacteristic
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×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×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
291C2×C4×Dic7C2311yescharacteristic
292C2×C4×Dic7C2311yescharacteristic
293#6455—42no—
294#6452—42no—
295#6452—42no—
296(C22⋊D7)⋊C4—24no—
297#6440—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#2750D711yescharacteristic, complemented
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#2313—71no—
382#2293—71no—
383C24×C7C2411yescharacteristic
384C24×C7C2411yescharacteristic
385C23×D7C2411yescharacteristic
386C2×C7×D4—22no—
387C2×C7×D4—41no—
388C2×C7×D4—41no—
389C22×C4×C7—22no—
390C22×C4×C7—41no—
391C22×C4×C7—41no—
392C22×C4×C7—41no—
393C22×C4×C7—41no—
394C22×C4×C7—41no—
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
408C2×C22⋊D7—22no—
409C2×C22⋊D7—22no—
410C2×C22⋊D7—41no—
411C2×C22⋊D7—41no—
412C2×C22⋊D7—41no—
413C2×C22⋊D7—41no—
414C22×Dic7—22no—
415C22×Dic7—41no—
416C22×Dic7—41no—
417C22×Dic7—41no—
418C22×Dic7—41no—
419C22×Dic7#4114yes—
420C22×Dic7C2411yescharacteristic
421C22×Dic7C2411yescharacteristic
422C22×Dic7C2411yescharacteristic
423C22×Dic7C2411yescharacteristic
424C22×Dic7C2411yescharacteristic
425C22×Dic7C2411yescharacteristic
426C22×Dic7C2411yescharacteristic
427C22×Dic7C2411yescharacteristic
428C22×Dic7C2411yescharacteristic
429C22×Dic7C2411yescharacteristic
430C22×Dic7C2411yescharacteristic
431C22×Dic7C2411yescharacteristic
432C22×Dic7C2411yescharacteristic
433C22×Dic7C2411yescharacteristic
434C22×Dic7C2411yescharacteristic
435C2×C4×D7—22no—
436C2×C4×D7—41no—
437C2×C4×D7—41no—
438C7×C4⋊C4—41no—
439C7×C4⋊C4—41no—
440C7×C4⋊C4—41no—
441C7×C4⋊C4—41no—
442C7×C4⋊C4—41no—
443C7×C4⋊C4—41no—
444C7×C4⋊C4—41no—
445C7×C22⋊C4—22no—
446C7×C22⋊C4—41no—
447C7×C22⋊C4—41no—
448C7×C22⋊C4—41no—
449C7×C22⋊C4—41no—
450C7×C22⋊C4—41no—
451C7×C22⋊C4—41no—
452C7×C22⋊C4—41no—
453C7×C22⋊C4—41no—
454C7×C22⋊C4—41no—
455C42×C7—41no—
456C22⋊Dic7—22no—
457C22⋊Dic7—22no—
458C22⋊Dic7—22no—
459C22⋊Dic7—22no—
460C22⋊Dic7—22no—
461C22⋊Dic7—22no—
462C22⋊Dic7—41no—
463C22⋊Dic7—41no—
464C22⋊Dic7—41no—
465C22⋊Dic7—41no—
466C22⋊Dic7—41no—
467C22⋊Dic7—41no—
468(C2×D7)⋊C4—22no—
469(C2×D7)⋊C4—22no—
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—
480C4⋊Dic7—22no—
481C4⋊Dic7—22no—
482C4⋊Dic7—22no—
483C4⋊Dic7—22no—
484C4⋊Dic7—22no—
485C4⋊Dic7—22no—
486C4⋊Dic7—41no—
487C4⋊Dic7—41no—
488C4⋊Dic7—41no—
489C4⋊Dic7—41no—
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—41no—
499Dic7⋊C4—41no—
500Dic7⋊C4—41no—
501Dic7⋊C4—41no—
502Dic7⋊C4—41no—
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—
518C4×Dic7—22no—
519C4×Dic7—22no—
520C4×Dic7—22no—
521C4×Dic7—41no—
522C4×Dic7—41no—
523C4×Dic7—41no—
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⋊C4—71no—
540#400—71no—
541#400—71no—
542#400—71no—
543#400—71no—
544#400—71no—
545#400—71no—
546#400C2×D711yescharacteristic
547#400C2×D711yescharacteristic
548#400C2×D711yescharacteristic
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#397C2×D711yescharacteristic
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#396C2×D711yescharacteristic
582#394—71no—
583#394—71no—
584#394—71no—
585#394—71no—
586#394C2×D711yescharacteristic
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#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#387—71no—
642#387—71no—
643#387—71no—
644#387—71no—
645#387—71no—
646#387—71no—
647#387—71no—
648#387—71no—
649#387—71no—
650#387—71no—
651#387—71no—
652#387—71no—
653#387C2×D711yescharacteristic
654#386—71no—
655#386—71no—
656#386—71no—
657#386C2×D711yescharacteristic
658#386C2×D711yescharacteristic
659#385—71no—
660#385—71no—
661#385—71no—
662#385—71no—
663#385—71no—
664#385—71no—
665#385—71no—
666#385C2×D711yescharacteristic
667#385C2×D711yescharacteristic
668#384—71no—
669#383—71no—
670#382—71no—
671#382—71no—
672#381—71no—
673#381—71no—
674#381C2×D711yescharacteristic
675#380—71no—
676#380—71no—
677#380—71no—
678#380C2×D711yescharacteristic
679C4×C4⋊C4—71no—
680C4×C4⋊C4—71no—
681C4×C22⋊C4—71no—
682C4×C22⋊C4—71no—
683C4×C22⋊C4—71no—
684C4×C22⋊C4—71no—
685C43—71no—
686C23×C7—21no—
687C23×C7—21no—
688C23×C7—21no—
689C23×C7—21no—
690C23×C7—21no—
691C23×C7—21no—
692C23×C7—21no—
693C23×C7—21no—
694C23×C7—21no—
695C23×C7—21no—
696C23×C7—21no—
697C23×C7—21no—
698C23×C7—21no—
699C23×C7C2×#4112yes—
700C23×C7C2511yescharacteristic
701C22×D7—21no—
702C22×D7—21no—
703C22×D7—21no—
704C22×D7—21no—
705C22×D7—21no—
706C22×D7—21no—
707C22×D7—21no—
708C7×D4—82no—
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—82no—
750C22⋊D7—44no—
751C22⋊D7—82no—
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—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—44no—
794C2×Dic7—82no—
795C2×Dic7C2×#4112yes—
796C2×Dic7C2×#4112yes—
797C2×Dic7H(5,𝔽2)12yes—
798C2×Dic72−1+412yes—
799C4×D7—44no—
800C22×D4—71no—
801C22×D4—71no—
802C22×D4C22×D711yescharacteristic
803C23×C4—71no—
804C23×C4—71no—
805C23×C4—71no—
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—71no—
817C2×C4⋊C4—71no—
818C2×C4⋊C4—71no—
819C2×C4⋊C4—71no—
820C2×C4⋊C4—71no—
821C2×C4⋊C4—71no—
822C2×C4⋊C4—71no—
823C2×C4⋊C4—71no—
824C2×C4⋊C4—71no—
825C2×C4⋊C4—71no—
826C2×C4⋊C4—71no—
827C2×C4⋊C4—71no—
828C2×C4⋊C4—71no—
829C2×C4⋊C4—71no—
830C2×C4⋊C4—71no—
831C2×C4⋊C4—71no—
832C2×C4⋊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⋊C4—144no—
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⋊C4C22×D711yescharacteristic
887C2×C22⋊C4C22×D711yescharacteristic
888C2×C22⋊C4C22×D711yescharacteristic
889C2×C22⋊C4C22×D711yescharacteristic
890C2×C22⋊C4C22×D711yescharacteristic
891C2×C22⋊C4C22×D711yescharacteristic
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×C42—71no—
907C2×C42—71no—
908C2×C42—71no—
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#95—71no—
949#95—71no—
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×C7—41no—
972C22×C7—41no—
973C22×C7—41no—
974C22×C7—41no—
975C22×C7—41no—
976C22×C7—41no—
977C22×C7—41no—
978C22×C7C22×#4111yescharacteristic
979C22×C7C2×H(5,𝔽2)11yescharacteristic
980C22×C7C2×2−1+411yescharacteristic
981C22×C7#58511yescharacteristic
982C22×C7#58511yescharacteristic
983C22×C7#58511yescharacteristic
984C22×C7#58511yescharacteristic
985C2×D7—41no—
986C2×D7—41no—
987C2×D7—41no—
988C2×D7—41no—
989C2×D7—41no—
990C2×D7—41no—
991C2×D7—41no—
992C4×C7—41no—
993C4×C7—41no—
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—
1005Dic7—22no—
1006Dic7—22no—
1007Dic7—22no—
1008Dic7—22no—
1009Dic7—41no—
1010Dic7—41no—
1011Dic7—41no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7—41no—
1020C24—71no—
1021C24C23×D711yescharacteristic
1022C24C23×D711yescharacteristic
1023C2×D4—22no—
1024C2×D4—41no—
1025C2×D4—41no—
1026C2×D4—142no—
1027C2×D4—142no—
1028C2×D4—281no—
1029C2×D4—281no—
1030C2×D4—281no—
1031C2×D4—281no—
1032C22×C4—22no—
1033C22×C4—41no—
1034C22×C4—41no—
1035C22×C4—41no—
1036C22×C4—41no—
1037C22×C4—41no—
1038C22×C4—71no—
1039C22×C4—71no—
1040C22×C4—71no—
1041C22×C4—71no—
1042C22×C4—74no—
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—142no—
1056C22×C4—281no—
1057C22×C4—281no—
1058C22×C4—281no—
1059C22×C4—281no—
1060C22×C4—281no—
1061C22×C4—281no—
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—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
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—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—22no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—41no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—142no—
1131C22⋊C4—142no—
1132C22⋊C4—142no—
1133C22⋊C4—142no—
1134C22⋊C4—142no—
1135C22⋊C4—142no—
1136C22⋊C4—142no—
1137C22⋊C4—142no—
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—142no—
1156C42—142no—
1157C42—142no—
1158C42—281no—
1159C42—281no—
1160C42—281no—
1161C42—281no—
1162C42—281no—
1163C42—281no—
1164C42—281no—
1165C42—281no—
1166C42—281no—
1167C42—281no—
1168C2×C7—42no—
1169C2×C7—81no—
1170C2×C7#345511yescharacteristic
1171C2×C7#349511yescharacteristic
1172C2×C7#350511yescharacteristic
1173C2×C7#355711yescharacteristic
1174C2×C7#355911yescharacteristic
1175C2×C7#356211yescharacteristic
1176C2×C7#356711yescharacteristic
1177D7—81no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—141no—
1192C23—141no—
1193C23—141no—
1194C23—141no—
1195C23—141no—
1196C23—141no—
1197C23—141no—
1198C23D7×#4112yes—
1199C23C24×D711yescharacteristic
1200D4—82no—
1201D4—284no—
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—44no—
1243C2×C4—72no—
1244C2×C4—72no—
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—141no—
1289C2×C4—284no—
1290C2×C4—284no—
1291C2×C4—562no—
1292C7#3699411yescharacteristic, complemented, Sylow
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—281no—
1308C22—281no—
1309C22—281no—
1310C22—281no—
1311C22—281no—
1312C22—281no—
1313C22—281no—
1314C22C2×D7×#4111yescharacteristic
1315C22#9061611yescharacteristic
1316C22#9061611yescharacteristic
1317C22D7×H(5,𝔽2)11yescharacteristic
1318C22#9061811yescharacteristic
1319C22#9061811yescharacteristic
1320C22D7×2−1+411yescharacteristic
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—142no—
1335C4—142no—
1336C4—142no—
1337C4—142no—
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—81no—
1351C2—561no—
1352C2#1174345511yescharacteristic
1353C2#1174347511yescharacteristic
1354C2#1174350911yescharacteristic
1355C2#1174388511yescharacteristic
1356C2#1174389711yescharacteristic
1357C2#1174397511yescharacteristic
1358C2#1174418211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2750C2
prime radical#89995C22
hypercenter#2750D7
hypocenterC7#36994
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2750

Complements

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

NH ≅ G/Ntype
1. C7×#2750C2semidirect
2. #11735754C2semidirect
3. #11735730C2semidirect
4. #11735690C2semidirect
5. #11735670C2semidirect
6. #11735642C2semidirect
7. #11735587C2semidirect
8. #11735064C2semidirect
9. #11734996C2semidirect
10. #11734819C2semidirect
11. #11734734C2semidirect
12. #11734472C2semidirect
14. #11733267C2semidirect
15. #11733247C2semidirect
16. #11733160C2semidirect
17. #11732895C2semidirect
18. #11732737C2semidirect
19. #11732705C2semidirect
22. #11732136C2semidirect
23. #11732115C2semidirect
24. #11732020C2semidirect
25. #11732007C2semidirect
26. #11731930C2semidirect
27. #11731883C2semidirect
28. #11731555C2semidirect
29. #11731499C2semidirect
30. #11731415C2semidirect
31. #11731392C2semidirect
363. #2750D7semidirect
1292. C7#36994semidirect

Maximal subgroups

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

subgroupindex
C7×#27502
#117357542
#117357302
#117356902
#117356702
#117356422
#117355872
#117350642
#117349962
#117348192
#117347342
#117344722
#117344112
#117332672
#117332472
#117331602
#117328952
#117327372
#117327052
#117322902
#117322632
#117321362
#117321152
#117320202
#117320072
#117319302
#117318832
#117315552
#117314992
#117314152
#117313922
#369947