Finite Group Databasebeta

← #14216697

Subgroups — #14216697

Order 1792.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2359C211yesmaximal, characteristic, complemented
2#11740300C211yesmaximal, characteristic
3#11740296C211yesmaximal, characteristic, complemented
4#11739810C211yesmaximal, characteristic
5#11739782C211yesmaximal, characteristic, complemented
6#11739695C211yesmaximal, characteristic, complemented
7#11739674C211yesmaximal, characteristic, complemented
8#11733499C211yesmaximal, characteristic, complemented
9#11733498C211yesmaximal, characteristic, complemented
10#11733191C211yesmaximal, characteristic, complemented
11#11733065C211yesmaximal, characteristic, complemented
12#11733034C211yesmaximal, characteristic, complemented
13#11733005C211yesmaximal, characteristic, complemented
14#11732702C211yesmaximal, characteristic, complemented
15#11732485C211yesmaximal, characteristic, complemented
16#11732409C211yesmaximal, characteristic, complemented
17#11732384C211yesmaximal, characteristic, complemented
18#11732291C211yesmaximal, characteristic
19#11732219C211yesmaximal, characteristic, complemented
20#11731987C211yesmaximal, characteristic, complemented
21#11731916C211yesmaximal, characteristic, complemented
22#11731893C211yesmaximal, characteristic, complemented
23#11731893C211yesmaximal, characteristic, complemented
24#11731135C211yesmaximal, characteristic, complemented
25#11731092C211yesmaximal, characteristic, complemented
26#11730994C211yesmaximal, characteristic, complemented
27#11730978C211yesmaximal, characteristic, complemented
28#11730920C211yesmaximal, characteristic, complemented
29#11730885C211yesmaximal, characteristic, complemented
30#11730801C211yesmaximal, characteristic, complemented
31#11730780C211yesmaximal, characteristic, complemented
32C2×C7×#123C2211yescharacteristic
33C2×C4×C7×D4C2211yescharacteristic
34C2×C7×#117C2211yescharacteristic
35C2×#6489C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C2×#6460C2211yescharacteristic
38C2×#6455C2211yescharacteristic
39C2×#6450C2211yescharacteristic
40C2×#6448C2211yescharacteristic
41C7×#389C2211yescharacteristic
42C7×#388C2211yescharacteristic
43C7×#388C2211yescharacteristic
44C7×#387C2211yescharacteristic
45C7×#387C2211yescharacteristic
46C7×#386C2211yescharacteristic
47C7×#385C2211yescharacteristic
48C7×#385C2211yescharacteristic
49C4×C7×C4⋊C4C2211yescharacteristic
50C4×C7×C22⋊C4C2211yescharacteristic
51C4×C7×C22⋊C4C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53#89995C2211yescharacteristic
54#89994C2211yescharacteristic
55#89993C2211yescharacteristic
56#89993C2211yescharacteristic
57#89985C2211yescharacteristic
58#89985C2211yescharacteristic
59#89985C2211yescharacteristic
60#89985C2211yescharacteristic
61#89984C2211yescharacteristic
62#89984C2211yescharacteristic
63#89983C2211yescharacteristic
64#89982C2211yescharacteristic
65#89982C2211yescharacteristic
66#89982C2211yescharacteristic
67C4×C22⋊Dic7C2211yescharacteristic
68C4×C22⋊Dic7C2211yescharacteristic
69C4×C22⋊Dic7C2211yescharacteristic
70C4×C22⋊Dic7C2211yescharacteristic
71#89766C2211yescharacteristic
72#89766C2211yescharacteristic
73#89762C2211yescharacteristic
74#89762C2211yescharacteristic
75#89762C2211yescharacteristic
76#89758C2211yescharacteristic
77#89758C2211yescharacteristic
78#89757C2211yescharacteristic
79#89756C2211yescharacteristic
80#89755C2211yescharacteristic
81#89754C2211yescharacteristic
82#89753C2211yescharacteristic
83#89753C2211yescharacteristic
84#89753C2211yescharacteristic
85#89753C2211yescharacteristic
86#89753C2211yescharacteristic
87#89753C2211yescharacteristic
88#89753C2211yescharacteristic
89#89751C2211yescharacteristic
90#89750C2211yescharacteristic
91#89750C2211yescharacteristic
92#89750C2211yescharacteristic
93#89750C2211yescharacteristic
94C4⋊C4×Dic7C2211yescharacteristic
95C4⋊C4×Dic7C2211yescharacteristic
96#89733C2211yescharacteristic
97#89731C2211yescharacteristic
98#89731C2211yescharacteristic
99#89731C2211yescharacteristic
100#89729C2211yescharacteristic
101#89728C2211yescharacteristic
102#89728C2211yescharacteristic
103#89725C2211yescharacteristic
104#89725C2211yescharacteristic
105#89724C2211yescharacteristic
106#89724C2211yescharacteristic
107#89723C2211yescharacteristic
108#89723C2211yescharacteristic
109#89723C2211yescharacteristic
110#89723C2211yescharacteristic
111#89723C2211yescharacteristic
112#89723C2211yescharacteristic
113#89723C2211yescharacteristic
114#89723C2211yescharacteristic
115#89721C2211yescharacteristic
116#89719C2211yescharacteristic
117#89719C2211yescharacteristic
118#89719C2211yescharacteristic
119#89717C2211yescharacteristic
120#89717C2211yescharacteristic
121#89717C2211yescharacteristic
122#89716C2211yescharacteristic
123#89716C2211yescharacteristic
124#89716C2211yescharacteristic
125#89716C2211yescharacteristic
126#89716C2211yescharacteristic
127#89712C2211yescharacteristic
128#89712C2211yescharacteristic
129#89712C2211yescharacteristic
130#89712C2211yescharacteristic
131C4×(C2×D7)⋊C4C2211yescharacteristic
132#89707C2211yescharacteristic
133C4×C4⋊Dic7C2211yescharacteristic
134C4×C4⋊Dic7C2211yescharacteristic
135C4×C4⋊Dic7C2211yescharacteristic
136#89705C2211yescharacteristic
137#89704C2211yescharacteristic
138#89704C2211yescharacteristic
139C4×Dic7⋊C4C2211yescharacteristic
140C4×Dic7⋊C4C2211yescharacteristic
141C42×Dic7C2211yescharacteristic
142#89701C2211yescharacteristic
143#89701C2211yescharacteristic
144#89701C2211yescharacteristic
145#89701C2211yescharacteristic
146#89700C2211yescharacteristic
147#89447C2211yescharacteristic
148#89446C2211yescharacteristic
149#89446C2211yescharacteristic
150#89442C2211yescharacteristic
151#89442C2211yescharacteristic
152#89442C2211yescharacteristic
153#89442C2211yescharacteristic
154#89441C2211yescharacteristic
155#89438C2211yescharacteristic
156#89438C2211yescharacteristic
157C7⋊#401C2211yescharacteristic
158#89432C2211yescharacteristic
159#89432C2211yescharacteristic
160#89432C2211yescharacteristic
161#89432C2211yescharacteristic
162#89429C2211yescharacteristic
163#89429C2211yescharacteristic
164#89427C2211yescharacteristic
165#89426C2211yescharacteristic
166#89426C2211yescharacteristic
167#89426C2211yescharacteristic
168#89426C2211yescharacteristic
169#89426C2211yescharacteristic
170#89425C2211yescharacteristic
171#89425C2211yescharacteristic
172#89425C2211yescharacteristic
173#89425C2211yescharacteristic
174#89425C2211yescharacteristic
175#89423C2211yescharacteristic
176#89423C2211yescharacteristic
177#89423C2211yescharacteristic
178#89422C2211yescharacteristic
179#89422C2211yescharacteristic
180#89421C2211yescharacteristic
181#89421C2211yescharacteristic
182#89420C2211yescharacteristic
183#89420C2211yescharacteristic
184#89418C2211yescharacteristic
185#89418C2211yescharacteristic
186#89418C2211yescharacteristic
187#60024—71nomaximal, Sylow
188C22×C7×D4C2311yescharacteristic
189C23×C4×C7C2311yescharacteristic
190C23×C4×C7C2311yescharacteristic
191C23×C4×C7C2311yescharacteristic
192C23×C4×C7C2311yescharacteristic
193C22×C22⋊D7C2311yescharacteristic
194C22×C22⋊D7C2311yescharacteristic
195C22×C4×D7C2311yescharacteristic
196C22×Dic14C2311yescharacteristic
197C22×Dic14C2311yescharacteristic
198C7×#123—24no—
199C4×C7×D4—24no—
200C7×#117—24no—
201C2×C7×C4⋊C4C2311yescharacteristic
202C2×C7×C4⋊C4C2311yescharacteristic
203C2×C7×C4⋊C4C2311yescharacteristic
204C2×C7×C4⋊C4C2311yescharacteristic
205C2×C7×C4⋊C4C2311yescharacteristic
206C2×C7×C4⋊C4C2311yescharacteristic
207C2×C7×C4⋊C4C2311yescharacteristic
208C2×C7×C22⋊C4C2311yescharacteristic
209C2×C7×C22⋊C4C2311yescharacteristic
210C2×C7×C22⋊C4C2311yescharacteristic
211C2×C7×C22⋊C4C2311yescharacteristic
212C2×C7×C22⋊C4C2311yescharacteristic
213C2×C7×C22⋊C4C2311yescharacteristic
214C2×C7×C22⋊C4C2311yescharacteristic
215C2×C7×C22⋊C4C2311yescharacteristic
216C2×C42×C7C2311yescharacteristic
217C2×C42×C7C2311yescharacteristic
218C2×C42×C7C2311yescharacteristic
219C2×C42×C7C2311yescharacteristic
220C2×C42×C7C2311yescharacteristic
221C2×C22⋊Dic7C2311yescharacteristic
222C2×C22⋊Dic7C2311yescharacteristic
223C2×C22⋊Dic7C2311yescharacteristic
224C2×C22⋊Dic7C2311yescharacteristic
225C2×C22⋊Dic7C2311yescharacteristic
226C2×C22⋊Dic7C2311yescharacteristic
227C2×C22⋊Dic7C2311yescharacteristic
228C2×C22⋊Dic7C2311yescharacteristic
229C2×C22⋊Dic7C2311yescharacteristic
230C2×C22⋊Dic7C2311yescharacteristic
231C2×C22⋊Dic7C2311yescharacteristic
232C2×C22⋊Dic7C2311yescharacteristic
233C2×C22⋊Dic7C2311yescharacteristic
234C2×C22⋊Dic7C2311yescharacteristic
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
246C2×(C2×D7)⋊C4C2311yescharacteristic
247#6489—24no—
248#6489—24no—
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×C4⋊Dic7C2311yescharacteristic
259C2×C4⋊Dic7C2311yescharacteristic
260C2×C4⋊Dic7C2311yescharacteristic
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×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
290#6460—24no—
291#6455—24no—
292#6450—24no—
293#6448—24no—
294C7×#95C2311yescharacteristic
295C7×#95C2311yescharacteristic
296C7×#95C2311yescharacteristic
297C7×#95C2311yescharacteristic
298C7×#95C2311yescharacteristic
299C7×#95C2311yescharacteristic
300C7×#95C2311yescharacteristic
301C7×#95C2311yescharacteristic
302C7×#95C2311yescharacteristic
303C7×#95C2311yescharacteristic
304C7⋊#95C2311yescharacteristic
305C7⋊#95C2311yescharacteristic
306C7⋊#95C2311yescharacteristic
307C7⋊#95C2311yescharacteristic
308C7⋊#95C2311yescharacteristic
309C7⋊#95C2311yescharacteristic
310C7⋊#95C2311yescharacteristic
311C7⋊#95C2311yescharacteristic
312C7⋊#95C2311yescharacteristic
313C7⋊#95C2311yescharacteristic
314C7⋊#95C2311yescharacteristic
315C7⋊#95C2311yescharacteristic
316C7⋊#95C2311yescharacteristic
317C7⋊#95C2311yescharacteristic
318C7⋊#95C2311yescharacteristic
319C7⋊#95C2311yescharacteristic
320C7⋊#95C2311yescharacteristic
321C7⋊#95C2311yescharacteristic
322C7⋊#95C2311yescharacteristic
323C7⋊#95C2311yescharacteristic
324C7⋊#95C2311yescharacteristic
325C7⋊#95C2311yescharacteristic
326C7⋊#95C2311yescharacteristic
327C7⋊#95C2311yescharacteristic
328C7⋊#95C2311yescharacteristic
329C7⋊#95C2311yescharacteristic
330C7⋊#95C2311yescharacteristic
331C7⋊#95C2311yescharacteristic
332C7⋊#95C2311yescharacteristic
333C7⋊#95C2311yescharacteristic
334C7⋊#95C2311yescharacteristic
335C7⋊#95C2311yescharacteristic
336C7⋊#95C2311yescharacteristic
337C7⋊#95C2311yescharacteristic
338C7⋊#95C2311yescharacteristic
339C7⋊#95C2311yescharacteristic
340C7⋊#95C2311yescharacteristic
341C7⋊#95C2311yescharacteristic
342C7⋊#95C2311yescharacteristic
343C7⋊#95C2311yescharacteristic
344C7⋊#95C2311yescharacteristic
345C7⋊#95C2311yescharacteristic
346C7⋊#95C2311yescharacteristic
347C7⋊#95C2311yescharacteristic
348C7⋊#95C2311yescharacteristic
349C7⋊#95C2311yescharacteristic
350C7⋊#95C2311yescharacteristic
351C7⋊#95C2311yescharacteristic
352#2793—71no—
353#2759—71no—
354#2753—71no—
355#2738—71no—
356#2597—71no—
357#2593—71no—
358#2589—71no—
359#2532—71no—
360#2531—71no—
361#2530—71no—
362#2528—71no—
363#2525—71no—
364#2520—71no—
365#2518—71no—
366#2511—71no—
367#2510—71no—
368#2477—71no—
369#2477—71no—
370#2474—71no—
371#2471—71no—
372#2459—71no—
373#2458—71no—
374#2372—71no—
375#2362—71no—
376#2359D711yescharacteristic, complemented
377#2356—71no—
378#2354—71no—
379#2343—71no—
380#2298—71no—
381#2298—71no—
382#2298—71no—
383C24×C7C2411yescharacteristic
384C24×C7C2411yescharacteristic
385C23×D7C2411yescharacteristic
386C2×C7×D4—22no—
387C2×C7×D4—22no—
388C2×C7×D4—41no—
389C22×C4×C7—22no—
390C22×C4×C7—22no—
391C22×C4×C7—22no—
392C22×C4×C7—22no—
393C22×C4×C7—22no—
394C22×C4×C7—22no—
395C22×C4×C7—41no—
396C22×C4×C7—41no—
397C22×C4×C7—41no—
398C22×C4×C7—41no—
399C22×C4×C7—41no—
400C22×C4×C7—41no—
401C22×C4×C7C2411yescharacteristic
402C22×C4×C7C2411yescharacteristic
403C22×C4×C7C2411yescharacteristic
404C22×C4×C7C2411yescharacteristic
405C22×C4×C7C2411yescharacteristic
406C22×C4×C7C2411yescharacteristic
407C22×C4×C7C2411yescharacteristic
408C22×C4×C7C2411yescharacteristic
409C22×C4×C7C2411yescharacteristic
410C22×C4×C7C2411yescharacteristic
411C22×C4×C7C2411yescharacteristic
412C22×C4×C7C2411yescharacteristic
413C22×C4×C7C2411yescharacteristic
414C2×C22⋊D7—22no—
415C2×C22⋊D7—41no—
416C2×C22⋊D7—41no—
417C2×C22⋊D7—41no—
418C2×C22⋊D7—41no—
419C2×C22⋊D7—41no—
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—22no—
437C2×C4×D7—41no—
438C2×Dic14—22no—
439C2×Dic14—22no—
440C2×Dic14—22no—
441C2×Dic14—41no—
442C2×Dic14—41no—
443C2×Dic14—41no—
444C7×C4⋊C4—22no—
445C7×C4⋊C4—22no—
446C7×C4⋊C4—22no—
447C7×C4⋊C4—22no—
448C7×C4⋊C4—22no—
449C7×C4⋊C4—41no—
450C7×C4⋊C4#4114yes—
451C7×C22⋊C4—22no—
452C7×C22⋊C4—22no—
453C7×C22⋊C4—22no—
454C7×C22⋊C4—22no—
455C7×C22⋊C4—22no—
456C7×C22⋊C4—41no—
457C7×C22⋊C4—41no—
458C7×C22⋊C4#4114yes—
459C42×C7—22no—
460C42×C7—22no—
461C42×C7—22no—
462C42×C7—41no—
463C42×C7—41no—
464C22⋊Dic7—22no—
465C22⋊Dic7—22no—
466C22⋊Dic7—22no—
467C22⋊Dic7—22no—
468C22⋊Dic7—22no—
469C22⋊Dic7—41no—
470C22⋊Dic7—41no—
471C22⋊Dic7—41no—
472C22⋊Dic7—41no—
473C22⋊Dic7—41no—
474C22⋊Dic7—41no—
475C22⋊Dic7—41no—
476C22⋊Dic7—41no—
477C22⋊Dic7—41no—
478(C2×D7)⋊C4—22no—
479(C2×D7)⋊C4—22no—
480(C2×D7)⋊C4—22no—
481(C2×D7)⋊C4—22no—
482(C2×D7)⋊C4—22no—
483(C2×D7)⋊C4—22no—
484(C2×D7)⋊C4—41no—
485(C2×D7)⋊C4—41no—
486(C2×D7)⋊C4—41no—
487(C2×D7)⋊C4—41no—
488(C2×D7)⋊C4—41no—
489(C2×D7)⋊C4—41no—
490C4⋊Dic7—22no—
491C4⋊Dic7—22no—
492C4⋊Dic7—22no—
493C4⋊Dic7—22no—
494C4⋊Dic7—41no—
495C4⋊Dic7—41no—
496C4⋊Dic7—41no—
497C4⋊Dic7—41no—
498C4⋊Dic7—41no—
499C4⋊Dic7—41no—
500C4⋊Dic7—41no—
501C4⋊Dic7#4114yes—
502Dic7⋊C4—22no—
503Dic7⋊C4—22no—
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—
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—41no—
525C4×Dic7—41no—
526C4×Dic7—41no—
527C4×Dic7—41no—
528C4×Dic7—41no—
529C4×Dic7—41no—
530C4×Dic7—41no—
531C2×#124—71no—
532C2×#123C2×D711yescharacteristic
533C2×C22⋊Q8—71no—
534C2×C4×Q8—71no—
535C2×C4×D4C2×D711yescharacteristic
536C2×#117—71no—
537C2×#117—71no—
538C2×#117—71no—
539C2×#117C2×D711yescharacteristic
540#401—71no—
541#400—71no—
542#400—71no—
543#400—71no—
544#400—71no—
545#400—71no—
546#400—71no—
547#400—71no—
548#399—71no—
549#398—71no—
550#398—71no—
551#398—71no—
552#398—71no—
553#397—71no—
554#397—71no—
555#397—71no—
556#397—71no—
557#397—71no—
558#397—71no—
559#397—71no—
560#396—71no—
561#396—71no—
562#395—71no—
563#394—71no—
564#394—71no—
565#394—71no—
566#394—71no—
567#394—71no—
568#393—71no—
569#393—71no—
570#393—71no—
571#392—71no—
572#391—71no—
573#391—71no—
574#391—71no—
575#391—71no—
576#391—71no—
577#391—71no—
578#391—71no—
579#390—71no—
580#390—71no—
581#390—71no—
582#389—71no—
583#389—71no—
584#389C2×D711yescharacteristic
585#388—71no—
586#388—71no—
587#388—71no—
588#388—71no—
589#388—71no—
590#388—71no—
591#388—71no—
592#388—71no—
593#388—71no—
594#388—71no—
595#388—71no—
596#388—71no—
597#388—71no—
598#388—71no—
599#388—71no—
600#388—71no—
601#388—71no—
602#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#388C2×D711yescharacteristic
614#388C2×D711yescharacteristic
615#387—71no—
616#387—71no—
617#387—71no—
618#387—71no—
619#387—71no—
620#387—71no—
621#387—71no—
622#387—71no—
623#387—71no—
624#387—71no—
625#387—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#387C2×D711yescharacteristic
639#387C2×D711yescharacteristic
640#386—71no—
641#386—71no—
642#386—71no—
643#386—71no—
644#386—71no—
645#386—71no—
646#386C2×D711yescharacteristic
647#385—71no—
648#385—71no—
649#385—71no—
650#385C2×D711yescharacteristic
651#385C2×D711yescharacteristic
652#384—71no—
653#383—71no—
654#383—71no—
655#383—71no—
656#382—71no—
657#382—71no—
658#381—71no—
659#380—71no—
660#380—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⋊C4C2×D711yescharacteristic
671C4×C22⋊C4—71no—
672C4×C22⋊C4—71no—
673C4×C22⋊C4—71no—
674C4×C22⋊C4—71no—
675C4×C22⋊C4—71no—
676C4×C22⋊C4—71no—
677C4×C22⋊C4—71no—
678C4×C22⋊C4C2×D711yescharacteristic
679C4×C22⋊C4C2×D711yescharacteristic
680#376—71no—
681#376—71no—
682#376—71no—
683#376—71no—
684C2×#95C2×D711yescharacteristic
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—44no—
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—44no—
743C2×C4×C7—44no—
744C2×C4×C7—44no—
745C2×C4×C7—82no—
746C2×C4×C7C2×#4112yes—
747C2×C4×C7C2×#4112yes—
748C2×C4×C7C2×#4112yes—
749C2×C4×C7C2×#4112yes—
750C2×C4×C7C2×#4112yes—
751C2×C4×C7C2×#4112yes—
752C22⋊D7—82no—
753C22⋊D7—82no—
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—21no—
794C2×Dic7—21no—
795C2×Dic7—21no—
796C2×Dic7—21no—
797C2×Dic7C2×#4112yes—
798C2×Dic7C2×#4112yes—
799C4×D7—44no—
800Dic14—44no—
801Dic14—82no—
802C22×Q8—71no—
803C22×Q8—71no—
804C22×D4—71no—
805C22×D4—71no—
806C22×D4C22×D711yescharacteristic
807C23×C4—71no—
808C23×C4C22×D711yescharacteristic
809C23×C4C22×D711yescharacteristic
810C23×C4C22×D711yescharacteristic
811C23×C4C22×D711yescharacteristic
812#124—144no—
813#123—24no—
814C22⋊Q8—144no—
815C4×Q8—144no—
816C4×D4—24no—
817#117—24no—
818#117—144no—
819#117—144no—
820#117—144no—
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⋊C4C22×D711yescharacteristic
846C2×C4⋊C4C22×D711yescharacteristic
847C2×C4⋊C4C22×D711yescharacteristic
848C2×C4⋊C4C22×D711yescharacteristic
849C2×C4⋊C4C22×D711yescharacteristic
850C2×C4⋊C4C22×D711yescharacteristic
851C2×C4⋊C4C22×D711yescharacteristic
852C2×C22⋊C4—71no—
853C2×C22⋊C4—71no—
854C2×C22⋊C4—71no—
855C2×C22⋊C4—71no—
856C2×C22⋊C4—71no—
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⋊C4—71no—
877C2×C22⋊C4—71no—
878C2×C22⋊C4C22×D711yescharacteristic
879C2×C22⋊C4C22×D711yescharacteristic
880C2×C22⋊C4C22×D711yescharacteristic
881C2×C22⋊C4C22×D711yescharacteristic
882C2×C22⋊C4C22×D711yescharacteristic
883C2×C22⋊C4C22×D711yescharacteristic
884C2×C22⋊C4C22×D711yescharacteristic
885C2×C22⋊C4C22×D711yescharacteristic
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×C42C22×D711yescharacteristic
904C2×C42C22×D711yescharacteristic
905C2×C42C22×D711yescharacteristic
906C2×C42C22×D711yescharacteristic
907C2×C42C22×D711yescharacteristic
908#95—71no—
909#95—71no—
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#95—71no—
951#95—71no—
952#95—71no—
953#95—71no—
954#95—71no—
955#95—71no—
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
966C22×C7—22no—
967C22×C7—22no—
968C22×C7—22no—
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×C7—41no—
979C22×C7—41no—
980C22×C7C22×#4111yescharacteristic
981C22×C7C22×#4111yescharacteristic
982C22×C7C22×#4111yescharacteristic
983C22×C7#58511yescharacteristic
984C22×C7#58511yescharacteristic
985C22×C7#58511yescharacteristic
986C22×C7#58511yescharacteristic
987C2×D7—41no—
988C2×D7—41no—
989C2×D7—41no—
990C2×D7—41no—
991C2×D7—41no—
992C2×D7—41no—
993C2×D7—41no—
994C4×C7—22no—
995C4×C7—22no—
996C4×C7—22no—
997C4×C7—22no—
998C4×C7—22no—
999C4×C7—22no—
1000C4×C7—41no—
1001C4×C7—41no—
1002C4×C7—41no—
1003C4×C7—41no—
1004C4×C7—41no—
1005C4×C7—41no—
1006C4×C7—41no—
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—
1020Dic7—41no—
1021Dic7—41no—
1022C24—71no—
1023C24C23×D711yescharacteristic
1024C24C23×D711yescharacteristic
1025C2×Q8—142no—
1026C2×Q8—142no—
1027C2×Q8—142no—
1028C2×Q8—281no—
1029C2×Q8—281no—
1030C2×Q8—281no—
1031C2×D4—22no—
1032C2×D4—22no—
1033C2×D4—41no—
1034C2×D4—142no—
1035C2×D4—281no—
1036C2×D4—281no—
1037C2×D4—281no—
1038C2×D4—281no—
1039C2×D4—281no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—41no—
1047C22×C4—41no—
1048C22×C4—41no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4—41no—
1052C22×C4—71no—
1053C22×C4—71no—
1054C22×C4—71no—
1055C22×C4—71no—
1056C22×C4—71no—
1057C22×C4—71no—
1058C22×C4—71no—
1059C22×C4—71no—
1060C22×C4—71no—
1061C22×C4—71no—
1062C22×C4—71no—
1063C22×C4—71no—
1064C22×C4—71no—
1065C22×C4—71no—
1066C22×C4—71no—
1067C22×C4—142no—
1068C22×C4—142no—
1069C22×C4—281no—
1070C22×C4C23×D711yescharacteristic
1071C22×C4C23×D711yescharacteristic
1072C22×C4C23×D711yescharacteristic
1073C22×C4C23×D711yescharacteristic
1074C22×C4C23×D711yescharacteristic
1075C22×C4C23×D711yescharacteristic
1076C22×C4C23×D711yescharacteristic
1077C22×C4C23×D711yescharacteristic
1078C22×C4C23×D711yescharacteristic
1079C22×C4C23×D711yescharacteristic
1080C22×C4C23×D711yescharacteristic
1081C22×C4C23×D711yescharacteristic
1082C22×C4C23×D711yescharacteristic
1083C4⋊C4—22no—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—22no—
1087C4⋊C4—22no—
1088C4⋊C4—41no—
1089C4⋊C4—74no—
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#115714yes—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—22no—
1117C22⋊C4—22no—
1118C22⋊C4—22no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—142no—
1122C22⋊C4—142no—
1123C22⋊C4—142no—
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—281no—
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#115914yes—
1148C42—22no—
1149C42—22no—
1150C42—22no—
1151C42—41no—
1152C42—41no—
1153C42—142no—
1154C42—142no—
1155C42—142no—
1156C42—142no—
1157C42—142no—
1158C42—142no—
1159C42—142no—
1160C42—142no—
1161C42—142no—
1162C42—142no—
1163C42—281no—
1164C42—281no—
1165C42—281no—
1166C42—281no—
1167C42—281no—
1168C42—281no—
1169C42—281no—
1170C2×C7—42no—
1171C2×C7—81no—
1172C2×C7#347511yescharacteristic
1173C2×C7#347511yescharacteristic
1174C2×C7#347511yescharacteristic
1175C2×C7#352111yescharacteristic
1176C2×C7#352411yescharacteristic
1177C2×C7#352411yescharacteristic
1178C2×C7#356811yescharacteristic
1179D7—81no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—141no—
1194C23—141no—
1195C23—141no—
1196C23—141no—
1197C23—141no—
1198C23—141no—
1199C23—141no—
1200C23C2×#115912yes—
1201C23C24×D711yescharacteristic
1202Q8—284no—
1203Q8—562no—
1204D4—44no—
1205D4—562no—
1206D4—562no—
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—44no—
1241C2×C4—44no—
1242C2×C4—44no—
1243C2×C4—72no—
1244C2×C4—72no—
1245C2×C4—82no—
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—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×C4C2×#115712yes—
1291C2×C4C2×#115712yes—
1292C2×C4C2×#115712yes—
1293C2×C4C2×#115912yes—
1294C2×C4C2×#115912yes—
1295C2×C4D7×#4112yes—
1296C7#6002411yescharacteristic, complemented, Sylow
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—281no—
1312C22—281no—
1313C22—281no—
1314C22—281no—
1315C22—281no—
1316C22—281no—
1317C22—281no—
1318C22C22×#115711yescharacteristic
1319C22C22×#115911yescharacteristic
1320C22C2×D7×#4111yescharacteristic
1321C22#9061611yescharacteristic
1322C22#9061611yescharacteristic
1323C22#9061811yescharacteristic
1324C22#9062011yescharacteristic
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—142no—
1339C4—142no—
1340C4—281no—
1341C4—281no—
1342C4—281no—
1343C4—281no—
1344C4—281no—
1345C4—281no—
1346C4—281no—
1347C4—281no—
1348C4—281no—
1349C4—281no—
1350C4—281no—
1351C4—281no—
1352C4—281no—
1353C2—42no—
1354C2—81no—
1355C2—561no—
1356C2#1174283211yescharacteristic
1357C2#1174290811yescharacteristic
1358C2#1174296611yescharacteristic
1359C2#1174369511yescharacteristic
1360C2#1174375511yescharacteristic
1361C2#1174388111yescharacteristic
1362C2#1174391111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2359C2
prime radical#89995C22
hypercenter#2359D7
hypocenterC7#60024
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2359

Complements

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

NH ≅ G/Ntype
1. C7×#2359C2semidirect
3. #11740296C2semidirect
5. #11739782C2semidirect
6. #11739695C2semidirect
7. #11739674C2semidirect
8. #11733499C2semidirect
9. #11733498C2semidirect
10. #11733191C2semidirect
11. #11733065C2semidirect
12. #11733034C2semidirect
13. #11733005C2semidirect
14. #11732702C2semidirect
15. #11732485C2semidirect
16. #11732409C2semidirect
17. #11732384C2semidirect
19. #11732219C2semidirect
20. #11731987C2semidirect
21. #11731916C2semidirect
22. #11731893C2semidirect
23. #11731893C2semidirect
24. #11731135C2semidirect
25. #11731092C2semidirect
26. #11730994C2semidirect
27. #11730978C2semidirect
28. #11730920C2semidirect
29. #11730885C2semidirect
30. #11730801C2semidirect
31. #11730780C2semidirect
376. #2359D7semidirect
1296. C7#60024semidirect

Maximal subgroups

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

subgroupindex
C7×#23592
#117403002
#117402962
#117398102
#117397822
#117396952
#117396742
#117334992
#117334982
#117331912
#117330652
#117330342
#117330052
#117327022
#117324852
#117324092
#117323842
#117322912
#117322192
#117319872
#117319162
#117318932
#117311352
#117310922
#117309942
#117309782
#117309202
#117308852
#117308012
#117307802
#600247