Finite Group Databasebeta

← #34502804

Subgroups — #34502804

Order 20224.

1526 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23771737C211yesmaximal, characteristic, complemented
2#23771719C211yesmaximal, characteristic
3#23771390C211yesmaximal, characteristic, complemented
4#23771384C211yesmaximal, characteristic, complemented
5#23771323C211yesmaximal, characteristic, complemented
6#23771279C211yesmaximal, characteristic, complemented
7#23771219C211yesmaximal, characteristic, complemented
8#23771216C211yesmaximal, characteristic, complemented
9#23771192C211yesmaximal, characteristic, complemented
10#23771171C211yesmaximal, characteristic, complemented
11#23771156C211yesmaximal, characteristic, complemented
12#23771135C211yesmaximal, characteristic, complemented
13#23771092C211yesmaximal, characteristic, complemented
14#23770995C211yesmaximal, characteristic, complemented
15#23770966C211yesmaximal, characteristic, complemented
16#23770915C211yesmaximal, characteristic, complemented
17#23770864C211yesmaximal, characteristic, complemented
18#23770554C211yesmaximal, characteristic, complemented
19#23769373C211yesmaximal, characteristic, complemented
20#23769355C211yesmaximal, characteristic
21#23767903C211yesmaximal, characteristic, complemented
22#23767842C211yesmaximal, characteristic
23#23767785C211yesmaximal, characteristic, complemented
24#23767684C211yesmaximal, characteristic, complemented
25#23767218C211yesmaximal, characteristic
26#23767082C211yesmaximal, characteristic, complemented
27#23766803C211yesmaximal, characteristic
28#23766065C211yesmaximal, characteristic
29#23766019C211yesmaximal, characteristic, complemented
30C2×#19098445C211yesmaximal, characteristic, complemented
31C79×#2419C211yesmaximal, characteristic
32C2×#14579142C2211yescharacteristic
33C2×#14579138C2211yescharacteristic
34C2×#14579117C2211yescharacteristic
35C2×#14579117C2211yescharacteristic
36C22×Dic79⋊C4C2211yescharacteristic
37C22×Dic79⋊C4C2211yescharacteristic
38C22×C4×Dic79C2211yescharacteristic
39C79⋊#401C2211yescharacteristic
40C79⋊#401C2211yescharacteristic
41#19098505C2211yescharacteristic
42#19098505C2211yescharacteristic
43#19098505C2211yescharacteristic
44#19098505C2211yescharacteristic
45#19098504C2211yescharacteristic
46#19098504C2211yescharacteristic
47#19098504C2211yescharacteristic
48#19098504C2211yescharacteristic
49#19098504C2211yescharacteristic
50#19098504C2211yescharacteristic
51#19098504C2211yescharacteristic
52#19098503C2211yescharacteristic
53#19098503C2211yescharacteristic
54#19098503C2211yescharacteristic
55#19098502C2211yescharacteristic
56#19098502C2211yescharacteristic
57#19098502C2211yescharacteristic
58#19098501C2211yescharacteristic
59#19098499C2211yescharacteristic
60#19098497C2211yescharacteristic
61#19098497C2211yescharacteristic
62#19098497C2211yescharacteristic
63#19098497C2211yescharacteristic
64#19098496C2211yescharacteristic
65#19098496C2211yescharacteristic
66#19098496C2211yescharacteristic
67#19098495C2211yescharacteristic
68#19098495C2211yescharacteristic
69#19098494C2211yescharacteristic
70#19098494C2211yescharacteristic
71#19098494C2211yescharacteristic
72#19098493C2211yescharacteristic
73#19098491C2211yescharacteristic
74#19098491C2211yescharacteristic
75#19098491C2211yescharacteristic
76#19098488C2211yescharacteristic
77#19098486C2211yescharacteristic
78#19098486C2211yescharacteristic
79#19098486C2211yescharacteristic
80#19098486C2211yescharacteristic
81#19098483C2211yescharacteristic
82#19098475C2211yescharacteristic
83#19098469C2211yescharacteristic
84#19098467C2211yescharacteristic
85#19098467C2211yescharacteristic
86#19098467C2211yescharacteristic
87#19098460C2211yescharacteristic
88#19098460C2211yescharacteristic
89#19098460C2211yescharacteristic
90#19098460C2211yescharacteristic
91#19098460C2211yescharacteristic
92#19098459C2211yescharacteristic
93#19098459C2211yescharacteristic
94#19098458C2211yescharacteristic
95#19098458C2211yescharacteristic
96#19098458C2211yescharacteristic
97#19098458C2211yescharacteristic
98#19098458C2211yescharacteristic
99#19098457C2211yescharacteristic
100#19098457C2211yescharacteristic
101#19098457C2211yescharacteristic
102#19098456C2211yescharacteristic
103#19098451C2211yescharacteristic
104#19098451C2211yescharacteristic
105#19098451C2211yescharacteristic
106#19098451C2211yescharacteristic
107#19098451C2211yescharacteristic
108#19098451C2211yescharacteristic
109#19098450C2211yescharacteristic
110#19098450C2211yescharacteristic
111#19098450C2211yescharacteristic
112#19098449C2211yescharacteristic
113#19098449C2211yescharacteristic
114#19098448C2211yescharacteristic
115#19098447C2211yescharacteristic
116#19098447C2211yescharacteristic
117#19098447C2211yescharacteristic
118#19098446C2211yescharacteristic
119#19098446C2211yescharacteristic
120#19098446C2211yescharacteristic
121#19098446C2211yescharacteristic
122#19098446C2211yescharacteristic
123#19098445C2211yescharacteristic
124#19098445C2211yescharacteristic
125#19098445C2211yescharacteristic
126#19098445C2211yescharacteristic
127#19098445C2211yescharacteristic
128#19098445C2211yescharacteristic
129#19098445C2211yescharacteristic
130#19098445C2211yescharacteristic
131#19098445C2211yescharacteristic
132#19098445C2211yescharacteristic
133#19098445C2211yescharacteristic
134#19098445C2211yescharacteristic
135#19098445C2211yescharacteristic
136#19098444C2211yescharacteristic
137#19098444C2211yescharacteristic
138#19098444C2211yescharacteristic
139#19098444C2211yescharacteristic
140#19098444C2211yescharacteristic
141#19098443C2211yescharacteristic
142#19098443C2211yescharacteristic
143#19098443C2211yescharacteristic
144#19098438C2211yescharacteristic
145#19098438C2211yescharacteristic
146#19098438C2211yescharacteristic
147#19098436C2211yescharacteristic
148#19098436C2211yescharacteristic
149#19098436C2211yescharacteristic
150#19098436C2211yescharacteristic
151#19098436C2211yescharacteristic
152#19098435C2211yescharacteristic
153#19098435C2211yescharacteristic
154#19098435C2211yescharacteristic
155#19098435C2211yescharacteristic
156#19098432C2211yescharacteristic
157#19098432C2211yescharacteristic
158#19098430C2211yescharacteristic
159#19098427C2211yescharacteristic
160#19098427C2211yescharacteristic
161#19098427C2211yescharacteristic
162#19098426C2211yescharacteristic
163#19098426C2211yescharacteristic
164#19098424C2211yescharacteristic
165#19098423C2211yescharacteristic
166#19098423C2211yescharacteristic
167#19098421C2211yescharacteristic
168C4×C22⋊Dic79C2211yescharacteristic
169C2×C79⋊#95C2211yescharacteristic
170C2×C79⋊#95C2211yescharacteristic
171C2×C79⋊#95C2211yescharacteristic
172C2×#123×C79C2211yescharacteristic
173C2×C4×D4×C79C2211yescharacteristic
174#400×C79C2211yescharacteristic
175#398×C79C2211yescharacteristic
176#397×C79C2211yescharacteristic
177#397×C79C2211yescharacteristic
178#387×C79C2211yescharacteristic
179#387×C79C2211yescharacteristic
180#386×C79C2211yescharacteristic
181#385×C79C2211yescharacteristic
182#385×C79C2211yescharacteristic
183#381×C79C2211yescharacteristic
184#381×C79C2211yescharacteristic
185#380×C79C2211yescharacteristic
186C2×#95×C79C2211yescharacteristic
187C22×Dic158C2311yescharacteristic
188C23×Dic79C2311yescharacteristic
189C23×Dic79C2311yescharacteristic
190C23×Dic79C2311yescharacteristic
191C23×Dic79C2311yescharacteristic
192#14579142—24no—
193#14579138—42no—
194#14579117—24no—
195#14579117—42no—
196C2×C4⋊Dic79C2311yescharacteristic
197C2×C4⋊Dic79C2311yescharacteristic
198C2×C4⋊Dic79C2311yescharacteristic
199C2×C4⋊Dic79C2311yescharacteristic
200C2×C4⋊Dic79C2311yescharacteristic
201C2×C4⋊Dic79C2311yescharacteristic
202C2×C4⋊Dic79C2311yescharacteristic
203C2×C4⋊Dic79C2311yescharacteristic
204C2×C4⋊Dic79C2311yescharacteristic
205C2×Dic79⋊C4—24no—
206C2×Dic79⋊C4—42no—
207C2×Dic79⋊C4C2311yescharacteristic
208C2×Dic79⋊C4C2311yescharacteristic
209C2×Dic79⋊C4C2311yescharacteristic
210C2×Dic79⋊C4C2311yescharacteristic
211C2×Dic79⋊C4C2311yescharacteristic
212C2×Dic79⋊C4C2311yescharacteristic
213C2×Dic79⋊C4C2311yescharacteristic
214C2×Dic79⋊C4C2311yescharacteristic
215C2×Dic79⋊C4C2311yescharacteristic
216C2×Dic79⋊C4C2311yescharacteristic
217C2×Dic79⋊C4C2311yescharacteristic
218C2×Dic79⋊C4C2311yescharacteristic
219C2×Dic79⋊C4C2311yescharacteristic
220C2×Dic79⋊C4C2311yescharacteristic
221C2×Dic79⋊C4C2311yescharacteristic
222C2×Dic79⋊C4C2311yescharacteristic
223C2×Dic79⋊C4C2311yescharacteristic
224C2×Dic79⋊C4C2311yescharacteristic
225C2×Dic79⋊C4C2311yescharacteristic
226C2×Dic79⋊C4C2311yescharacteristic
227C2×Dic79⋊C4C2311yescharacteristic
228C2×Dic79⋊C4C2311yescharacteristic
229C2×Dic79⋊C4C2311yescharacteristic
230C2×Dic79⋊C4C2311yescharacteristic
231C2×Dic79⋊C4C2311yescharacteristic
232C2×Dic79⋊C4C2311yescharacteristic
233C2×Dic79⋊C4C2311yescharacteristic
234C2×Dic79⋊C4C2311yescharacteristic
235C2×Dic79⋊C4C2311yescharacteristic
236C2×Dic79⋊C4C2311yescharacteristic
237C2×C22⋊Dic79C2311yescharacteristic
238C2×C22⋊Dic79C2311yescharacteristic
239C2×C22⋊Dic79C2311yescharacteristic
240C2×C22⋊Dic79C2311yescharacteristic
241C2×C22⋊Dic79C2311yescharacteristic
242C2×C22⋊Dic79C2311yescharacteristic
243C2×C22⋊Dic79C2311yescharacteristic
244C2×C22⋊Dic79C2311yescharacteristic
245C2×C22⋊Dic79C2311yescharacteristic
246C2×C22⋊Dic79C2311yescharacteristic
247C2×C22⋊Dic79C2311yescharacteristic
248C2×C22⋊Dic79C2311yescharacteristic
249C2×C4×Dic79—42no—
250C2×C4×Dic79C2311yescharacteristic
251C2×C4×Dic79C2311yescharacteristic
252C2×C4×Dic79C2311yescharacteristic
253C2×C4×Dic79C2311yescharacteristic
254C2×C4×Dic79C2311yescharacteristic
255C2×C4×Dic79C2311yescharacteristic
256C2×C4×Dic79C2311yescharacteristic
257C2×C4×Dic79C2311yescharacteristic
258C2×C4×Dic79C2311yescharacteristic
259C2×C4×Dic79C2311yescharacteristic
260C79⋊#95C2311yescharacteristic
261C79⋊#95C2311yescharacteristic
262C79⋊#95C2311yescharacteristic
263C79⋊#95C2311yescharacteristic
264C79⋊#95C2311yescharacteristic
265C79⋊#95C2311yescharacteristic
266C79⋊#95C2311yescharacteristic
267C79⋊#95C2311yescharacteristic
268C79⋊#95C2311yescharacteristic
269C79⋊#95C2311yescharacteristic
270C79⋊#95C2311yescharacteristic
271C79⋊#95C2311yescharacteristic
272C79⋊#95C2311yescharacteristic
273C79⋊#95C2311yescharacteristic
274C79⋊#95C2311yescharacteristic
275C79⋊#95C2311yescharacteristic
276C79⋊#95C2311yescharacteristic
277C79⋊#95C2311yescharacteristic
278C79⋊#95C2311yescharacteristic
279C79⋊#95C2311yescharacteristic
280C79⋊#95C2311yescharacteristic
281C79⋊#95C2311yescharacteristic
282C79⋊#95C2311yescharacteristic
283C79⋊#95C2311yescharacteristic
284C79⋊#95C2311yescharacteristic
285C79⋊#95C2311yescharacteristic
286C79⋊#95C2311yescharacteristic
287C79⋊#95C2311yescharacteristic
288C79⋊#95C2311yescharacteristic
289C79⋊#95C2311yescharacteristic
290C79⋊#95C2311yescharacteristic
291C79⋊#95C2311yescharacteristic
292C79⋊#95C2311yescharacteristic
293C79⋊#95C2311yescharacteristic
294C79⋊#95C2311yescharacteristic
295C79⋊#95C2311yescharacteristic
296C79⋊#95C2311yescharacteristic
297C79⋊#95C2311yescharacteristic
298C79⋊#95C2311yescharacteristic
299C79⋊#95C2311yescharacteristic
300C79⋊#95C2311yescharacteristic
301C79⋊#95C2311yescharacteristic
302C79⋊#95C2311yescharacteristic
303C79⋊#95C2311yescharacteristic
304C79⋊#95C2311yescharacteristic
305C79⋊#95C2311yescharacteristic
306C79⋊#95C2311yescharacteristic
307C79⋊#95C2311yescharacteristic
308C79⋊#95C2311yescharacteristic
309C79⋊#95C2311yescharacteristic
310C79⋊#95C2311yescharacteristic
311C79⋊#95C2311yescharacteristic
312C79⋊#95C2311yescharacteristic
313C79⋊#95C2311yescharacteristic
314C22×D4×C79C2311yescharacteristic
315C23×C4×C79C2311yescharacteristic
316C23×C4×C79C2311yescharacteristic
317C23×C4×C79C2311yescharacteristic
318C23×C4×C79C2311yescharacteristic
319#123×C79—42no—
320C4×D4×C79—42no—
321C2×C4⋊C4×C79C2311yescharacteristic
322C2×C4⋊C4×C79C2311yescharacteristic
323C2×C4⋊C4×C79C2311yescharacteristic
324C2×C4⋊C4×C79C2311yescharacteristic
325C2×C4⋊C4×C79C2311yescharacteristic
326C2×C4⋊C4×C79C2311yescharacteristic
327C2×C4⋊C4×C79C2311yescharacteristic
328C2×C22⋊C4×C79C2311yescharacteristic
329C2×C22⋊C4×C79C2311yescharacteristic
330C2×C22⋊C4×C79C2311yescharacteristic
331C2×C22⋊C4×C79C2311yescharacteristic
332C2×C22⋊C4×C79C2311yescharacteristic
333C2×C22⋊C4×C79C2311yescharacteristic
334C2×C22⋊C4×C79C2311yescharacteristic
335C2×C22⋊C4×C79C2311yescharacteristic
336C2×C42×C79C2311yescharacteristic
337#95×C79C2311yescharacteristic
338#95×C79C2311yescharacteristic
339#95×C79C2311yescharacteristic
340#95×C79C2311yescharacteristic
341#95×C79C2311yescharacteristic
342#95×C79C2311yescharacteristic
343#95×C79C2311yescharacteristic
344#95×C79C2311yescharacteristic
345#95×C79C2311yescharacteristic
346#95×C79C2311yescharacteristic
347#95×C79C2311yescharacteristic
348#95×C79C2311yescharacteristic
349#95×C79C2311yescharacteristic
350#95×C79C2311yescharacteristic
351C2×Dic158—22no—
352C2×Dic158—41no—
353C2×Dic158—41no—
354C22×Dic79—22no—
355C22×Dic79—22no—
356C22×Dic79—22no—
357C22×Dic79—22no—
358C22×Dic79—22no—
359C22×Dic79—22no—
360C22×Dic79—41no—
361C22×Dic79—41no—
362C22×Dic79—41no—
363C22×Dic79—41no—
364C22×Dic79—41no—
365C22×Dic79#4114yes—
366C22×Dic79C2411yescharacteristic
367C22×Dic79C2411yescharacteristic
368C22×Dic79C2411yescharacteristic
369C22×Dic79C2411yescharacteristic
370C22×Dic79C2411yescharacteristic
371C22×Dic79C2411yescharacteristic
372C22×Dic79C2411yescharacteristic
373C22×Dic79C2411yescharacteristic
374C22×Dic79C2411yescharacteristic
375C22×Dic79C2411yescharacteristic
376C22×Dic79C2411yescharacteristic
377C22×Dic79C2411yescharacteristic
378C22×Dic79C2411yescharacteristic
379C22×Dic79C2411yescharacteristic
380C22×Dic79C2411yescharacteristic
381C22×Dic79C2411yescharacteristic
382C4⋊Dic79—41no—
383C4⋊Dic79—41no—
384C4⋊Dic79—41no—
385C4⋊Dic79—41no—
386C4⋊Dic79—41no—
387C4⋊Dic79—41no—
388C4⋊Dic79—41no—
389C4⋊Dic79—41no—
390C4⋊Dic79—41no—
391Dic79⋊C4—22no—
392Dic79⋊C4—22no—
393Dic79⋊C4—22no—
394Dic79⋊C4—22no—
395Dic79⋊C4—22no—
396Dic79⋊C4—22no—
397Dic79⋊C4—22no—
398Dic79⋊C4—22no—
399Dic79⋊C4—22no—
400Dic79⋊C4—22no—
401Dic79⋊C4—41no—
402Dic79⋊C4—41no—
403Dic79⋊C4—41no—
404Dic79⋊C4—41no—
405Dic79⋊C4—41no—
406Dic79⋊C4—41no—
407Dic79⋊C4—41no—
408Dic79⋊C4—41no—
409Dic79⋊C4—41no—
410Dic79⋊C4—41no—
411Dic79⋊C4—41no—
412Dic79⋊C4—41no—
413Dic79⋊C4—41no—
414Dic79⋊C4—41no—
415Dic79⋊C4—41no—
416Dic79⋊C4—41no—
417Dic79⋊C4—41no—
418Dic79⋊C4—41no—
419Dic79⋊C4—41no—
420Dic79⋊C4—41no—
421C22⋊Dic79—22no—
422C22⋊Dic79—22no—
423C22⋊Dic79—22no—
424C22⋊Dic79—22no—
425C22⋊Dic79—22no—
426C22⋊Dic79—22no—
427C22⋊Dic79—22no—
428C22⋊Dic79—41no—
429C22⋊Dic79—41no—
430C22⋊Dic79—41no—
431C22⋊Dic79—41no—
432C22⋊Dic79—41no—
433C4×Dic79—22no—
434C4×Dic79—22no—
435C4×Dic79—41no—
436C4×Dic79—41no—
437C4×Dic79—41no—
438C4×Dic79—41no—
439C4×Dic79—41no—
440C4×Dic79—41no—
441C4×Dic79—41no—
442C4×Dic79—41no—
443C24×C79C2411yescharacteristic
444C24×C79C2411yescharacteristic
445C2×D4×C79—22no—
446C2×D4×C79—22no—
447C2×D4×C79—22no—
448C22×C4×C79—22no—
449C22×C4×C79—22no—
450C22×C4×C79—22no—
451C22×C4×C79—22no—
452C22×C4×C79—22no—
453C22×C4×C79—41no—
454C22×C4×C79—41no—
455C22×C4×C79—41no—
456C22×C4×C79—41no—
457C22×C4×C79—41no—
458C22×C4×C79—41no—
459C22×C4×C79—41no—
460C22×C4×C79C2411yescharacteristic
461C22×C4×C79C2411yescharacteristic
462C22×C4×C79C2411yescharacteristic
463C22×C4×C79C2411yescharacteristic
464C22×C4×C79C2411yescharacteristic
465C22×C4×C79C2411yescharacteristic
466C22×C4×C79C2411yescharacteristic
467C22×C4×C79C2411yescharacteristic
468C22×C4×C79C2411yescharacteristic
469C22×C4×C79C2411yescharacteristic
470C22×C4×C79C2411yescharacteristic
471C22×C4×C79C2411yescharacteristic
472C22×C4×C79C2411yescharacteristic
473C4⋊C4×C79—41no—
474C4⋊C4×C79—41no—
475C4⋊C4×C79—41no—
476C4⋊C4×C79—41no—
477C4⋊C4×C79—41no—
478C4⋊C4×C79—41no—
479C4⋊C4×C79—41no—
480C22⋊C4×C79—22no—
481C22⋊C4×C79—22no—
482C22⋊C4×C79—22no—
483C22⋊C4×C79—41no—
484C22⋊C4×C79—41no—
485C22⋊C4×C79—41no—
486C22⋊C4×C79—41no—
487C22⋊C4×C79—41no—
488C42×C79—41no—
489C23×C79—21no—
490C23×C79—21no—
491C23×C79—21no—
492C23×C79—21no—
493C23×C79—21no—
494C23×C79—21no—
495C23×C79—21no—
496C23×C79—21no—
497C23×C79—21no—
498C23×C79—21no—
499C23×C79—21no—
500C23×C79C2×#4112yes—
501C23×C79H(5,𝔽2)12yes—
502C23×C792−1+412yes—
503C23×C79C2511yescharacteristic
504D4×C79—44no—
505C2×C4×C79—21no—
506C2×C4×C79—21no—
507C2×C4×C79—21no—
508C2×C4×C79—21no—
509C2×C4×C79—21no—
510C2×C4×C79—21no—
511C2×C4×C79—21no—
512C2×C4×C79—21no—
513C2×C4×C79—21no—
514C2×C4×C79—21no—
515C2×C4×C79—21no—
516C2×C4×C79—21no—
517C2×C4×C79—21no—
518C2×C4×C79—21no—
519C2×C4×C79—21no—
520C2×C4×C79—21no—
521C2×C4×C79—21no—
522C2×C4×C79—21no—
523C2×C4×C79—21no—
524C2×C4×C79—21no—
525C2×C4×C79—21no—
526C2×C4×C79—21no—
527C2×C4×C79—21no—
528C2×C4×C79—21no—
529C2×C4×C79—21no—
530C2×C4×C79—21no—
531C2×C4×C79—21no—
532C2×C4×C79—21no—
533C2×C4×C79—21no—
534C2×C4×C79—21no—
535C2×C4×C79—21no—
536C2×C4×C79—21no—
537C2×C4×C79—21no—
538C2×C4×C79—21no—
539C2×C4×C79—21no—
540C2×C4×C79—21no—
541C2×C4×C79—21no—
542C2×C4×C79—21no—
543C2×C4×C79—21no—
544C2×C4×C79—44no—
545C2×C4×C79—82no—
546C2×C4×C79—82no—
547C2×C4×C79—82no—
548C2×Dic79—28no—
549C2×Dic79—21no—
550C2×Dic79—21no—
551C2×Dic79—21no—
552C2×Dic79—21no—
553C2×Dic79—21no—
554C2×Dic79—21no—
555C2×Dic79—21no—
556C2×Dic79—21no—
557C2×Dic79—21no—
558C2×Dic79—21no—
559C2×Dic79—21no—
560C2×Dic79—21no—
561C2×Dic79—21no—
562C2×Dic79—21no—
563C2×Dic79—21no—
564C2×Dic79—21no—
565C2×Dic79—21no—
566C2×Dic79—21no—
567C2×Dic79—21no—
568C2×Dic79—21no—
569C2×Dic79—21no—
570C2×Dic79—21no—
571C2×Dic79—21no—
572C2×Dic79—21no—
573C2×Dic79—21no—
574C2×Dic79—21no—
575C2×Dic79—21no—
576C2×Dic79—21no—
577C2×Dic79—21no—
578C2×Dic79—21no—
579C2×Dic79—21no—
580C2×Dic79—21no—
581C2×Dic79—21no—
582C2×Dic79—21no—
583C2×Dic79—21no—
584C2×Dic79—21no—
585C2×Dic79—21no—
586C2×Dic79—21no—
587C2×Dic79—21no—
588C2×Dic79—21no—
589C2×Dic79—21no—
590C2×Dic79—21no—
591C2×Dic79—21no—
592C2×Dic79—21no—
593C2×Dic79—21no—
594C2×Dic79—44no—
595C2×Dic79—44no—
596C2×Dic79—44no—
597C2×Dic79C2×#4112yes—
598C2×Dic79C2×#4112yes—
599C2×Dic792−1+412yes—
600Dic158—82no—
601C22×C79—22no—
602C22×C79—22no—
603C22×C79—22no—
604C22×C79—22no—
605C22×C79—22no—
606C22×C79—22no—
607C22×C79—41no—
608C22×C79—41no—
609C22×C79—41no—
610C22×C79—41no—
611C22×C79—41no—
612C22×C79—41no—
613C22×C79—41no—
614C22×C79#53914yes—
615C22×C79C22×#4111yescharacteristic
616C22×C79C2×H(5,𝔽2)11yescharacteristic
617C22×C79C2×2−1+411yescharacteristic
618C22×C79C2×2−1+411yescharacteristic
619C22×C79#58511yescharacteristic
620C22×C79#58511yescharacteristic
621C22×C79#58511yescharacteristic
622C4×C79—41no—
623C4×C79—41no—
624C4×C79—41no—
625C4×C79—41no—
626C4×C79—41no—
627C4×C79—41no—
628C4×C79—41no—
629C4×C79—41no—
630C4×C79—41no—
631C4×C79—41no—
632C4×C79—41no—
633C4×C79—41no—
634C4×C79—41no—
635Dic79—22no—
636Dic79—22no—
637Dic79—22no—
638Dic79—41no—
639Dic79—41no—
640Dic79—41no—
641Dic79—41no—
642Dic79—41no—
643Dic79—41no—
644Dic79—41no—
645Dic79—41no—
646Dic79—41no—
647Dic79—41no—
648Dic79—41no—
649Dic79—41no—
650Dic79—41no—
651#36998—791nomaximal, Sylow
652C2×C79—24no—
653C2×C79—81no—
654C2×C79C2×#53911yescharacteristic
655C2×C79#349311yescharacteristic
656C2×C79#350711yescharacteristic
657C2×C79#353311yescharacteristic
658C2×C79#353511yescharacteristic
659C2×C79#356311yescharacteristic
660C2×C79#356411yescharacteristic
661#2855—791no—
662#2853—791no—
663#2810—791no—
664#2809—791no—
665#2802—791no—
666#2798—791no—
667#2794—791no—
668#2793—791no—
669#2791—791no—
670#2790—791no—
671#2789—791no—
672#2787—791no—
673#2783—791no—
674#2776—791no—
675#2775—791no—
676#2771—791no—
677#2767—791no—
678#2744—791no—
679#2646—791no—
680#2643—791no—
681#2505—791no—
682#2498—791no—
683#2493—791no—
684#2484—791no—
685#2450—791no—
686#2438—791no—
687#2419D7911yescharacteristic
688#2413—791no—
689#2322—791no—
690#2317—791no—
691C2×#387—791no—
692C79#3699811yescharacteristic, complemented, Sylow
693C2×#123—791no—
694C2×#123C2×D7911yescharacteristic
695C2×C22⋊Q8—791no—
696C2×C4×D4C2×D7911yescharacteristic
697C2×#117—791no—
698C2×#117—791no—
699C22×C4⋊C4—791no—
700C22×C4⋊C4—791no—
701C22×C42—791no—
702#401—791no—
703#401—791no—
704#400—791no—
705#400—791no—
706#400—791no—
707#400—791no—
708#400—791no—
709#400—791no—
710#400—791no—
711#400—791no—
712#400—791no—
713#400—791no—
714#400—791no—
715#400—791no—
716#400—791no—
717#400—791no—
718#400—791no—
719#400—791no—
720#400—791no—
721#400—791no—
722#400C2×D7911yescharacteristic
723#399—791no—
724#398—791no—
725#398—791no—
726#398—791no—
727#398—791no—
728#398—791no—
729#398—791no—
730#398—791no—
731#398—791no—
732#398—791no—
733#398—791no—
734#398—791no—
735#398—791no—
736#398—791no—
737#398C2×D7911yescharacteristic
738#397—791no—
739#397—791no—
740#397—791no—
741#397—791no—
742#397C2×D7911yescharacteristic
743#397C2×D7911yescharacteristic
744#396—791no—
745#396—791no—
746#396—791no—
747#396—791no—
748#395—791no—
749#393—791no—
750#391—791no—
751#391—791no—
752#391—791no—
753#391—791no—
754#389—791no—
755#389—791no—
756#389—791no—
757#389—791no—
758#389—791no—
759#389—791no—
760#389—791no—
761#389—791no—
762#389—791no—
763#389—791no—
764#389—791no—
765#389—791no—
766#388—791no—
767#388—791no—
768#388—791no—
769#388—791no—
770#388—791no—
771#388—791no—
772#388—791no—
773#388—791no—
774#388—791no—
775#388—791no—
776#387—791no—
777#387—791no—
778#387—791no—
779#387—791no—
780#387—791no—
781#387—791no—
782#387—791no—
783#387—791no—
784#387—791no—
785#387—791no—
786#387—791no—
787#387—791no—
788#387—791no—
789#387—791no—
790#387—791no—
791#387—791no—
792#387—791no—
793#387—791no—
794#387—791no—
795#387—791no—
796#387—791no—
797#387—791no—
798#387—791no—
799#387—791no—
800#387—791no—
801#387—791no—
802#387—791no—
803#387—791no—
804#387—791no—
805#387—791no—
806#387—791no—
807#387—791no—
808#387C2×D7911yescharacteristic
809#387C2×D7911yescharacteristic
810#386—791no—
811#386—791no—
812#386—791no—
813#386C2×D7911yescharacteristic
814#385—791no—
815#385—791no—
816#385—791no—
817#385—791no—
818#385—791no—
819#385—791no—
820#385—791no—
821#385—791no—
822#385—791no—
823#385—791no—
824#385—791no—
825#385—791no—
826#385C2×D7911yescharacteristic
827#385C2×D7911yescharacteristic
828#384—791no—
829#384—791no—
830#383—791no—
831#382—791no—
832#382—791no—
833#382—791no—
834#381—791no—
835#381—791no—
836#381—791no—
837#381C2×D7911yescharacteristic
838#381C2×D7911yescharacteristic
839#380—791no—
840#380—791no—
841#380—791no—
842#380C2×D7911yescharacteristic
843C4×C22⋊C4—791no—
844C2×#95—791no—
845C2×#95—791no—
846C2×#95—791no—
847C2×#95C2×D7911yescharacteristic
848C22×Q8—791no—
849C22×D4C22×D7911yescharacteristic
850C23×C4—791no—
851C23×C4—791no—
852C23×C4—791no—
853C23×C4—791no—
854C23×C4C22×D7911yescharacteristic
855C23×C4C22×D7911yescharacteristic
856C23×C4C22×D7911yescharacteristic
857C23×C4C22×D7911yescharacteristic
858#123—42no—
859#123—1584no—
860C22⋊Q8—3162no—
861C4×D4—42no—
862#117—3162no—
863#117—1584no—
864C2×C4⋊C4—3162no—
865C2×C4⋊C4—791no—
866C2×C4⋊C4—791no—
867C2×C4⋊C4—791no—
868C2×C4⋊C4—791no—
869C2×C4⋊C4—791no—
870C2×C4⋊C4—791no—
871C2×C4⋊C4—791no—
872C2×C4⋊C4—791no—
873C2×C4⋊C4—791no—
874C2×C4⋊C4—791no—
875C2×C4⋊C4—791no—
876C2×C4⋊C4—791no—
877C2×C4⋊C4—791no—
878C2×C4⋊C4—791no—
879C2×C4⋊C4—791no—
880C2×C4⋊C4—791no—
881C2×C4⋊C4—791no—
882C2×C4⋊C4—791no—
883C2×C4⋊C4—791no—
884C2×C4⋊C4—791no—
885C2×C4⋊C4—791no—
886C2×C4⋊C4—791no—
887C2×C4⋊C4—791no—
888C2×C4⋊C4—791no—
889C2×C4⋊C4—791no—
890C2×C4⋊C4—791no—
891C2×C4⋊C4—791no—
892C2×C4⋊C4—791no—
893C2×C4⋊C4—791no—
894C2×C4⋊C4—791no—
895C2×C4⋊C4—791no—
896C2×C4⋊C4—791no—
897C2×C4⋊C4—791no—
898C2×C4⋊C4—791no—
899C2×C4⋊C4—791no—
900C2×C4⋊C4—791no—
901C2×C4⋊C4—791no—
902C2×C4⋊C4—791no—
903C2×C4⋊C4—791no—
904C2×C4⋊C4—1584no—
905C2×C4⋊C4C22×D7911yescharacteristic
906C2×C4⋊C4C22×D7911yescharacteristic
907C2×C4⋊C4C22×D7911yescharacteristic
908C2×C4⋊C4C22×D7911yescharacteristic
909C2×C4⋊C4C22×D7911yescharacteristic
910C2×C4⋊C4C22×D7911yescharacteristic
911C2×C4⋊C4C22×D7911yescharacteristic
912C2×C22⋊C4—791no—
913C2×C22⋊C4—791no—
914C2×C22⋊C4—791no—
915C2×C22⋊C4—791no—
916C2×C22⋊C4—791no—
917C2×C22⋊C4—791no—
918C2×C22⋊C4—791no—
919C2×C22⋊C4—791no—
920C2×C22⋊C4—791no—
921C2×C22⋊C4—791no—
922C2×C22⋊C4—791no—
923C2×C22⋊C4—791no—
924C2×C22⋊C4C22×D7911yescharacteristic
925C2×C22⋊C4C22×D7911yescharacteristic
926C2×C22⋊C4C22×D7911yescharacteristic
927C2×C22⋊C4C22×D7911yescharacteristic
928C2×C22⋊C4C22×D7911yescharacteristic
929C2×C22⋊C4C22×D7911yescharacteristic
930C2×C22⋊C4C22×D7911yescharacteristic
931C2×C22⋊C4C22×D7911yescharacteristic
932C2×C42—3162no—
933C2×C42—791no—
934C2×C42—791no—
935C2×C42—791no—
936C2×C42—791no—
937C2×C42—791no—
938C2×C42—791no—
939C2×C42—791no—
940C2×C42—791no—
941C2×C42—791no—
942C2×C42—791no—
943C2×C42C22×D7911yescharacteristic
944#95—791no—
945#95—791no—
946#95—791no—
947#95—791no—
948#95—791no—
949#95—791no—
950#95—791no—
951#95—791no—
952#95—791no—
953#95—791no—
954#95—791no—
955#95—791no—
956#95—791no—
957#95—791no—
958#95—791no—
959#95—791no—
960#95—791no—
961#95—791no—
962#95—791no—
963#95—791no—
964#95—791no—
965#95—791no—
966#95—791no—
967#95—791no—
968#95—791no—
969#95—791no—
970#95—791no—
971#95—791no—
972#95—791no—
973#95—791no—
974#95—791no—
975#95—791no—
976#95—791no—
977#95—791no—
978#95—791no—
979#95—791no—
980#95—791no—
981#95—791no—
982#95—791no—
983#95—791no—
984#95—791no—
985#95—791no—
986#95—791no—
987#95—791no—
988#95—791no—
989#95—791no—
990#95—791no—
991#95—791no—
992#95—791no—
993#95—791no—
994#95—791no—
995#95—791no—
996#95—791no—
997#95—791no—
998#95C22×D7911yescharacteristic
999#95C22×D7911yescharacteristic
1000#95C22×D7911yescharacteristic
1001#95C22×D7911yescharacteristic
1002#95C22×D7911yescharacteristic
1003#95C22×D7911yescharacteristic
1004#95C22×D7911yescharacteristic
1005#95C22×D7911yescharacteristic
1006#95C22×D7911yescharacteristic
1007#95C22×D7911yescharacteristic
1008#95C22×D7911yescharacteristic
1009#95C22×D7911yescharacteristic
1010#95C22×D7911yescharacteristic
1011#95C22×D7911yescharacteristic
1012C24C23×D7911yescharacteristic
1013C24C23×D7911yescharacteristic
1014C2×Q8—3161no—
1015C2×Q8—3161no—
1016C2×Q8—1582no—
1017C2×D4—22no—
1018C2×D4—22no—
1019C2×D4—22no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—3161no—
1033C22×C4—3161no—
1034C22×C4—3161no—
1035C22×C4—3161no—
1036C22×C4—3161no—
1037C22×C4—794no—
1038C22×C4—791no—
1039C22×C4—791no—
1040C22×C4—791no—
1041C22×C4—791no—
1042C22×C4—791no—
1043C22×C4—791no—
1044C22×C4—791no—
1045C22×C4—791no—
1046C22×C4—791no—
1047C22×C4—791no—
1048C22×C4—791no—
1049C22×C4—791no—
1050C22×C4—791no—
1051C22×C4—791no—
1052C22×C4—791no—
1053C22×C4—791no—
1054C22×C4—1582no—
1055C22×C4—1582no—
1056C22×C4—1582no—
1057C22×C4—1582no—
1058C22×C4—1582no—
1059C22×C4—1582no—
1060C22×C4C23×D7911yescharacteristic
1061C22×C4C23×D7911yescharacteristic
1062C22×C4C23×D7911yescharacteristic
1063C22×C4C23×D7911yescharacteristic
1064C22×C4C23×D7911yescharacteristic
1065C22×C4C23×D7911yescharacteristic
1066C22×C4C23×D7911yescharacteristic
1067C22×C4C23×D7911yescharacteristic
1068C22×C4C23×D7911yescharacteristic
1069C22×C4C23×D7911yescharacteristic
1070C22×C4C23×D7911yescharacteristic
1071C22×C4C23×D7911yescharacteristic
1072C22×C4C23×D7911yescharacteristic
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—3161no—
1081C4⋊C4—3161no—
1082C4⋊C4—3161no—
1083C4⋊C4—3161no—
1084C4⋊C4—3161no—
1085C4⋊C4—3161no—
1086C4⋊C4—3161no—
1087C4⋊C4—3161no—
1088C4⋊C4—3161no—
1089C4⋊C4—3161no—
1090C4⋊C4—3161no—
1091C4⋊C4—3161no—
1092C4⋊C4—3161no—
1093C4⋊C4—3161no—
1094C4⋊C4—3161no—
1095C4⋊C4—3161no—
1096C4⋊C4—3161no—
1097C4⋊C4—3161no—
1098C4⋊C4—3161no—
1099C4⋊C4—3161no—
1100C4⋊C4—3161no—
1101C4⋊C4—3161no—
1102C4⋊C4—3161no—
1103C4⋊C4—3161no—
1104C4⋊C4—3161no—
1105C4⋊C4—3161no—
1106C4⋊C4—3161no—
1107C4⋊C4—3161no—
1108C4⋊C4—3161no—
1109C4⋊C4—1582no—
1110C4⋊C4—1582no—
1111C4⋊C4—1582no—
1112C4⋊C4—1582no—
1113C4⋊C4—1582no—
1114C4⋊C4—1582no—
1115C4⋊C4—1582no—
1116C4⋊C4—1582no—
1117C4⋊C4—1582no—
1118C4⋊C4—1582no—
1119C22⋊C4—22no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—41no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—3161no—
1128C22⋊C4—3161no—
1129C22⋊C4—3161no—
1130C22⋊C4—3161no—
1131C22⋊C4—3161no—
1132C22⋊C4—1582no—
1133C22⋊C4—1582no—
1134C22⋊C4—1582no—
1135C22⋊C4—1582no—
1136C22⋊C4—1582no—
1137C22⋊C4—1582no—
1138C22⋊C4—1582no—
1139C42—41no—
1140C42—3161no—
1141C42—3161no—
1142C42—3161no—
1143C42—3161no—
1144C42—3161no—
1145C42—3161no—
1146C42—3161no—
1147C42—3161no—
1148C42—1582no—
1149C42—1582no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23#41×D7912yes—
1162C23#1457920612yes—
1163C23#1457920812yes—
1164C23C24×D7911yescharacteristic
1165Q8—6322no—
1166D4—44no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
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—44no—
1207C2×C4—82no—
1208C2×C4—82no—
1209C2×C4—82no—
1210C2×C4—3164no—
1211C2×C4—3164no—
1212C2×C4—3164no—
1213C2×C4—792no—
1214C2×C4—792no—
1215C2×C4—792no—
1216C2×C4—1581no—
1217C2×C4—1581no—
1218C2×C4—1581no—
1219C2×C4—1581no—
1220C2×C4—1581no—
1221C2×C4—1581no—
1222C2×C4—1581no—
1223C2×C4—1581no—
1224C2×C4—1581no—
1225C2×C4—1581no—
1226C2×C4—1581no—
1227C2×C4—1581no—
1228C2×C4—1581no—
1229C2×C4—1581no—
1230C2×C4—1581no—
1231C2×C4—1581no—
1232C2×C4—1581no—
1233C2×C4—1581no—
1234C2×C4—1581no—
1235C2×C4—1581no—
1236C2×C4—1581no—
1237C2×C4—1581no—
1238C2×C4—1581no—
1239C2×C4—1581no—
1240C2×C4—1581no—
1241C2×C4—1581no—
1242C2×C4—1581no—
1243C2×C4—1581no—
1244C2×C4—1581no—
1245C2×C4—1581no—
1246C2×C4—1581no—
1247C2×C4—1581no—
1248C2×C4—1581no—
1249C2×C4—1581no—
1250C2×C4—1581no—
1251C2×C4—1581no—
1252C2×C4—1581no—
1253C2×C4—1581no—
1254C2×C4—1581no—
1255C2×C4—1581no—
1256C2×C4—1581no—
1257C2×C4—1581no—
1258C2×C4—1581no—
1259C2×C4—1581no—
1260C2×C4—1581no—
1261C2×C4—1588no—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22#1909915614yes—
1276C22C2×#41×D7911yescharacteristic
1277C22C2×#1457920611yescharacteristic
1278C222−1+4×D7911yescharacteristic
1279C22C2×#1457920811yescharacteristic
1280C22#1909939811yescharacteristic
1281C22#1909939911yescharacteristic
1282C22#1909939911yescharacteristic
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—3161no—
1297C4—3161no—
1298C4—3161no—
1299C4—3161no—
1300C4—3161no—
1301C4—3161no—
1302C4—3161no—
1303C4—3161no—
1304C4—3161no—
1305C4—3161no—
1306C4—3161no—
1307C4—3161no—
1308C4—3161no—
1309C4—1582no—
1310C4—1582no—
1311C4—1582no—
1312C2—24no—
1313C2—81no—
1314C2C2×#1909915611yescharacteristic
1315C2#2377711211yescharacteristic
1316C2#2377726011yescharacteristic
1317C2#2377755911yescharacteristic
1318C2#2377760111yescharacteristic
1319C2#2377799711yescharacteristic
1320C2#2377801211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutator, socle, cosocleC23×C79C25
FittingC79×#2419C2
prime radicalC22×D4×C79C23
hypercenter#2419D79
hypocenterC79#36998
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2419

Complements

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

NH ≅ G/Ntype
1. #23771737C2semidirect
3. #23771390C2semidirect
4. #23771384C2semidirect
5. #23771323C2semidirect
6. #23771279C2semidirect
7. #23771219C2semidirect
8. #23771216C2semidirect
9. #23771192C2semidirect
10. #23771171C2semidirect
11. #23771156C2semidirect
12. #23771135C2semidirect
13. #23771092C2semidirect
14. #23770995C2semidirect
15. #23770966C2semidirect
16. #23770915C2semidirect
17. #23770864C2semidirect
18. #23770554C2semidirect
19. #23769373C2semidirect
21. #23767903C2semidirect
23. #23767785C2semidirect
24. #23767684C2semidirect
26. #23767082C2semidirect
29. #23766019C2semidirect
30. C2×#19098445C2semidirect
692. C79#36998semidirect

Maximal subgroups

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

subgroupindex
#237717372
#237717192
#237713902
#237713842
#237713232
#237712792
#237712192
#237712162
#237711922
#237711712
#237711562
#237711352
#237710922
#237709952
#237709662
#237709152
#237708642
#237705542
#237693732
#237693552
#237679032
#237678422
#237677852
#237676842
#237672182
#237670822
#237668032
#237660652
#237660192
C2×#190984452
C79×#24192
#3699879