Finite Group Databasebeta

← #34503612

Subgroups — #34503612

Order 20224.

1420 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23771793C211yesmaximal, characteristic, complemented
2#23771791C211yesmaximal, characteristic, complemented
3#23771390C211yesmaximal, characteristic, complemented
4#23771389C211yesmaximal, characteristic, complemented
5#23771329C211yesmaximal, characteristic
6#23771326C211yesmaximal, characteristic
7#23771301C211yesmaximal, characteristic, complemented
8#23771296C211yesmaximal, characteristic, complemented
9#23770947C211yesmaximal, characteristic, complemented
10#23770942C211yesmaximal, characteristic, complemented
11#23770593C211yesmaximal, characteristic, complemented
12#23770592C211yesmaximal, characteristic, complemented
13#23770548C211yesmaximal, characteristic, complemented
14#23770547C211yesmaximal, characteristic, complemented
15#23770520C211yesmaximal, characteristic, complemented
16#23770518C211yesmaximal, characteristic, complemented
17#23770505C211yesmaximal, characteristic, complemented
18#23770498C211yesmaximal, characteristic, complemented
19#23769405C211yesmaximal, characteristic, complemented
20#23769403C211yesmaximal, characteristic, complemented
21#23769094C211yesmaximal, characteristic, complemented
22#23769059C211yesmaximal, characteristic, complemented
23#23768962C211yesmaximal, characteristic
24#23768945C211yesmaximal, characteristic, complemented
25#23768564C211yesmaximal, characteristic, complemented
26#23768219C211yesmaximal, characteristic, complemented
27#23768217C211yesmaximal, characteristic, complemented
28#23766199C211yesmaximal, characteristic, complemented
29#23766041C211yesmaximal, characteristic, complemented
30#23765896C211yesmaximal, characteristic, complemented
31C79×#2597C211yesmaximal, characteristic, complemented
32C2×#14579151C2211yescharacteristic
33C2×(C22⋊D79)⋊C4C2211yescharacteristic
34C2×#14579120C2211yescharacteristic
35#19098505C2211yescharacteristic
36#19098505C2211yescharacteristic
37#19098505C2211yescharacteristic
38#19098505C2211yescharacteristic
39#19098504C2211yescharacteristic
40#19098504C2211yescharacteristic
41#19098504C2211yescharacteristic
42#19098504C2211yescharacteristic
43#19098503C2211yescharacteristic
44#19098502C2211yescharacteristic
45#19098501C2211yescharacteristic
46#19098499C2211yescharacteristic
47#19098499C2211yescharacteristic
48#19098499C2211yescharacteristic
49#19098499C2211yescharacteristic
50#19098497C2211yescharacteristic
51#19098497C2211yescharacteristic
52#19098496C2211yescharacteristic
53#19098496C2211yescharacteristic
54#19098494C2211yescharacteristic
55#19098494C2211yescharacteristic
56#19098494C2211yescharacteristic
57#19098492C2211yescharacteristic
58#19098492C2211yescharacteristic
59#19098492C2211yescharacteristic
60#19098491C2211yescharacteristic
61#19098491C2211yescharacteristic
62#19098491C2211yescharacteristic
63#19098491C2211yescharacteristic
64#19098491C2211yescharacteristic
65#19098488C2211yescharacteristic
66#19098486C2211yescharacteristic
67#19098486C2211yescharacteristic
68#19098485C2211yescharacteristic
69#19098485C2211yescharacteristic
70#19098479C2211yescharacteristic
71#19098479C2211yescharacteristic
72#19098479C2211yescharacteristic
73#19098478C2211yescharacteristic
74#19098478C2211yescharacteristic
75#19098478C2211yescharacteristic
76#19098477C2211yescharacteristic
77#19098477C2211yescharacteristic
78#19098471C2211yescharacteristic
79#19098463C2211yescharacteristic
80#19098463C2211yescharacteristic
81#19098463C2211yescharacteristic
82#19098462C2211yescharacteristic
83#19098461C2211yescharacteristic
84#19098460C2211yescharacteristic
85#19098460C2211yescharacteristic
86#19098460C2211yescharacteristic
87#19098460C2211yescharacteristic
88#19098459C2211yescharacteristic
89#19098458C2211yescharacteristic
90#19098458C2211yescharacteristic
91#19098458C2211yescharacteristic
92#19098457C2211yescharacteristic
93#19098457C2211yescharacteristic
94#19098457C2211yescharacteristic
95#19098457C2211yescharacteristic
96#19098457C2211yescharacteristic
97#19098457C2211yescharacteristic
98#19098456C2211yescharacteristic
99#19098456C2211yescharacteristic
100#19098456C2211yescharacteristic
101#19098456C2211yescharacteristic
102#19098455C2211yescharacteristic
103#19098455C2211yescharacteristic
104#19098454C2211yescharacteristic
105#19098454C2211yescharacteristic
106#19098454C2211yescharacteristic
107#19098454C2211yescharacteristic
108#19098453C2211yescharacteristic
109#19098453C2211yescharacteristic
110#19098453C2211yescharacteristic
111#19098452C2211yescharacteristic
112#19098452C2211yescharacteristic
113#19098452C2211yescharacteristic
114#19098451C2211yescharacteristic
115#19098451C2211yescharacteristic
116#19098451C2211yescharacteristic
117#19098451C2211yescharacteristic
118#19098451C2211yescharacteristic
119#19098451C2211yescharacteristic
120#19098450C2211yescharacteristic
121#19098450C2211yescharacteristic
122#19098450C2211yescharacteristic
123#19098450C2211yescharacteristic
124#19098449C2211yescharacteristic
125#19098449C2211yescharacteristic
126#19098448C2211yescharacteristic
127#19098448C2211yescharacteristic
128#19098448C2211yescharacteristic
129#19098448C2211yescharacteristic
130#19098448C2211yescharacteristic
131#19098448C2211yescharacteristic
132#19098447C2211yescharacteristic
133#19098447C2211yescharacteristic
134#19098447C2211yescharacteristic
135#19098447C2211yescharacteristic
136#19098447C2211yescharacteristic
137#19098446C2211yescharacteristic
138#19098446C2211yescharacteristic
139#19098446C2211yescharacteristic
140#19098446C2211yescharacteristic
141#19098445C2211yescharacteristic
142#19098445C2211yescharacteristic
143#19098445C2211yescharacteristic
144#19098445C2211yescharacteristic
145#19098444C2211yescharacteristic
146#19098444C2211yescharacteristic
147#19098444C2211yescharacteristic
148#19098443C2211yescharacteristic
149#19098442C2211yescharacteristic
150#19098439C2211yescharacteristic
151#19098438C2211yescharacteristic
152#19098437C2211yescharacteristic
153#19098436C2211yescharacteristic
154#19098430C2211yescharacteristic
155#19098429C2211yescharacteristic
156#19098427C2211yescharacteristic
157#19098425C2211yescharacteristic
158#19098424C2211yescharacteristic
159#19098422C2211yescharacteristic
160#19098422C2211yescharacteristic
161#19098421C2211yescharacteristic
162#19098421C2211yescharacteristic
163#19098421C2211yescharacteristic
164#19098420C2211yescharacteristic
165C4×Dic79⋊C4C2211yescharacteristic
166C4×Dic79⋊C4C2211yescharacteristic
167C4×Dic79⋊C4C2211yescharacteristic
168C4×C22⋊Dic79C2211yescharacteristic
169#19098409C2211yescharacteristic
170#19098408C2211yescharacteristic
171C42×Dic79C2211yescharacteristic
172#400×C79C2211yescharacteristic
173#397×C79C2211yescharacteristic
174#397×C79C2211yescharacteristic
175#394×C79C2211yescharacteristic
176#390×C79C2211yescharacteristic
177#388×C79C2211yescharacteristic
178#388×C79C2211yescharacteristic
179#388×C79C2211yescharacteristic
180#388×C79C2211yescharacteristic
181#387×C79C2211yescharacteristic
182#387×C79C2211yescharacteristic
183#386×C79C2211yescharacteristic
184#385×C79C2211yescharacteristic
185C4×C4⋊C4×C79C2211yescharacteristic
186C4×C22⋊C4×C79C2211yescharacteristic
187C22×C22⋊D79C2311yescharacteristic
188C22×C22⋊D79C2311yescharacteristic
189C23×Dic79C2311yescharacteristic
190C22×C4×D79C2311yescharacteristic
191#14579151—24no—
192(C22⋊D79)⋊C4—24no—
193#14579120—24no—
194C2×C4⋊Dic79C2311yescharacteristic
195C2×C4⋊Dic79C2311yescharacteristic
196C2×C4⋊Dic79C2311yescharacteristic
197C2×C4⋊Dic79C2311yescharacteristic
198C2×C4⋊Dic79C2311yescharacteristic
199C2×C4⋊Dic79C2311yescharacteristic
200C2×C4⋊Dic79C2311yescharacteristic
201C2×C4⋊Dic79C2311yescharacteristic
202C2×C4⋊Dic79C2311yescharacteristic
203C2×Dic79⋊C4C2311yescharacteristic
204C2×Dic79⋊C4C2311yescharacteristic
205C2×Dic79⋊C4C2311yescharacteristic
206C2×Dic79⋊C4C2311yescharacteristic
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×C22⋊Dic79C2311yescharacteristic
228C2×C22⋊Dic79C2311yescharacteristic
229C2×C22⋊Dic79C2311yescharacteristic
230C2×C22⋊Dic79C2311yescharacteristic
231C2×C22⋊Dic79C2311yescharacteristic
232C2×C22⋊Dic79C2311yescharacteristic
233C2×C22⋊Dic79C2311yescharacteristic
234C2×C22⋊Dic79C2311yescharacteristic
235C2×C22⋊Dic79C2311yescharacteristic
236C2×C22⋊Dic79C2311yescharacteristic
237C2×C22⋊Dic79C2311yescharacteristic
238C2×C22⋊Dic79C2311yescharacteristic
239C2×C22⋊Dic79C2311yescharacteristic
240C2×(C2×D79)⋊C4C2311yescharacteristic
241C2×(C2×D79)⋊C4C2311yescharacteristic
242C2×(C2×D79)⋊C4C2311yescharacteristic
243C2×(C2×D79)⋊C4C2311yescharacteristic
244C2×(C2×D79)⋊C4C2311yescharacteristic
245C2×(C2×D79)⋊C4C2311yescharacteristic
246C2×(C2×D79)⋊C4C2311yescharacteristic
247C2×(C2×D79)⋊C4C2311yescharacteristic
248C2×(C2×D79)⋊C4C2311yescharacteristic
249C2×(C2×D79)⋊C4C2311yescharacteristic
250C2×(C2×D79)⋊C4C2311yescharacteristic
251C2×(C2×D79)⋊C4C2311yescharacteristic
252C2×C4×Dic79C2311yescharacteristic
253C2×C4×Dic79C2311yescharacteristic
254C2×C4×Dic79C2311yescharacteristic
255C2×C4×Dic79C2311yescharacteristic
256C2×C4×Dic79C2311yescharacteristic
257C2×C4×Dic79C2311yescharacteristic
258C2×C4×Dic79C2311yescharacteristic
259C2×C4×Dic79C2311yescharacteristic
260C2×C4×Dic79C2311yescharacteristic
261C2×C4×Dic79C2311yescharacteristic
262C2×C4×Dic79C2311yescharacteristic
263C2×C4×Dic79C2311yescharacteristic
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
310C22×D4×C79C2311yescharacteristic
311C23×C4×C79C2311yescharacteristic
312C2×C4⋊C4×C79C2311yescharacteristic
313C2×C4⋊C4×C79C2311yescharacteristic
314C2×C4⋊C4×C79C2311yescharacteristic
315C2×C4⋊C4×C79C2311yescharacteristic
316C2×C4⋊C4×C79C2311yescharacteristic
317C2×C4⋊C4×C79C2311yescharacteristic
318C2×C22⋊C4×C79C2311yescharacteristic
319C2×C22⋊C4×C79C2311yescharacteristic
320C2×C22⋊C4×C79C2311yescharacteristic
321C2×C22⋊C4×C79C2311yescharacteristic
322C2×C22⋊C4×C79C2311yescharacteristic
323C2×C22⋊C4×C79C2311yescharacteristic
324C2×C22⋊C4×C79C2311yescharacteristic
325C2×C22⋊C4×C79C2311yescharacteristic
326C2×C22⋊C4×C79C2311yescharacteristic
327C2×C22⋊C4×C79C2311yescharacteristic
328C2×C22⋊C4×C79C2311yescharacteristic
329C2×C42×C79C2311yescharacteristic
330C2×C42×C79C2311yescharacteristic
331C2×C42×C79C2311yescharacteristic
332C2×C42×C79C2311yescharacteristic
333#95×C79C2311yescharacteristic
334#95×C79C2311yescharacteristic
335#95×C79C2311yescharacteristic
336#95×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
345C23×D79C2411yescharacteristic
346C2×C22⋊D79—22no—
347C2×C22⋊D79—41no—
348C2×C22⋊D79—41no—
349C2×C22⋊D79—41no—
350C2×C22⋊D79—41no—
351C2×C22⋊D79—41no—
352C22×Dic79—22no—
353C22×Dic79—41no—
354C22×Dic79—41no—
355C22×Dic79C2411yescharacteristic
356C22×Dic79C2411yescharacteristic
357C22×Dic79C2411yescharacteristic
358C22×Dic79C2411yescharacteristic
359C22×Dic79C2411yescharacteristic
360C22×Dic79C2411yescharacteristic
361C22×Dic79C2411yescharacteristic
362C22×Dic79C2411yescharacteristic
363C22×Dic79C2411yescharacteristic
364C22×Dic79C2411yescharacteristic
365C22×Dic79C2411yescharacteristic
366C22×Dic79C2411yescharacteristic
367C22×Dic79C2411yescharacteristic
368C22×Dic79C2411yescharacteristic
369C22×Dic79C2411yescharacteristic
370C2×C4×D79—22no—
371C2×C4×D79—41no—
372C2×C4×D79—41no—
373C4⋊Dic79—22no—
374C4⋊Dic79—22no—
375C4⋊Dic79—22no—
376C4⋊Dic79—41no—
377C4⋊Dic79—41no—
378C4⋊Dic79—41no—
379C4⋊Dic79—41no—
380C4⋊Dic79—41no—
381C4⋊Dic79—41no—
382Dic79⋊C4—22no—
383Dic79⋊C4—22no—
384Dic79⋊C4—22no—
385Dic79⋊C4—22no—
386Dic79⋊C4—22no—
387Dic79⋊C4—41no—
388Dic79⋊C4—41no—
389Dic79⋊C4—41no—
390Dic79⋊C4—41no—
391Dic79⋊C4—41no—
392Dic79⋊C4—41no—
393Dic79⋊C4—41no—
394Dic79⋊C4—41no—
395Dic79⋊C4—41no—
396Dic79⋊C4—41no—
397Dic79⋊C4—41no—
398Dic79⋊C4—41no—
399Dic79⋊C4—41no—
400Dic79⋊C4—41no—
401Dic79⋊C4—41no—
402Dic79⋊C4—41no—
403Dic79⋊C4—41no—
404Dic79⋊C4—41no—
405Dic79⋊C4—41no—
406C22⋊Dic79—22no—
407C22⋊Dic79—22no—
408C22⋊Dic79—41no—
409C22⋊Dic79—41no—
410C22⋊Dic79—41no—
411C22⋊Dic79—41no—
412C22⋊Dic79—41no—
413C22⋊Dic79—41no—
414C22⋊Dic79—41no—
415C22⋊Dic79—41no—
416C22⋊Dic79—41no—
417C22⋊Dic79—41no—
418C22⋊Dic79—41no—
419(C2×D79)⋊C4—22no—
420(C2×D79)⋊C4—41no—
421(C2×D79)⋊C4—41no—
422(C2×D79)⋊C4—41no—
423(C2×D79)⋊C4—41no—
424(C2×D79)⋊C4—41no—
425(C2×D79)⋊C4—41no—
426(C2×D79)⋊C4—41no—
427(C2×D79)⋊C4—41no—
428(C2×D79)⋊C4—41no—
429(C2×D79)⋊C4—41no—
430(C2×D79)⋊C4—41no—
431C4×Dic79—22no—
432C4×Dic79—41no—
433C4×Dic79—41no—
434C4×Dic79—41no—
435C4×Dic79—41no—
436C4×Dic79—41no—
437C4×Dic79—41no—
438C4×Dic79—41no—
439C4×Dic79—41no—
440C4×Dic79—41no—
441C4×Dic79—41no—
442C4×Dic79#4114yes—
443C24×C79C2411yescharacteristic
444C24×C79C2411yescharacteristic
445C2×D4×C79—41no—
446C2×D4×C79—41no—
447C2×D4×C79—41no—
448C22×C4×C79—22no—
449C22×C4×C79—41no—
450C22×C4×C79—41no—
451C22×C4×C79C2411yescharacteristic
452C22×C4×C79C2411yescharacteristic
453C22×C4×C79C2411yescharacteristic
454C22×C4×C79C2411yescharacteristic
455C22×C4×C79C2411yescharacteristic
456C22×C4×C79C2411yescharacteristic
457C22×C4×C79C2411yescharacteristic
458C22×C4×C79C2411yescharacteristic
459C22×C4×C79C2411yescharacteristic
460C22×C4×C79C2411yescharacteristic
461C22×C4×C79C2411yescharacteristic
462C22×C4×C79C2411yescharacteristic
463C22×C4×C79C2411yescharacteristic
464C4⋊C4×C79—22no—
465C4⋊C4×C79—41no—
466C4⋊C4×C79—41no—
467C4⋊C4×C79—41no—
468C4⋊C4×C79—41no—
469C4⋊C4×C79—41no—
470C22⋊C4×C79—22no—
471C22⋊C4×C79—41no—
472C22⋊C4×C79—41no—
473C22⋊C4×C79—41no—
474C22⋊C4×C79—41no—
475C22⋊C4×C79—41no—
476C22⋊C4×C79—41no—
477C22⋊C4×C79—41no—
478C22⋊C4×C79—41no—
479C22⋊C4×C79—41no—
480C22⋊C4×C79—41no—
481C42×C79—41no—
482C42×C79—41no—
483C42×C79—41no—
484C42×C79—41no—
485C23×C79—21no—
486C23×C79—21no—
487C23×C79—21no—
488C23×C79—21no—
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×C79C2511yescharacteristic
500C22×D79—21no—
501C22×D79—21no—
502C22×D79—21no—
503C22×D79—21no—
504C22×D79—21no—
505C22×D79—21no—
506C22×D79—21no—
507D4×C79—82no—
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—21no—
545C2×C4×C79—21no—
546C2×C4×C79—44no—
547C2×C4×C79C2×#4112yes—
548C22⋊D79—44no—
549C22⋊D79—82no—
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—82no—
594C2×Dic79C2×#4112yes—
595C2×Dic79C2×#4112yes—
596C4×D79—82no—
597C22×C79—41no—
598C22×C79—41no—
599C22×C79—41no—
600C22×C79—41no—
601C22×C79—41no—
602C22×C79—41no—
603C22×C79—41no—
604C22×C79—41no—
605C22×C79—41no—
606C22×C79—41no—
607C22×C79—41no—
608C22×C79—41no—
609C22×C79—41no—
610C22×C79—41no—
611C22×C79C22×#4111yescharacteristic
612C22×C79#58511yescharacteristic
613C22×C79#58511yescharacteristic
614C22×C79#58511yescharacteristic
615C22×C79#58511yescharacteristic
616C22×C79#58511yescharacteristic
617C22×C79#58511yescharacteristic
618C2×D79—41no—
619C2×D79—41no—
620C2×D79—41no—
621C2×D79—41no—
622C2×D79—41no—
623C2×D79—41no—
624C2×D79—41no—
625C4×C79—22no—
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—
635C4×C79—41no—
636C4×C79—41no—
637C4×C79—41no—
638Dic79—22no—
639Dic79—22no—
640Dic79—41no—
641Dic79—41no—
642Dic79—41no—
643Dic79—41no—
644Dic79—41no—
645Dic79—41no—
646Dic79—41no—
647Dic79—41no—
648Dic79—41no—
649Dic79—41no—
650Dic79—41no—
651Dic79—41no—
652Dic79—41no—
653#37030—791nomaximal, Sylow
654C2×C79—81no—
655C2×C79—81no—
656C2×C79#345511yescharacteristic
657C2×C79#349311yescharacteristic
658C2×C79#351011yescharacteristic
659C2×C79#356611yescharacteristic
660C2×C79#356611yescharacteristic
661C2×C79#356711yescharacteristic
662C2×C79#356711yescharacteristic
663D79—81no—
664#2866—791no—
665#2866—791no—
666#2810—791no—
667#2810—791no—
668#2803—791no—
669#2803—791no—
670#2800—791no—
671#2800—791no—
672#2773—791no—
673#2773—791no—
674#2747—791no—
675#2747—791no—
676#2744—791no—
677#2744—791no—
678#2741—791no—
679#2741—791no—
680#2740—791no—
681#2740—791no—
682#2649—791no—
683#2649—791no—
684#2611—791no—
685#2606—791no—
686#2598—791no—
687#2597—791no—
688#2597D7911yescharacteristic, complemented
689#2562—791no—
690#2529—791no—
691#2529—791no—
692#2336—791no—
693#2319—791no—
694#2298—791no—
695C79#3703011yescharacteristic, complemented, Sylow
696C2×#125—791no—
697C2×C4×D4—791no—
698C2×#117—791no—
699#400—791no—
700#400—791no—
701#400—791no—
702#400—791no—
703#400—791no—
704#400—791no—
705#400—791no—
706#400—791no—
707#400—791no—
708#400—791no—
709#400—791no—
710#400C2×D7911yescharacteristic
711#399—791no—
712#399—791no—
713#399—791no—
714#399—791no—
715#398—791no—
716#398—791no—
717#398—791no—
718#398—791no—
719#398—791no—
720#398—791no—
721#398—791no—
722#397—791no—
723#397—791no—
724#397—791no—
725#397—791no—
726#397—791no—
727#397—791no—
728#397—791no—
729#397—791no—
730#397—791no—
731#397C2×D7911yescharacteristic
732#397C2×D7911yescharacteristic
733#396—791no—
734#396—791no—
735#396—791no—
736#396—791no—
737#394—791no—
738#394—791no—
739#394—791no—
740#394—791no—
741#394—791no—
742#394—791no—
743#394—791no—
744#394—791no—
745#394C2×D7911yescharacteristic
746#392—791no—
747#390—791no—
748#390—791no—
749#390—791no—
750#390C2×D7911yescharacteristic
751#389—791no—
752#389—791no—
753#389—791no—
754#389—791no—
755#389—791no—
756#389—791no—
757#389—791no—
758#389—791no—
759#389—791no—
760#389—791no—
761#388—791no—
762#388—791no—
763#388—791no—
764#388—791no—
765#388—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#388—791no—
777#388—791no—
778#388—791no—
779#388—791no—
780#388—791no—
781#388—791no—
782#388—791no—
783#388—791no—
784#388—791no—
785#388—791no—
786#388—791no—
787#388—791no—
788#388—791no—
789#388C2×D7911yescharacteristic
790#388C2×D7911yescharacteristic
791#388C2×D7911yescharacteristic
792#388C2×D7911yescharacteristic
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#387—791no—
809#387—791no—
810#387—791no—
811#387—791no—
812#387—791no—
813#387—791no—
814#387—791no—
815#387—791no—
816#387—791no—
817#387—791no—
818#387—791no—
819#387—791no—
820#387—791no—
821#387C2×D7911yescharacteristic
822#387C2×D7911yescharacteristic
823#386—791no—
824#386—791no—
825#386—791no—
826#386C2×D7911yescharacteristic
827#385—791no—
828#385—791no—
829#385—791no—
830#385C2×D7911yescharacteristic
831#383—791no—
832#382—791no—
833#382—791no—
834#381—791no—
835#381—791no—
836#380—791no—
837#380—791no—
838#380—791no—
839#380—791no—
840#380—791no—
841#380—791no—
842C4×C4⋊C4—791no—
843C4×C4⋊C4—791no—
844C4×C4⋊C4—791no—
845C4×C4⋊C4C2×D7911yescharacteristic
846C4×C22⋊C4—791no—
847C4×C22⋊C4C2×D7911yescharacteristic
848#376—791no—
849#376—791no—
850C43—791no—
851C22×D4—791no—
852C22×D4—791no—
853C22×D4C22×D7911yescharacteristic
854C23×C4—791no—
855C23×C4—791no—
856C23×C4C22×D7911yescharacteristic
857#125—1584no—
858C4×D4—1584no—
859#117—1584no—
860C2×C4⋊C4—791no—
861C2×C4⋊C4—791no—
862C2×C4⋊C4—791no—
863C2×C4⋊C4—791no—
864C2×C4⋊C4—791no—
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⋊C4C22×D7911yescharacteristic
894C2×C4⋊C4C22×D7911yescharacteristic
895C2×C4⋊C4C22×D7911yescharacteristic
896C2×C4⋊C4C22×D7911yescharacteristic
897C2×C4⋊C4C22×D7911yescharacteristic
898C2×C4⋊C4C22×D7911yescharacteristic
899C2×C22⋊C4—791no—
900C2×C22⋊C4—791no—
901C2×C22⋊C4—791no—
902C2×C22⋊C4—791no—
903C2×C22⋊C4—791no—
904C2×C22⋊C4—791no—
905C2×C22⋊C4—791no—
906C2×C22⋊C4—791no—
907C2×C22⋊C4—791no—
908C2×C22⋊C4—791no—
909C2×C22⋊C4—791no—
910C2×C22⋊C4—791no—
911C2×C22⋊C4—791no—
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×C22⋊C4C22×D7911yescharacteristic
933C2×C22⋊C4C22×D7911yescharacteristic
934C2×C22⋊C4C22×D7911yescharacteristic
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×C42—791no—
944C2×C42—791no—
945C2×C42—791no—
946C2×C42—791no—
947C2×C42C22×D7911yescharacteristic
948C2×C42C22×D7911yescharacteristic
949C2×C42C22×D7911yescharacteristic
950C2×C42C22×D7911yescharacteristic
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#95C22×D7911yescharacteristic
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
1009C24—791no—
1010C24C23×D7911yescharacteristic
1011C24C23×D7911yescharacteristic
1012C2×D4—41no—
1013C2×D4—41no—
1014C2×D4—41no—
1015C2×D4—3161no—
1016C2×D4—3161no—
1017C2×D4—3161no—
1018C2×D4—3161no—
1019C2×D4—3161no—
1020C2×D4—1582no—
1021C22×C4—22no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—3161no—
1025C22×C4—3161no—
1026C22×C4—3161no—
1027C22×C4—3161no—
1028C22×C4—791no—
1029C22×C4—791no—
1030C22×C4—791no—
1031C22×C4—791no—
1032C22×C4—791no—
1033C22×C4—791no—
1034C22×C4—791no—
1035C22×C4—791no—
1036C22×C4—791no—
1037C22×C4—791no—
1038C22×C4—791no—
1039C22×C4—791no—
1040C22×C4—791no—
1041C22×C4—791no—
1042C22×C4—791no—
1043C22×C4—1582no—
1044C22×C4—1582no—
1045C22×C4C23×D7911yescharacteristic
1046C22×C4C23×D7911yescharacteristic
1047C22×C4C23×D7911yescharacteristic
1048C22×C4C23×D7911yescharacteristic
1049C22×C4C23×D7911yescharacteristic
1050C22×C4C23×D7911yescharacteristic
1051C22×C4C23×D7911yescharacteristic
1052C22×C4C23×D7911yescharacteristic
1053C22×C4C23×D7911yescharacteristic
1054C22×C4C23×D7911yescharacteristic
1055C22×C4C23×D7911yescharacteristic
1056C22×C4C23×D7911yescharacteristic
1057C22×C4C23×D7911yescharacteristic
1058C4⋊C4—22no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—3161no—
1065C4⋊C4—3161no—
1066C4⋊C4—3161no—
1067C4⋊C4—3161no—
1068C4⋊C4—3161no—
1069C4⋊C4—3161no—
1070C4⋊C4—3161no—
1071C4⋊C4—3161no—
1072C4⋊C4—3161no—
1073C4⋊C4—3161no—
1074C4⋊C4—3161no—
1075C4⋊C4—3161no—
1076C4⋊C4—3161no—
1077C4⋊C4—3161no—
1078C4⋊C4—3161no—
1079C4⋊C4—3161no—
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—1582no—
1090C4⋊C4—1582no—
1091C4⋊C4—1582no—
1092C4⋊C4—1582no—
1093C4⋊C4—1582no—
1094C4⋊C4—1582no—
1095C4⋊C4—1582no—
1096C4⋊C4—1582no—
1097C22⋊C4—22no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—41no—
1108C22⋊C4—3161no—
1109C22⋊C4—3161no—
1110C22⋊C4—3161no—
1111C22⋊C4—3161no—
1112C22⋊C4—3161no—
1113C22⋊C4—3161no—
1114C22⋊C4—3161no—
1115C22⋊C4—3161no—
1116C22⋊C4—3161no—
1117C22⋊C4—3161no—
1118C22⋊C4—3161no—
1119C22⋊C4—3161no—
1120C22⋊C4—3161no—
1121C22⋊C4—3161no—
1122C22⋊C4—3161no—
1123C22⋊C4—3161no—
1124C22⋊C4—3161no—
1125C22⋊C4—3161no—
1126C22⋊C4—3161no—
1127C22⋊C4—3161no—
1128C22⋊C4—3161no—
1129C22⋊C4—3161no—
1130C22⋊C4—1582no—
1131C22⋊C4—1582no—
1132C22⋊C4—1582no—
1133C42—41no—
1134C42—41no—
1135C42—41no—
1136C42—41no—
1137C42—3161no—
1138C42—3161no—
1139C42—3161no—
1140C42—3161no—
1141C42—3161no—
1142C42—3161no—
1143C42—3161no—
1144C42—3161no—
1145C42—3161no—
1146C42—3161no—
1147C42—794no—
1148C42—1582no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—1581no—
1164C23—1581no—
1165C23—1581no—
1166C23—1581no—
1167C23—1581no—
1168C23—1581no—
1169C23—1581no—
1170C23C24×D7911yescharacteristic
1171D4—82no—
1172D4—3164no—
1173D4—6322no—
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—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—44no—
1213C2×C4—792no—
1214C2×C4—792no—
1215C2×C4—6322no—
1216C2×C4—6322no—
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#41×D7912yes—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—3161no—
1276C22—3161no—
1277C22—3161no—
1278C22—3161no—
1279C22—3161no—
1280C22—3161no—
1281C22—3161no—
1282C22C2×#41×D7911yescharacteristic
1283C22#1909939811yescharacteristic
1284C22#1909939811yescharacteristic
1285C22#1909939911yescharacteristic
1286C22#1909939911yescharacteristic
1287C22#1909939911yescharacteristic
1288C22#1909939911yescharacteristic
1289C4—22no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—3161no—
1303C4—3161no—
1304C4—3161no—
1305C4—3161no—
1306C4—3161no—
1307C4—3161no—
1308C4—3161no—
1309C4—3161no—
1310C4—3161no—
1311C4—3161no—
1312C4—3161no—
1313C4—3161no—
1314C4—3161no—
1315C4—1582no—
1316C4—1582no—
1317C2—81no—
1318C2—81no—
1319C2—6321no—
1320C2#2377678311yescharacteristic
1321C2#2377711511yescharacteristic
1322C2#2377728911yescharacteristic
1323C2#2377806111yescharacteristic
1324C2#2377806911yescharacteristic
1325C2#2377808411yescharacteristic
1326C2#2377808411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutator, socle, cosocleC23×C79C25
FittingC79×#2597C2
prime radical#19098471C22
hypercenter#2597D79
hypocenterC79#37030
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2597

Complements

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

NH ≅ G/Ntype
1. #23771793C2semidirect
2. #23771791C2semidirect
3. #23771390C2semidirect
4. #23771389C2semidirect
7. #23771301C2semidirect
8. #23771296C2semidirect
9. #23770947C2semidirect
10. #23770942C2semidirect
11. #23770593C2semidirect
12. #23770592C2semidirect
13. #23770548C2semidirect
14. #23770547C2semidirect
15. #23770520C2semidirect
16. #23770518C2semidirect
17. #23770505C2semidirect
18. #23770498C2semidirect
19. #23769405C2semidirect
20. #23769403C2semidirect
21. #23769094C2semidirect
22. #23769059C2semidirect
24. #23768945C2semidirect
25. #23768564C2semidirect
26. #23768219C2semidirect
27. #23768217C2semidirect
28. #23766199C2semidirect
29. #23766041C2semidirect
30. #23765896C2semidirect
31. C79×#2597C2semidirect
688. #2597D79semidirect
695. C79#37030semidirect

Maximal subgroups

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

subgroupindex
#237717932
#237717912
#237713902
#237713892
#237713292
#237713262
#237713012
#237712962
#237709472
#237709422
#237705932
#237705922
#237705482
#237705472
#237705202
#237705182
#237705052
#237704982
#237694052
#237694032
#237690942
#237690592
#237689622
#237689452
#237685642
#237682192
#237682172
#237661992
#237660412
#237658962
C79×#25972
#3703079