Finite Group Databasebeta

← C79×#17604 #34129293

Subgroups — C79×#17604 #34129293

Order 20224.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3494C211yesmaximal, characteristic
2C79×#2924C211yesmaximal, characteristic, complemented
3C79×#2343C211yesmaximal, characteristic, complemented
4C79×#1521C211yesmaximal, characteristic, complemented
5C79×#1517C211yesmaximal, characteristic, complemented
6C79×#1516C211yesmaximal, characteristic, complemented
7C79×#1514C211yesmaximal, characteristic, complemented
8C79×#1512C211yesmaximal, characteristic, complemented
9C79×#1510C211yesmaximal, characteristic, complemented
10C79×#1509C211yesmaximal, characteristic, complemented
11C79×#1505C211yesmaximal, characteristic, complemented
12C79×#1504C211yesmaximal, characteristic, complemented
13C79×#1502C211yesmaximal, characteristic, complemented
14C79×#1500C211yesmaximal, characteristic, complemented
15C2×#327×C79C211yesmaximal, characteristic, complemented
16#555×C79—21no—
17#553×C79—21no—
18#553×C79—21no—
19#551×C79—21no—
20#551×C79—21no—
21#547×C79—21no—
22#546×C79—21no—
23#546×C79—21no—
24#544×C79C411yescharacteristic, complemented
25#542×C79C411yescharacteristic, complemented
26#542×C79C411yescharacteristic, complemented
27#540×C79C411yescharacteristic, complemented
28#540×C79C411yescharacteristic, complemented
29#535×C79C411yescharacteristic, complemented
30#532×C79C2211yescharacteristic
31#532×C79C2211yescharacteristic
32#529×C79C2211yescharacteristic
33#529×C79C2211yescharacteristic
34#525×C79C2211yescharacteristic
35C2×#121×C79C2211yescharacteristic
36#520×C79C411yescharacteristic, complemented
37#518×C79C411yescharacteristic, complemented
38C2×#117×C79C2211yescharacteristic
39#433×C79—21no—
40#433×C79—21no—
41#432×C79C2211yescharacteristic, complemented
42#432×C79C2211yescharacteristic, complemented
43#431×C79C2211yescharacteristic, complemented
44#431×C79C2211yescharacteristic, complemented
45#424×C79—21no—
46#407×C79C2211yescharacteristic
47C2×C22⋊C8×C79C2211yescharacteristic
48#405×C79—21no—
49#387×C79—21no—
50#387×C79—21no—
51#385×C79—21no—
52#383×C79C2211yescharacteristic, complemented
53#382×C79C2211yescharacteristic, complemented
54#381×C79C2211yescharacteristic
55C4×C4⋊C4×C79C2211yescharacteristic, complemented
56C4×C22⋊C4×C79—21no—
57#376×C79C2211yescharacteristic, complemented
58C2×#95×C79C2211yescharacteristic
59#328×C79C2211yescharacteristic, complemented
60#328×C79C2211yescharacteristic, complemented
61#328×C79C2211yescharacteristic, complemented
62#328×C79C2211yescharacteristic, complemented
63#327×C79C2211yescharacteristic
64#327×C79C2211yescharacteristic
65#327×C79C2211yescharacteristic
66#327×C79C2211yescharacteristic
67#327×C79C2211yescharacteristic
68#327×C79C2211yescharacteristic
69#327×C79C2211yescharacteristic
70#327×C79C2211yescharacteristic
71#327×C79C2211yescharacteristic, complemented
72#327×C79C2211yescharacteristic, complemented
73#327×C79C2211yescharacteristic, complemented
74#327×C79C2211yescharacteristic, complemented
75C2×#41×C79—21no—
76C2×#41×C79—21no—
77C2×#41×C79C2×C411yescharacteristic
78C22×D4×C79—21no—
79C22×D4×C79C2×C411yescharacteristic
80C23×C4×C79—21no—
81C23×C4×C79C2311yescharacteristic
82C2×M16×C79—21no—
83C22×C8×C79—21no—
84C4⋊Q8×C79—21no—
85C4⋊Q8×C79C2×C411yescharacteristic, complemented
86C4⋊Q8×C79C2×C411yescharacteristic, complemented
87#127×C79C2×C411yescharacteristic, complemented
88#127×C79C2×C411yescharacteristic, complemented
89#126×C79—21no—
90#126×C79—21no—
91#126×C79—21no—
92#126×C79—21no—
93#125×C79—21no—
94#125×C79C2×C411yescharacteristic, complemented
95#125×C79C2×C411yescharacteristic, complemented
96#124×C79—21no—
97#124×C79—21no—
98#124×C79—21no—
99#124×C79—21no—
100#124×C79C2×C411yescharacteristic, complemented
101#124×C79C2×C411yescharacteristic, complemented
102#123×C79—21no—
103#123×C79—21no—
104#123×C79—21no—
105#123×C79—21no—
106#123×C79—21no—
107#123×C79—21no—
108#123×C79—21no—
109#123×C79—21no—
110#123×C79—21no—
111C22⋊Q8×C79—21no—
112C22⋊Q8×C79—21no—
113C22⋊Q8×C79—21no—
114C22⋊Q8×C79—21no—
115C22⋊Q8×C79C2×C411yescharacteristic
116C22⋊Q8×C79C2311yescharacteristic
117#121×C79—21no—
118#121×C79—21no—
119#121×C79—21no—
120#121×C79—21no—
121#121×C79—21no—
122#121×C79—21no—
123#121×C79—21no—
124#121×C79—21no—
125#121×C79—21no—
126#121×C79—21no—
127#121×C79C2×C411yescharacteristic
128#121×C79C2×C411yescharacteristic
129#121×C79C2×C411yescharacteristic
130#121×C79C2311yescharacteristic
131#121×C79C2311yescharacteristic
132#121×C79C2311yescharacteristic
133#120×C79—21no—
134#120×C79—21no—
135#120×C79—21no—
136C4×Q8×C79C2×C411yescharacteristic, complemented
137C4×Q8×C79C2×C411yescharacteristic, complemented
138C4×D4×C79—21no—
139C4×D4×C79—21no—
140C4×D4×C79—21no—
141C4×D4×C79—21no—
142C4×D4×C79—21no—
143C4×D4×C79—21no—
144C4×D4×C79—21no—
145C4×D4×C79—21no—
146C4×D4×C79—21no—
147C4×D4×C79—21no—
148C4×D4×C79C2×C411yescharacteristic, complemented
149C4×D4×C79C2×C411yescharacteristic, complemented
150C4×D4×C79C2×C411yescharacteristic, complemented
151C4×D4×C79C2×C411yescharacteristic, complemented
152C4×D4×C79C2×C411yescharacteristic, complemented
153C4×D4×C79C2×C411yescharacteristic, complemented
154#117×C79—21no—
155#117×C79—21no—
156#117×C79—21no—
157#117×C79C2×C411yescharacteristic
158#117×C79C2×C411yescharacteristic
159#117×C79C2×C411yescharacteristic
160#117×C79C2×C411yescharacteristic
161#117×C79C2×C411yescharacteristic
162#117×C79D411yescharacteristic
163#117×C79D411yescharacteristic
164#117×C79D411yescharacteristic
165#117×C79D411yescharacteristic
166C2×C4⋊C4×C79—21no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79C2×C411yescharacteristic
170C2×C4⋊C4×C79D411yescharacteristic
171C2×C4⋊C4×C79D411yescharacteristic
172C2×C22⋊C4×C79—21no—
173C2×C22⋊C4×C79—21no—
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176C2×C22⋊C4×C79D411yescharacteristic
177C2×C22⋊C4×C79D411yescharacteristic
178C2×C42×C79—21no—
179C2×C42×C79—21no—
180C2×C42×C79C2311yescharacteristic
181C2×C42×C79C2311yescharacteristic
182C4⋊C8×C79—21no—
183C4⋊C8×C79—21no—
184C4⋊C8×C79—21no—
185C4⋊C8×C79—21no—
186C22⋊C8×C79—21no—
187C22⋊C8×C79—21no—
188C22⋊C8×C79C2311yescharacteristic
189C22⋊C8×C79C2311yescharacteristic
190C22⋊C8×C79C2311yescharacteristic
191C22⋊C8×C79C2311yescharacteristic
192#97×C79—21no—
193#97×C79—21no—
194C4×C8×C79—21no—
195C4×C8×C79—21no—
196#95×C79—21no—
197#95×C79—21no—
198#95×C79—21no—
199#95×C79—21no—
200#95×C79—21no—
201#95×C79—21no—
202#95×C79C2311yescharacteristic
203#95×C79C2311yescharacteristic
204#95×C79C2311yescharacteristic
205#95×C79C2311yescharacteristic
206C24×C79—21no—
207C24×C79C2×D411yescharacteristic
208#41×C79—42no—
209#41×C79—81no—
210#41×C79—81no—
211#41×C79—81no—
212#41×C79—81no—
213C2×Q8×C79—21no—
214C2×Q8×C79—21no—
215C2×Q8×C79C22×C411yescharacteristic
216C2×D4×C79—21no—
217C2×D4×C79—21no—
218C2×D4×C79—21no—
219C2×D4×C79—21no—
220C2×D4×C79—21no—
221C2×D4×C79—21no—
222C2×D4×C79—21no—
223C2×D4×C79—21no—
224C2×D4×C79—21no—
225C2×D4×C79—21no—
226C2×D4×C79—21no—
227C2×D4×C79—21no—
228C2×D4×C79—42no—
229C2×D4×C79—81no—
230C2×D4×C79—81no—
231C2×D4×C79C22×C411yescharacteristic
232C2×D4×C79C22×C411yescharacteristic
233C2×D4×C79C22×C411yescharacteristic
234C22×C4×C79—21no—
235C22×C4×C79—21no—
236C22×C4×C79—21no—
237C22×C4×C79—21no—
238C22×C4×C79—21no—
239C22×C4×C79—21no—
240C22×C4×C79—21no—
241C22×C4×C79—21no—
242C22×C4×C79—21no—
243C22×C4×C79—21no—
244C22×C4×C79—21no—
245C22×C4×C79—21no—
246C22×C4×C79—42no—
247C22×C4×C79—42no—
248C22×C4×C79—42no—
249C22×C4×C79—81no—
250C22×C4×C79C22×C411yescharacteristic
251C22×C4×C79C22×C411yescharacteristic
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D411yescharacteristic
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2411yescharacteristic
260M16×C79—42no—
261C2×C8×C79—21no—
262C2×C8×C79—21no—
263C2×C8×C79—21no—
264C2×C8×C79—21no—
265C2×C8×C79—42no—
266C4⋊C4×C79—21no—
267C4⋊C4×C79—21no—
268C4⋊C4×C79—21no—
269C4⋊C4×C79—21no—
270C4⋊C4×C79—21no—
271C4⋊C4×C79—21no—
272C4⋊C4×C79—21no—
273C4⋊C4×C79—21no—
274C4⋊C4×C79—21no—
275C4⋊C4×C79—21no—
276C4⋊C4×C79—21no—
277C4⋊C4×C79—42no—
278C4⋊C4×C79—81no—
279C4⋊C4×C79C22⋊C411yescharacteristic
280C4⋊C4×C79C22⋊C411yescharacteristic
281C4⋊C4×C79C22⋊C411yescharacteristic
282C4⋊C4×C79C22⋊C411yescharacteristic
283C4⋊C4×C79C22⋊C411yescharacteristic
284C4⋊C4×C79C22⋊C411yescharacteristic
285C4⋊C4×C79C22⋊C411yescharacteristic
286C4⋊C4×C79C22⋊C411yescharacteristic
287C4⋊C4×C79C22×C411yescharacteristic
288C4⋊C4×C79C22×C411yescharacteristic
289C4⋊C4×C79C22×C411yescharacteristic
290C4⋊C4×C79C22×C411yescharacteristic
291C22⋊C4×C79—21no—
292C22⋊C4×C79—21no—
293C22⋊C4×C79—21no—
294C22⋊C4×C79—21no—
295C22⋊C4×C79—21no—
296C22⋊C4×C79—21no—
297C22⋊C4×C79—21no—
298C22⋊C4×C79—21no—
299C22⋊C4×C79—21no—
300C22⋊C4×C79—21no—
301C22⋊C4×C79—21no—
302C22⋊C4×C79—21no—
303C22⋊C4×C79—21no—
304C22⋊C4×C79—21no—
305C22⋊C4×C79—21no—
306C22⋊C4×C79—21no—
307C22⋊C4×C79—21no—
308C22⋊C4×C79—21no—
309C22⋊C4×C79—21no—
310C22⋊C4×C79—42no—
311C22⋊C4×C79C22⋊C411yescharacteristic
312C22⋊C4×C79C22⋊C411yescharacteristic
313C22⋊C4×C79C22⋊C411yescharacteristic
314C22⋊C4×C79C22⋊C411yescharacteristic
315C22⋊C4×C79C22⋊C411yescharacteristic
316C22⋊C4×C79C22⋊C411yescharacteristic
317C22⋊C4×C79C22⋊C411yescharacteristic
318C22⋊C4×C79C22⋊C411yescharacteristic
319C42×C79—21no—
320C42×C79—21no—
321C42×C79—21no—
322C42×C79—42no—
323C42×C79—81no—
324C42×C79C22×C411yescharacteristic
325C42×C79C22×C411yescharacteristic
326C42×C79C22×C411yescharacteristic
327C42×C79C22×C411yescharacteristic
328C42×C79C2×D411yescharacteristic
329C42×C79C2×D411yescharacteristic
330C42×C79C2×D411yescharacteristic
331C42×C79C2×D411yescharacteristic
332C23×C79—21no—
333C23×C79—21no—
334C23×C79—22no—
335C23×C79—21no—
336C23×C79—21no—
337C23×C79—21no—
338C23×C79—41no—
339C23×C79—42no—
340C23×C79—81no—
341C23×C79—81no—
342C23×C79C2×C22⋊C411yescharacteristic
343C23×C79C2×C22⋊C411yescharacteristic
344C23×C79C22×D411yescharacteristic
345Q8×C79—41no—
346Q8×C79—81no—
347Q8×C79—81no—
348D4×C79—41no—
349D4×C79—41no—
350D4×C79—41no—
351D4×C79—42no—
352D4×C79—41no—
353D4×C79—41no—
354D4×C79—41no—
355D4×C79—41no—
356D4×C79—41no—
357D4×C79—41no—
358D4×C79—42no—
359D4×C79—81no—
360D4×C79—81no—
361D4×C79—81no—
362D4×C79—81no—
363D4×C79—81no—
364D4×C79—81no—
365D4×C79—81no—
366C2×C4×C79—21no—
367C2×C4×C79—21no—
368C2×C4×C79—21no—
369C2×C4×C79—21no—
370C2×C4×C79—22no—
371C2×C4×C79—22no—
372C2×C4×C79—22no—
373C2×C4×C79—21no—
374C2×C4×C79—21no—
375C2×C4×C79—21no—
376C2×C4×C79—21no—
377C2×C4×C79—21no—
378C2×C4×C79—41no—
379C2×C4×C79—41no—
380C2×C4×C79—41no—
381C2×C4×C79—41no—
382C2×C4×C79—41no—
383C2×C4×C79—41no—
384C2×C4×C79—42no—
385C2×C4×C79—41no—
386C2×C4×C79—41no—
387C2×C4×C79—41no—
388C2×C4×C79—41no—
389C2×C4×C79—41no—
390C2×C4×C79—41no—
391C2×C4×C79—41no—
392C2×C4×C79—41no—
393C2×C4×C79—41no—
394C2×C4×C79—41no—
395C2×C4×C79—41no—
396C2×C4×C79—81no—
397C2×C4×C79—81no—
398C2×C4×C79—81no—
399C2×C4×C79—81no—
400C2×C4×C79—81no—
401C2×C4×C79—81no—
402C2×C4×C79—81no—
403C2×C4×C79—84no—
404C2×C4×C79C2×C22⋊C411yescharacteristic
405C2×C4×C79C2×C22⋊C411yescharacteristic
406C2×C4×C79C2×C22⋊C411yescharacteristic
407C2×C4×C79C2×C22⋊C411yescharacteristic
408C2×C4×C79C2×C22⋊C411yescharacteristic
409C2×C4×C79C2×C22⋊C411yescharacteristic
410C2×C4×C79C2×C22⋊C411yescharacteristic
411C2×C4×C79C2×C22⋊C411yescharacteristic
412C2×C4×C79C2×C22⋊C411yescharacteristic
413C2×C4×C79C2×C22⋊C411yescharacteristic
414C2×C4×C79C23×C411yescharacteristic
415C2×C4×C79C22×D411yescharacteristic
416C8×C79—41no—
417C8×C79—41no—
418C8×C79—41no—
419C8×C79—41no—
420C22×C79—21no—
421C22×C79—21no—
422C22×C79—21no—
423C22×C79—21no—
424C22×C79—21no—
425C22×C79—21no—
426C22×C79—21no—
427C22×C79—42no—
428C22×C79—42no—
429C22×C79—41no—
430C22×C79—41no—
431C22×C79—41no—
432C22×C79—41no—
433C22×C79—41no—
434C22×C79—41no—
435C22×C79—41no—
436C22×C79—41no—
437C22×C79—41no—
438C22×C79—162no—
439C22×C79#41012yes—
440C22×C79C22×C22⋊C411yescharacteristic
441C22×C79#57611yescharacteristic
442C22×C79#57711yescharacteristic
443C4×C79—21no—
444C4×C79—21no—
445C4×C79—21no—
446C4×C79—21no—
447C4×C79—21no—
448C4×C79—21no—
449C4×C79—21no—
450C4×C79—21no—
451C4×C79—21no—
452C4×C79—21no—
453C4×C79—21no—
454C4×C79—21no—
455C4×C79—42no—
456C4×C79—41no—
457C4×C79—41no—
458C4×C79—41no—
459C4×C79—41no—
460C4×C79—41no—
461C4×C79—81no—
462C4×C79—81no—
463C4×C79—81no—
464#17604C7911yesmaximal, characteristic, direct product factor, Sylow
465C2×C79—21no—
466C2×C79—21no—
467C2×C79—22no—
468C2×C79—41no—
469C2×C79—81no—
470C2×C79—81no—
471C2×C79—81no—
472C2×C79C2×#41011yescharacteristic
473C2×C79#289711yescharacteristic
474C2×C79#290111yescharacteristic
475#3494C2×C7911yescharacteristic
476#2924C2×C7911yescharacteristic, complemented
477#2343C2×C7911yescharacteristic, complemented
478#1521C2×C7911yescharacteristic, complemented
479#1517C2×C7911yescharacteristic, complemented
480#1516C2×C7911yescharacteristic, complemented
481#1514C2×C7911yescharacteristic, complemented
482#1512C2×C7911yescharacteristic, complemented
483#1510C2×C7911yescharacteristic, complemented
484#1509C2×C7911yescharacteristic, complemented
485#1505C2×C7911yescharacteristic, complemented
486#1504C2×C7911yescharacteristic, complemented
487#1502C2×C7911yescharacteristic, complemented
488#1500C2×C7911yescharacteristic, complemented
489C2×#327C2×C7911yescharacteristic, complemented
490C79#1760411yescharacteristic, direct product factor, Sylow
491#555—21no—
492#553—21no—
493#553—21no—
494#551—21no—
495#551—21no—
496#547—21no—
497#546—21no—
498#546—21no—
499#544C4×C7911yescharacteristic, complemented
500#542C4×C7911yescharacteristic, complemented
501#542C4×C7911yescharacteristic, complemented
502#540C4×C7911yescharacteristic, complemented
503#540C4×C7911yescharacteristic, complemented
504#535C4×C7911yescharacteristic, complemented
505#532C22×C7911yescharacteristic
506#532C22×C7911yescharacteristic
507#529C22×C7911yescharacteristic
508#529C22×C7911yescharacteristic
509#525C22×C7911yescharacteristic
510C2×#121C22×C7911yescharacteristic
511#520C4×C7911yescharacteristic, complemented
512#518C4×C7911yescharacteristic, complemented
513C2×#117C22×C7911yescharacteristic
514#433—21no—
515#433—21no—
516#432C22×C7911yescharacteristic, complemented
517#432C22×C7911yescharacteristic, complemented
518#431C22×C7911yescharacteristic, complemented
519#431C22×C7911yescharacteristic, complemented
520#424—21no—
521#407C22×C7911yescharacteristic
522C2×C22⋊C8C22×C7911yescharacteristic
523#405—21no—
524#387—21no—
525#387—21no—
526#385—21no—
527#383C22×C7911yescharacteristic, complemented
528#382C22×C7911yescharacteristic, complemented
529#381C22×C7911yescharacteristic
530C4×C4⋊C4C22×C7911yescharacteristic, complemented
531C4×C22⋊C4—21no—
532#376C22×C7911yescharacteristic, complemented
533C2×#95C22×C7911yescharacteristic
534#328C22×C7911yescharacteristic, complemented
535#328C22×C7911yescharacteristic, complemented
536#328C22×C7911yescharacteristic, complemented
537#328C22×C7911yescharacteristic, complemented
538#327C22×C7911yescharacteristic
539#327C22×C7911yescharacteristic
540#327C22×C7911yescharacteristic
541#327C22×C7911yescharacteristic
542#327C22×C7911yescharacteristic
543#327C22×C7911yescharacteristic
544#327C22×C7911yescharacteristic
545#327C22×C7911yescharacteristic
546#327C22×C7911yescharacteristic, complemented
547#327C22×C7911yescharacteristic, complemented
548#327C22×C7911yescharacteristic, complemented
549#327C22×C7911yescharacteristic, complemented
550C2×#41—21no—
551C2×#41—21no—
552C2×#41C2×C4×C7911yescharacteristic
553C22×D4—21no—
554C22×D4C2×C4×C7911yescharacteristic
555C23×C4—21no—
556C23×C4C23×C7911yescharacteristic
557C2×M16—21no—
558C22×C8—21no—
559C4⋊Q8—21no—
560C4⋊Q8C2×C4×C7911yescharacteristic, complemented
561C4⋊Q8C2×C4×C7911yescharacteristic, complemented
562#127C2×C4×C7911yescharacteristic, complemented
563#127C2×C4×C7911yescharacteristic, complemented
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#125—21no—
569#125C2×C4×C7911yescharacteristic, complemented
570#125C2×C4×C7911yescharacteristic, complemented
571#124—21no—
572#124—21no—
573#124—21no—
574#124—21no—
575#124C2×C4×C7911yescharacteristic, complemented
576#124C2×C4×C7911yescharacteristic, complemented
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8C2×C4×C7911yescharacteristic
591C22⋊Q8C23×C7911yescharacteristic
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121C2×C4×C7911yescharacteristic
603#121C2×C4×C7911yescharacteristic
604#121C2×C4×C7911yescharacteristic
605#121C23×C7911yescharacteristic
606#121C23×C7911yescharacteristic
607#121C23×C7911yescharacteristic
608#120—21no—
609#120—21no—
610#120—21no—
611C4×Q8C2×C4×C7911yescharacteristic, complemented
612C4×Q8C2×C4×C7911yescharacteristic, complemented
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4C2×C4×C7911yescharacteristic, complemented
624C4×D4C2×C4×C7911yescharacteristic, complemented
625C4×D4C2×C4×C7911yescharacteristic, complemented
626C4×D4C2×C4×C7911yescharacteristic, complemented
627C4×D4C2×C4×C7911yescharacteristic, complemented
628C4×D4C2×C4×C7911yescharacteristic, complemented
629#117—21no—
630#117—21no—
631#117—21no—
632#117C2×C4×C7911yescharacteristic
633#117C2×C4×C7911yescharacteristic
634#117C2×C4×C7911yescharacteristic
635#117C2×C4×C7911yescharacteristic
636#117C2×C4×C7911yescharacteristic
637#117D4×C7911yescharacteristic
638#117D4×C7911yescharacteristic
639#117D4×C7911yescharacteristic
640#117D4×C7911yescharacteristic
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4C2×C4×C7911yescharacteristic
645C2×C4⋊C4D4×C7911yescharacteristic
646C2×C4⋊C4D4×C7911yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C7911yescharacteristic
652C2×C22⋊C4D4×C7911yescharacteristic
653C2×C42—21no—
654C2×C42—21no—
655C2×C42C23×C7911yescharacteristic
656C2×C42C23×C7911yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—21no—
660C4⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8C23×C7911yescharacteristic
664C22⋊C8C23×C7911yescharacteristic
665C22⋊C8C23×C7911yescharacteristic
666C22⋊C8C23×C7911yescharacteristic
667#97—21no—
668#97—21no—
669C4×C8—21no—
670C4×C8—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95C23×C7911yescharacteristic
678#95C23×C7911yescharacteristic
679#95C23×C7911yescharacteristic
680#95C23×C7911yescharacteristic
681C24—21no—
682C24C2×D4×C7911yescharacteristic
683#41—42no—
684#41—81no—
685#41—81no—
686#41—81no—
687#41—81no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8C22×C4×C7911yescharacteristic
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4C22×C4×C7911yescharacteristic
707C2×D4C22×C4×C7911yescharacteristic
708C2×D4C22×C4×C7911yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—81no—
725C22×C4C22×C4×C7911yescharacteristic
726C22×C4C22×C4×C7911yescharacteristic
727C22×C4C2×D4×C7911yescharacteristic
728C22×C4C2×D4×C7911yescharacteristic
729C22×C4C2×D4×C7911yescharacteristic
730C22×C4C2×D4×C7911yescharacteristic
731C22×C4C2×D4×C7911yescharacteristic
732C22×C4C2×D4×C7911yescharacteristic
733C22×C4C2×D4×C7911yescharacteristic
734C22×C4C24×C7911yescharacteristic
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—42no—
753C4⋊C4—81no—
754C4⋊C4C22⋊C4×C7911yescharacteristic
755C4⋊C4C22⋊C4×C7911yescharacteristic
756C4⋊C4C22⋊C4×C7911yescharacteristic
757C4⋊C4C22⋊C4×C7911yescharacteristic
758C4⋊C4C22⋊C4×C7911yescharacteristic
759C4⋊C4C22⋊C4×C7911yescharacteristic
760C4⋊C4C22⋊C4×C7911yescharacteristic
761C4⋊C4C22⋊C4×C7911yescharacteristic
762C4⋊C4C22×C4×C7911yescharacteristic
763C4⋊C4C22×C4×C7911yescharacteristic
764C4⋊C4C22×C4×C7911yescharacteristic
765C4⋊C4C22×C4×C7911yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—42no—
786C22⋊C4C22⋊C4×C7911yescharacteristic
787C22⋊C4C22⋊C4×C7911yescharacteristic
788C22⋊C4C22⋊C4×C7911yescharacteristic
789C22⋊C4C22⋊C4×C7911yescharacteristic
790C22⋊C4C22⋊C4×C7911yescharacteristic
791C22⋊C4C22⋊C4×C7911yescharacteristic
792C22⋊C4C22⋊C4×C7911yescharacteristic
793C22⋊C4C22⋊C4×C7911yescharacteristic
794C42—21no—
795C42—21no—
796C42—21no—
797C42—42no—
798C42—81no—
799C42C22×C4×C7911yescharacteristic
800C42C22×C4×C7911yescharacteristic
801C42C22×C4×C7911yescharacteristic
802C42C22×C4×C7911yescharacteristic
803C42C2×D4×C7911yescharacteristic
804C42C2×D4×C7911yescharacteristic
805C42C2×D4×C7911yescharacteristic
806C42C2×D4×C7911yescharacteristic
807C23—21no—
808C23—21no—
809C23—22no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—42no—
815C23—81no—
816C23—81no—
817C23C2×C22⋊C4×C7911yescharacteristic
818C23C2×C22⋊C4×C7911yescharacteristic
819C23C22×D4×C7911yescharacteristic
820Q8—41no—
821Q8—81no—
822Q8—81no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—42no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—81no—
835D4—81no—
836D4—81no—
837D4—81no—
838D4—81no—
839D4—81no—
840D4—81no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—84no—
879C2×C4C2×C22⋊C4×C7911yescharacteristic
880C2×C4C2×C22⋊C4×C7911yescharacteristic
881C2×C4C2×C22⋊C4×C7911yescharacteristic
882C2×C4C2×C22⋊C4×C7911yescharacteristic
883C2×C4C2×C22⋊C4×C7911yescharacteristic
884C2×C4C2×C22⋊C4×C7911yescharacteristic
885C2×C4C2×C22⋊C4×C7911yescharacteristic
886C2×C4C2×C22⋊C4×C7911yescharacteristic
887C2×C4C2×C22⋊C4×C7911yescharacteristic
888C2×C4C2×C22⋊C4×C7911yescharacteristic
889C2×C4C23×C4×C7911yescharacteristic
890C2×C4C22×D4×C7911yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—162no—
914C22#410×C7912yes—
915C22C22×C22⋊C4×C7911yescharacteristic
916C22#576×C7911yescharacteristic
917C22#577×C7911yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—42no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—81no—
946C2C2×#410×C7911yescharacteristic
947C2C79×#289711yescharacteristic
948C2C79×#290111yescharacteristic
subgroupG/H
center, socleC22×C79C22×C22⋊C4
commutatorC2×C4C23×C4×C79
Frattini, cosocleC22×C4C24×C79
prime radicalC79×#3494C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C79 ◁ C2×#117×C79 ◁ G

Complements

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

NH ≅ G/Ntype
2. C79×#2924C2semidirect
3. C79×#2343C2semidirect
4. C79×#1521C2semidirect
5. C79×#1517C2semidirect
6. C79×#1516C2semidirect
7. C79×#1514C2semidirect
8. C79×#1512C2semidirect
9. C79×#1510C2semidirect
10. C79×#1509C2semidirect
11. C79×#1505C2semidirect
12. C79×#1504C2semidirect
13. C79×#1502C2semidirect
14. C79×#1500C2semidirect
15. C2×#327×C79C2semidirect
24. #544×C79C4semidirect
25. #542×C79C4semidirect
26. #542×C79C4semidirect
27. #540×C79C4semidirect
28. #540×C79C4semidirect
29. #535×C79C4semidirect
36. #520×C79C4semidirect
37. #518×C79C4semidirect
41. #432×C79C22semidirect
42. #432×C79C22semidirect
43. #431×C79C22semidirect
44. #431×C79C22semidirect
52. #383×C79C22semidirect
53. #382×C79C22semidirect
55. C4×C4⋊C4×C79C22semidirect
57. #376×C79C22semidirect
59. #328×C79C22semidirect
60. #328×C79C22semidirect
61. #328×C79C22semidirect
62. #328×C79C22semidirect
71. #327×C79C22semidirect
72. #327×C79C22semidirect
73. #327×C79C22semidirect
74. #327×C79C22semidirect
85. C4⋊Q8×C79C2×C4semidirect
86. C4⋊Q8×C79C2×C4semidirect
87. #127×C79C2×C4semidirect
88. #127×C79C2×C4semidirect
94. #125×C79C2×C4semidirect
95. #125×C79C2×C4semidirect
100. #124×C79C2×C4semidirect
101. #124×C79C2×C4semidirect
136. C4×Q8×C79C2×C4semidirect
137. C4×Q8×C79C2×C4semidirect
148. C4×D4×C79C2×C4semidirect
149. C4×D4×C79C2×C4semidirect
150. C4×D4×C79C2×C4semidirect
151. C4×D4×C79C2×C4semidirect
152. C4×D4×C79C2×C4semidirect
153. C4×D4×C79C2×C4semidirect
464. #17604C79direct (N × H)
476. #2924C2×C79semidirect
477. #2343C2×C79semidirect
478. #1521C2×C79semidirect
479. #1517C2×C79semidirect
480. #1516C2×C79semidirect
481. #1514C2×C79semidirect
482. #1512C2×C79semidirect
483. #1510C2×C79semidirect
484. #1509C2×C79semidirect
485. #1505C2×C79semidirect
486. #1504C2×C79semidirect
487. #1502C2×C79semidirect
488. #1500C2×C79semidirect
489. C2×#327C2×C79semidirect
490. C79#17604direct (N × H)
499. #544C4×C79semidirect
500. #542C4×C79semidirect
501. #542C4×C79semidirect
502. #540C4×C79semidirect
503. #540C4×C79semidirect
504. #535C4×C79semidirect
511. #520C4×C79semidirect
512. #518C4×C79semidirect
516. #432C22×C79semidirect
517. #432C22×C79semidirect
518. #431C22×C79semidirect
519. #431C22×C79semidirect
527. #383C22×C79semidirect
528. #382C22×C79semidirect
530. C4×C4⋊C4C22×C79semidirect
532. #376C22×C79semidirect
534. #328C22×C79semidirect
535. #328C22×C79semidirect
536. #328C22×C79semidirect
537. #328C22×C79semidirect
546. #327C22×C79semidirect
547. #327C22×C79semidirect
548. #327C22×C79semidirect
549. #327C22×C79semidirect
560. C4⋊Q8C2×C4×C79semidirect
561. C4⋊Q8C2×C4×C79semidirect
562. #127C2×C4×C79semidirect
563. #127C2×C4×C79semidirect
569. #125C2×C4×C79semidirect
570. #125C2×C4×C79semidirect
575. #124C2×C4×C79semidirect
576. #124C2×C4×C79semidirect
611. C4×Q8C2×C4×C79semidirect
612. C4×Q8C2×C4×C79semidirect
623. C4×D4C2×C4×C79semidirect
624. C4×D4C2×C4×C79semidirect
625. C4×D4C2×C4×C79semidirect
626. C4×D4C2×C4×C79semidirect
627. C4×D4C2×C4×C79semidirect
628. C4×D4C2×C4×C79semidirect

Maximal subgroups

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

subgroupindex
C79×#34942
C79×#29242
C79×#23432
C79×#15212
C79×#15172
C79×#15162
C79×#15142
C79×#15122
C79×#15102
C79×#15092
C79×#15052
C79×#15042
C79×#15022
C79×#15002
C2×#327×C792
#1760479