Finite Group Databasebeta

← C79×#17516 #34129205

Subgroups — C79×#17516 #34129205

Order 20224.

948 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3480C211yesmaximal, characteristic
2C79×#2965C211yesmaximal, characteristic, complemented
3C79×#2925C211yesmaximal, characteristic, complemented
4C79×#1496C211yesmaximal, characteristic, complemented
5C79×#1495C211yesmaximal, characteristic, complemented
6C79×#1494C211yesmaximal, characteristic, complemented
7C79×#1491C211yesmaximal, characteristic, complemented
8C79×#1489C211yesmaximal, characteristic, complemented
9C79×#1488C211yesmaximal, characteristic, complemented
10C79×#1484C211yesmaximal, characteristic, complemented
11C79×#1483C211yesmaximal, characteristic, complemented
12C79×#1482C211yesmaximal, characteristic, complemented
13C79×#1479C211yesmaximal, characteristic, complemented
14C79×#1477C211yesmaximal, characteristic, complemented
15C79×#1476C211yesmaximal, characteristic, complemented
16#559×C79—21no—
17#559×C79C411yescharacteristic
18#557×C79C411yescharacteristic
19#556×C79—21no—
20#556×C79C411yescharacteristic
21#553×C79—21no—
22#553×C79—21no—
23#553×C79C411yescharacteristic
24#553×C79C411yescharacteristic
25#550×C79C411yescharacteristic
26#548×C79C411yescharacteristic
27#548×C79C411yescharacteristic
28#532×C79—21no—
29#532×C79C2211yescharacteristic
30#529×C79—21no—
31#529×C79—21no—
32#529×C79C2211yescharacteristic
33#529×C79C2211yescharacteristic
34C4×#41×C79—21no—
35C4×#41×C79C2211yescharacteristic
36C4×#41×C79C2211yescharacteristic
37C4×#41×C79C2211yescharacteristic
38C2×C4×Q8×C79C2211yescharacteristic
39#446×C79—21no—
40#436×C79—21no—
41#435×C79—21no—
42#435×C79—21no—
43#433×C79—21no—
44#433×C79—21no—
45#432×C79C2211yescharacteristic
46#432×C79C2211yescharacteristic
47#431×C79C2211yescharacteristic
48#431×C79C2211yescharacteristic
49#431×C79C2211yescharacteristic
50#431×C79C2211yescharacteristic
51#431×C79C2211yescharacteristic
52#423×C79C2211yescharacteristic
53C2×C4⋊C8×C79C2211yescharacteristic
54#408×C79—21no—
55#405×C79—21no—
56C4×M16×C79C2211yescharacteristic
57C4×M16×C79C2211yescharacteristic
58C2×C4×C8×C79C2211yescharacteristic
59Q8⋊C8×C79C2211yescharacteristic
60Q8⋊C8×C79C2211yescharacteristic
61Q8⋊C8×C79C2211yescharacteristic
62Q8⋊C8×C79C2211yescharacteristic
63Q8⋊C8×C79C2211yescharacteristic
64Q8⋊C8×C79C2211yescharacteristic
65Q8⋊C8×C79C2211yescharacteristic
66Q8⋊C8×C79C2211yescharacteristic
67D4⋊C8×C79C2211yescharacteristic
68D4⋊C8×C79C2211yescharacteristic
69D4⋊C8×C79C2211yescharacteristic
70D4⋊C8×C79C2211yescharacteristic
71D4⋊C8×C79C2211yescharacteristic
72D4⋊C8×C79C2211yescharacteristic
73D4⋊C8×C79C2211yescharacteristic
74D4⋊C8×C79C2211yescharacteristic
75C2×#41×C79—21no—
76C2×#41×C79C2×C411yescharacteristic
77C2×#41×C79C2×C411yescharacteristic
78C2×#41×C79D411yescharacteristic
79C22×Q8×C79C2×C411yescharacteristic
80C2×M16×C79—21no—
81C2×M16×C79—21no—
82C2×M16×C79—21no—
83C22×C8×C79—21no—
84C22×C8×C79—21no—
85C4⋊Q8×C79—21no—
86C4⋊Q8×C79C2×C411yescharacteristic
87#127×C79—21no—
88#127×C79C2×C411yescharacteristic
89#126×C79—21no—
90#126×C79—21no—
91#126×C79—21no—
92#126×C79—21no—
93#126×C79—21no—
94#126×C79—21no—
95#125×C79—21no—
96#125×C79—21no—
97#125×C79C2×C411yescharacteristic
98#125×C79C2×C411yescharacteristic
99#124×C79—21no—
100#124×C79—21no—
101#124×C79—21no—
102#124×C79—21no—
103#124×C79—21no—
104#124×C79C2×C411yescharacteristic
105#124×C79C2×C411yescharacteristic
106#123×C79—21no—
107#123×C79—21no—
108#123×C79—21no—
109#123×C79—21no—
110#123×C79—21no—
111#123×C79—21no—
112C22⋊Q8×C79—21no—
113C22⋊Q8×C79—21no—
114C22⋊Q8×C79C2×C411yescharacteristic
115C22⋊Q8×C79C2×C411yescharacteristic
116#121×C79—21no—
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×C79C2×C411yescharacteristic
124#121×C79C2×C411yescharacteristic
125#121×C79C2×C411yescharacteristic
126#121×C79C2×C411yescharacteristic
127C4×Q8×C79—21no—
128C4×Q8×C79—21no—
129C4×Q8×C79—21no—
130C4×Q8×C79—21no—
131C4×Q8×C79C2×C411yescharacteristic
132C4×Q8×C79C2×C411yescharacteristic
133C4×Q8×C79C2×C411yescharacteristic
134C4×Q8×C79C2×C411yescharacteristic
135C4×Q8×C79C2×C411yescharacteristic
136C4×Q8×C79D411yescharacteristic
137C4×Q8×C79C2311yescharacteristic
138C4×Q8×C79C2311yescharacteristic
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×C79—21no—
149C4×D4×C79—21no—
150C4×D4×C79—21no—
151C4×D4×C79—21no—
152C4×D4×C79C2×C411yescharacteristic
153C4×D4×C79C2×C411yescharacteristic
154C4×D4×C79C2×C411yescharacteristic
155C4×D4×C79C2×C411yescharacteristic
156C4×D4×C79C2×C411yescharacteristic
157C4×D4×C79D411yescharacteristic
158C4×D4×C79D411yescharacteristic
159C4×D4×C79D411yescharacteristic
160C4×D4×C79C2311yescharacteristic
161C4×D4×C79C2311yescharacteristic
162#117×C79—21no—
163#117×C79—21no—
164#117×C79—21no—
165#117×C79—21no—
166#117×C79C2×C411yescharacteristic
167#117×C79C2×C411yescharacteristic
168#117×C79D411yescharacteristic
169#117×C79D411yescharacteristic
170#117×C79D411yescharacteristic
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79C2×C411yescharacteristic
173C2×C42×C79—21no—
174C2×C42×C79—21no—
175C2×C42×C79—21no—
176C2×C42×C79C2311yescharacteristic
177C2×C42×C79C2311yescharacteristic
178C2×C42×C79C2311yescharacteristic
179C4⋊C8×C79—21no—
180C4⋊C8×C79—21no—
181C4⋊C8×C79—21no—
182C4⋊C8×C79—21no—
183C4⋊C8×C79—21no—
184C4⋊C8×C79C2311yescharacteristic
185C4⋊C8×C79C2311yescharacteristic
186C4⋊C8×C79C2311yescharacteristic
187C4⋊C8×C79C2311yescharacteristic
188C22⋊C8×C79—21no—
189C22⋊C8×C79—21no—
190C22⋊C8×C79—21no—
191C22⋊C8×C79—21no—
192C22⋊C8×C79—21no—
193C22⋊C8×C79—21no—
194C22⋊C8×C79—21no—
195#97×C79—21no—
196#97×C79—21no—
197#97×C79—21no—
198#97×C79—21no—
199C4×C8×C79—21no—
200C4×C8×C79—21no—
201C4×C8×C79—21no—
202C4×C8×C79C2311yescharacteristic
203C4×C8×C79C2311yescharacteristic
204C4×C8×C79C2311yescharacteristic
205C4×C8×C79C2311yescharacteristic
206#41×C79—22no—
207#41×C79—22no—
208#41×C79—41no—
209#41×C79—41no—
210#41×C79—41no—
211#41×C79—41no—
212#41×C79—42no—
213#41×C79—42no—
214C2×Q8×C79—21no—
215C2×Q8×C79—21no—
216C2×Q8×C79—22no—
217C2×Q8×C79—41no—
218C2×Q8×C79C22⋊C411yescharacteristic
219C2×Q8×C79C22×C411yescharacteristic
220C2×Q8×C79C22×C411yescharacteristic
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—21no—
229C2×D4×C79C22⋊C411yescharacteristic
230C2×D4×C79C22⋊C411yescharacteristic
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×C79C22×C411yescharacteristic
243C22×C4×C79C22×C411yescharacteristic
244C22×C4×C79C22×C411yescharacteristic
245C22×C4×C79C2×D411yescharacteristic
246C22×C4×C79C2×D411yescharacteristic
247C22×C4×C79C2×D411yescharacteristic
248C22×C4×C79C2×D411yescharacteristic
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2×D411yescharacteristic
251M16×C79—42no—
252M16×C79—42no—
253M16×C79—42no—
254C2×C8×C79—21no—
255C2×C8×C79—21no—
256C2×C8×C79—21no—
257C2×C8×C79—21no—
258C2×C8×C79—21no—
259C2×C8×C79—21no—
260C2×C8×C79—21no—
261C2×C8×C79—21no—
262C2×C8×C79—42no—
263C2×C8×C79—42no—
264C4⋊C4×C79—21no—
265C4⋊C4×C79—21no—
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—21no—
278C4⋊C4×C79C22⋊C411yescharacteristic
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
288C22⋊C4×C79—21no—
289C22⋊C4×C79—21no—
290C22⋊C4×C79—21no—
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×C79C22⋊C411yescharacteristic
305C22⋊C4×C79C22⋊C411yescharacteristic
306C22⋊C4×C79C22⋊C411yescharacteristic
307C22⋊C4×C79C22⋊C411yescharacteristic
308C22⋊C4×C79C22⋊C411yescharacteristic
309C22⋊C4×C79C22⋊C411yescharacteristic
310C42×C79—21no—
311C42×C79—21no—
312C42×C79—21no—
313C42×C79—21no—
314C42×C79—21no—
315C42×C79—21no—
316C42×C79—21no—
317C42×C79—21no—
318C42×C79C22×C411yescharacteristic
319C42×C79C22×C411yescharacteristic
320C42×C79C22×C411yescharacteristic
321C42×C79C2×D411yescharacteristic
322C42×C79C2×D411yescharacteristic
323C42×C79C2×D411yescharacteristic
324C42×C79C2×D411yescharacteristic
325C42×C79C2×D411yescharacteristic
326C42×C79C2×D411yescharacteristic
327C42×C79C2411yescharacteristic
328C23×C79—21no—
329C23×C79—21no—
330C23×C79C2×C22⋊C411yescharacteristic
331C23×C79C2×C22⋊C411yescharacteristic
332C23×C79C2×C22⋊C411yescharacteristic
333Q8×C79—21no—
334Q8×C79—21no—
335Q8×C79—21no—
336Q8×C79—41no—
337Q8×C79—42no—
338Q8×C79—42no—
339Q8×C79#13112yes—
340D4×C79—21no—
341D4×C79—21no—
342D4×C79—21no—
343D4×C79—21no—
344D4×C79—41no—
345D4×C79—41no—
346D4×C79—41no—
347D4×C79—42no—
348D4×C79—42no—
349D4×C79—42no—
350D4×C79—42no—
351D4×C79—42no—
352D4×C79—81no—
353D4×C79—81no—
354D4×C79—81no—
355C2×C4×C79—21no—
356C2×C4×C79—21no—
357C2×C4×C79—21no—
358C2×C4×C79—21no—
359C2×C4×C79—21no—
360C2×C4×C79—21no—
361C2×C4×C79—21no—
362C2×C4×C79—21no—
363C2×C4×C79—21no—
364C2×C4×C79—21no—
365C2×C4×C79—21no—
366C2×C4×C79—21no—
367C2×C4×C79—21no—
368C2×C4×C79—21no—
369C2×C4×C79—21no—
370C2×C4×C79—21no—
371C2×C4×C79—21no—
372C2×C4×C79—21no—
373C2×C4×C79—41no—
374C2×C4×C79—41no—
375C2×C4×C79—41no—
376C2×C4×C79—42no—
377C2×C4×C79—42no—
378C2×C4×C79—42no—
379C2×C4×C79—41no—
380C2×C4×C79—41no—
381C2×C4×C79—41no—
382C2×C4×C79—41no—
383C2×C4×C79—81no—
384C2×C4×C79—81no—
385C2×C4×C79—81no—
386C2×C4×C79C2×C22⋊C411yescharacteristic
387C2×C4×C79C2×C22⋊C411yescharacteristic
388C2×C4×C79C2×C22⋊C411yescharacteristic
389C2×C4×C79C2×C22⋊C411yescharacteristic
390C2×C4×C79C2×C22⋊C411yescharacteristic
391C2×C4×C79C2×C22⋊C411yescharacteristic
392C2×C4×C79C2×C22⋊C411yescharacteristic
393C2×C4×C79C2×C22⋊C411yescharacteristic
394C2×C4×C79C2×C22⋊C411yescharacteristic
395C2×C4×C79C23×C411yescharacteristic
396C2×C4×C79C22×D411yescharacteristic
397C2×C4×C79C22×D411yescharacteristic
398C8×C79—22no—
399C8×C79—41no—
400C8×C79—41no—
401C8×C79—41no—
402C8×C79—41no—
403C8×C79—41no—
404C8×C79—41no—
405C8×C79—41no—
406C22×C79—21no—
407C22×C79—21no—
408C22×C79—21no—
409C22×C79—21no—
410C22×C79—21no—
411C22×C79—21no—
412C22×C79—21no—
413C22×C79—21no—
414C22×C79—21no—
415C22×C79—41no—
416C22×C79—41no—
417C22×C79—41no—
418C22×C79—41no—
419C22×C79—41no—
420C22×C79—41no—
421C22×C79C22×C22⋊C411yescharacteristic
422C4×C79—21no—
423C4×C79—21no—
424C4×C79—21no—
425C4×C79—22no—
426C4×C79—21no—
427C4×C79—21no—
428C4×C79—21no—
429C4×C79—21no—
430C4×C79—21no—
431C4×C79—21no—
432C4×C79—21no—
433C4×C79—41no—
434C4×C79—41no—
435C4×C79—41no—
436C4×C79—41no—
437C4×C79—41no—
438C4×C79C2×#13111yescharacteristic
439C4×C79#56811yescharacteristic
440C4×C79#57511yescharacteristic
441C4×C79#57511yescharacteristic
442#17516C7911yesmaximal, characteristic, direct product factor, Sylow
443C2×C79—41no—
444C2×C79—41no—
445C2×C79—41no—
446C2×C79—81no—
447C2×C79—81no—
448C2×C79#288011yescharacteristic
449C2×C79#289611yescharacteristic
450C2×C79#290111yescharacteristic
451#3480C2×C7911yescharacteristic
452#2965C2×C7911yescharacteristic, complemented
453#2925C2×C7911yescharacteristic, complemented
454#1496C2×C7911yescharacteristic, complemented
455#1495C2×C7911yescharacteristic, complemented
456#1494C2×C7911yescharacteristic, complemented
457#1491C2×C7911yescharacteristic, complemented
458#1489C2×C7911yescharacteristic, complemented
459#1488C2×C7911yescharacteristic, complemented
460#1484C2×C7911yescharacteristic, complemented
461#1483C2×C7911yescharacteristic, complemented
462#1482C2×C7911yescharacteristic, complemented
463#1479C2×C7911yescharacteristic, complemented
464#1477C2×C7911yescharacteristic, complemented
465#1476C2×C7911yescharacteristic, complemented
466C79#1751611yescharacteristic, direct product factor, Sylow
467#559—21no—
468#559C4×C7911yescharacteristic
469#557C4×C7911yescharacteristic
470#556—21no—
471#556C4×C7911yescharacteristic
472#553—21no—
473#553—21no—
474#553C4×C7911yescharacteristic
475#553C4×C7911yescharacteristic
476#550C4×C7911yescharacteristic
477#548C4×C7911yescharacteristic
478#548C4×C7911yescharacteristic
479#532—21no—
480#532C22×C7911yescharacteristic
481#529—21no—
482#529—21no—
483#529C22×C7911yescharacteristic
484#529C22×C7911yescharacteristic
485C4×#41—21no—
486C4×#41C22×C7911yescharacteristic
487C4×#41C22×C7911yescharacteristic
488C4×#41C22×C7911yescharacteristic
489C2×C4×Q8C22×C7911yescharacteristic
490#446—21no—
491#436—21no—
492#435—21no—
493#435—21no—
494#433—21no—
495#433—21no—
496#432C22×C7911yescharacteristic
497#432C22×C7911yescharacteristic
498#431C22×C7911yescharacteristic
499#431C22×C7911yescharacteristic
500#431C22×C7911yescharacteristic
501#431C22×C7911yescharacteristic
502#431C22×C7911yescharacteristic
503#423C22×C7911yescharacteristic
504C2×C4⋊C8C22×C7911yescharacteristic
505#408—21no—
506#405—21no—
507C4×M16C22×C7911yescharacteristic
508C4×M16C22×C7911yescharacteristic
509C2×C4×C8C22×C7911yescharacteristic
510Q8⋊C8C22×C7911yescharacteristic
511Q8⋊C8C22×C7911yescharacteristic
512Q8⋊C8C22×C7911yescharacteristic
513Q8⋊C8C22×C7911yescharacteristic
514Q8⋊C8C22×C7911yescharacteristic
515Q8⋊C8C22×C7911yescharacteristic
516Q8⋊C8C22×C7911yescharacteristic
517Q8⋊C8C22×C7911yescharacteristic
518D4⋊C8C22×C7911yescharacteristic
519D4⋊C8C22×C7911yescharacteristic
520D4⋊C8C22×C7911yescharacteristic
521D4⋊C8C22×C7911yescharacteristic
522D4⋊C8C22×C7911yescharacteristic
523D4⋊C8C22×C7911yescharacteristic
524D4⋊C8C22×C7911yescharacteristic
525D4⋊C8C22×C7911yescharacteristic
526C2×#41—21no—
527C2×#41C2×C4×C7911yescharacteristic
528C2×#41C2×C4×C7911yescharacteristic
529C2×#41D4×C7911yescharacteristic
530C22×Q8C2×C4×C7911yescharacteristic
531C2×M16—21no—
532C2×M16—21no—
533C2×M16—21no—
534C22×C8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8C2×C4×C7911yescharacteristic
538#127—21no—
539#127C2×C4×C7911yescharacteristic
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#125—21no—
547#125—21no—
548#125C2×C4×C7911yescharacteristic
549#125C2×C4×C7911yescharacteristic
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124C2×C4×C7911yescharacteristic
556#124C2×C4×C7911yescharacteristic
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8C2×C4×C7911yescharacteristic
566C22⋊Q8C2×C4×C7911yescharacteristic
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121C2×C4×C7911yescharacteristic
575#121C2×C4×C7911yescharacteristic
576#121C2×C4×C7911yescharacteristic
577#121C2×C4×C7911yescharacteristic
578C4×Q8—21no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8C2×C4×C7911yescharacteristic
583C4×Q8C2×C4×C7911yescharacteristic
584C4×Q8C2×C4×C7911yescharacteristic
585C4×Q8C2×C4×C7911yescharacteristic
586C4×Q8C2×C4×C7911yescharacteristic
587C4×Q8D4×C7911yescharacteristic
588C4×Q8C23×C7911yescharacteristic
589C4×Q8C23×C7911yescharacteristic
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4C2×C4×C7911yescharacteristic
604C4×D4C2×C4×C7911yescharacteristic
605C4×D4C2×C4×C7911yescharacteristic
606C4×D4C2×C4×C7911yescharacteristic
607C4×D4C2×C4×C7911yescharacteristic
608C4×D4D4×C7911yescharacteristic
609C4×D4D4×C7911yescharacteristic
610C4×D4D4×C7911yescharacteristic
611C4×D4C23×C7911yescharacteristic
612C4×D4C23×C7911yescharacteristic
613#117—21no—
614#117—21no—
615#117—21no—
616#117—21no—
617#117C2×C4×C7911yescharacteristic
618#117C2×C4×C7911yescharacteristic
619#117D4×C7911yescharacteristic
620#117D4×C7911yescharacteristic
621#117D4×C7911yescharacteristic
622C2×C4⋊C4—21no—
623C2×C4⋊C4C2×C4×C7911yescharacteristic
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42C23×C7911yescharacteristic
628C2×C42C23×C7911yescharacteristic
629C2×C42C23×C7911yescharacteristic
630C4⋊C8—21no—
631C4⋊C8—21no—
632C4⋊C8—21no—
633C4⋊C8—21no—
634C4⋊C8—21no—
635C4⋊C8C23×C7911yescharacteristic
636C4⋊C8C23×C7911yescharacteristic
637C4⋊C8C23×C7911yescharacteristic
638C4⋊C8C23×C7911yescharacteristic
639C22⋊C8—21no—
640C22⋊C8—21no—
641C22⋊C8—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646#97—21no—
647#97—21no—
648#97—21no—
649#97—21no—
650C4×C8—21no—
651C4×C8—21no—
652C4×C8—21no—
653C4×C8C23×C7911yescharacteristic
654C4×C8C23×C7911yescharacteristic
655C4×C8C23×C7911yescharacteristic
656C4×C8C23×C7911yescharacteristic
657#41—22no—
658#41—22no—
659#41—41no—
660#41—41no—
661#41—41no—
662#41—41no—
663#41—42no—
664#41—42no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C22⋊C4×C7911yescharacteristic
670C2×Q8C22×C4×C7911yescharacteristic
671C2×Q8C22×C4×C7911yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4C22⋊C4×C7911yescharacteristic
681C2×D4C22⋊C4×C7911yescharacteristic
682C2×D4C22⋊C4×C7911yescharacteristic
683C2×D4C22×C4×C7911yescharacteristic
684C2×D4C22×C4×C7911yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4C22×C4×C7911yescharacteristic
694C22×C4C22×C4×C7911yescharacteristic
695C22×C4C22×C4×C7911yescharacteristic
696C22×C4C2×D4×C7911yescharacteristic
697C22×C4C2×D4×C7911yescharacteristic
698C22×C4C2×D4×C7911yescharacteristic
699C22×C4C2×D4×C7911yescharacteristic
700C22×C4C2×D4×C7911yescharacteristic
701C22×C4C2×D4×C7911yescharacteristic
702M16—42no—
703M16—42no—
704M16—42no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—42no—
714C2×C8—42no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4C22⋊C4×C7911yescharacteristic
730C4⋊C4C22⋊C4×C7911yescharacteristic
731C4⋊C4C22⋊C4×C7911yescharacteristic
732C4⋊C4C22⋊C4×C7911yescharacteristic
733C4⋊C4C22⋊C4×C7911yescharacteristic
734C4⋊C4C22⋊C4×C7911yescharacteristic
735C4⋊C4C22×C4×C7911yescharacteristic
736C4⋊C4C22×C4×C7911yescharacteristic
737C4⋊C4C22×C4×C7911yescharacteristic
738C4⋊C4C22×C4×C7911yescharacteristic
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4C22⋊C4×C7911yescharacteristic
756C22⋊C4C22⋊C4×C7911yescharacteristic
757C22⋊C4C22⋊C4×C7911yescharacteristic
758C22⋊C4C22⋊C4×C7911yescharacteristic
759C22⋊C4C22⋊C4×C7911yescharacteristic
760C22⋊C4C22⋊C4×C7911yescharacteristic
761C42—21no—
762C42—21no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42C22×C4×C7911yescharacteristic
770C42C22×C4×C7911yescharacteristic
771C42C22×C4×C7911yescharacteristic
772C42C2×D4×C7911yescharacteristic
773C42C2×D4×C7911yescharacteristic
774C42C2×D4×C7911yescharacteristic
775C42C2×D4×C7911yescharacteristic
776C42C2×D4×C7911yescharacteristic
777C42C2×D4×C7911yescharacteristic
778C42C24×C7911yescharacteristic
779C23—21no—
780C23—21no—
781C23C2×C22⋊C4×C7911yescharacteristic
782C23C2×C22⋊C4×C7911yescharacteristic
783C23C2×C22⋊C4×C7911yescharacteristic
784Q8—21no—
785Q8—21no—
786Q8—21no—
787Q8—41no—
788Q8—42no—
789Q8—42no—
790Q8#131×C7912yes—
791D4—21no—
792D4—21no—
793D4—21no—
794D4—21no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—81no—
804D4—81no—
805D4—81no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4C2×C22⋊C4×C7911yescharacteristic
838C2×C4C2×C22⋊C4×C7911yescharacteristic
839C2×C4C2×C22⋊C4×C7911yescharacteristic
840C2×C4C2×C22⋊C4×C7911yescharacteristic
841C2×C4C2×C22⋊C4×C7911yescharacteristic
842C2×C4C2×C22⋊C4×C7911yescharacteristic
843C2×C4C2×C22⋊C4×C7911yescharacteristic
844C2×C4C2×C22⋊C4×C7911yescharacteristic
845C2×C4C2×C22⋊C4×C7911yescharacteristic
846C2×C4C23×C4×C7911yescharacteristic
847C2×C4C22×D4×C7911yescharacteristic
848C2×C4C22×D4×C7911yescharacteristic
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C8—41no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22C22×C22⋊C4×C7911yescharacteristic
873C4—21no—
874C4—21no—
875C4—21no—
876C4—22no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4C2×#131×C7911yescharacteristic
890C4#568×C7911yescharacteristic
891C4#575×C7911yescharacteristic
892C4#575×C7911yescharacteristic
893C2—41no—
894C2—41no—
895C2—41no—
896C2—81no—
897C2—81no—
898C2C79×#288011yescharacteristic
899C2C79×#289611yescharacteristic
900C2C79×#290111yescharacteristic
subgroupG/H
centerC2×C4×C79C22×D4
commutatorC2×C4C23×C4×C79
Frattini, cosocleC42C24×C79
socleC22×C79C22×C22⋊C4
prime radicalC79×#3480C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C79 ◁ C4×#41×C79 ◁ G

Complements

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

NH ≅ G/Ntype
2. C79×#2965C2semidirect
3. C79×#2925C2semidirect
4. C79×#1496C2semidirect
5. C79×#1495C2semidirect
6. C79×#1494C2semidirect
7. C79×#1491C2semidirect
8. C79×#1489C2semidirect
9. C79×#1488C2semidirect
10. C79×#1484C2semidirect
11. C79×#1483C2semidirect
12. C79×#1482C2semidirect
13. C79×#1479C2semidirect
14. C79×#1477C2semidirect
15. C79×#1476C2semidirect
442. #17516C79direct (N × H)
452. #2965C2×C79semidirect
453. #2925C2×C79semidirect
454. #1496C2×C79semidirect
455. #1495C2×C79semidirect
456. #1494C2×C79semidirect
457. #1491C2×C79semidirect
458. #1489C2×C79semidirect
459. #1488C2×C79semidirect
460. #1484C2×C79semidirect
461. #1483C2×C79semidirect
462. #1482C2×C79semidirect
463. #1479C2×C79semidirect
464. #1477C2×C79semidirect
465. #1476C2×C79semidirect
466. C79#17516direct (N × H)

Maximal subgroups

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

subgroupindex
C79×#34802
C79×#29652
C79×#29252
C79×#14962
C79×#14952
C79×#14942
C79×#14912
C79×#14892
C79×#14882
C79×#14842
C79×#14832
C79×#14822
C79×#14792
C79×#14772
C79×#14762
#1751679