Finite Group Databasebeta

← C79×#18416 #34130105

Subgroups — C79×#18416 #34130105

Order 20224.

978 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×#3535C211yesmaximal, characteristic, complemented
2C79×#3194C211yesmaximal, characteristic, complemented
3C79×#3187C211yesmaximal, characteristic, complemented
4C79×#2661C211yesmaximal, characteristic, complemented
5C79×#1612C211yesmaximal, characteristic, complemented
6C79×#1611C211yesmaximal, characteristic, complemented
7C79×#1609C211yesmaximal, characteristic, complemented
8C79×#1608C211yesmaximal, characteristic, complemented
9C79×#1600C211yesmaximal, characteristic, complemented
10C79×#1599C211yesmaximal, characteristic, complemented
11C79×#1597C211yesmaximal, characteristic, complemented
12C79×#1596C211yesmaximal, characteristic, complemented
13C79×#1508C211yesmaximal, characteristic, complemented
14C79×#1501C211yesmaximal, characteristic, complemented
15C79×#1468C211yesmaximal, characteristic, complemented
16#563×C79—21no—
17#562×C79—21no—
18#554×C79—21no—
19#552×C79—21no—
20#551×C79—21no—
21#551×C79—21no—
22#547×C79—21no—
23#546×C79—21no—
24#544×C79C2211yescharacteristic
25#543×C79C2211yescharacteristic
26#542×C79—21no—
27#539×C79—21no—
28#539×C79—21no—
29#539×C79C2211yescharacteristic
30#538×C79C2211yescharacteristic
31#536×C79—21no—
32#525×C79C2211yescharacteristic
33C2×#123×C79C2211yescharacteristic
34C2×C22⋊Q8×C79C2211yescharacteristic
35C2×#121×C79C2211yescharacteristic
36#483×C79C2211yescharacteristic
37#483×C79C2211yescharacteristic
38#483×C79C2211yescharacteristic
39#482×C79—21no—
40#481×C79—21no—
41#480×C79C2211yescharacteristic
42#469×C79—21no—
43#468×C79—21no—
44#465×C79—21no—
45#465×C79—21no—
46#450×C79C2211yescharacteristic
47#450×C79C2211yescharacteristic
48#450×C79C2211yescharacteristic
49#449×C79—21no—
50#448×C79—21no—
51#447×C79C2211yescharacteristic
52#407×C79C2211yescharacteristic
53C2×C22⋊C8×C79C2211yescharacteristic
54#398×C79C2211yescharacteristic
55#397×C79C2211yescharacteristic
56#394×C79—21no—
57#394×C79C2211yescharacteristic
58#392×C79—21no—
59#392×C79C2211yescharacteristic
60#390×C79—21no—
61#388×C79—21no—
62C4×C22⋊C4×C79C2211yescharacteristic
63#328×C79C2211yescharacteristic
64#328×C79C2211yescharacteristic
65#328×C79C2211yescharacteristic
66#328×C79C2211yescharacteristic
67#328×C79C2211yescharacteristic
68#328×C79C2211yescharacteristic
69#327×C79C2211yescharacteristic
70#327×C79C2211yescharacteristic
71#324×C79C2211yescharacteristic
72#324×C79C2211yescharacteristic
73#323×C79C2211yescharacteristic
74#323×C79C2211yescharacteristic
75C2×#41×C79—21no—
76C2×#41×C79D411yescharacteristic, complemented
77C22×Q8×C79D411yescharacteristic, complemented
78C22×D4×C79—21no—
79C22×D4×C79—21no—
80C22×D4×C79D411yescharacteristic
81C22×D4×C79C2311yescharacteristic
82C23×C4×C79C2311yescharacteristic
83C2×SD16×C79—21no—
84C2×SD16×C79—21no—
85C2×SD16×C79—21no—
86C2×D8×C79—21no—
87C2×M16×C79—21no—
88C22×C8×C79—21no—
89C4⋊Q8×C79—21no—
90C4⋊Q8×C79—21no—
91C4⋊Q8×C79—21no—
92#126×C79—21no—
93#126×C79—21no—
94#126×C79—21no—
95#126×C79—21no—
96#126×C79—21no—
97#126×C79—21no—
98#125×C79—21no—
99#125×C79—21no—
100#125×C79—21no—
101#125×C79—21no—
102#125×C79—21no—
103#124×C79—21no—
104#124×C79—21no—
105#124×C79—21no—
106#124×C79—21no—
107#123×C79—21no—
108#123×C79—21no—
109#123×C79—21no—
110#123×C79—21no—
111#123×C79—21no—
112#123×C79—21no—
113#123×C79—21no—
114#123×C79—21no—
115#123×C79—21no—
116#123×C79—21no—
117#123×C79—21no—
118#123×C79—21no—
119#123×C79—21no—
120#123×C79—21no—
121C22⋊Q8×C79—21no—
122C22⋊Q8×C79—21no—
123C22⋊Q8×C79—21no—
124C22⋊Q8×C79—21no—
125C22⋊Q8×C79—21no—
126C22⋊Q8×C79—21no—
127C22⋊Q8×C79—21no—
128C22⋊Q8×C79—21no—
129C22⋊Q8×C79—21no—
130C22⋊Q8×C79—21no—
131C22⋊Q8×C79—21no—
132C22⋊Q8×C79—21no—
133C22⋊Q8×C79—21no—
134C22⋊Q8×C79—21no—
135C22⋊Q8×C79D411yescharacteristic, complemented
136C22⋊Q8×C79D411yescharacteristic, complemented
137C22⋊Q8×C79D411yescharacteristic, complemented
138C22⋊Q8×C79C2311yescharacteristic
139C22⋊Q8×C79C2311yescharacteristic
140C22⋊Q8×C79C2311yescharacteristic
141#121×C79—21no—
142#121×C79—21no—
143#121×C79—21no—
144#121×C79—21no—
145#121×C79—21no—
146#121×C79—21no—
147#121×C79—21no—
148#121×C79—21no—
149#121×C79D411yescharacteristic, complemented
150#121×C79C2311yescharacteristic
151#120×C79—21no—
152#120×C79—21no—
153C4×Q8×C79—21no—
154C4×D4×C79—21no—
155C4×D4×C79—21no—
156C4×D4×C79—21no—
157C4×D4×C79—21no—
158C4×D4×C79—21no—
159C4×D4×C79—21no—
160C4×D4×C79—21no—
161#117×C79—21no—
162#117×C79—21no—
163#117×C79—21no—
164#117×C79D411yescharacteristic, complemented
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79—21no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79D411yescharacteristic
169C2×C4⋊C4×C79D411yescharacteristic, complemented
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C22⋊C4×C79—21no—
173C2×C22⋊C4×C79—21no—
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176C2×C22⋊C4×C79—21no—
177C2×C22⋊C4×C79—21no—
178C2×C22⋊C4×C79—21no—
179C2×C22⋊C4×C79—21no—
180C2×C22⋊C4×C79D411yescharacteristic
181C2×C22⋊C4×C79D411yescharacteristic
182C2×C22⋊C4×C79C2311yescharacteristic
183C2×C42×C79—21no—
184#107×C79—21no—
185#106×C79—21no—
186#106×C79—21no—
187#106×C79—21no—
188#103×C79—21no—
189#103×C79—21no—
190#103×C79—21no—
191#102×C79—21no—
192#102×C79—21no—
193#102×C79—21no—
194#102×C79—21no—
195#102×C79—21no—
196C22⋊C8×C79—21no—
197C22⋊C8×C79—21no—
198C22⋊C8×C79C2311yescharacteristic
199C22⋊C8×C79C2311yescharacteristic
200C22⋊C8×C79C2311yescharacteristic
201C22⋊C8×C79C2311yescharacteristic
202#95×C79—21no—
203#95×C79—21no—
204#95×C79C2311yescharacteristic
205#95×C79C2311yescharacteristic
206C24×C79—21no—
207C24×C79C2×D411yescharacteristic
208C24×C79C2×D411yescharacteristic
209#41×C79—82no—
210#41×C79—81no—
211C2×Q8×C79—21no—
212C2×Q8×C79—21no—
213C2×Q8×C79—21no—
214C2×Q8×C79—81no—
215C2×Q8×C79C2×D411yescharacteristic
216C2×Q8×C79C2×D411yescharacteristic
217C2×Q8×C79C2×D411yescharacteristic
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—42no—
228C2×D4×C79—41no—
229C2×D4×C79—41no—
230C2×D4×C79—81no—
231C2×D4×C79—81no—
232C2×D4×C79—81no—
233C2×D4×C79—81no—
234C2×D4×C79—81no—
235C2×D4×C79—81no—
236C2×D4×C79C2×D411yescharacteristic
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—21no—
247C22×C4×C79—81no—
248C22×C4×C79C2×D411yescharacteristic
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2411yescharacteristic
257SD16×C79—81no—
258SD16×C79—81no—
259SD16×C79—81no—
260D8×C79—81no—
261M16×C79—81no—
262C2×C8×C79—21no—
263C2×C8×C79—21no—
264C2×C8×C79—21no—
265C2×C8×C79—21no—
266C2×C8×C79—81no—
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×C79—21no—
279C4⋊C4×C79—21no—
280C4⋊C4×C79—21no—
281C4⋊C4×C79—21no—
282C4⋊C4×C79—21no—
283C4⋊C4×C79—21no—
284C4⋊C4×C79—21no—
285C4⋊C4×C79—21no—
286C4⋊C4×C79—21no—
287C4⋊C4×C79—21no—
288C4⋊C4×C79—21no—
289C4⋊C4×C79—21no—
290C4⋊C4×C79—21no—
291C4⋊C4×C79—21no—
292C4⋊C4×C79—81no—
293C4⋊C4×C79C2×D411yescharacteristic
294C4⋊C4×C79C2×D411yescharacteristic
295C4⋊C4×C79C2×D411yescharacteristic
296C4⋊C4×C79C2×D411yescharacteristic
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—21no—
311C22⋊C4×C79—21no—
312C22⋊C4×C79—21no—
313C22⋊C4×C79—21no—
314C22⋊C4×C79—21no—
315C22⋊C4×C79—21no—
316C22⋊C4×C79—21no—
317C22⋊C4×C79—21no—
318C22⋊C4×C79—21no—
319C22⋊C4×C79—21no—
320C22⋊C4×C79—42no—
321C22⋊C4×C79—42no—
322C22⋊C4×C79—41no—
323C22⋊C4×C79—41no—
324C22⋊C4×C79—81no—
325C22⋊C4×C79—81no—
326C22⋊C4×C79—81no—
327C42×C79—21no—
328C42×C79—21no—
329C42×C79—21no—
330C42×C79—21no—
331C42×C79—21no—
332C42×C79—81no—
333C23×C79—21no—
334C23×C79—21no—
335C23×C79—21no—
336C23×C79—21no—
337C23×C79—21no—
338C23×C79—21no—
339C23×C79—41no—
340C23×C79—41no—
341C23×C79—41no—
342C23×C79—41no—
343C23×C79—41no—
344C23×C79—41no—
345C23×C79—41no—
346C23×C79—41no—
347C23×C79—41no—
348C23×C79—41no—
349C23×C79—41no—
350C23×C79#12011yescharacteristic
351C23×C79#12011yescharacteristic
352C23×C79C22×D411yescharacteristic
353Q8×C79—41no—
354Q8×C79—41no—
355Q8×C79—41no—
356Q8×C79—81no—
357Q8×C79—81no—
358Q8×C79—81no—
359D4×C79—41no—
360D4×C79—41no—
361D4×C79—41no—
362D4×C79—41no—
363D4×C79—41no—
364D4×C79—42no—
365D4×C79—42no—
366D4×C79—41no—
367D4×C79—41no—
368D4×C79—81no—
369D4×C79—81no—
370D4×C79—81no—
371D4×C79—81no—
372D4×C79—84no—
373D4×C79—82no—
374D4×C79—82no—
375C2×C4×C79—22no—
376C2×C4×C79—21no—
377C2×C4×C79—21no—
378C2×C4×C79—21no—
379C2×C4×C79—21no—
380C2×C4×C79—21no—
381C2×C4×C79—21no—
382C2×C4×C79—21no—
383C2×C4×C79—21no—
384C2×C4×C79—21no—
385C2×C4×C79—21no—
386C2×C4×C79—21no—
387C2×C4×C79—21no—
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—42no—
396C2×C4×C79—41no—
397C2×C4×C79—41no—
398C2×C4×C79—41no—
399C2×C4×C79—41no—
400C2×C4×C79—41no—
401C2×C4×C79—41no—
402C2×C4×C79—41no—
403C2×C4×C79—41no—
404C2×C4×C79—41no—
405C2×C4×C79—81no—
406C2×C4×C79—81no—
407C2×C4×C79—81no—
408C2×C4×C79—81no—
409C2×C4×C79—81no—
410C2×C4×C79—81no—
411C2×C4×C79#12011yescharacteristic
412C2×C4×C79#12011yescharacteristic
413C2×C4×C79C22×D411yescharacteristic
414C2×C4×C79C22×D411yescharacteristic
415C8×C79—41no—
416C8×C79—41no—
417C8×C79—41no—
418C8×C79—41no—
419C22×C79—21no—
420C22×C79—21no—
421C22×C79—21no—
422C22×C79—21no—
423C22×C79—21no—
424C22×C79—21no—
425C22×C79—21no—
426C22×C79—21no—
427C22×C79—41no—
428C22×C79—41no—
429C22×C79—41no—
430C22×C79—41no—
431C22×C79—41no—
432C22×C79—41no—
433C22×C79—81no—
434C22×C79—81no—
435C22×C79—81no—
436C22×C79—81no—
437C22×C79—81no—
438C22×C79—81no—
439C22×C79—81no—
440C22×C79—81no—
441C22×C79—81no—
442C22×C79—81no—
443C22×C79—81no—
444C22×C79C2×#12011yescharacteristic
445C22×C79#57711yescharacteristic
446C22×C79#57711yescharacteristic
447C4×C79—21no—
448C4×C79—21no—
449C4×C79—21no—
450C4×C79—21no—
451C4×C79—42no—
452C4×C79—41no—
453C4×C79—41no—
454C4×C79—41no—
455C4×C79—41no—
456C4×C79—41no—
457C4×C79—41no—
458C4×C79—41no—
459C4×C79—41no—
460C4×C79—41no—
461C4×C79—41no—
462C4×C79—81no—
463C4×C79—81no—
464#18416C7911yesmaximal, characteristic, direct product factor, Sylow
465C2×C79—21no—
466C2×C79—21no—
467C2×C79—41no—
468C2×C79—41no—
469C2×C79—81no—
470C2×C79—81no—
471C2×C79—161no—
472C2×C79#301011yescharacteristic
473C2×C79#301811yescharacteristic
474C2×C79#302611yescharacteristic
475#3535C2×C7911yescharacteristic, complemented
476#3194C2×C7911yescharacteristic, complemented
477#3187C2×C7911yescharacteristic, complemented
478#2661C2×C7911yescharacteristic, complemented
479#1612C2×C7911yescharacteristic, complemented
480#1611C2×C7911yescharacteristic, complemented
481#1609C2×C7911yescharacteristic, complemented
482#1608C2×C7911yescharacteristic, complemented
483#1600C2×C7911yescharacteristic, complemented
484#1599C2×C7911yescharacteristic, complemented
485#1597C2×C7911yescharacteristic, complemented
486#1596C2×C7911yescharacteristic, complemented
487#1508C2×C7911yescharacteristic, complemented
488#1501C2×C7911yescharacteristic, complemented
489#1468C2×C7911yescharacteristic, complemented
490C79#1841611yescharacteristic, direct product factor, Sylow
491#563—21no—
492#562—21no—
493#554—21no—
494#552—21no—
495#551—21no—
496#551—21no—
497#547—21no—
498#546—21no—
499#544C22×C7911yescharacteristic
500#543C22×C7911yescharacteristic
501#542—21no—
502#539—21no—
503#539—21no—
504#539C22×C7911yescharacteristic
505#538C22×C7911yescharacteristic
506#536—21no—
507#525C22×C7911yescharacteristic
508C2×#123C22×C7911yescharacteristic
509C2×C22⋊Q8C22×C7911yescharacteristic
510C2×#121C22×C7911yescharacteristic
511#483C22×C7911yescharacteristic
512#483C22×C7911yescharacteristic
513#483C22×C7911yescharacteristic
514#482—21no—
515#481—21no—
516#480C22×C7911yescharacteristic
517#469—21no—
518#468—21no—
519#465—21no—
520#465—21no—
521#450C22×C7911yescharacteristic
522#450C22×C7911yescharacteristic
523#450C22×C7911yescharacteristic
524#449—21no—
525#448—21no—
526#447C22×C7911yescharacteristic
527#407C22×C7911yescharacteristic
528C2×C22⋊C8C22×C7911yescharacteristic
529#398C22×C7911yescharacteristic
530#397C22×C7911yescharacteristic
531#394—21no—
532#394C22×C7911yescharacteristic
533#392—21no—
534#392C22×C7911yescharacteristic
535#390—21no—
536#388—21no—
537C4×C22⋊C4C22×C7911yescharacteristic
538#328C22×C7911yescharacteristic
539#328C22×C7911yescharacteristic
540#328C22×C7911yescharacteristic
541#328C22×C7911yescharacteristic
542#328C22×C7911yescharacteristic
543#328C22×C7911yescharacteristic
544#327C22×C7911yescharacteristic
545#327C22×C7911yescharacteristic
546#324C22×C7911yescharacteristic
547#324C22×C7911yescharacteristic
548#323C22×C7911yescharacteristic
549#323C22×C7911yescharacteristic
550C2×#41—21no—
551C2×#41D4×C7911yescharacteristic, complemented
552C22×Q8D4×C7911yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C7911yescharacteristic
556C22×D4C23×C7911yescharacteristic
557C23×C4C23×C7911yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C7911yescharacteristic, complemented
611C22⋊Q8D4×C7911yescharacteristic, complemented
612C22⋊Q8D4×C7911yescharacteristic, complemented
613C22⋊Q8C23×C7911yescharacteristic
614C22⋊Q8C23×C7911yescharacteristic
615C22⋊Q8C23×C7911yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C7911yescharacteristic, complemented
625#121C23×C7911yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C7911yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C7911yescharacteristic
644C2×C4⋊C4D4×C7911yescharacteristic, complemented
645C2×C4⋊C4C23×C7911yescharacteristic
646C2×C4⋊C4C23×C7911yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C7911yescharacteristic
656C2×C22⋊C4D4×C7911yescharacteristic
657C2×C22⋊C4C23×C7911yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C7911yescharacteristic
674C22⋊C8C23×C7911yescharacteristic
675C22⋊C8C23×C7911yescharacteristic
676C22⋊C8C23×C7911yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C7911yescharacteristic
680#95C23×C7911yescharacteristic
681C24—21no—
682C24C2×D4×C7911yescharacteristic
683C24C2×D4×C7911yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C7911yescharacteristic
691C2×Q8C2×D4×C7911yescharacteristic
692C2×Q8C2×D4×C7911yescharacteristic
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—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C7911yescharacteristic
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—21no—
722C22×C4—81no—
723C22×C4C2×D4×C7911yescharacteristic
724C22×C4C2×D4×C7911yescharacteristic
725C22×C4C2×D4×C7911yescharacteristic
726C22×C4C2×D4×C7911yescharacteristic
727C22×C4C2×D4×C7911yescharacteristic
728C22×C4C2×D4×C7911yescharacteristic
729C22×C4C2×D4×C7911yescharacteristic
730C22×C4C2×D4×C7911yescharacteristic
731C22×C4C24×C7911yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
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—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C7911yescharacteristic
769C4⋊C4C2×D4×C7911yescharacteristic
770C4⋊C4C2×D4×C7911yescharacteristic
771C4⋊C4C2×D4×C7911yescharacteristic
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—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C7911yescharacteristic
826C23#120×C7911yescharacteristic
827C23C22×D4×C7911yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C7911yescharacteristic
887C2×C4#120×C7911yescharacteristic
888C2×C4C22×D4×C7911yescharacteristic
889C2×C4C22×D4×C7911yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C7911yescharacteristic
920C22#577×C7911yescharacteristic
921C22#577×C7911yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C79×#301011yescharacteristic
947C2C79×#301811yescharacteristic
948C2C79×#302611yescharacteristic
subgroupG/H
center, socleC22×C79C2×#120
commutator, Frattini, cosocleC22×C4C24×C79
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C79 ◁ C23×C4×C79 ◁ G

Complements

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

NH ≅ G/Ntype
1. C79×#3535C2semidirect
2. C79×#3194C2semidirect
3. C79×#3187C2semidirect
4. C79×#2661C2semidirect
5. C79×#1612C2semidirect
6. C79×#1611C2semidirect
7. C79×#1609C2semidirect
8. C79×#1608C2semidirect
9. C79×#1600C2semidirect
10. C79×#1599C2semidirect
11. C79×#1597C2semidirect
12. C79×#1596C2semidirect
13. C79×#1508C2semidirect
14. C79×#1501C2semidirect
15. C79×#1468C2semidirect
76. C2×#41×C79D4semidirect
77. C22×Q8×C79D4semidirect
135. C22⋊Q8×C79D4semidirect
136. C22⋊Q8×C79D4semidirect
137. C22⋊Q8×C79D4semidirect
149. #121×C79D4semidirect
164. #117×C79D4semidirect
169. C2×C4⋊C4×C79D4semidirect
464. #18416C79direct (N × H)
475. #3535C2×C79semidirect
476. #3194C2×C79semidirect
477. #3187C2×C79semidirect
478. #2661C2×C79semidirect
479. #1612C2×C79semidirect
480. #1611C2×C79semidirect
481. #1609C2×C79semidirect
482. #1608C2×C79semidirect
483. #1600C2×C79semidirect
484. #1599C2×C79semidirect
485. #1597C2×C79semidirect
486. #1596C2×C79semidirect
487. #1508C2×C79semidirect
488. #1501C2×C79semidirect
489. #1468C2×C79semidirect
490. C79#18416direct (N × H)
551. C2×#41D4×C79semidirect
552. C22×Q8D4×C79semidirect
610. C22⋊Q8D4×C79semidirect
611. C22⋊Q8D4×C79semidirect
612. C22⋊Q8D4×C79semidirect
624. #121D4×C79semidirect
639. #117D4×C79semidirect
644. C2×C4⋊C4D4×C79semidirect

Maximal subgroups

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

subgroupindex
C79×#35352
C79×#31942
C79×#31872
C79×#26612
C79×#16122
C79×#16112
C79×#16092
C79×#16082
C79×#16002
C79×#15992
C79×#15972
C79×#15962
C79×#15082
C79×#15012
C79×#14682
#1841679