Finite Group Databasebeta

← C79×#18434 #34130123

Subgroups — C79×#18434 #34130123

Order 20224.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3560C211yesmaximal, characteristic, complemented
2C79×#3213C211yesmaximal, characteristic, complemented
3C79×#3211C211yesmaximal, characteristic, complemented
4C79×#2662C211yesmaximal, characteristic, complemented
5C79×#1606C211yesmaximal, characteristic, complemented
6C79×#1604C211yesmaximal, characteristic, complemented
7C79×#1603C211yesmaximal, characteristic, complemented
8C79×#1601C211yesmaximal, characteristic, complemented
9C79×#1600C211yesmaximal, characteristic, complemented
10C79×#1598C211yesmaximal, characteristic, complemented
11C79×#1597C211yesmaximal, characteristic, complemented
12C79×#1595C211yesmaximal, characteristic, complemented
13C79×#1509C211yesmaximal, characteristic, complemented
14C79×#1502C211yesmaximal, characteristic, complemented
15C79×#1473C211yesmaximal, characteristic, complemented
16#563×C79—21no—
17#560×C79—21no—
18#553×C79—21no—
19#553×C79—21no—
20#551×C79—21no—
21#547×C79—21no—
22#546×C79—21no—
23#546×C79—21no—
24#542×C79—21no—
25#539×C79—21no—
26#539×C79C2211yescharacteristic
27#538×C79—21no—
28#538×C79—21no—
29#538×C79C2211yescharacteristic
30#537×C79C2211yescharacteristic
31#534×C79C2211yescharacteristic
32#532×C79C2211yescharacteristic
33#529×C79C2211yescharacteristic
34C2×#126×C79C2211yescharacteristic
35C2×#124×C79C2211yescharacteristic, complemented
36#496×C79—21no—
37#495×C79—21no—
38#489×C79—21no—
39#488×C79—21no—
40#464×C79—21no—
41#463×C79—21no—
42#463×C79—21no—
43#463×C79—21no—
44#451×C79C2211yescharacteristic, complemented
45#450×C79C2211yescharacteristic, complemented
46#448×C79C2211yescharacteristic
47#448×C79C2211yescharacteristic
48#448×C79C2211yescharacteristic, complemented
49#447×C79C2211yescharacteristic
50#447×C79C2211yescharacteristic
51#447×C79C2211yescharacteristic, complemented
52#432×C79C2211yescharacteristic, complemented
53#431×C79C2211yescharacteristic, complemented
54#396×C79—21no—
55#395×C79C2211yescharacteristic, complemented
56#394×C79—21no—
57#394×C79C2211yescharacteristic, complemented
58#393×C79C2211yescharacteristic
59#392×C79C2211yescharacteristic
60#390×C79—21no—
61#388×C79—21no—
62C4×C4⋊C4×C79C2211yescharacteristic, complemented
63#328×C79C2211yescharacteristic, complemented
64#328×C79C2211yescharacteristic, complemented
65#327×C79C2211yescharacteristic
66#327×C79C2211yescharacteristic
67#327×C79C2211yescharacteristic
68#327×C79C2211yescharacteristic
69#327×C79C2211yescharacteristic, complemented
70#327×C79C2211yescharacteristic, complemented
71#324×C79C2211yescharacteristic, complemented
72#324×C79C2211yescharacteristic, complemented
73#323×C79C2211yescharacteristic
74#323×C79C2211yescharacteristic
75C2×#41×C79—21no—
76C2×#41×C79—21no—
77C22×Q8×C79C2311yescharacteristic
78C22×D4×C79—21no—
79C22×D4×C79—21no—
80C22×D4×C79C2311yescharacteristic
81C2×Q16×C79—21no—
82C2×SD16×C79—21no—
83C2×SD16×C79—21no—
84C2×SD16×C79—21no—
85C2×SD16×C79—21no—
86C2×D8×C79—21no—
87C2×D8×C79—21no—
88C2×D8×C79—21no—
89C4⋊Q8×C79—21no—
90C4⋊Q8×C79D411yescharacteristic, complemented
91#127×C79D411yescharacteristic, complemented
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#126×C79—21no—
99#126×C79—21no—
100#126×C79—21no—
101#125×C79—21no—
102#125×C79—21no—
103#125×C79D411yescharacteristic, complemented
104#124×C79—21no—
105#124×C79—21no—
106#124×C79—21no—
107#124×C79—21no—
108#124×C79—21no—
109#124×C79—21no—
110#124×C79—21no—
111#124×C79—21no—
112#124×C79D411yescharacteristic, complemented
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—
121#123×C79—21no—
122#123×C79—21no—
123#123×C79—21no—
124#123×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×C79C2311yescharacteristic
133#121×C79—21no—
134#121×C79—21no—
135#121×C79—21no—
136#121×C79—21no—
137#121×C79—21no—
138#121×C79—21no—
139#121×C79—21no—
140#121×C79—21no—
141#121×C79—21no—
142#121×C79—21no—
143#121×C79—21no—
144#121×C79—21no—
145#121×C79C2311yescharacteristic
146#121×C79C2311yescharacteristic
147#121×C79C2311yescharacteristic
148#120×C79—21no—
149#120×C79—21no—
150#120×C79—21no—
151#120×C79—21no—
152#120×C79—21no—
153C4×Q8×C79D411yescharacteristic, complemented
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—
161C4×D4×C79—21no—
162C4×D4×C79D411yescharacteristic, complemented
163C4×D4×C79D411yescharacteristic, complemented
164C4×D4×C79D411yescharacteristic, complemented
165#117×C79—21no—
166#117×C79—21no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79D411yescharacteristic
171C2×C4⋊C4×C79D411yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
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×C79—21no—
181C2×C22⋊C4×C79D411yescharacteristic
182C2×C22⋊C4×C79D411yescharacteristic
183C2×C22⋊C4×C79C2311yescharacteristic
184C2×C42×C79—21no—
185C2×C42×C79C2311yescharacteristic
186C4⋊C8×C79—21no—
187C4⋊C8×C79—21no—
188#103×C79—21no—
189#103×C79—21no—
190#103×C79—21no—
191#103×C79—21no—
192#102×C79—21no—
193#102×C79—21no—
194#102×C79—21no—
195#102×C79—21no—
196C22⋊C8×C79C2311yescharacteristic
197C22⋊C8×C79C2311yescharacteristic
198C22⋊C8×C79C2311yescharacteristic
199C22⋊C8×C79C2311yescharacteristic
200#97×C79—21no—
201C4×C8×C79—21no—
202#95×C79—21no—
203#95×C79—21no—
204#95×C79C2311yescharacteristic
205#95×C79C2311yescharacteristic
206C24×C79—21no—
207C24×C79—21no—
208C24×C79C2×D411yescharacteristic
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×C79—21no—
216C2×Q8×C79—21no—
217C2×Q8×C79—81no—
218C2×Q8×C79C2×D411yescharacteristic
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—21no—
229C2×D4×C79—21no—
230C2×D4×C79—21no—
231C2×D4×C79—21no—
232C2×D4×C79—21no—
233C2×D4×C79—42no—
234C2×D4×C79—81no—
235C2×D4×C79—81no—
236C2×D4×C79—81no—
237C2×D4×C79—81no—
238C2×D4×C79—81no—
239C2×D4×C79C2×D411yescharacteristic
240C2×D4×C79C2×D411yescharacteristic
241C2×D4×C79C2×D411yescharacteristic
242C22×C4×C79—21no—
243C22×C4×C79—21no—
244C22×C4×C79—21no—
245C22×C4×C79—21no—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79—21no—
252C22×C4×C79—21no—
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D411yescharacteristic
258C22×C4×C79C2411yescharacteristic
259Q16×C79—81no—
260SD16×C79—81no—
261SD16×C79—81no—
262SD16×C79—81no—
263SD16×C79—81no—
264D8×C79—81no—
265D8×C79—81no—
266D8×C79—81no—
267C2×C8×C79—21no—
268C2×C8×C79—21no—
269C2×C8×C79—21no—
270C2×C8×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—42no—
289C4⋊C4×C79—81no—
290C4⋊C4×C79C2×D411yescharacteristic
291C4⋊C4×C79C2×D411yescharacteristic
292C4⋊C4×C79C2×D411yescharacteristic
293C4⋊C4×C79C2×D411yescharacteristic
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—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—42no—
320C22⋊C4×C79—41no—
321C22⋊C4×C79—41no—
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—81no—
331C42×C79C2×D411yescharacteristic
332C42×C79C2×D411yescharacteristic
333C42×C79C2×D411yescharacteristic
334C42×C79C2×D411yescharacteristic
335C23×C79—21no—
336C23×C79—21no—
337C23×C79—21no—
338C23×C79—21no—
339C23×C79—21no—
340C23×C79—21no—
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—81no—
351C23×C79—81no—
352C23×C79—81no—
353C23×C79C22×D411yescharacteristic
354Q8×C79—41no—
355Q8×C79—41no—
356Q8×C79—41no—
357Q8×C79—41no—
358Q8×C79—41no—
359Q8×C79—81no—
360Q8×C79—81no—
361D4×C79—41no—
362D4×C79—41no—
363D4×C79—41no—
364D4×C79—41no—
365D4×C79—41no—
366D4×C79—41no—
367D4×C79—41no—
368D4×C79—41no—
369D4×C79—41no—
370D4×C79—41no—
371D4×C79—41no—
372D4×C79—41no—
373D4×C79—41no—
374D4×C79—81no—
375D4×C79—81no—
376D4×C79—81no—
377D4×C79—81no—
378D4×C79—81no—
379D4×C79—81no—
380D4×C79—81no—
381D4×C79—81no—
382D4×C79—81no—
383D4×C79—84no—
384C2×C4×C79—21no—
385C2×C4×C79—21no—
386C2×C4×C79—22no—
387C2×C4×C79—21no—
388C2×C4×C79—21no—
389C2×C4×C79—21no—
390C2×C4×C79—21no—
391C2×C4×C79—21no—
392C2×C4×C79—21no—
393C2×C4×C79—21no—
394C2×C4×C79—21no—
395C2×C4×C79—21no—
396C2×C4×C79—21no—
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—41no—
406C2×C4×C79—41no—
407C2×C4×C79—41no—
408C2×C4×C79—41no—
409C2×C4×C79—81no—
410C2×C4×C79—81no—
411C2×C4×C79—81no—
412C2×C4×C79—81no—
413C2×C4×C79—81no—
414C2×C4×C79—81no—
415C2×C4×C79—81no—
416C2×C4×C79—81no—
417C2×C4×C79#12011yescharacteristic
418C2×C4×C79#12011yescharacteristic
419C2×C4×C79#12011yescharacteristic
420C2×C4×C79#12011yescharacteristic
421C2×C4×C79C22×D411yescharacteristic
422C2×C4×C79C22×D411yescharacteristic
423C8×C79—41no—
424C8×C79—41no—
425C8×C79—41no—
426C8×C79—41no—
427C22×C79—21no—
428C22×C79—21no—
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—41no—
439C22×C79—41no—
440C22×C79—41no—
441C22×C79—81no—
442C22×C79—81no—
443C22×C79—81no—
444C22×C79—81no—
445C22×C79—81no—
446C22×C79—81no—
447C22×C79—81no—
448C22×C79—81no—
449C22×C79—81no—
450C22×C79—162no—
451C22×C79C2×#12011yescharacteristic
452C22×C79#57611yescharacteristic
453C22×C79#57711yescharacteristic
454C4×C79—21no—
455C4×C79—21no—
456C4×C79—21no—
457C4×C79—21no—
458C4×C79—21no—
459C4×C79—21no—
460C4×C79—42no—
461C4×C79—41no—
462C4×C79—41no—
463C4×C79—41no—
464C4×C79—41no—
465C4×C79—41no—
466C4×C79—41no—
467C4×C79—41no—
468C4×C79—41no—
469C4×C79—81no—
470C4×C79—81no—
471#18434C7911yesmaximal, characteristic, direct product factor, Sylow
472C2×C79—21no—
473C2×C79—21no—
474C2×C79—81no—
475C2×C79—81no—
476C2×C79—81no—
477C2×C79—81no—
478C2×C79—161no—
479C2×C79#301211yescharacteristic
480C2×C79#301811yescharacteristic
481C2×C79#302711yescharacteristic
482#3560C2×C7911yescharacteristic, complemented
483#3213C2×C7911yescharacteristic, complemented
484#3211C2×C7911yescharacteristic, complemented
485#2662C2×C7911yescharacteristic, complemented
486#1606C2×C7911yescharacteristic, complemented
487#1604C2×C7911yescharacteristic, complemented
488#1603C2×C7911yescharacteristic, complemented
489#1601C2×C7911yescharacteristic, complemented
490#1600C2×C7911yescharacteristic, complemented
491#1598C2×C7911yescharacteristic, complemented
492#1597C2×C7911yescharacteristic, complemented
493#1595C2×C7911yescharacteristic, complemented
494#1509C2×C7911yescharacteristic, complemented
495#1502C2×C7911yescharacteristic, complemented
496#1473C2×C7911yescharacteristic, complemented
497C79#1843411yescharacteristic, direct product factor, Sylow
498#563—21no—
499#560—21no—
500#553—21no—
501#553—21no—
502#551—21no—
503#547—21no—
504#546—21no—
505#546—21no—
506#542—21no—
507#539—21no—
508#539C22×C7911yescharacteristic
509#538—21no—
510#538—21no—
511#538C22×C7911yescharacteristic
512#537C22×C7911yescharacteristic
513#534C22×C7911yescharacteristic
514#532C22×C7911yescharacteristic
515#529C22×C7911yescharacteristic
516C2×#126C22×C7911yescharacteristic
517C2×#124C22×C7911yescharacteristic, complemented
518#496—21no—
519#495—21no—
520#489—21no—
521#488—21no—
522#464—21no—
523#463—21no—
524#463—21no—
525#463—21no—
526#451C22×C7911yescharacteristic, complemented
527#450C22×C7911yescharacteristic, complemented
528#448C22×C7911yescharacteristic
529#448C22×C7911yescharacteristic
530#448C22×C7911yescharacteristic, complemented
531#447C22×C7911yescharacteristic
532#447C22×C7911yescharacteristic
533#447C22×C7911yescharacteristic, complemented
534#432C22×C7911yescharacteristic, complemented
535#431C22×C7911yescharacteristic, complemented
536#396—21no—
537#395C22×C7911yescharacteristic, complemented
538#394—21no—
539#394C22×C7911yescharacteristic, complemented
540#393C22×C7911yescharacteristic
541#392C22×C7911yescharacteristic
542#390—21no—
543#388—21no—
544C4×C4⋊C4C22×C7911yescharacteristic, complemented
545#328C22×C7911yescharacteristic, complemented
546#328C22×C7911yescharacteristic, complemented
547#327C22×C7911yescharacteristic
548#327C22×C7911yescharacteristic
549#327C22×C7911yescharacteristic
550#327C22×C7911yescharacteristic
551#327C22×C7911yescharacteristic, complemented
552#327C22×C7911yescharacteristic, complemented
553#324C22×C7911yescharacteristic, complemented
554#324C22×C7911yescharacteristic, complemented
555#323C22×C7911yescharacteristic
556#323C22×C7911yescharacteristic
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C7911yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C7911yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C7911yescharacteristic, complemented
573#127D4×C7911yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C7911yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C7911yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C7911yescharacteristic
615#121—21no—
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#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C7911yescharacteristic
628#121C23×C7911yescharacteristic
629#121C23×C7911yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C7911yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C7911yescharacteristic, complemented
645C4×D4D4×C7911yescharacteristic, complemented
646C4×D4D4×C7911yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C7911yescharacteristic
653C2×C4⋊C4D4×C7911yescharacteristic
654C2×C4⋊C4C23×C7911yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C7911yescharacteristic
664C2×C22⋊C4D4×C7911yescharacteristic
665C2×C22⋊C4C23×C7911yescharacteristic
666C2×C42—21no—
667C2×C42C23×C7911yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C7911yescharacteristic
679C22⋊C8C23×C7911yescharacteristic
680C22⋊C8C23×C7911yescharacteristic
681C22⋊C8C23×C7911yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C7911yescharacteristic
687#95C23×C7911yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C7911yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C7911yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C7911yescharacteristic
722C2×D4C2×D4×C7911yescharacteristic
723C2×D4C2×D4×C7911yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C7911yescharacteristic
736C22×C4C2×D4×C7911yescharacteristic
737C22×C4C2×D4×C7911yescharacteristic
738C22×C4C2×D4×C7911yescharacteristic
739C22×C4C2×D4×C7911yescharacteristic
740C22×C4C24×C7911yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—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—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C7911yescharacteristic
773C4⋊C4C2×D4×C7911yescharacteristic
774C4⋊C4C2×D4×C7911yescharacteristic
775C4⋊C4C2×D4×C7911yescharacteristic
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—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C7911yescharacteristic
814C42C2×D4×C7911yescharacteristic
815C42C2×D4×C7911yescharacteristic
816C42C2×D4×C7911yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C7911yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C7911yescharacteristic
900C2×C4#120×C7911yescharacteristic
901C2×C4#120×C7911yescharacteristic
902C2×C4#120×C7911yescharacteristic
903C2×C4C22×D4×C7911yescharacteristic
904C2×C4C22×D4×C7911yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C7911yescharacteristic
934C22#576×C7911yescharacteristic
935C22#577×C7911yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C79×#301211yescharacteristic
961C2C79×#301811yescharacteristic
962C2C79×#302711yescharacteristic
subgroupG/H
center, socleC22×C79C2×#120
commutator, Frattini, cosocleC22×C4C24×C79
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G

Complements

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

NH ≅ G/Ntype
1. C79×#3560C2semidirect
2. C79×#3213C2semidirect
3. C79×#3211C2semidirect
4. C79×#2662C2semidirect
5. C79×#1606C2semidirect
6. C79×#1604C2semidirect
7. C79×#1603C2semidirect
8. C79×#1601C2semidirect
9. C79×#1600C2semidirect
10. C79×#1598C2semidirect
11. C79×#1597C2semidirect
12. C79×#1595C2semidirect
13. C79×#1509C2semidirect
14. C79×#1502C2semidirect
15. C79×#1473C2semidirect
35. C2×#124×C79C22semidirect
44. #451×C79C22semidirect
45. #450×C79C22semidirect
48. #448×C79C22semidirect
51. #447×C79C22semidirect
52. #432×C79C22semidirect
53. #431×C79C22semidirect
55. #395×C79C22semidirect
57. #394×C79C22semidirect
62. C4×C4⋊C4×C79C22semidirect
63. #328×C79C22semidirect
64. #328×C79C22semidirect
69. #327×C79C22semidirect
70. #327×C79C22semidirect
71. #324×C79C22semidirect
72. #324×C79C22semidirect
90. C4⋊Q8×C79D4semidirect
91. #127×C79D4semidirect
103. #125×C79D4semidirect
112. #124×C79D4semidirect
153. C4×Q8×C79D4semidirect
162. C4×D4×C79D4semidirect
163. C4×D4×C79D4semidirect
164. C4×D4×C79D4semidirect
471. #18434C79direct (N × H)
482. #3560C2×C79semidirect
483. #3213C2×C79semidirect
484. #3211C2×C79semidirect
485. #2662C2×C79semidirect
486. #1606C2×C79semidirect
487. #1604C2×C79semidirect
488. #1603C2×C79semidirect
489. #1601C2×C79semidirect
490. #1600C2×C79semidirect
491. #1598C2×C79semidirect
492. #1597C2×C79semidirect
493. #1595C2×C79semidirect
494. #1509C2×C79semidirect
495. #1502C2×C79semidirect
496. #1473C2×C79semidirect
497. C79#18434direct (N × H)
517. C2×#124C22×C79semidirect
526. #451C22×C79semidirect
527. #450C22×C79semidirect
530. #448C22×C79semidirect
533. #447C22×C79semidirect
534. #432C22×C79semidirect
535. #431C22×C79semidirect
537. #395C22×C79semidirect
539. #394C22×C79semidirect
544. C4×C4⋊C4C22×C79semidirect
545. #328C22×C79semidirect
546. #328C22×C79semidirect
551. #327C22×C79semidirect
552. #327C22×C79semidirect
553. #324C22×C79semidirect
554. #324C22×C79semidirect
572. C4⋊Q8D4×C79semidirect
573. #127D4×C79semidirect
585. #125D4×C79semidirect
594. #124D4×C79semidirect
635. C4×Q8D4×C79semidirect
644. C4×D4D4×C79semidirect
645. C4×D4D4×C79semidirect
646. C4×D4D4×C79semidirect

Maximal subgroups

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

subgroupindex
C79×#35602
C79×#32132
C79×#32112
C79×#26622
C79×#16062
C79×#16042
C79×#16032
C79×#16012
C79×#16002
C79×#15982
C79×#15972
C79×#15952
C79×#15092
C79×#15022
C79×#14732
#1843479