Finite Group Databasebeta

← C79×#17597 #34129286

Subgroups — C79×#17597 #34129286

Order 20224.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3519C211yesmaximal, characteristic
2C79×#2974C211yesmaximal, characteristic, complemented
3C79×#2318C211yesmaximal, characteristic, complemented
4C79×#1521C211yesmaximal, characteristic, complemented
5C79×#1519C211yesmaximal, characteristic, complemented
6C79×#1517C211yesmaximal, characteristic, complemented
7C79×#1516C211yesmaximal, characteristic, complemented
8C79×#1514C211yesmaximal, characteristic, complemented
9C79×#1513C211yesmaximal, characteristic, complemented
10C79×#1512C211yesmaximal, characteristic, complemented
11C79×#1510C211yesmaximal, characteristic, complemented
12C79×#1507C211yesmaximal, characteristic, complemented
13C79×#1504C211yesmaximal, characteristic, complemented
14C79×#1501C211yesmaximal, characteristic, complemented
15C2×#327×C79C211yesmaximal, characteristic, complemented
16#555×C79C411yescharacteristic, complemented
17#554×C79C411yescharacteristic, complemented
18#553×C79—21no—
19#553×C79C411yescharacteristic, complemented
20#553×C79C411yescharacteristic, complemented
21#550×C79C411yescharacteristic, complemented
22#546×C79—21no—
23#546×C79—21no—
24#546×C79C411yescharacteristic, complemented
25#546×C79C411yescharacteristic, complemented
26D42×C79—21no—
27D42×C79C411yescharacteristic, complemented
28#540×C79—21no—
29#538×C79—21no—
30#538×C79—21no—
31#532×C79C2211yescharacteristic
32#529×C79C2211yescharacteristic
33#525×C79C2211yescharacteristic
34#525×C79C2211yescharacteristic
35C2×#121×C79C2211yescharacteristic
36C2×#121×C79C2211yescharacteristic
37#518×C79—21no—
38C2×C4×D4×C79C2211yescharacteristic
39#436×C79—21no—
40#435×C79—21no—
41#435×C79—21no—
42C8×D4×C79—21no—
43#432×C79C2211yescharacteristic, complemented
44#431×C79C2211yescharacteristic, complemented
45#407×C79C2211yescharacteristic, complemented
46#407×C79C2211yescharacteristic, complemented
47C2×C22⋊C8×C79C2211yescharacteristic, complemented
48C2×C22⋊C8×C79C2211yescharacteristic, complemented
49#388×C79—21no—
50#387×C79—21no—
51#386×C79—21no—
52#385×C79—21no—
53#383×C79C2211yescharacteristic, complemented
54#382×C79C2211yescharacteristic, complemented
55#381×C79C2211yescharacteristic, complemented
56#380×C79C2211yescharacteristic, complemented
57C4×C22⋊C4×C79C2211yescharacteristic, complemented
58C2×#95×C79C2211yescharacteristic, complemented
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, complemented
68#327×C79C2211yescharacteristic, complemented
69#327×C79C2211yescharacteristic, complemented
70#327×C79C2211yescharacteristic, complemented
71#327×C79C2211yescharacteristic, complemented
72#327×C79C2211yescharacteristic, complemented
73#327×C79C2211yescharacteristic, complemented
74#327×C79C2211yescharacteristic, complemented
75C2×#41×C79—21no—
76C2×#41×C79C2×C411yescharacteristic
77C2×#41×C79C2×C411yescharacteristic, complemented
78C22×D4×C79—21no—
79C22×D4×C79—21no—
80C22×D4×C79—21no—
81C22×D4×C79C2×C411yescharacteristic
82C22×D4×C79C2×C411yescharacteristic, complemented
83C22×D4×C79D411yescharacteristic
84C23×C4×C79—21no—
85C23×C4×C79C2311yescharacteristic
86C23×C4×C79C2311yescharacteristic
87C2×M16×C79—21no—
88C2×M16×C79—21no—
89C22×C8×C79—21no—
90C22×C8×C79—21no—
91C4⋊Q8×C79C2×C411yescharacteristic, complemented
92#127×C79—21no—
93#127×C79C2×C411yescharacteristic, complemented
94#126×C79—21no—
95#126×C79—21no—
96#126×C79—21no—
97#125×C79—21no—
98#125×C79C2×C411yescharacteristic, complemented
99#124×C79—21no—
100#124×C79—21no—
101#124×C79—21no—
102#124×C79C2×C411yescharacteristic, complemented
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—
110C22⋊Q8×C79—21no—
111C22⋊Q8×C79—21no—
112C22⋊Q8×C79C2×C411yescharacteristic
113C22⋊Q8×C79C2×C411yescharacteristic, complemented
114C22⋊Q8×C79C2311yescharacteristic
115#121×C79—21no—
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×C79—21no—
124#121×C79—21no—
125#121×C79—21no—
126#121×C79—21no—
127#121×C79—21no—
128#121×C79C2×C411yescharacteristic
129#121×C79C2×C411yescharacteristic
130#121×C79C2×C411yescharacteristic
131#121×C79C2×C411yescharacteristic, complemented
132#121×C79C2×C411yescharacteristic, complemented
133#121×C79C2×C411yescharacteristic, complemented
134#121×C79C2311yescharacteristic
135#121×C79C2311yescharacteristic
136#121×C79C2311yescharacteristic
137#120×C79—21no—
138#120×C79—21no—
139#120×C79—21no—
140#120×C79—21no—
141#120×C79—21no—
142#120×C79—21no—
143C4×Q8×C79C2×C411yescharacteristic, complemented
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×C79—21no—
153C4×D4×C79—21no—
154C4×D4×C79C2×C411yescharacteristic
155C4×D4×C79C2×C411yescharacteristic
156C4×D4×C79C2×C411yescharacteristic
157C4×D4×C79C2×C411yescharacteristic
158C4×D4×C79C2×C411yescharacteristic, complemented
159C4×D4×C79C2×C411yescharacteristic, complemented
160C4×D4×C79C2×C411yescharacteristic, complemented
161C4×D4×C79D411yescharacteristic
162C4×D4×C79D411yescharacteristic
163C4×D4×C79D411yescharacteristic
164C4×D4×C79D411yescharacteristic
165#117×C79—21no—
166#117×C79—21no—
167#117×C79C2×C411yescharacteristic
168#117×C79C2×C411yescharacteristic, complemented
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79—21no—
171C2×C4⋊C4×C79C2×C411yescharacteristic
172C2×C4⋊C4×C79C2×C411yescharacteristic, complemented
173C2×C4⋊C4×C79D411yescharacteristic
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×C42×C79—21no—
184C2×C42×C79C2311yescharacteristic
185C4⋊C8×C79—21no—
186C4⋊C8×C79—21no—
187C22⋊C8×C79—21no—
188C22⋊C8×C79—21no—
189C22⋊C8×C79—21no—
190C22⋊C8×C79—21no—
191C22⋊C8×C79C2311yescharacteristic
192C22⋊C8×C79C2311yescharacteristic
193C22⋊C8×C79C2311yescharacteristic
194C22⋊C8×C79C2311yescharacteristic
195#97×C79—21no—
196C4×C8×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×C79—21no—
208C24×C79C2×D411yescharacteristic
209C24×C79C2×D411yescharacteristic
210#41×C79—81no—
211#41×C79—81no—
212#41×C79—81no—
213#41×C79—81no—
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—21no—
229C2×D4×C79—21no—
230C2×D4×C79—21no—
231C2×D4×C79—42no—
232C2×D4×C79—44no—
233C2×D4×C79—81no—
234C2×D4×C79—81no—
235C2×D4×C79—81no—
236C2×D4×C79—81no—
237C2×D4×C79—81no—
238C2×D4×C79—81no—
239C2×D4×C79C22⋊C411yescharacteristic
240C2×D4×C79C22⋊C411yescharacteristic
241C2×D4×C79C22⋊C411yescharacteristic
242C2×D4×C79C22⋊C411yescharacteristic
243C2×D4×C79C22×C411yescharacteristic
244C2×D4×C79C22×C411yescharacteristic
245C2×D4×C79C22×C411yescharacteristic
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×C79—21no—
254C22×C4×C79—21no—
255C22×C4×C79—21no—
256C22×C4×C79—21no—
257C22×C4×C79—42no—
258C22×C4×C79—81no—
259C22×C4×C79—81no—
260C22×C4×C79—81no—
261C22×C4×C79—81no—
262C22×C4×C79C22×C411yescharacteristic
263C22×C4×C79C22×C411yescharacteristic
264C22×C4×C79C22×C411yescharacteristic
265C22×C4×C79C22×C411yescharacteristic
266C22×C4×C79C2×D411yescharacteristic
267C22×C4×C79C2×D411yescharacteristic
268C22×C4×C79C2×D411yescharacteristic
269C22×C4×C79C2×D411yescharacteristic
270C22×C4×C79C2×D411yescharacteristic
271C22×C4×C79C2×D411yescharacteristic
272C22×C4×C79C2×D411yescharacteristic
273C22×C4×C79C2×D411yescharacteristic
274C22×C4×C79C2411yescharacteristic
275M16×C79—81no—
276M16×C79—81no—
277C2×C8×C79—21no—
278C2×C8×C79—21no—
279C2×C8×C79—21no—
280C2×C8×C79—21no—
281C2×C8×C79—81no—
282C2×C8×C79—81no—
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×C79—81no—
294C4⋊C4×C79C22⋊C411yescharacteristic
295C4⋊C4×C79C22⋊C411yescharacteristic
296C4⋊C4×C79C22⋊C411yescharacteristic
297C4⋊C4×C79C22⋊C411yescharacteristic
298C4⋊C4×C79C22×C411yescharacteristic
299C4⋊C4×C79C22×C411yescharacteristic
300C4⋊C4×C79C22×C411yescharacteristic
301C4⋊C4×C79C22×C411yescharacteristic
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—21no—
321C22⋊C4×C79—42no—
322C22⋊C4×C79—81no—
323C22⋊C4×C79—81no—
324C22⋊C4×C79C22⋊C411yescharacteristic
325C22⋊C4×C79C22⋊C411yescharacteristic
326C22⋊C4×C79C22⋊C411yescharacteristic
327C22⋊C4×C79C22⋊C411yescharacteristic
328C22⋊C4×C79C22⋊C411yescharacteristic
329C22⋊C4×C79C22⋊C411yescharacteristic
330C22⋊C4×C79C22⋊C411yescharacteristic
331C22⋊C4×C79C22⋊C411yescharacteristic
332C42×C79—21no—
333C42×C79—21no—
334C42×C79—21no—
335C42×C79—81no—
336C42×C79C22×C411yescharacteristic
337C42×C79C22×C411yescharacteristic
338C42×C79C2×D411yescharacteristic
339C42×C79C2×D411yescharacteristic
340C23×C79—21no—
341C23×C79—21no—
342C23×C79—22no—
343C23×C79—21no—
344C23×C79—21no—
345C23×C79—21no—
346C23×C79—21no—
347C23×C79—21no—
348C23×C79—41no—
349C23×C79—41no—
350C23×C79—41no—
351C23×C79—42no—
352C23×C79—42no—
353C23×C79—81no—
354C23×C79—81no—
355C23×C79—81no—
356C23×C79—81no—
357C23×C79C2×C22⋊C411yescharacteristic
358C23×C79C2×C22⋊C411yescharacteristic
359C23×C79C2×C22⋊C411yescharacteristic
360C23×C79C2×C22⋊C411yescharacteristic
361C23×C79C22×D411yescharacteristic
362Q8×C79—41no—
363Q8×C79—81no—
364D4×C79—22no—
365D4×C79—22no—
366D4×C79—41no—
367D4×C79—41no—
368D4×C79—41no—
369D4×C79—41no—
370D4×C79—41no—
371D4×C79—42no—
372D4×C79—42no—
373D4×C79—41no—
374D4×C79—41no—
375D4×C79—41no—
376D4×C79—41no—
377D4×C79—41no—
378D4×C79—41no—
379D4×C79—42no—
380D4×C79—81no—
381D4×C79—81no—
382D4×C79—81no—
383D4×C79—81no—
384D4×C79—81no—
385D4×C79—81no—
386D4×C79—81no—
387D4×C79—81no—
388D4×C79—81no—
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—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—41no—
406C2×C4×C79—41no—
407C2×C4×C79—41no—
408C2×C4×C79—42no—
409C2×C4×C79—41no—
410C2×C4×C79—41no—
411C2×C4×C79—41no—
412C2×C4×C79—41no—
413C2×C4×C79—41no—
414C2×C4×C79—41no—
415C2×C4×C79—41no—
416C2×C4×C79—41no—
417C2×C4×C79—41no—
418C2×C4×C79—41no—
419C2×C4×C79—41no—
420C2×C4×C79—41no—
421C2×C4×C79—81no—
422C2×C4×C79—81no—
423C2×C4×C79—81no—
424C2×C4×C79—81no—
425C2×C4×C79—81no—
426C2×C4×C79—81no—
427C2×C4×C79—84no—
428C2×C4×C79C2×C22⋊C411yescharacteristic
429C2×C4×C79C2×C22⋊C411yescharacteristic
430C2×C4×C79C2×C22⋊C411yescharacteristic
431C2×C4×C79C2×C22⋊C411yescharacteristic
432C2×C4×C79C2×C22⋊C411yescharacteristic
433C2×C4×C79C2×C22⋊C411yescharacteristic
434C2×C4×C79C2×C22⋊C411yescharacteristic
435C2×C4×C79C2×C22⋊C411yescharacteristic
436C2×C4×C79C23×C411yescharacteristic
437C2×C4×C79C22×D411yescharacteristic
438C8×C79—41no—
439C8×C79—41no—
440C8×C79—41no—
441C8×C79—41no—
442C22×C79—21no—
443C22×C79—21no—
444C22×C79—21no—
445C22×C79—21no—
446C22×C79—21no—
447C22×C79—21no—
448C22×C79—21no—
449C22×C79—21no—
450C22×C79—21no—
451C22×C79—21no—
452C22×C79—21no—
453C22×C79—21no—
454C22×C79—21no—
455C22×C79—42no—
456C22×C79—42no—
457C22×C79—41no—
458C22×C79—41no—
459C22×C79—41no—
460C22×C79—41no—
461C22×C79—41no—
462C22×C79—41no—
463C22×C79—41no—
464C22×C79—41no—
465C22×C79—41no—
466C22×C79—81no—
467C22×C79—81no—
468C22×C79—162no—
469C22×C79—162no—
470C22×C79#42112yes—
471C22×C79C22×C22⋊C411yescharacteristic
472C22×C79#57611yescharacteristic
473C22×C79#57711yescharacteristic
474C4×C79—21no—
475C4×C79—21no—
476C4×C79—21no—
477C4×C79—21no—
478C4×C79—21no—
479C4×C79—21no—
480C4×C79—21no—
481C4×C79—21no—
482C4×C79—21no—
483C4×C79—21no—
484C4×C79—41no—
485C4×C79—41no—
486C4×C79—41no—
487C4×C79—41no—
488C4×C79—41no—
489C4×C79—81no—
490C4×C79—81no—
491C4×C79—81no—
492C4×C79—81no—
493#17597C7911yesmaximal, characteristic, direct product factor, Sylow
494C2×C79—21no—
495C2×C79—21no—
496C2×C79—22no—
497C2×C79—41no—
498C2×C79—41no—
499C2×C79—41no—
500C2×C79—81no—
501C2×C79—81no—
502C2×C79—81no—
503C2×C79#288311yescharacteristic
504C2×C79#289711yescharacteristic
505C2×C79C2×#42111yescharacteristic
506#3519C2×C7911yescharacteristic
507#2974C2×C7911yescharacteristic, complemented
508#2318C2×C7911yescharacteristic, complemented
509#1521C2×C7911yescharacteristic, complemented
510#1519C2×C7911yescharacteristic, complemented
511#1517C2×C7911yescharacteristic, complemented
512#1516C2×C7911yescharacteristic, complemented
513#1514C2×C7911yescharacteristic, complemented
514#1513C2×C7911yescharacteristic, complemented
515#1512C2×C7911yescharacteristic, complemented
516#1510C2×C7911yescharacteristic, complemented
517#1507C2×C7911yescharacteristic, complemented
518#1504C2×C7911yescharacteristic, complemented
519#1501C2×C7911yescharacteristic, complemented
520C2×#327C2×C7911yescharacteristic, complemented
521C79#1759711yescharacteristic, direct product factor, Sylow
522#555C4×C7911yescharacteristic, complemented
523#554C4×C7911yescharacteristic, complemented
524#553—21no—
525#553C4×C7911yescharacteristic, complemented
526#553C4×C7911yescharacteristic, complemented
527#550C4×C7911yescharacteristic, complemented
528#546—21no—
529#546—21no—
530#546C4×C7911yescharacteristic, complemented
531#546C4×C7911yescharacteristic, complemented
532D42—21no—
533D42C4×C7911yescharacteristic, complemented
534#540—21no—
535#538—21no—
536#538—21no—
537#532C22×C7911yescharacteristic
538#529C22×C7911yescharacteristic
539#525C22×C7911yescharacteristic
540#525C22×C7911yescharacteristic
541C2×#121C22×C7911yescharacteristic
542C2×#121C22×C7911yescharacteristic
543#518—21no—
544C2×C4×D4C22×C7911yescharacteristic
545#436—21no—
546#435—21no—
547#435—21no—
548C8×D4—21no—
549#432C22×C7911yescharacteristic, complemented
550#431C22×C7911yescharacteristic, complemented
551#407C22×C7911yescharacteristic, complemented
552#407C22×C7911yescharacteristic, complemented
553C2×C22⋊C8C22×C7911yescharacteristic, complemented
554C2×C22⋊C8C22×C7911yescharacteristic, complemented
555#388—21no—
556#387—21no—
557#386—21no—
558#385—21no—
559#383C22×C7911yescharacteristic, complemented
560#382C22×C7911yescharacteristic, complemented
561#381C22×C7911yescharacteristic, complemented
562#380C22×C7911yescharacteristic, complemented
563C4×C22⋊C4C22×C7911yescharacteristic, complemented
564C2×#95C22×C7911yescharacteristic, complemented
565#328C22×C7911yescharacteristic, complemented
566#328C22×C7911yescharacteristic, complemented
567#328C22×C7911yescharacteristic, complemented
568#328C22×C7911yescharacteristic, complemented
569#327C22×C7911yescharacteristic
570#327C22×C7911yescharacteristic
571#327C22×C7911yescharacteristic
572#327C22×C7911yescharacteristic
573#327C22×C7911yescharacteristic, complemented
574#327C22×C7911yescharacteristic, complemented
575#327C22×C7911yescharacteristic, complemented
576#327C22×C7911yescharacteristic, complemented
577#327C22×C7911yescharacteristic, complemented
578#327C22×C7911yescharacteristic, complemented
579#327C22×C7911yescharacteristic, complemented
580#327C22×C7911yescharacteristic, complemented
581C2×#41—21no—
582C2×#41C2×C4×C7911yescharacteristic
583C2×#41C2×C4×C7911yescharacteristic, complemented
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4C2×C4×C7911yescharacteristic
588C22×D4C2×C4×C7911yescharacteristic, complemented
589C22×D4D4×C7911yescharacteristic
590C23×C4—21no—
591C23×C4C23×C7911yescharacteristic
592C23×C4C23×C7911yescharacteristic
593C2×M16—21no—
594C2×M16—21no—
595C22×C8—21no—
596C22×C8—21no—
597C4⋊Q8C2×C4×C7911yescharacteristic, complemented
598#127—21no—
599#127C2×C4×C7911yescharacteristic, complemented
600#126—21no—
601#126—21no—
602#126—21no—
603#125—21no—
604#125C2×C4×C7911yescharacteristic, complemented
605#124—21no—
606#124—21no—
607#124—21no—
608#124C2×C4×C7911yescharacteristic, complemented
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8C2×C4×C7911yescharacteristic
619C22⋊Q8C2×C4×C7911yescharacteristic, complemented
620C22⋊Q8C23×C7911yescharacteristic
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121C2×C4×C7911yescharacteristic
635#121C2×C4×C7911yescharacteristic
636#121C2×C4×C7911yescharacteristic
637#121C2×C4×C7911yescharacteristic, complemented
638#121C2×C4×C7911yescharacteristic, complemented
639#121C2×C4×C7911yescharacteristic, complemented
640#121C23×C7911yescharacteristic
641#121C23×C7911yescharacteristic
642#121C23×C7911yescharacteristic
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648#120—21no—
649C4×Q8C2×C4×C7911yescharacteristic, complemented
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4C2×C4×C7911yescharacteristic
661C4×D4C2×C4×C7911yescharacteristic
662C4×D4C2×C4×C7911yescharacteristic
663C4×D4C2×C4×C7911yescharacteristic
664C4×D4C2×C4×C7911yescharacteristic, complemented
665C4×D4C2×C4×C7911yescharacteristic, complemented
666C4×D4C2×C4×C7911yescharacteristic, complemented
667C4×D4D4×C7911yescharacteristic
668C4×D4D4×C7911yescharacteristic
669C4×D4D4×C7911yescharacteristic
670C4×D4D4×C7911yescharacteristic
671#117—21no—
672#117—21no—
673#117C2×C4×C7911yescharacteristic
674#117C2×C4×C7911yescharacteristic, complemented
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4C2×C4×C7911yescharacteristic
678C2×C4⋊C4C2×C4×C7911yescharacteristic, complemented
679C2×C4⋊C4D4×C7911yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4D4×C7911yescharacteristic
688C2×C22⋊C4D4×C7911yescharacteristic
689C2×C42—21no—
690C2×C42C23×C7911yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8C23×C7911yescharacteristic
698C22⋊C8C23×C7911yescharacteristic
699C22⋊C8C23×C7911yescharacteristic
700C22⋊C8C23×C7911yescharacteristic
701#97—21no—
702C4×C8—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95C23×C7911yescharacteristic
709#95C23×C7911yescharacteristic
710#95C23×C7911yescharacteristic
711#95C23×C7911yescharacteristic
712C24—21no—
713C24—21no—
714C24C2×D4×C7911yescharacteristic
715C24C2×D4×C7911yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719#41—81no—
720C2×Q8—21no—
721C2×Q8C22×C4×C7911yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C22⋊C4×C7911yescharacteristic
746C2×D4C22⋊C4×C7911yescharacteristic
747C2×D4C22⋊C4×C7911yescharacteristic
748C2×D4C22⋊C4×C7911yescharacteristic
749C2×D4C22×C4×C7911yescharacteristic
750C2×D4C22×C4×C7911yescharacteristic
751C2×D4C22×C4×C7911yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—42no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—81no—
767C22×C4—81no—
768C22×C4C22×C4×C7911yescharacteristic
769C22×C4C22×C4×C7911yescharacteristic
770C22×C4C22×C4×C7911yescharacteristic
771C22×C4C22×C4×C7911yescharacteristic
772C22×C4C2×D4×C7911yescharacteristic
773C22×C4C2×D4×C7911yescharacteristic
774C22×C4C2×D4×C7911yescharacteristic
775C22×C4C2×D4×C7911yescharacteristic
776C22×C4C2×D4×C7911yescharacteristic
777C22×C4C2×D4×C7911yescharacteristic
778C22×C4C2×D4×C7911yescharacteristic
779C22×C4C2×D4×C7911yescharacteristic
780C22×C4C24×C7911yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—81no—
799C4⋊C4—81no—
800C4⋊C4C22⋊C4×C7911yescharacteristic
801C4⋊C4C22⋊C4×C7911yescharacteristic
802C4⋊C4C22⋊C4×C7911yescharacteristic
803C4⋊C4C22⋊C4×C7911yescharacteristic
804C4⋊C4C22×C4×C7911yescharacteristic
805C4⋊C4C22×C4×C7911yescharacteristic
806C4⋊C4C22×C4×C7911yescharacteristic
807C4⋊C4C22×C4×C7911yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—42no—
828C22⋊C4—81no—
829C22⋊C4—81no—
830C22⋊C4C22⋊C4×C7911yescharacteristic
831C22⋊C4C22⋊C4×C7911yescharacteristic
832C22⋊C4C22⋊C4×C7911yescharacteristic
833C22⋊C4C22⋊C4×C7911yescharacteristic
834C22⋊C4C22⋊C4×C7911yescharacteristic
835C22⋊C4C22⋊C4×C7911yescharacteristic
836C22⋊C4C22⋊C4×C7911yescharacteristic
837C22⋊C4C22⋊C4×C7911yescharacteristic
838C42—21no—
839C42—21no—
840C42—21no—
841C42—81no—
842C42C22×C4×C7911yescharacteristic
843C42C22×C4×C7911yescharacteristic
844C42C2×D4×C7911yescharacteristic
845C42C2×D4×C7911yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23C2×C22⋊C4×C7911yescharacteristic
864C23C2×C22⋊C4×C7911yescharacteristic
865C23C2×C22⋊C4×C7911yescharacteristic
866C23C2×C22⋊C4×C7911yescharacteristic
867C23C22×D4×C7911yescharacteristic
868Q8—41no—
869Q8—81no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—42no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—42no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—84no—
934C2×C4C2×C22⋊C4×C7911yescharacteristic
935C2×C4C2×C22⋊C4×C7911yescharacteristic
936C2×C4C2×C22⋊C4×C7911yescharacteristic
937C2×C4C2×C22⋊C4×C7911yescharacteristic
938C2×C4C2×C22⋊C4×C7911yescharacteristic
939C2×C4C2×C22⋊C4×C7911yescharacteristic
940C2×C4C2×C22⋊C4×C7911yescharacteristic
941C2×C4C2×C22⋊C4×C7911yescharacteristic
942C2×C4C23×C4×C7911yescharacteristic
943C2×C4C22×D4×C7911yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—81no—
973C22—81no—
974C22—162no—
975C22—162no—
976C22#421×C7912yes—
977C22C22×C22⋊C4×C7911yescharacteristic
978C22#576×C7911yescharacteristic
979C22#577×C7911yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C4—81no—
998C4—81no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—81no—
1006C2—81no—
1007C2—81no—
1008C2C79×#288311yescharacteristic
1009C2C79×#289711yescharacteristic
1010C2C2×#421×C7911yescharacteristic
subgroupG/H
center, socleC22×C79C22×C22⋊C4
commutatorC2×C4C23×C4×C79
Frattini, cosocleC22×C4C24×C79
prime radicalC79×#3519C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C79 ◁ C2×C4×D4×C79 ◁ G

Complements

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

NH ≅ G/Ntype
2. C79×#2974C2semidirect
3. C79×#2318C2semidirect
4. C79×#1521C2semidirect
5. C79×#1519C2semidirect
6. C79×#1517C2semidirect
7. C79×#1516C2semidirect
8. C79×#1514C2semidirect
9. C79×#1513C2semidirect
10. C79×#1512C2semidirect
11. C79×#1510C2semidirect
12. C79×#1507C2semidirect
13. C79×#1504C2semidirect
14. C79×#1501C2semidirect
15. C2×#327×C79C2semidirect
16. #555×C79C4semidirect
17. #554×C79C4semidirect
19. #553×C79C4semidirect
20. #553×C79C4semidirect
21. #550×C79C4semidirect
24. #546×C79C4semidirect
25. #546×C79C4semidirect
27. D42×C79C4semidirect
43. #432×C79C22semidirect
44. #431×C79C22semidirect
45. #407×C79C22semidirect
46. #407×C79C22semidirect
47. C2×C22⋊C8×C79C22semidirect
48. C2×C22⋊C8×C79C22semidirect
53. #383×C79C22semidirect
54. #382×C79C22semidirect
55. #381×C79C22semidirect
56. #380×C79C22semidirect
57. C4×C22⋊C4×C79C22semidirect
58. C2×#95×C79C22semidirect
59. #328×C79C22semidirect
60. #328×C79C22semidirect
61. #328×C79C22semidirect
62. #328×C79C22semidirect
67. #327×C79C22semidirect
68. #327×C79C22semidirect
69. #327×C79C22semidirect
70. #327×C79C22semidirect
71. #327×C79C22semidirect
72. #327×C79C22semidirect
73. #327×C79C22semidirect
74. #327×C79C22semidirect
77. C2×#41×C79C2×C4semidirect
82. C22×D4×C79C2×C4semidirect
91. C4⋊Q8×C79C2×C4semidirect
93. #127×C79C2×C4semidirect
98. #125×C79C2×C4semidirect
102. #124×C79C2×C4semidirect
113. C22⋊Q8×C79C2×C4semidirect
131. #121×C79C2×C4semidirect
132. #121×C79C2×C4semidirect
133. #121×C79C2×C4semidirect
143. C4×Q8×C79C2×C4semidirect
158. C4×D4×C79C2×C4semidirect
159. C4×D4×C79C2×C4semidirect
160. C4×D4×C79C2×C4semidirect
168. #117×C79C2×C4semidirect
172. C2×C4⋊C4×C79C2×C4semidirect
493. #17597C79direct (N × H)
507. #2974C2×C79semidirect
508. #2318C2×C79semidirect
509. #1521C2×C79semidirect
510. #1519C2×C79semidirect
511. #1517C2×C79semidirect
512. #1516C2×C79semidirect
513. #1514C2×C79semidirect
514. #1513C2×C79semidirect
515. #1512C2×C79semidirect
516. #1510C2×C79semidirect
517. #1507C2×C79semidirect
518. #1504C2×C79semidirect
519. #1501C2×C79semidirect
520. C2×#327C2×C79semidirect
521. C79#17597direct (N × H)
522. #555C4×C79semidirect
523. #554C4×C79semidirect
525. #553C4×C79semidirect
526. #553C4×C79semidirect
527. #550C4×C79semidirect
530. #546C4×C79semidirect
531. #546C4×C79semidirect
533. D42C4×C79semidirect
549. #432C22×C79semidirect
550. #431C22×C79semidirect
551. #407C22×C79semidirect
552. #407C22×C79semidirect
553. C2×C22⋊C8C22×C79semidirect
554. C2×C22⋊C8C22×C79semidirect
559. #383C22×C79semidirect
560. #382C22×C79semidirect
561. #381C22×C79semidirect
562. #380C22×C79semidirect
563. C4×C22⋊C4C22×C79semidirect
564. C2×#95C22×C79semidirect
565. #328C22×C79semidirect
566. #328C22×C79semidirect
567. #328C22×C79semidirect
568. #328C22×C79semidirect
573. #327C22×C79semidirect
574. #327C22×C79semidirect
575. #327C22×C79semidirect
576. #327C22×C79semidirect
577. #327C22×C79semidirect
578. #327C22×C79semidirect
579. #327C22×C79semidirect
580. #327C22×C79semidirect
583. C2×#41C2×C4×C79semidirect
588. C22×D4C2×C4×C79semidirect
597. C4⋊Q8C2×C4×C79semidirect
599. #127C2×C4×C79semidirect
604. #125C2×C4×C79semidirect
608. #124C2×C4×C79semidirect
619. C22⋊Q8C2×C4×C79semidirect
637. #121C2×C4×C79semidirect
638. #121C2×C4×C79semidirect
639. #121C2×C4×C79semidirect
649. C4×Q8C2×C4×C79semidirect
664. C4×D4C2×C4×C79semidirect
665. C4×D4C2×C4×C79semidirect
666. C4×D4C2×C4×C79semidirect
674. #117C2×C4×C79semidirect
678. C2×C4⋊C4C2×C4×C79semidirect

Maximal subgroups

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

subgroupindex
C79×#35192
C79×#29742
C79×#23182
C79×#15212
C79×#15192
C79×#15172
C79×#15162
C79×#15142
C79×#15132
C79×#15122
C79×#15102
C79×#15072
C79×#15042
C79×#15012
C2×#327×C792
#1759779