Finite Group Databasebeta

← #34448591

Subgroups — #34448591

Order 20224.

3038 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D79C211yesmaximal, characteristic
2C2×#19099039C211yesmaximal, characteristic, complemented
3C2×#117×D79C211yesmaximal, characteristic
4#23766430C212yesmaximal, complemented
5#23766424C212yesmaximal, complemented
6#23766408C212yesmaximal, complemented
7#23766402C212yesmaximal, complemented
8#23766268C212yesmaximal, complemented
9#23766266C212yesmaximal, complemented
10#23766248C212yesmaximal
11#23766244C212yesmaximal
12#23766084C211yesmaximal, characteristic, complemented
13#23766082C211yesmaximal, characteristic, complemented
14#23766078C211yesmaximal, characteristic, complemented
15#23766015C211yesmaximal, characteristic, complemented
16#23765983C211yesmaximal, characteristic, complemented
17#23765938C211yesmaximal, characteristic, complemented
18C4×#14579141C211yesmaximal, characteristic, complemented
19#23765930C211yesmaximal, characteristic, complemented
20C4×#14579137C211yesmaximal, characteristic, complemented
21#23765782C211yesmaximal, characteristic
22#23765754C211yesmaximal, characteristic, complemented
23C79×#2323C211yesmaximal, characteristic, complemented
24C22×Q8×D79C2211yescharacteristic
25C23×C4×D79C2211yescharacteristic
26C2×#14579141C2211yescharacteristic
27C2×#14579140C2211yescharacteristic
28C2×#14579139C2212yes—
29C2×#14579138C2212yes—
30C2×#14579137C2211yescharacteristic
31C22⋊Q8×D79C4116yescomplemented
32#19099039—28no—
33C2×Q8×Dic79C2211yescharacteristic, complemented
34C2×C4×Dic158C2211yescharacteristic, complemented
35C2×C4×Dic158C2212yescomplemented
36C2×#14579126C2211yescharacteristic, complemented
37C2×#14579126C2212yescomplemented
38C2×#14579120C2211yescharacteristic
39C2×#14579119C2211yescharacteristic
40C2×#14579119C2211yescharacteristic
41C2×#14579119C2211yescharacteristic
42C2×#14579119C2211yescharacteristic
43C2×#14579119C2212yes—
44C2×#14579118C2211yescharacteristic
45C2×#14579118C2212yes—
46C2×#14579118C2211yescharacteristic
47C2×#14579117C2211yescharacteristic
48C2×#14579117C2211yescharacteristic
49#117×D79—28no—
50C2×C4⋊C4×D79C2211yescharacteristic
51C2×C4⋊C4×D79C2211yescharacteristic
52C2×C4⋊C4×D79C2211yescharacteristic
53C2×C4⋊C4×D79C2212yes—
54C2×C22⋊C4×D79C2211yescharacteristic
55C2×C22⋊C4×D79C2211yescharacteristic
56C2×C22⋊C4×D79C2212yes—
57C2×C42×D79C2211yescharacteristic
58C2×C42×D79C2211yescharacteristic
59#19098470C2211yescharacteristic, complemented
60#19098469C2211yescharacteristic, complemented
61#19098468C2211yescharacteristic, complemented
62#19098467C2212yescomplemented
63#19098467C2212yescomplemented
64#19098462C2212yescomplemented
65#19098462C2211yescharacteristic, complemented
66#19098461C2211yescharacteristic, complemented
67#19098460C2212yescomplemented
68#19098460C2212yescomplemented
69#19098459C2211yescharacteristic, complemented
70#19098458C2212yescomplemented
71#19098458C2212yescomplemented
72#19098457C2212yes—
73#19098457C2212yes—
74#19098456C2212yes—
75#19098456C2212yes—
76#19098451C2212yes—
77#19098451C2212yes—
78#19098450C2212yescomplemented
79#19098450C2212yescomplemented
80#19098449C2212yescomplemented
81#19098448C2212yescomplemented
82#19098446C2212yescomplemented
83#19098444C2212yescomplemented
84#19098444C2212yescomplemented
85#19098437C2212yes—
86#19098437C2212yes—
87#19098434C2212yes—
88#19098434C2212yes—
89#19098425C2212yes—
90#19098425C2212yes—
91#19098425C2212yes—
92#19098423C2211yescharacteristic
93#19098422C2212yes—
94#19098420C2211yescharacteristic
95#19098420C2211yescharacteristic
96#19098420C2212yes—
97#19098418C2212yes—
98C4⋊C4×Dic79C2211yescharacteristic, complemented
99C4⋊C4×Dic79C2211yescharacteristic, complemented
100C4⋊C4×Dic79C2212yescomplemented
101C4×Dic79⋊C4C2212yescomplemented
102C4×Dic79⋊C4C2212yescomplemented
103C4×C4⋊Dic79C2211yescharacteristic, complemented
104C4×C4⋊Dic79C2212yescomplemented
105#19098414C2212yescomplemented
106#19098414C2212yescomplemented
107C22⋊C4×Dic79C2212yes—
108C4×(C2×D79)⋊C4C2212yes—
109C4×(C2×D79)⋊C4C2212yes—
110C4×(C2×D79)⋊C4C2212yes—
111#19098410C2212yes—
112#19098410C2212yes—
113#19098410C2212yes—
114#19098410C2212yes—
115C2×C22⋊Q8×C79C2211yescharacteristic
116C2×C4×Q8×C79C2211yescharacteristic, complemented
117C2×#117×C79C2211yescharacteristic
118#391×C79C2211yescharacteristic, complemented
119#389×C79C2212yescomplemented
120#389×C79C2211yescharacteristic, complemented
121#388×C79C2212yes—
122#388×C79C2212yes—
123#387×C79C2212yescomplemented
124#380×C79C2211yescharacteristic
125C4×C4⋊C4×C79C2211yescharacteristic, complemented
126C24×D79C2311yescharacteristic
127C22×Dic158C2312yes—
128C22×Dic158C2311yescharacteristic
129C2×Q8×D79—24no—
130C2×Q8×D79—24no—
131C2×Q8×D79C2×C418yescomplemented
132C23×Dic79C2311yescharacteristic
133C22×C4×D79—24no—
134C22×C4×D79—24no—
135C22×C4×D79C2×C418yes—
136C22×C4×D79C2311yescharacteristic
137C22×C4×D79C2311yescharacteristic
138C22×C4×D79C2311yescharacteristic
139C22×C4×D79C2311yescharacteristic
140C22×C4×D79C2311yescharacteristic
141C22×C4×D79C2311yescharacteristic
142C22×C4×D79C2312yes—
143C22×C4×D79C2311yescharacteristic
144C22×C4×D79C2312yes—
145C22×C4×D79C2311yescharacteristic
146#14579141C2×C418yes—
147#14579140C2×C418yescomplemented
148#14579139C2×C4116yes—
149#14579138C2×C4116yescomplemented
150#14579137C2×C418yes—
151Q8×Dic79—24no—
152C4×Dic158—24no—
153C4×Dic158—28no—
154#14579126—28no—
155#14579126—24no—
156#14579120—24no—
157#14579119—24no—
158#14579119—24no—
159#14579119—24no—
160#14579119—24no—
161#14579119—28no—
162#14579118—24no—
163#14579118—28no—
164#14579118D418yes—
165#14579117—24no—
166#14579117—24no—
167C2×C4⋊Dic79C2311yescharacteristic
168C2×C4⋊Dic79C2311yescharacteristic
169C2×C4⋊Dic79C2312yes—
170C2×C4⋊Dic79C2311yescharacteristic
171C2×C4⋊Dic79C2311yescharacteristic
172C2×C4⋊Dic79C2312yes—
173C2×C4⋊Dic79C2312yes—
174C2×C4⋊Dic79C2311yescharacteristic
175C2×Dic79⋊C4C2312yes—
176C2×Dic79⋊C4C2312yes—
177C2×Dic79⋊C4C2311yescharacteristic
178C2×Dic79⋊C4C2311yescharacteristic
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2312yes—
182C2×Dic79⋊C4C2312yes—
183C2×Dic79⋊C4C2312yes—
184C2×Dic79⋊C4C2311yescharacteristic
185C2×Dic79⋊C4C2311yescharacteristic
186C4⋊C4×D79—24no—
187C4⋊C4×D79—24no—
188C4⋊C4×D79C2×C4116yescomplemented
189C4⋊C4×D79C2×C418yescomplemented
190C2×C22⋊Dic79C2311yescharacteristic
191C2×C22⋊Dic79C2311yescharacteristic
192C2×C22⋊Dic79C2312yes—
193C2×C22⋊Dic79C2312yes—
194C2×(C2×D79)⋊C4C2312yes—
195C2×(C2×D79)⋊C4C2312yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×(C2×D79)⋊C4C2311yescharacteristic
199C2×(C2×D79)⋊C4C2311yescharacteristic
200C2×(C2×D79)⋊C4C2312yes—
201C2×(C2×D79)⋊C4C2312yes—
202C2×(C2×D79)⋊C4C2311yescharacteristic
203C2×(C2×D79)⋊C4C2311yescharacteristic
204C22⋊C4×D79—24no—
205C22⋊C4×D79—24no—
206C22⋊C4×D79C2×C4116yes—
207C2×C4×Dic79C2312yes—
208C2×C4×Dic79C2312yes—
209C2×C4×Dic79C2312yes—
210C2×C4×Dic79C2312yes—
211C2×C4×Dic79C2312yes—
212C2×C4×Dic79C2311yescharacteristic
213C2×C4×Dic79C2311yescharacteristic
214C2×C4×Dic79C2311yescharacteristic
215C2×C4×Dic79C2311yescharacteristic
216C2×C4×Dic79C2311yescharacteristic
217C2×C4×Dic79C2312yes—
218C2×C4×Dic79C2312yes—
219C2×C4×Dic79C2312yes—
220C2×C4×Dic79C2311yescharacteristic
221C42×D79—24no—
222C42×D79—24no—
223C79⋊#95C2312yes—
224C79⋊#95C2312yes—
225C79⋊#95C2312yes—
226C79⋊#95C2312yes—
227C79⋊#95C2312yes—
228C79⋊#95C2312yes—
229C79⋊#95C2312yes—
230C79⋊#95C2312yes—
231C79⋊#95C2312yes—
232C79⋊#95C2312yes—
233C79⋊#95C2312yes—
234C79⋊#95C2312yes—
235C79⋊#95C2312yes—
236C79⋊#95C2312yes—
237C79⋊#95C2312yes—
238C22×Q8×C79C2311yescharacteristic
239C23×C4×C79C2311yescharacteristic
240C22⋊Q8×C79C2×C418yescomplemented
241C4×Q8×C79—24no—
242#117×C79—24no—
243C2×C4⋊C4×C79C2311yescharacteristic
244C2×C4⋊C4×C79C2311yescharacteristic
245C2×C4⋊C4×C79C2312yes—
246C2×C4⋊C4×C79C2311yescharacteristic
247C2×C4⋊C4×C79C2311yescharacteristic
248C2×C4⋊C4×C79C2312yes—
249C2×C4⋊C4×C79C2311yescharacteristic
250C2×C4⋊C4×C79C2312yes—
251C2×C22⋊C4×C79C2311yescharacteristic
252C2×C22⋊C4×C79C2311yescharacteristic
253C2×C22⋊C4×C79C2312yes—
254C2×C22⋊C4×C79C2312yes—
255C2×C42×C79C2312yes—
256C2×C42×C79C2311yescharacteristic
257C2×C42×C79C2312yes—
258C2×C42×C79C2311yescharacteristic
259#95×C79C2312yes—
260#95×C79C2312yes—
261#95×C79C2312yes—
262#95×C79C2312yes—
263#95×C79C2312yes—
264C23×D79—22no—
265C23×D79—22no—
266C23×D79—22no—
267C23×D79—22no—
268C23×D79—41no—
269C23×D79—41no—
270C23×D79C22×C414yes—
271C23×D79C2411yescharacteristic
272C23×D79C2411yescharacteristic
273C2×Dic158—24no—
274C2×Dic158—24no—
275C2×Dic158—22no—
276C2×Dic158—22no—
277C2×Dic158C22×C418yes—
278C2×Dic158C22×C414yes—
279Q8×D79—232no—
280C22×Dic79—22no—
281C22×Dic79—22no—
282C22×Dic79C22×C414yes—
283C22×Dic79C2412yes—
284C22×Dic79C2411yescharacteristic
285C22×Dic79C2411yescharacteristic
286C22×Dic79C2412yes—
287C22×Dic79C2412yes—
288C22×Dic79C2411yescharacteristic
289C22×Dic79C2412yes—
290C22×Dic79C2411yescharacteristic
291C22×Dic79C2411yescharacteristic
292C22×Dic79C2411yescharacteristic
293C2×C4×D79—22no—
294C2×C4×D79—22no—
295C2×C4×D79—232no—
296C2×C4×D79—22no—
297C2×C4×D79—22no—
298C2×C4×D79—24no—
299C2×C4×D79—22no—
300C2×C4×D79—24no—
301C2×C4×D79—22no—
302C2×C4×D79—22no—
303C2×C4×D79—22no—
304C2×C4×D79—22no—
305C2×C4×D79—22no—
306C2×C4×D79—22no—
307C2×C4×D79—22no—
308C2×C4×D79—22no—
309C2×C4×D79—22no—
310C2×C4×D79—41no—
311C2×C4×D79—42no—
312C2×C4×D79—41no—
313C2×C4×D79—42no—
314C2×C4×D79—41no—
315C2×C4×D79—41no—
316C2×C4×D79C22×C418yes—
317C2×C4×D79C22×C414yes—
318C2×C4×D79C22×C414yes—
319C2×C4×D79C22×C414yes—
320C2×C4×D79C22×C418yes—
321C2×C4×D79C22×C414yes—
322C2×C4×D79C2×D414yes—
323C2×C4×D79#4114yes—
324C4⋊Dic79—22no—
325C4⋊Dic79—22no—
326C4⋊Dic79—24no—
327C4⋊Dic79—22no—
328C4⋊Dic79—22no—
329C4⋊Dic79—42no—
330C4⋊Dic79C22×C414yes—
331C4⋊Dic79C22×C418yes—
332Dic79⋊C4—22no—
333Dic79⋊C4—22no—
334Dic79⋊C4—24no—
335Dic79⋊C4—24no—
336Dic79⋊C4—42no—
337Dic79⋊C4—42no—
338Dic79⋊C4C22×C418yes—
339Dic79⋊C4C22×C418yes—
340Dic79⋊C4C22×C418yes—
341Dic79⋊C4C2×D414yes—
342Dic79⋊C4C2×D414yes—
343C22⋊Dic79—22no—
344C22⋊Dic79—22no—
345C22⋊Dic79—42no—
346C22⋊Dic79C22×C418yes—
347(C2×D79)⋊C4—22no—
348(C2×D79)⋊C4—22no—
349(C2×D79)⋊C4—24no—
350(C2×D79)⋊C4—24no—
351(C2×D79)⋊C4—24no—
352(C2×D79)⋊C4—24no—
353(C2×D79)⋊C4C22×C418yes—
354(C2×D79)⋊C4C22×C418yes—
355(C2×D79)⋊C4C2×D414yes—
356(C2×D79)⋊C4C2×D414yes—
357C4×Dic79—22no—
358C4×Dic79—22no—
359C4×Dic79—24no—
360C4×Dic79—24no—
361C4×Dic79—24no—
362C4×Dic79—24no—
363C4×Dic79—22no—
364C4×Dic79—22no—
365C4×Dic79—22no—
366C4×Dic79—24no—
367C4×Dic79—42no—
368C4×Dic79—42no—
369C4×Dic79—42no—
370C4×Dic79C2×D414yes—
371C24×C79C2411yescharacteristic
372C2×Q8×C79—22no—
373C2×Q8×C79—22no—
374C2×Q8×C79C22×C414yes—
375C22×C4×C79—22no—
376C22×C4×C79—22no—
377C22×C4×C79C22×C414yes—
378C22×C4×C79C2412yes—
379C22×C4×C79C2411yescharacteristic
380C22×C4×C79C2411yescharacteristic
381C22×C4×C79C2412yes—
382C22×C4×C79C2412yes—
383C22×C4×C79C2412yes—
384C22×C4×C79C2411yescharacteristic
385C22×C4×C79C2411yescharacteristic
386C22×C4×C79C2411yescharacteristic
387C22×C4×C79C2411yescharacteristic
388C4⋊C4×C79—22no—
389C4⋊C4×C79—22no—
390C4⋊C4×C79—24no—
391C4⋊C4×C79—22no—
392C4⋊C4×C79—22no—
393C4⋊C4×C79—42no—
394C4⋊C4×C79C22×C418yes—
395C4⋊C4×C79C22×C414yes—
396C22⋊C4×C79—22no—
397C22⋊C4×C79—22no—
398C22⋊C4×C79—42no—
399C22⋊C4×C79C22×C418yes—
400C42×C79—22no—
401C42×C79—24no—
402C42×C79—42no—
403C42×C79C2×D414yes—
404C23×C79—21no—
405C23×C79—21no—
406C23×C79—21no—
407C23×C79—21no—
408C23×C79—21no—
409C23×C79—21no—
410C23×C79C23×C412yes—
411C23×C79C2511yescharacteristic
412C22×D79—21no—
413C22×D79—21no—
414C22×D79—21no—
415C22×D79—21no—
416C22×D79—21no—
417C22×D79—21no—
418C22×D79—21no—
419C22×D79—21no—
420C22×D79—28no—
421C22×D79—28no—
422C22×D79—44no—
423C22×D79—44no—
424C22×D79—44no—
425C22×D79—44no—
426C22×D79—44no—
427C22×D79C23×C412yes—
428C22×D79C23×C412yes—
429C22×D79C22×D412yes—
430C22×D79C2×#4112yes—
431C22×D792−1+412yes—
432C22×D792−1+412yes—
433Q8×C79—28no—
434C2×C4×C79—22no—
435C2×C4×C79—21no—
436C2×C4×C79—21no—
437C2×C4×C79—22no—
438C2×C4×C79—21no—
439C2×C4×C79—21no—
440C2×C4×C79—21no—
441C2×C4×C79—22no—
442C2×C4×C79—21no—
443C2×C4×C79—22no—
444C2×C4×C79—28no—
445C2×C4×C79—22no—
446C2×C4×C79—21no—
447C2×C4×C79—21no—
448C2×C4×C79—22no—
449C2×C4×C79—22no—
450C2×C4×C79—22no—
451C2×C4×C79—21no—
452C2×C4×C79—21no—
453C2×C4×C79—22no—
454C2×C4×C79—21no—
455C2×C4×C79—22no—
456C2×C4×C79—21no—
457C2×C4×C79C23×C414yes—
458C2×C4×C79C23×C414yes—
459C2×C4×C79C23×C412yes—
460C2×C4×C79C23×C412yes—
461C2×C4×C79C22×D412yes—
462C2×C4×C79C22×D412yes—
463C2×C4×C79C22×D412yes—
464C2×C4×C79C2×#4112yes—
465C2×Dic79—21no—
466C2×Dic79—22no—
467C2×Dic79—21no—
468C2×Dic79—22no—
469C2×Dic79—21no—
470C2×Dic79—21no—
471C2×Dic79—21no—
472C2×Dic79—21no—
473C2×Dic79—22no—
474C2×Dic79—22no—
475C2×Dic79—28no—
476C2×Dic79—22no—
477C2×Dic79—21no—
478C2×Dic79—21no—
479C2×Dic79—22no—
480C2×Dic79—22no—
481C2×Dic79—22no—
482C2×Dic79—21no—
483C2×Dic79—21no—
484C2×Dic79—22no—
485C2×Dic79—22no—
486C2×Dic79—21no—
487C2×Dic79—21no—
488C2×Dic79C23×C414yes—
489C2×Dic79C23×C414yes—
490C2×Dic79C23×C412yes—
491C2×Dic79C23×C412yes—
492C2×Dic79C22×D412yes—
493C2×Dic79C22×D412yes—
494C2×Dic79C22×D412yes—
495C2×Dic79C2×#4112yes—
496C4×D79—28no—
497C4×D79—216no—
498C4×D79—28no—
499C4×D79—28no—
500C4×D79—48no—
501C4×D79—44no—
502C4×D79—44no—
503C4×D79—44no—
504C4×D79—44no—
505C4×D79C4×D4116yes—
506Dic158—28no—
507Dic158—216no—
508C22×C79—22no—
509C22×C79—22no—
510C22×C79—22no—
511C22×C79—41no—
512C22×C79—41no—
513C22×C79—41no—
514C22×C79—41no—
515C22×C79C24×C411yescharacteristic
516C22×C79C23×D411yescharacteristic
517C22×C79C22×#4111yescharacteristic
518C22×C79C2×2−1+411yescharacteristic
519C22×C79C2×2−1+411yescharacteristic
520C22×C79#58511yescharacteristic
521C22×C79#58511yescharacteristic
522C2×D79—22no—
523C2×D79—22no—
524C2×D79—22no—
525C2×D79—22no—
526C2×D79—22no—
527C2×D79—22no—
528C2×D79—22no—
529C2×D79—22no—
530C2×D79—22no—
531C2×D79—22no—
532C2×D79—22no—
533C2×D79—22no—
534C2×D79—416no—
535C2×D79C2×C4×D414yes—
536C2×D79#51914yescomplemented
537C4×C79—22no—
538C4×C79—24no—
539C4×C79—24no—
540C4×C79—22no—
541C4×C79—22no—
542C4×C79—42no—
543C4×C79—41no—
544C4×C79—41no—
545C4×C79—42no—
546C4×C79C2×C4×D414yes—
547Dic79—24no—
548Dic79—22no—
549Dic79—24no—
550Dic79—22no—
551Dic79—22no—
552Dic79—41no—
553Dic79—41no—
554Dic79—42no—
555Dic79—42no—
556Dic79C2×C4×D414yes—
557#34203—791nomaximal, Sylow
558C2×C79—42no—
559C2×C79C22×C4×D411yescharacteristic
560C2×C79C2×#51911yescharacteristic
561C2×C79#342811yescharacteristic
562C2×C79#348911yescharacteristic
563C2×C79#348911yescharacteristic
564C2×C79#349511yescharacteristic
565C2×C79#349511yescharacteristic
566D79—24no—
567D79—24no—
568C22×C22⋊Q8—791no—
569C2×#519—791no—
570C22×#117—791no—
571#2362—792no—
572#2362—792no—
573#2360—792no—
574#2360—792no—
575#2344—792no—
576#2344—792no—
577#2342—792no—
578#2342—792no—
579#2323—791no—
580#2323—791no—
581#2323—791no—
582#2323D7911yescharacteristic, complemented
583#2316—791no—
584#2310—791no—
585C4×C22⋊Q8—791no—
586C4×C22⋊Q8—791no—
587C4×C22⋊Q8—791no—
588C4×C22⋊Q8—791no—
589#2280—791no—
590#2274—791no—
591C79#3420311yescharacteristic, complemented, Sylow
592C23×Q8—791no—
593C24×C4—791no—
594C2×C22⋊Q8—791no—
595C2×C22⋊Q8—791no—
596C2×C22⋊Q8—7916no—
597C2×C22⋊Q8—792no—
598C2×C22⋊Q8—791no—
599C2×C22⋊Q8—792no—
600C2×C22⋊Q8C2×D7911yescharacteristic
601#519—1588no—
602C2×C4×Q8—791no—
603C2×C4×Q8—791no—
604C2×C4×Q8—792no—
605C2×C4×Q8—791no—
606C2×C4×Q8—792no—
607C2×C4×Q8C2×D7911yescharacteristic, complemented
608C2×#117—791no—
609C2×#117—791no—
610C2×#117—791no—
611C2×#117—792no—
612C2×#117—791no—
613C2×#117—791no—
614C2×#117—791no—
615C2×#117—791no—
616C2×#117—791no—
617C2×#117—791no—
618C2×#117—792no—
619C2×#117—1588no—
620C2×#117C2×D7911yescharacteristic
621C22×C4⋊C4—791no—
622C22×C4⋊C4—792no—
623C22×C4⋊C4—791no—
624C22×C4⋊C4—791no—
625C22×C22⋊C4—792no—
626C22×C22⋊C4—791no—
627C22×C22⋊C4—791no—
628C22×C42—791no—
629C22×C42—791no—
630#391—791no—
631#391—791no—
632#391—791no—
633#391—792no—
634#391—792no—
635#391C2×D7911yescharacteristic, complemented
636#389—791no—
637#389—791no—
638#389—792no—
639#389—792no—
640#389—792no—
641#389—791no—
642#389—792no—
643#389—792no—
644#389C2×D7911yescharacteristic, complemented
645#389C2×D7912yescomplemented
646#388—792no—
647#388—792no—
648#388—792no—
649#388—792no—
650#388—792no—
651#388—792no—
652#388C2×D7912yes—
653#388C2×D7912yes—
654#387—792no—
655#387—792no—
656#387—792no—
657#387—792no—
658#387—792no—
659#387—792no—
660#387—792no—
661#387C2×D7912yescomplemented
662#385—792no—
663#385—792no—
664#385—792no—
665#385—792no—
666#381—792no—
667#381—792no—
668#381—792no—
669#380—791no—
670#380—792no—
671#380—791no—
672#380—791no—
673#380—792no—
674#380C2×D7911yescharacteristic
675#379—792no—
676C4×C4⋊C4—791no—
677C4×C4⋊C4—791no—
678C4×C4⋊C4—792no—
679C4×C4⋊C4—791no—
680C4×C4⋊C4—792no—
681C4×C4⋊C4—792no—
682C4×C4⋊C4—792no—
683C4×C4⋊C4—792no—
684C4×C4⋊C4—792no—
685C4×C4⋊C4C2×D7911yescharacteristic, complemented
686C4×C22⋊C4—792no—
687C4×C22⋊C4—792no—
688C4×C22⋊C4—792no—
689C4×C22⋊C4—792no—
690C4×C22⋊C4—792no—
691C4×C22⋊C4—792no—
692C4×C22⋊C4—792no—
693C4×C22⋊C4—792no—
694C25—791no—
695C22×Q8—798no—
696C22×Q8—792no—
697C22×Q8—791no—
698C22×Q8—1584no—
699C22×Q8—1584no—
700C22×Q8C22×D7911yescharacteristic
701C23×C4—792no—
702C23×C4—791no—
703C23×C4—791no—
704C23×C4—791no—
705C23×C4—791no—
706C23×C4—791no—
707C23×C4—791no—
708C23×C4—798no—
709C23×C4—792no—
710C23×C4—791no—
711C23×C4—791no—
712C23×C4—791no—
713C23×C4—1584no—
714C23×C4—1584no—
715C23×C4C22×D7911yescharacteristic
716C22⋊Q8—798no—
717C22⋊Q8—798no—
718C22⋊Q8—7916no—
719C22⋊Q8—798no—
720C22⋊Q8—7916no—
721C22⋊Q8C4×D7918yescomplemented
722C4×Q8—24no—
723C4×Q8—1588no—
724C4×Q8—1584no—
725C4×Q8—1584no—
726C4×Q8—1588no—
727C4×Q8—1584no—
728#117—24no—
729#117—798no—
730#117—1588no—
731#117—1584no—
732#117—1584no—
733#117—1584no—
734#117—1584no—
735#117—1584no—
736#117—1584no—
737#117—1588no—
738#117—1584no—
739#117—1584no—
740C2×C4⋊C4—792no—
741C2×C4⋊C4—792no—
742C2×C4⋊C4—792no—
743C2×C4⋊C4—791no—
744C2×C4⋊C4—791no—
745C2×C4⋊C4—792no—
746C2×C4⋊C4—792no—
747C2×C4⋊C4—792no—
748C2×C4⋊C4—791no—
749C2×C4⋊C4—792no—
750C2×C4⋊C4—798no—
751C2×C4⋊C4—7916no—
752C2×C4⋊C4—791no—
753C2×C4⋊C4—791no—
754C2×C4⋊C4—791no—
755C2×C4⋊C4—791no—
756C2×C4⋊C4—791no—
757C2×C4⋊C4—792no—
758C2×C4⋊C4—792no—
759C2×C4⋊C4—792no—
760C2×C4⋊C4—791no—
761C2×C4⋊C4—1584no—
762C2×C4⋊C4—1584no—
763C2×C4⋊C4C22×D7911yescharacteristic
764C2×C4⋊C4C22×D7911yescharacteristic
765C2×C4⋊C4C22×D7911yescharacteristic
766C2×C4⋊C4C22×D7912yes—
767C2×C4⋊C4C22×D7911yescharacteristic
768C2×C4⋊C4C22×D7912yes—
769C2×C4⋊C4C22×D7911yescharacteristic
770C2×C4⋊C4C22×D7912yes—
771C2×C22⋊C4—792no—
772C2×C22⋊C4—792no—
773C2×C22⋊C4—791no—
774C2×C22⋊C4—791no—
775C2×C22⋊C4—792no—
776C2×C22⋊C4—792no—
777C2×C22⋊C4—7916no—
778C2×C22⋊C4—791no—
779C2×C22⋊C4—791no—
780C2×C22⋊C4—791no—
781C2×C22⋊C4—791no—
782C2×C22⋊C4—792no—
783C2×C22⋊C4—792no—
784C2×C22⋊C4—792no—
785C2×C22⋊C4—792no—
786C2×C22⋊C4—1584no—
787C2×C22⋊C4—1584no—
788C2×C22⋊C4C22×D7911yescharacteristic
789C2×C22⋊C4C22×D7911yescharacteristic
790C2×C22⋊C4C22×D7912yes—
791C2×C22⋊C4C22×D7912yes—
792C2×C42—792no—
793C2×C42—792no—
794C2×C42—792no—
795C2×C42—791no—
796C2×C42—791no—
797C2×C42—791no—
798C2×C42—791no—
799C2×C42—791no—
800C2×C42—791no—
801C2×C42—792no—
802C2×C42—792no—
803C2×C42—792no—
804C2×C42—792no—
805C2×C42—792no—
806C2×C42—1584no—
807C2×C42—1584no—
808C2×C42C22×D7911yescharacteristic
809C2×C42C22×D7912yes—
810C2×C42C22×D7912yes—
811C2×C42C22×D7911yescharacteristic
812#95—792no—
813#95—792no—
814#95—792no—
815#95—792no—
816#95—792no—
817#95—792no—
818#95—792no—
819#95—792no—
820#95—792no—
821#95—792no—
822#95—792no—
823#95—792no—
824#95—792no—
825#95—792no—
826#95—792no—
827#95C22×D7912yes—
828#95C22×D7912yes—
829#95C22×D7912yes—
830#95C22×D7912yes—
831#95C22×D7912yes—
832C24—3161no—
833C24—3161no—
834C24—794no—
835C24—791no—
836C24—791no—
837C24—1582no—
838C24—1582no—
839C24—1582no—
840C24—1582no—
841C24C23×D7911yescharacteristic
842C2×Q8—22no—
843C2×Q8—22no—
844C2×Q8—798no—
845C2×Q8—794no—
846C2×Q8—1584no—
847C2×Q8—1584no—
848C2×Q8—15832no—
849C2×Q8—1582no—
850C2×Q8—1582no—
851C2×Q8C2×C4×D7914yes—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—3161no—
855C22×C4—3162no—
856C22×C4—3161no—
857C22×C4—3162no—
858C22×C4—3161no—
859C22×C4—3161no—
860C22×C4—798no—
861C22×C4—791no—
862C22×C4—794no—
863C22×C4—794no—
864C22×C4—794no—
865C22×C4—791no—
866C22×C4—792no—
867C22×C4—792no—
868C22×C4—791no—
869C22×C4—791no—
870C22×C4—794no—
871C22×C4—798no—
872C22×C4—794no—
873C22×C4—794no—
874C22×C4—794no—
875C22×C4—792no—
876C22×C4—791no—
877C22×C4—791no—
878C22×C4—792no—
879C22×C4—1582no—
880C22×C4—1582no—
881C22×C4—1582no—
882C22×C4—1582no—
883C22×C4—1582no—
884C22×C4—1582no—
885C22×C4—1582no—
886C22×C4—1582no—
887C22×C4—15832no—
888C22×C4—1582no—
889C22×C4—1584no—
890C22×C4—1582no—
891C22×C4—1584no—
892C22×C4—1582no—
893C22×C4—1582no—
894C22×C4—1582no—
895C22×C4—1582no—
896C22×C4—1582no—
897C22×C4—1582no—
898C22×C4C2×C4×D7914yes—
899C22×C4C23×D7912yes—
900C22×C4C23×D7911yescharacteristic
901C22×C4C23×D7911yescharacteristic
902C22×C4C23×D7912yes—
903C22×C4C23×D7912yes—
904C22×C4C23×D7912yes—
905C22×C4C23×D7911yescharacteristic
906C22×C4C23×D7911yescharacteristic
907C22×C4C23×D7911yescharacteristic
908C22×C4C23×D7911yescharacteristic
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—24no—
913C4⋊C4—22no—
914C4⋊C4—42no—
915C4⋊C4—3162no—
916C4⋊C4—3162no—
917C4⋊C4—3162no—
918C4⋊C4—798no—
919C4⋊C4—798no—
920C4⋊C4—798no—
921C4⋊C4—794no—
922C4⋊C4—798no—
923C4⋊C4—794no—
924C4⋊C4—794no—
925C4⋊C4—1582no—
926C4⋊C4—1582no—
927C4⋊C4—1584no—
928C4⋊C4—1582no—
929C4⋊C4—1582no—
930C4⋊C4—1584no—
931C4⋊C4—1582no—
932C4⋊C4—1584no—
933C4⋊C4—1582no—
934C4⋊C4C2×C4×D7914yes—
935C4⋊C4C2×C4×D7918yes—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—42no—
939C22⋊C4—3162no—
940C22⋊C4—798no—
941C22⋊C4—798no—
942C22⋊C4—798no—
943C22⋊C4—794no—
944C22⋊C4—794no—
945C22⋊C4—1584no—
946C22⋊C4—1584no—
947C22⋊C4—1582no—
948C22⋊C4—1582no—
949C22⋊C4—1584no—
950C22⋊C4—1584no—
951C22⋊C4—1582no—
952C22⋊C4—1582no—
953C22⋊C4C2×C4×D7918yes—
954C42—22no—
955C42—24no—
956C42—42no—
957C42—3162no—
958C42—3162no—
959C42—3162no—
960C42—794no—
961C42—1582no—
962C42—1582no—
963C42—1584no—
964C42—1584no—
965C42—1584no—
966C42—1584no—
967C42—1582no—
968C42—1582no—
969C42—1582no—
970C42—1584no—
971C42D4×D7914yes—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—3164no—
979C23—3164no—
980C23—3164no—
981C23—3164no—
982C23—3164no—
983C23—792no—
984C23—792no—
985C23—792no—
986C23—792no—
987C23—792no—
988C23—792no—
989C23—1588no—
990C23—1588no—
991C23—1581no—
992C23—1581no—
993C23—1581no—
994C23—1581no—
995C23—1581no—
996C23—1581no—
997C23—1581no—
998C23—1581no—
999C23C22×C4×D7912yes—
1000C23C24×D7911yescharacteristic
1001Q8—28no—
1002Q8—15816no—
1003Q8—1588no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—28no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—3164no—
1028C2×C4—3164no—
1029C2×C4—3168no—
1030C2×C4—3164no—
1031C2×C4—3164no—
1032C2×C4—792no—
1033C2×C4—792no—
1034C2×C4—792no—
1035C2×C4—7916no—
1036C2×C4—794no—
1037C2×C4—794no—
1038C2×C4—792no—
1039C2×C4—792no—
1040C2×C4—792no—
1041C2×C4—1588no—
1042C2×C4—1588no—
1043C2×C4—15816no—
1044C2×C4—1582no—
1045C2×C4—1582no—
1046C2×C4—1581no—
1047C2×C4—1581no—
1048C2×C4—1581no—
1049C2×C4—1582no—
1050C2×C4—1582no—
1051C2×C4—1581no—
1052C2×C4—1582no—
1053C2×C4—1581no—
1054C2×C4—1581no—
1055C2×C4—1582no—
1056C2×C4—1588no—
1057C2×C4—1581no—
1058C2×C4—1581no—
1059C2×C4—1581no—
1060C2×C4—1582no—
1061C2×C4—1581no—
1062C2×C4—1582no—
1063C2×C4—1581no—
1064C2×C4—1582no—
1065C2×C4—1581no—
1066C2×C4—1582no—
1067C2×C4—1588no—
1068C2×C4C22×C4×D7914yes—
1069C2×C4C22×C4×D7914yes—
1070C2×C4C22×C4×D7912yes—
1071C2×C4C22×C4×D7912yes—
1072C2×C4C2×D4×D7912yes—
1073C2×C4C2×D4×D7912yes—
1074C2×C4C2×D4×D7912yes—
1075C2×C4#41×D7912yes—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22—41no—
1083C22—31616no—
1084C22—794no—
1085C22—794no—
1086C22—1582no—
1087C22—1582no—
1088C22—1582no—
1089C22—1582no—
1090C22—1582no—
1091C22—1582no—
1092C22—1582no—
1093C22—1582no—
1094C22—1582no—
1095C22—1582no—
1096C22—1582no—
1097C22—1582no—
1098C22C23×C4×D7911yescharacteristic
1099C22C22×D4×D7911yescharacteristic
1100C22C2×#41×D7911yescharacteristic
1101C222−1+4×D7911yescharacteristic
1102C222−1+4×D7911yescharacteristic
1103C22#1909939811yescharacteristic
1104C22#1909940011yescharacteristic
1105C4—22no—
1106C4—22no—
1107C4—22no—
1108C4—24no—
1109C4—24no—
1110C4—41no—
1111C4—42no—
1112C4—41no—
1113C4—42no—
1114C4—3161no—
1115C4—3161no—
1116C4—3162no—
1117C4—3162no—
1118C4—794no—
1119C4—1582no—
1120C4—1582no—
1121C4—1582no—
1122C4—1584no—
1123C4—1584no—
1124C4C4×D4×D7914yes—
1125C2—42no—
1126C2—1584no—
1127C2—1584no—
1128C2C2×C4×D4×D7911yescharacteristic
1129C2#519×D7911yescharacteristic
1130C2#2377660011yescharacteristic
1131C2#2377707511yescharacteristic
1132C2#2377707811yescharacteristic
1133C2#2377714411yescharacteristic
1134C2#2377715011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2323C2
socle, cosocleC23×C79C25
prime radicalC24×D79C23
hypercenter#2323D79
hypocenterC79#34203
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×#19099039C2semidirect
4. #23766430C2semidirect
5. #23766424C2semidirect
6. #23766408C2semidirect
7. #23766402C2semidirect
8. #23766268C2semidirect
9. #23766266C2semidirect
12. #23766084C2semidirect
13. #23766082C2semidirect
14. #23766078C2semidirect
15. #23766015C2semidirect
16. #23765983C2semidirect
17. #23765938C2semidirect
18. C4×#14579141C2semidirect
19. #23765930C2semidirect
20. C4×#14579137C2semidirect
22. #23765754C2semidirect
23. C79×#2323C2semidirect
31. C22⋊Q8×D79C4semidirect
33. C2×Q8×Dic79C22semidirect
34. C2×C4×Dic158C22semidirect
35. C2×C4×Dic158C22semidirect
36. C2×#14579126C22semidirect
37. C2×#14579126C22semidirect
59. #19098470C22semidirect
60. #19098469C22semidirect
61. #19098468C22semidirect
62. #19098467C22semidirect
63. #19098467C22semidirect
64. #19098462C22semidirect
65. #19098462C22semidirect
66. #19098461C22semidirect
67. #19098460C22semidirect
68. #19098460C22semidirect
69. #19098459C22semidirect
70. #19098458C22semidirect
71. #19098458C22semidirect
78. #19098450C22semidirect
79. #19098450C22semidirect
80. #19098449C22semidirect
81. #19098448C22semidirect
82. #19098446C22semidirect
83. #19098444C22semidirect
84. #19098444C22semidirect
98. C4⋊C4×Dic79C22semidirect
99. C4⋊C4×Dic79C22semidirect
100. C4⋊C4×Dic79C22semidirect
101. C4×Dic79⋊C4C22semidirect
102. C4×Dic79⋊C4C22semidirect
103. C4×C4⋊Dic79C22semidirect
104. C4×C4⋊Dic79C22semidirect
105. #19098414C22semidirect
106. #19098414C22semidirect
116. C2×C4×Q8×C79C22semidirect
118. #391×C79C22semidirect
119. #389×C79C22semidirect
120. #389×C79C22semidirect
123. #387×C79C22semidirect
125. C4×C4⋊C4×C79C22semidirect
131. C2×Q8×D79C2×C4semidirect
147. #14579140C2×C4semidirect
149. #14579138C2×C4semidirect
188. C4⋊C4×D79C2×C4semidirect
189. C4⋊C4×D79C2×C4semidirect
240. C22⋊Q8×C79C2×C4semidirect
536. C2×D79#519semidirect
582. #2323D79semidirect
591. C79#34203semidirect
607. C2×C4×Q8C2×D79semidirect
635. #391C2×D79semidirect
644. #389C2×D79semidirect
645. #389C2×D79semidirect
661. #387C2×D79semidirect
685. C4×C4⋊C4C2×D79semidirect
721. C22⋊Q8C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D792
C2×#190990392
C2×#117×D792
#237664302
#237664242
#237664082
#237664022
#237662682
#237662662
#237662482
#237662442
#237660842
#237660822
#237660782
#237660152
#237659832
#237659382
C4×#145791412
#237659302
C4×#145791372
#237657822
#237657542
C79×#23232
#3420379