Finite Group Databasebeta

← C2×#23765932 #34446716

Subgroups — C2×#23765932 #34446716

Order 20224.

3854 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579138C211yesmaximal, characteristic
2C22×#14579126C211yesmaximal, characteristic, complemented
3C23×C4×Dic79C211yesmaximal, characteristic
4#23765932C2116yesmaximal, direct product factor
5C2×#19098467C211yesmaximal, characteristic, complemented
6C2×#19098458C211yesmaximal, characteristic, complemented
7C2×#19098448C211yesmaximal, characteristic, complemented
8C2×#19098444C211yesmaximal, characteristic, complemented
9C2×#19098436C211yesmaximal, characteristic
10C2×#19098421C211yesmaximal, characteristic
11C2×C4⋊C4×Dic79C211yesmaximal, characteristic, complemented
12C2×#19098414C211yesmaximal, characteristic, complemented
13C2×#19098414C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic79C211yesmaximal, characteristic
15C2×C22⋊C4×Dic79C211yesmaximal, characteristic
16C2×#385×C79C211yesmaximal, characteristic
17C23×Dic158C2211yescharacteristic
18C24×Dic79C2211yescharacteristic
19C24×Dic79C2211yescharacteristic
20C2×#14579138C4116yescomplemented
21C2×#14579138C2218yes—
22C2×#14579126—28no—
23C2×#14579126C2218yescomplemented
24C22×C4⋊Dic79C2211yescharacteristic
25C22×Dic79⋊C4C2211yescharacteristic
26C22×Dic79⋊C4C2211yescharacteristic
27C22×Dic79⋊C4C2211yescharacteristic
28C22×Dic79⋊C4C2211yescharacteristic
29C22×Dic79⋊C4C2211yescharacteristic
30C22×Dic79⋊C4C2211yescharacteristic
31C22×C22⋊Dic79C2211yescharacteristic
32C22×C22⋊Dic79C2211yescharacteristic
33C22×C4×Dic79—28no—
34C22×C4×Dic79C2211yescharacteristic
35C22×C4×Dic79C2211yescharacteristic
36C22×C4×Dic79C2218yes—
37C22×C4×Dic79C2211yescharacteristic
38C22×C4×Dic79C2211yescharacteristic
39C22×C4×Dic79C2211yescharacteristic
40C22×C4×Dic79C2211yescharacteristic
41C22×C4×Dic79C2211yescharacteristic
42C22×C4×Dic79C2211yescharacteristic
43#19098467C2218yescomplemented
44#19098458C2218yescomplemented
45#19098448C2218yescomplemented
46#19098444C2218yescomplemented
47#19098436C2218yes—
48#19098421C2218yes—
49C4⋊C4×Dic79C2218yescomplemented
50#19098414C2218yescomplemented
51#19098414C2218yescomplemented
52C22⋊C4×Dic79C2218yes—
53C22⋊C4×Dic79C2218yes—
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C2×C79⋊#95C2211yescharacteristic
60C2×C79⋊#95C2211yescharacteristic
61C2×C79⋊#95C2211yescharacteristic
62C24×C4×C79C2211yescharacteristic
63C22×C4⋊C4×C79C2211yescharacteristic
64C22×C4⋊C4×C79C2211yescharacteristic
65C22×C22⋊C4×C79C2211yescharacteristic
66C22×C22⋊C4×C79C2211yescharacteristic
67#385×C79C2218yes—
68C2×#95×C79C2211yescharacteristic
69C2×#95×C79C2211yescharacteristic
70C22×Dic158—24no—
71C22×Dic158—24no—
72C22×Dic158C2×C418yescomplemented
73C22×Dic158C2314yes—
74C23×Dic79—24no—
75C23×Dic79—24no—
76C23×Dic79—24no—
77C23×Dic79—24no—
78C23×Dic79C2×C418yes—
79C23×Dic79Q818yescomplemented
80C23×Dic79C2311yescharacteristic
81C23×Dic79C2311yescharacteristic
82C23×Dic79C2311yescharacteristic
83C23×Dic79C2311yescharacteristic
84C23×Dic79C2311yescharacteristic
85C23×Dic79C2314yes—
86C23×Dic79C2311yescharacteristic
87C23×Dic79C2314yes—
88C23×Dic79C2311yescharacteristic
89C23×Dic79C2311yescharacteristic
90#14579138C2×C4164yescomplemented
91#14579126—232no—
92C2×C4⋊Dic79C2×C418yescomplemented
93C2×C4⋊Dic79C2314yes—
94C2×Dic79⋊C4—24no—
95C2×Dic79⋊C4—24no—
96C2×Dic79⋊C4—24no—
97C2×Dic79⋊C4—24no—
98C2×Dic79⋊C4C2×C418yescomplemented
99C2×Dic79⋊C4C2×C418yescomplemented
100C2×Dic79⋊C4C2314yes—
101C2×Dic79⋊C4C2314yes—
102C2×Dic79⋊C4C2314yes—
103C2×Dic79⋊C4C2314yes—
104C2×Dic79⋊C4C2314yes—
105C2×Dic79⋊C4C2314yes—
106C2×C22⋊Dic79—24no—
107C2×C22⋊Dic79C2×C418yes—
108C2×C22⋊Dic79C2314yes—
109C2×C22⋊Dic79C2314yes—
110C2×C4×Dic79—24no—
111C2×C4×Dic79—24no—
112C2×C4×Dic79—24no—
113C2×C4×Dic79—24no—
114C2×C4×Dic79—24no—
115C2×C4×Dic79—24no—
116C2×C4×Dic79—24no—
117C2×C4×Dic79—232no—
118C2×C4×Dic79D418yes—
119C2×C4×Dic79C2314yes—
120C2×C4×Dic79C2314yes—
121C2×C4×Dic79C2314yes—
122C2×C4×Dic79C2314yes—
123C2×C4×Dic79C2314yes—
124C2×C4×Dic79C2314yes—
125C2×C4×Dic79C2314yes—
126C2×C4×Dic79C2314yes—
127C79⋊#95C2314yes—
128C79⋊#95C2314yes—
129C79⋊#95C2314yes—
130C79⋊#95C2314yes—
131C79⋊#95C2314yes—
132C79⋊#95C2314yes—
133C79⋊#95C2314yes—
134C79⋊#95C2314yes—
135C25×C79C2311yescharacteristic
136C23×C4×C79—24no—
137C23×C4×C79—24no—
138C23×C4×C79—24no—
139C23×C4×C79C2311yescharacteristic
140C23×C4×C79C2311yescharacteristic
141C23×C4×C79C2314yes—
142C23×C4×C79C2311yescharacteristic
143C23×C4×C79C2311yescharacteristic
144C23×C4×C79C2311yescharacteristic
145C23×C4×C79C2311yescharacteristic
146C2×C4⋊C4×C79—24no—
147C2×C4⋊C4×C79—24no—
148C2×C4⋊C4×C79C2314yes—
149C2×C4⋊C4×C79C2314yes—
150C2×C22⋊C4×C79—24no—
151C2×C22⋊C4×C79C2×C418yes—
152C2×C22⋊C4×C79C2314yes—
153C2×C22⋊C4×C79C2314yes—
154#95×C79C2314yes—
155#95×C79C2314yes—
156C2×Dic158—232no—
157C2×Dic158—28no—
158C2×Dic158—28no—
159C2×Dic158C22×C4116yescomplemented
160C22×Dic79—232no—
161C22×Dic79—232no—
162C22×Dic79—28no—
163C22×Dic79—28no—
164C22×Dic79—28no—
165C22×Dic79—28no—
166C22×Dic79—22no—
167C22×Dic79—22no—
168C22×Dic79—22no—
169C22×Dic79—22no—
170C22×Dic79—22no—
171C22×Dic79—22no—
172C22×Dic79—22no—
173C22×Dic79—22no—
174C22×Dic79—22no—
175C22×Dic79—22no—
176C22×Dic79—22no—
177C22×Dic79—22no—
178C22×Dic79—22no—
179C22×Dic79—22no—
180C22×Dic79C22×C414yes—
181C22×Dic79C22×C414yes—
182C22×Dic79C22×C414yes—
183C22×Dic79C22×C4116yes—
184C22×Dic79C22×C414yes—
185C22×Dic79C2×D414yes—
186C22×Dic79C2×D414yes—
187C22×Dic79C2×Q814yes—
188C22×Dic79C2×Q814yes—
189C22×Dic79C2×Q8116yescomplemented
190C22×Dic79#4114yes—
191C22×Dic79#4114yes—
192C22×Dic79C2412yes—
193C22×Dic79C2412yes—
194C22×Dic79C2412yes—
195C22×Dic79C2412yes—
196C22×Dic79C2412yes—
197C22×Dic79C2412yes—
198C22×Dic79C2412yes—
199C22×Dic79C2412yes—
200C4⋊Dic79C22×C4116yescomplemented
201Dic79⋊C4—28no—
202Dic79⋊C4—28no—
203Dic79⋊C4—28no—
204Dic79⋊C4—28no—
205Dic79⋊C4C22×C4116yescomplemented
206Dic79⋊C4C22×C4116yescomplemented
207C22⋊Dic79—28no—
208C22⋊Dic79C22×C4116yes—
209C4×Dic79—28no—
210C4×Dic79—28no—
211C4×Dic79—28no—
212C4×Dic79—28no—
213C4×Dic79—28no—
214C4×Dic79—28no—
215C4×Dic79—28no—
216C4×Dic79C2×D4116yes—
217C24×C79—22no—
218C24×C79—22no—
219C24×C79—22no—
220C24×C79—22no—
221C24×C79C22×C414yes—
222C24×C79C2×Q814yes—
223C24×C79#4114yes—
224C24×C79C2412yes—
225C24×C79C2411yescharacteristic
226C22×C4×C79—232no—
227C22×C4×C79—22no—
228C22×C4×C79—22no—
229C22×C4×C79—22no—
230C22×C4×C79—22no—
231C22×C4×C79—28no—
232C22×C4×C79—22no—
233C22×C4×C79—22no—
234C22×C4×C79—22no—
235C22×C4×C79—22no—
236C22×C4×C79—28no—
237C22×C4×C79—28no—
238C22×C4×C79—22no—
239C22×C4×C79—22no—
240C22×C4×C79—22no—
241C22×C4×C79—22no—
242C22×C4×C79—22no—
243C22×C4×C79—22no—
244C22×C4×C79C22×C414yes—
245C22×C4×C79C22×C414yes—
246C22×C4×C79C2×D414yes—
247C22×C4×C79#4114yes—
248C22×C4×C79C2412yes—
249C22×C4×C79C2412yes—
250C22×C4×C79C2412yes—
251C22×C4×C79C2412yes—
252C22×C4×C79C2412yes—
253C22×C4×C79C2412yes—
254C4⋊C4×C79—28no—
255C4⋊C4×C79—28no—
256C22⋊C4×C79—28no—
257C22⋊C4×C79C22×C4116yes—
258C23×C79—28no—
259C23×C79—28no—
260C23×C79—28no—
261C23×C79—28no—
262C23×C79—28no—
263C23×C79—28no—
264C23×C79—22no—
265C23×C79—22no—
266C23×C79—22no—
267C23×C79—22no—
268C23×C79C4×Q8116yescomplemented
269C23×C79C23×C414yes—
270C23×C79C23×C412yes—
271C23×C79C22×D412yes—
272C23×C79C22×Q814yes—
273C23×C79C22×Q812yes—
274C23×C79C2×#4112yes—
275C23×C79C2×#4112yes—
276C23×C79C2×#4114yes—
277C23×C79C2×#4112yes—
278C23×C79C2×#4112yes—
279C23×C79C2511yescharacteristic
280C2×C4×C79—232no—
281C2×C4×C79—28no—
282C2×C4×C79—28no—
283C2×C4×C79—28no—
284C2×C4×C79—28no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—44no—
300C2×C4×C79—44no—
301C2×C4×C79C23×C414yes—
302C2×C4×C79C23×C414yes—
303C2×C4×C79C22×D414yes—
304C2×C4×C79C2×#4114yes—
305C2×Dic79—28no—
306C2×Dic79—28no—
307C2×Dic79—28no—
308C2×Dic79—28no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—232no—
318C2×Dic79—232no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—22no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—44no—
326C2×Dic79—44no—
327C2×Dic79C4×D4116yes—
328C2×Dic79C22⋊Q8116yescomplemented
329C2×Dic79C23×C414yes—
330C2×Dic79C23×C414yes—
331C2×Dic79C23×C414yes—
332C2×Dic79C23×C414yes—
333C2×Dic79C22×D414yes—
334C2×Dic79C22×D414yes—
335C2×Dic79C22×Q814yes—
336C2×Dic79C22×Q814yes—
337C2×Dic79C2×#4114yes—
338C2×Dic79C2×#4114yes—
339Dic158—232no—
340C22×C79—24no—
341C22×C79—24no—
342C22×C79—24no—
343C22×C79—24no—
344C22×C79—24no—
345C22×C79—24no—
346C22×C79—232no—
347C22×C79C2×C4×D414yes—
348C22×C79C2×C4×Q814yes—
349C22×C79C2×C4×Q818yescomplemented
350C22×C79C4×#4114yes—
351C22×C79C2×C22⋊Q814yes—
352C22×C79#52514yes—
353C22×C79#52914yes—
354C22×C79#53314yes—
355C22×C79C24×C411yescharacteristic
356C22×C79C23×D411yescharacteristic
357C22×C79C23×Q811yescharacteristic
358C22×C79C22×#4111yescharacteristic
359C22×C79C22×#4111yescharacteristic
360C22×C79C22×#4111yescharacteristic
361C22×C79C22×#4111yescharacteristic
362C4×C79—24no—
363C4×C79—24no—
364C4×C79—24no—
365C4×C79—24no—
366C4×C79—42no—
367C4×C79—42no—
368Dic79—24no—
369Dic79—24no—
370Dic79—24no—
371Dic79—24no—
372Dic79—42no—
373Dic79—42no—
374Dic79C2×C4×D418yes—
375Dic79C2×C22⋊Q818yescomplemented
376C2×C4×C22⋊Q8—791nomaximal, Sylow
377C2×C79—28no—
378C2×C79C4×C22⋊Q818yescomplemented
379C2×C79C22×C4×D411yescharacteristic
380C2×C79C22×C4×Q811yescharacteristic
381C2×C79C2×C4×#4111yescharacteristic
382C2×C79C22×C22⋊Q811yescharacteristic
383C2×C79C2×#52511yescharacteristic
384C2×C79C2×#52911yescharacteristic
385C2×C79C2×#53311yescharacteristic
386C22×C22⋊Q8—791no—
387C22×C4×Q8—791no—
388C23×C42—791no—
389C4×C22⋊Q8—7916no—
390C2×#391—791no—
391C2×#389—791no—
392C2×#387—791no—
393C2×#387—791no—
394C2×#385—791no—
395C2×#385D7911yescharacteristic
396C2×#380—791no—
397C2×C4×C4⋊C4—791no—
398C2×C4×C4⋊C4—791no—
399C2×C4×C4⋊C4—791no—
400C2×C4×C22⋊C4—791no—
401C2×C4×C22⋊C4—791no—
402C79C2×C4×C22⋊Q811yescharacteristic, complemented, Sylow
403C23×Q8—791no—
404C24×C4—791no—
405C24×C4—791no—
406C24×C4C2×D7911yescharacteristic
407C2×C22⋊Q8—798no—
408C2×C22⋊Q8—7916no—
409C2×C4×Q8—798no—
410C2×C4×Q8—1588no—
411C22×C4⋊C4—791no—
412C22×C4⋊C4—791no—
413C22×C4⋊C4—791no—
414C22×C4⋊C4—791no—
415C22×C4⋊C4—791no—
416C22×C4⋊C4—791no—
417C22×C4⋊C4—791no—
418C22×C4⋊C4C2×D7911yescharacteristic
419C22×C4⋊C4C2×D7911yescharacteristic
420C22×C22⋊C4—791no—
421C22×C22⋊C4—791no—
422C22×C22⋊C4C2×D7911yescharacteristic
423C22×C22⋊C4C2×D7911yescharacteristic
424C22×C42—791no—
425C22×C42—791no—
426C22×C42—791no—
427C22×C42—791no—
428C22×C42—798no—
429C22×C42—791no—
430C22×C42—791no—
431C22×C42—791no—
432C22×C42—791no—
433C22×C42—1588no—
434#391—798no—
435#389—798no—
436#387—798no—
437#387—798no—
438#385—798no—
439#385C2×D7918yes—
440#380—798no—
441C4×C4⋊C4—798no—
442C4×C4⋊C4—798no—
443C4×C4⋊C4—798no—
444C4×C22⋊C4—798no—
445C4×C22⋊C4—798no—
446C2×#95—791no—
447C2×#95—791no—
448C2×#95—791no—
449C2×#95—791no—
450C2×#95—791no—
451C2×#95—791no—
452C2×#95—791no—
453C2×#95—791no—
454C2×#95C2×D7911yescharacteristic
455C2×#95C2×D7911yescharacteristic
456C25C22×D7911yescharacteristic
457C22×Q8—798no—
458C22×Q8—794no—
459C22×Q8—1584no—
460C22×Q8—1584no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—791no—
465C23×C4—791no—
466C23×C4—798no—
467C23×C4—798no—
468C23×C4—794no—
469C23×C4—794no—
470C23×C4—791no—
471C23×C4—791no—
472C23×C4—791no—
473C23×C4—791no—
474C23×C4—791no—
475C23×C4—791no—
476C23×C4—1584no—
477C23×C4—1584no—
478C23×C4—1584no—
479C23×C4—1584no—
480C23×C4C22×D7914yes—
481C23×C4C22×D7911yescharacteristic
482C23×C4C22×D7911yescharacteristic
483C23×C4C22×D7911yescharacteristic
484C23×C4C22×D7911yescharacteristic
485C23×C4C22×D7911yescharacteristic
486C23×C4C22×D7911yescharacteristic
487C22⋊Q8—7964no—
488C4×Q8—15832no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—798no—
492C2×C4⋊C4—798no—
493C2×C4⋊C4—798no—
494C2×C4⋊C4—794no—
495C2×C4⋊C4—794no—
496C2×C4⋊C4—794no—
497C2×C4⋊C4—794no—
498C2×C4⋊C4—794no—
499C2×C4⋊C4—794no—
500C2×C4⋊C4—794no—
501C2×C4⋊C4—1584no—
502C2×C4⋊C4—1584no—
503C2×C4⋊C4—1584no—
504C2×C4⋊C4—1584no—
505C2×C4⋊C4C22×D7914yes—
506C2×C4⋊C4C22×D7914yes—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—798no—
509C2×C22⋊C4—794no—
510C2×C22⋊C4—794no—
511C2×C22⋊C4—1584no—
512C2×C22⋊C4C4×D7918yes—
513C2×C22⋊C4C22×D7914yes—
514C2×C22⋊C4C22×D7914yes—
515C2×C42—798no—
516C2×C42—794no—
517C2×C42—794no—
518C2×C42—794no—
519C2×C42—794no—
520C2×C42—794no—
521C2×C42—794no—
522C2×C42—794no—
523C2×C42—794no—
524C2×C42—15832no—
525C2×C42—1584no—
526C2×C42—1584no—
527C2×C42—1584no—
528C2×C42—1584no—
529C2×C42—1584no—
530C2×C42—1584no—
531C2×C42—1584no—
532#95—794no—
533#95—794no—
534#95—794no—
535#95—794no—
536#95—794no—
537#95—794no—
538#95—794no—
539#95—794no—
540#95C22×D7914yes—
541#95C22×D7914yes—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24C2×C4×D7914yes—
547C24Q8×D7914yes—
548C24#1192962314yes—
549C24C23×D7912yes—
550C24C23×D7911yescharacteristic
551C2×Q8—7916no—
552C2×Q8—1588no—
553C2×Q8—15832no—
554C2×Q8—1588no—
555C22×C4—232no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—28no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—794no—
574C22×C4—794no—
575C22×C4—794no—
576C22×C4—792no—
577C22×C4—792no—
578C22×C4—794no—
579C22×C4—794no—
580C22×C4—794no—
581C22×C4—794no—
582C22×C4—7916no—
583C22×C4—792no—
584C22×C4—792no—
585C22×C4—792no—
586C22×C4—792no—
587C22×C4—794no—
588C22×C4—794no—
589C22×C4—794no—
590C22×C4—7916no—
591C22×C4—792no—
592C22×C4—792no—
593C22×C4—1582no—
594C22×C4—1582no—
595C22×C4—1582no—
596C22×C4—1582no—
597C22×C4—1582no—
598C22×C4—1582no—
599C22×C4—1588no—
600C22×C4—1588no—
601C22×C4—15832no—
602C22×C4—15832no—
603C22×C4—1588no—
604C22×C4—1588no—
605C22×C4—1582no—
606C22×C4—1582no—
607C22×C4—1582no—
608C22×C4—1582no—
609C22×C4—1582no—
610C22×C4—1582no—
611C22×C4—1582no—
612C22×C4—1582no—
613C22×C4C2×C4×D7914yes—
614C22×C4C2×C4×D7914yes—
615C22×C4D4×D7914yes—
616C22×C4#1192962314yes—
617C22×C4C23×D7912yes—
618C22×C4C23×D7912yes—
619C22×C4C23×D7912yes—
620C22×C4C23×D7912yes—
621C22×C4C23×D7912yes—
622C22×C4C23×D7912yes—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—7916no—
626C4⋊C4—7916no—
627C4⋊C4—7916no—
628C4⋊C4—1588no—
629C4⋊C4—1588no—
630C4⋊C4—1588no—
631C4⋊C4—1588no—
632C22⋊C4—28no—
633C22⋊C4—7916no—
634C22⋊C4—1588no—
635C22⋊C4C2×C4×D79116yes—
636C42—7916no—
637C42—1588no—
638C42—1588no—
639C42—1588no—
640C42—1588no—
641C42—1588no—
642C42—1588no—
643C42—1588no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—28no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23#14579126116yescomplemented
655C23C22×C4×D7914yes—
656C23C22×C4×D7912yes—
657C23C2×D4×D7912yes—
658C23C2×Q8×D7914yes—
659C23C2×Q8×D7912yes—
660C23#41×D7912yes—
661C23#41×D7912yes—
662C23C2×#1192962314yes—
663C23C2×#1192962312yes—
664C23C2×#1192962312yes—
665C23C24×D7911yescharacteristic
666Q8—15832no—
667C2×C4—232no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—3164no—
689C2×C4—3164no—
690C2×C4—7916no—
691C2×C4—7916no—
692C2×C4—794no—
693C2×C4—794no—
694C2×C4—794no—
695C2×C4—794no—
696C2×C4—794no—
697C2×C4—794no—
698C2×C4—794no—
699C2×C4—794no—
700C2×C4—794no—
701C2×C4—794no—
702C2×C4—1582no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4—1582no—
708C2×C4—15832no—
709C2×C4—15832no—
710C2×C4—1588no—
711C2×C4—1588no—
712C2×C4—1588no—
713C2×C4—1588no—
714C2×C4—1582no—
715C2×C4—1582no—
716C2×C4—1582no—
717C2×C4—1582no—
718C2×C4—1582no—
719C2×C4—1582no—
720C2×C4—1582no—
721C2×C4—1582no—
722C2×C4C22×C4×D7914yes—
723C2×C4C22×C4×D7914yes—
724C2×C4C2×D4×D7914yes—
725C2×C4C2×#1192962314yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—232no—
732C22—24no—
733C22C4×D4×D7914yes—
734C22C2×#1457912614yes—
735C22C2×#1457912618yescomplemented
736C22C4×#1192962314yes—
737C22C22⋊Q8×D7914yes—
738C22#1909906914yes—
739C22#1909909014yes—
740C22#1909911514yes—
741C22C23×C4×D7911yescharacteristic
742C22C22×D4×D7911yescharacteristic
743C22C22×Q8×D7911yescharacteristic
744C22C2×#41×D7911yescharacteristic
745C22C2×#41×D7911yescharacteristic
746C22C22×#1192962311yescharacteristic
747C22C22×#1192962311yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—3162no—
755C4—3162no—
756C4—798no—
757C4—798no—
758C4—1584no—
759C4—1584no—
760C4—1584no—
761C4—1584no—
762C2—28no—
763C2#2376593218yesdirect product factor
764C2C2×C4×D4×D7911yescharacteristic
765C2C22×#1457912611yescharacteristic
766C2C2×C4×#1192962311yescharacteristic
767C2C2×C22⋊Q8×D7911yescharacteristic
768C2C2×#1909906911yescharacteristic
769C2C2×#1909909011yescharacteristic
770C2C2×#1909911511yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#385×C79C2
socleC24×C79C24
prime radicalC25×C79C23
cosocleC23×C79C25
hypercenterC2×#385D79
hypocenterC79C2×C4×C22⋊Q8
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#14579126C2semidirect
4. #23765932C2direct (N × H)
5. C2×#19098467C2semidirect
6. C2×#19098458C2semidirect
7. C2×#19098448C2semidirect
8. C2×#19098444C2semidirect
11. C2×C4⋊C4×Dic79C2semidirect
12. C2×#19098414C2semidirect
13. C2×#19098414C2semidirect
20. C2×#14579138C4semidirect
23. C2×#14579126C22semidirect
43. #19098467C22semidirect
44. #19098458C22semidirect
45. #19098448C22semidirect
46. #19098444C22semidirect
49. C4⋊C4×Dic79C22semidirect
50. #19098414C22semidirect
51. #19098414C22semidirect
72. C22×Dic158C2×C4semidirect
79. C23×Dic79Q8semidirect
90. #14579138C2×C4semidirect
92. C2×C4⋊Dic79C2×C4semidirect
98. C2×Dic79⋊C4C2×C4semidirect
99. C2×Dic79⋊C4C2×C4semidirect
159. C2×Dic158C22×C4semidirect
189. C22×Dic79C2×Q8semidirect
200. C4⋊Dic79C22×C4semidirect
205. Dic79⋊C4C22×C4semidirect
206. Dic79⋊C4C22×C4semidirect
268. C23×C79C4×Q8semidirect
328. C2×Dic79C22⋊Q8semidirect
349. C22×C79C2×C4×Q8semidirect
375. Dic79C2×C22⋊Q8semidirect
378. C2×C79C4×C22⋊Q8semidirect
402. C79C2×C4×C22⋊Q8semidirect
654. C23#14579126semidirect
735. C22C2×#14579126semidirect
763. C2#23765932direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791382
C22×#145791262
C23×C4×Dic792
#237659322
C2×#190984672
C2×#190984582
C2×#190984482
C2×#190984442
C2×#190984362
C2×#190984212
C2×C4⋊C4×Dic792
C2×#190984142
C2×C22⋊C4×Dic792
C2×#385×C792
C2×C4×C22⋊Q879