Finite Group Databasebeta

← C2×#23765989 #34446833

Subgroups — C2×#23765989 #34446833

Order 20224.

5822 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11929624C211yesmaximal, characteristic
2C22×#14579119C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D79C211yesmaximal, characteristic, complemented
4#23765989C2116yesmaximal, direct product factor
5C2×#19098467C212yesmaximal, complemented
6C2×#19098463C212yesmaximal, complemented
7C2×#19098441C212yesmaximal, complemented
8C2×#19098439C212yesmaximal, complemented
9C2×#19098423C211yesmaximal, characteristic, complemented
10C2×#19098420C211yesmaximal, characteristic, complemented
11C2×#19098420C211yesmaximal, characteristic, complemented
12C2×#380×C79C211yesmaximal, characteristic, complemented
13C22×#11929624—28no—
14C22×#11929624—28no—
15C22×#11929624C4116yescomplemented
16C22×#11929624C2218yes—
17C23×Dic158C2211yescharacteristic
18C23×D316C2211yescharacteristic
19C23×C22⋊D79C2211yescharacteristic
20C23×C22⋊D79C2211yescharacteristic
21C23×C4×D79C2211yescharacteristic
22C23×C4×D79C2212yes—
23C23×C4×D79C2211yescharacteristic
24C2×#14579119—28no—
25C2×#14579119C2218yescomplemented
26C22×C4⋊Dic79C2211yescharacteristic
27C22×C4⋊Dic79C2211yescharacteristic
28C22×Dic79⋊C4C2212yes—
29C2×C4⋊C4×D79—28no—
30C2×C4⋊C4×D79C2218yescomplemented
31C22×C22⋊Dic79C2212yes—
32C22×(C2×D79)⋊C4C2212yes—
33C22×(C2×D79)⋊C4C2212yes—
34C22×(C2×D79)⋊C4C2212yes—
35C22×C4×Dic79C2212yes—
36#19098467C22116yescomplemented
37#19098463C22116yescomplemented
38#19098441C22116yescomplemented
39#19098439C22116yescomplemented
40#19098423C2218yescomplemented
41#19098420C2218yescomplemented
42#19098420C2218yescomplemented
43C2×C79⋊#95C2212yes—
44C2×C79⋊#95C2212yes—
45C2×C79⋊#95C2212yes—
46C24×C4×C79C2211yescharacteristic
47C22×C4⋊C4×C79C2211yescharacteristic
48C22×C4⋊C4×C79C2211yescharacteristic
49C22×C22⋊C4×C79C2212yes—
50#380×C79C2218yescomplemented
51C2×#95×C79C2212yes—
52C24×D79C2311yescharacteristic
53C24×D79C2311yescharacteristic
54C2×#11929624—2128no—
55C2×#11929624—232no—
56C2×#11929624—232no—
57C2×#11929624C2×C4164yescomplemented
58C22×Dic158—24no—
59C22×Dic158—24no—
60C22×Dic158C2×C418yescomplemented
61C22×Dic158C2314yes—
62C22×D316—24no—
63C22×D316—24no—
64C22×D316C2×C418yes—
65C22×D316C2314yes—
66C22×C22⋊D79—24no—
67C22×C22⋊D79—24no—
68C22×C22⋊D79—24no—
69C22×C22⋊D79—24no—
70C22×C22⋊D79C2×C418yes—
71C22×C22⋊D79C2×C418yescomplemented
72C22×C22⋊D79C2314yes—
73C22×C22⋊D79C2314yes—
74C23×Dic79C2312yes—
75C23×Dic79C2312yes—
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C22×C4×D79—24no—
79C22×C4×D79—24no—
80C22×C4×D79—28no—
81C22×C4×D79—44no—
82C22×C4×D79—44no—
83C22×C4×D79C2×C418yes—
84C22×C4×D79C2×C418yescomplemented
85C22×C4×D79D418yes—
86C22×C4×D79D418yes—
87C22×C4×D79C2314yes—
88C22×C4×D79C2318yes—
89C22×C4×D79C2314yes—
90#14579119—232no—
91C2×C4⋊Dic79—24no—
92C2×C4⋊Dic79—24no—
93C2×C4⋊Dic79C2314yes—
94C2×C4⋊Dic79C2314yes—
95C2×Dic79⋊C4—28no—
96C2×Dic79⋊C4C2318yes—
97C4⋊C4×D79—232no—
98C2×C22⋊Dic79—44no—
99C2×C22⋊Dic79C2318yes—
100C2×(C2×D79)⋊C4—28no—
101C2×(C2×D79)⋊C4—44no—
102C2×(C2×D79)⋊C4—44no—
103C2×(C2×D79)⋊C4C2318yes—
104C2×(C2×D79)⋊C4C2318yes—
105C2×(C2×D79)⋊C4C2318yes—
106C2×C4×Dic79—28no—
107C2×C4×Dic79C2318yes—
108C79⋊#95C2318yes—
109C79⋊#95C2318yes—
110C79⋊#95C2318yes—
111C25×C79C2311yescharacteristic
112C23×C4×C79—24no—
113C23×C4×C79—24no—
114C23×C4×C79C2×C418yescomplemented
115C23×C4×C79C2312yes—
116C23×C4×C79C2312yes—
117C23×C4×C79C2311yescharacteristic
118C23×C4×C79C2314yes—
119C23×C4×C79C2311yescharacteristic
120C2×C4⋊C4×C79—24no—
121C2×C4⋊C4×C79—24no—
122C2×C4⋊C4×C79C2314yes—
123C2×C4⋊C4×C79C2314yes—
124C2×C22⋊C4×C79—44no—
125C2×C22⋊C4×C79C2318yes—
126#95×C79C2318yes—
127C23×D79—22no—
128C23×D79—22no—
129C23×D79—22no—
130C23×D79—22no—
131C23×D79—22no—
132C23×D79—22no—
133C23×D79—22no—
134C23×D79—22no—
135C23×D79—22no—
136C23×D79—22no—
137C23×D79C22×C414yes—
138C23×D79C22×C414yes—
139C23×D79C2×D414yes—
140C23×D79C2×D414yes—
141C23×D79C2412yes—
142C23×D79C2412yes—
143#11929624—2256no—
144C2×Dic158—232no—
145C2×Dic158—28no—
146C2×Dic158—28no—
147C2×Dic158C22×C4116yescomplemented
148C2×D316—232no—
149C2×D316—28no—
150C2×D316—28no—
151C2×D316C22×C4116yes—
152C2×C22⋊D79—232no—
153C2×C22⋊D79—28no—
154C2×C22⋊D79—28no—
155C2×C22⋊D79—232no—
156C2×C22⋊D79—28no—
157C2×C22⋊D79—28no—
158C2×C22⋊D79C22×C4116yes—
159C2×C22⋊D79C22×C4116yescomplemented
160C22×Dic79—22no—
161C22×Dic79—22no—
162C22×Dic79—24no—
163C22×Dic79—24no—
164C22×Dic79—24no—
165C22×Dic79—24no—
166C22×Dic79—24no—
167C22×Dic79—24no—
168C22×Dic79C22×C414yes—
169C22×Dic79C22×C414yes—
170C22×Dic79C2×D414yes—
171C22×Dic79C2×D414yes—
172C22×Dic79C2414yes—
173C22×Dic79C2414yes—
174C22×Dic79C2412yes—
175C22×Dic79C2412yes—
176C2×C4×D79—216no—
177C2×C4×D79—232no—
178C2×C4×D79—28no—
179C2×C4×D79—28no—
180C2×C4×D79—48no—
181C2×C4×D79—48no—
182C2×C4×D79—432no—
183C2×C4×D79C22⋊C4164yescomplemented
184C2×C4×D79C22×C4116yes—
185C2×C4×D79C22×C4116yescomplemented
186C2×C4×D79C2×D4116yes—
187C2×C4×D79C2×D4116yes—
188C4⋊Dic79—28no—
189C4⋊Dic79—28no—
190Dic79⋊C4—216no—
191C22⋊Dic79—48no—
192(C2×D79)⋊C4—216no—
193(C2×D79)⋊C4—48no—
194(C2×D79)⋊C4—48no—
195C4×Dic79—216no—
196C24×C79—22no—
197C24×C79—22no—
198C24×C79—22no—
199C24×C79—22no—
200C24×C79—22no—
201C24×C79—22no—
202C24×C79C22×C414yes—
203C24×C79C2412yes—
204C24×C79C2411yescharacteristic
205C22×C4×C79—22no—
206C22×C4×C79—22no—
207C22×C4×C79—232no—
208C22×C4×C79—28no—
209C22×C4×C79—28no—
210C22×C4×C79—24no—
211C22×C4×C79—24no—
212C22×C4×C79—24no—
213C22×C4×C79—24no—
214C22×C4×C79—24no—
215C22×C4×C79—24no—
216C22×C4×C79C22×C414yes—
217C22×C4×C79C22×C414yes—
218C22×C4×C79C22×C4116yescomplemented
219C22×C4×C79C2×D414yes—
220C22×C4×C79C2×D414yes—
221C22×C4×C79C2414yes—
222C22×C4×C79C2414yes—
223C22×C4×C79C2412yes—
224C22×C4×C79C2412yes—
225C4⋊C4×C79—28no—
226C4⋊C4×C79—28no—
227C22⋊C4×C79—48no—
228C23×C79—28no—
229C23×C79—28no—
230C23×C79—28no—
231C23×C79—22no—
232C23×C79—22no—
233C23×C79—22no—
234C23×C79—22no—
235C23×C79—22no—
236C23×C79—22no—
237C23×C79—44no—
238C23×C79—44no—
239C23×C79—44no—
240C23×C79—44no—
241C23×C79C23×C414yes—
242C23×C79C23×C412yes—
243C23×C79C22×D412yes—
244C23×C79C22×D412yes—
245C23×C79H(5,𝔽2)12yes—
246C23×C79H(5,𝔽2)12yes—
247C23×C792−1+412yes—
248C23×C792−1+412yes—
249C23×C79C2511yescharacteristic
250C22×D79—28no—
251C22×D79—28no—
252C22×D79—28no—
253C22×D79—28no—
254C22×D79—28no—
255C22×D79—28no—
256C22×D79—22no—
257C22×D79—22no—
258C22×D79—22no—
259C22×D79—22no—
260C22×D79—28no—
261C22×D79—28no—
262C22×D79—28no—
263C22×D79—22no—
264C22×D79—22no—
265C22×D79—22no—
266C22×D79—22no—
267C22×D79—22no—
268C22×D79—22no—
269C22×D79—44no—
270C22×D79—44no—
271C22×D79—44no—
272C22×D79—44no—
273C22×D79C2×C22⋊C4116yes—
274C22×D79C23×C414yes—
275C22×D79C23×C414yes—
276C22×D79C22×D414yes—
277C22×D79C22×D414yes—
278C2×C4×C79—28no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—232no—
282C2×C4×C79—24no—
283C2×C4×C79—24no—
284C2×C4×C79—24no—
285C2×C4×C79—24no—
286C2×C4×C79—24no—
287C2×C4×C79—24no—
288C2×C4×C79—48no—
289C2×C4×C79—48no—
290C2×C4×C79C2×C22⋊C4116yes—
291C2×C4×C79C23×C414yes—
292C2×C4×C79C23×C414yes—
293C2×C4×C79C22×D414yes—
294C2×C4×C79C22×D414yes—
295C22⋊D79—232no—
296C22⋊D79—232no—
297C2×Dic79—28no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—24no—
301C2×Dic79—24no—
302C2×Dic79—24no—
303C2×Dic79—24no—
304C2×Dic79—24no—
305C2×Dic79—24no—
306C2×Dic79—48no—
307C2×Dic79—48no—
308C2×Dic79C2×C22⋊C4116yes—
309C2×Dic79C23×C414yes—
310C2×Dic79C23×C414yes—
311C2×Dic79C22×D414yes—
312C2×Dic79C22×D414yes—
313D316—232no—
314C4×D79—232no—
315C4×D79—432no—
316C4×D79C2×C22⋊C4164yescomplemented
317Dic158—232no—
318C22×C79—24no—
319C22×C79—24no—
320C22×C79—24no—
321C22×C79—416no—
322C22×C79—42no—
323C22×C79—42no—
324C22×C79—42no—
325C22×C79—42no—
326C22×C79C22×C22⋊C414yes—
327C22×C79#52014yes—
328C22×C79#52014yes—
329C22×C79#53514yes—
330C22×C79#53614yes—
331C22×C79#53714yes—
332C22×C79#53714yes—
333C22×C79C24×C411yescharacteristic
334C22×C79C23×D411yescharacteristic
335C22×C79C23×D411yescharacteristic
336C22×C79C2×H(5,𝔽2)11yescharacteristic
337C22×C79C2×H(5,𝔽2)11yescharacteristic
338C22×C79C2×2−1+411yescharacteristic
339C22×C79C2×2−1+411yescharacteristic
340C2×D79—232no—
341C2×D79—24no—
342C2×D79—24no—
343C2×D79—24no—
344C2×D79—24no—
345C2×D79—24no—
346C2×D79—24no—
347C2×D79—24no—
348C2×D79—24no—
349C2×D79—24no—
350C2×D79—416no—
351C2×D79—42no—
352C2×D79—42no—
353C2×D79—42no—
354C2×D79—42no—
355C2×D79C22×C22⋊C418yes—
356C4×C79—24no—
357C4×C79—44no—
358C4×C79—44no—
359C4×C79C22×C22⋊C418yes—
360Dic79—24no—
361Dic79—44no—
362Dic79—44no—
363Dic79C22×C22⋊C418yes—
364C2×#2311—791nomaximal, Sylow
365C2×C79—44no—
366C2×C79#231118yescomplemented
367C2×C79C23×C22⋊C411yescharacteristic
368C2×C79C2×#52011yescharacteristic
369C2×C79C2×#52011yescharacteristic
370C2×C79C2×#53511yescharacteristic
371C2×C79C2×#53611yescharacteristic
372C2×C79C2×#53711yescharacteristic
373C2×C79C2×#53711yescharacteristic
374D79—28no—
375D79—44no—
376C23×#41—791no—
377C22×#117—791no—
378C23×C4⋊C4—791no—
379#2311—7916no—
380C2×#391—792no—
381C2×#390—792no—
382C2×#386—792no—
383C2×#386—792no—
384C2×#380—791no—
385C2×#380—791no—
386C2×#380—791no—
387C2×#380D7911yescharacteristic, complemented
388C79C2×#231111yescharacteristic, complemented, Sylow
389C22×#41—798no—
390C22×#41—7916no—
391C22×#41—1588no—
392C22×#41—1588no—
393C23×Q8—791no—
394C23×D4—791no—
395C23×D4—791no—
396C23×D4—791no—
397C24×C4—792no—
398C24×C4—791no—
399C24×C4—791no—
400C24×C4C2×D7911yescharacteristic
401C2×#117—798no—
402C2×#117—1588no—
403C22×C4⋊C4—792no—
404C22×C4⋊C4—791no—
405C22×C4⋊C4—791no—
406C22×C4⋊C4—798no—
407C22×C4⋊C4—1588no—
408C22×C4⋊C4C2×D7911yescharacteristic
409C22×C4⋊C4C2×D7911yescharacteristic
410C22×C22⋊C4—792no—
411C22×C22⋊C4—792no—
412C22×C22⋊C4—792no—
413C22×C22⋊C4—792no—
414C22×C22⋊C4C2×D7912yes—
415C22×C42—792no—
416#391—7916no—
417#390—7916no—
418#386—7916no—
419#386—7916no—
420#380—798no—
421#380—798no—
422#380—798no—
423#380C2×D7918yescomplemented
424C2×#95—792no—
425C2×#95—792no—
426C2×#95—792no—
427C2×#95C2×D7912yes—
428C25—791no—
429C25—791no—
430C25C22×D7911yescharacteristic
431C2×#41—7964no—
432C2×#41—158128no—
433C2×#41—15832no—
434C2×#41—15832no—
435C22×Q8—798no—
436C22×Q8—794no—
437C22×Q8—1584no—
438C22×Q8—1584no—
439C22×D4—798no—
440C22×D4—798no—
441C22×D4—794no—
442C22×D4—794no—
443C22×D4—798no—
444C22×D4—794no—
445C22×D4—1584no—
446C22×D4—1584no—
447C22×D4—1584no—
448C22×D4—1584no—
449C22×D4—1584no—
450C22×D4—1584no—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—3164no—
454C23×C4—3164no—
455C23×C4—798no—
456C23×C4—791no—
457C23×C4—798no—
458C23×C4—798no—
459C23×C4—798no—
460C23×C4—794no—
461C23×C4—791no—
462C23×C4—798no—
463C23×C4—794no—
464C23×C4—792no—
465C23×C4—792no—
466C23×C4—1588no—
467C23×C4—1584no—
468C23×C4—1584no—
469C23×C4C4×D7918yescomplemented
470C23×C4C22×D7912yes—
471C23×C4C22×D7912yes—
472C23×C4C22×D7911yescharacteristic
473C23×C4C22×D7914yes—
474C23×C4C22×D7911yescharacteristic
475#117—15832no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—794no—
479C2×C4⋊C4—798no—
480C2×C4⋊C4—794no—
481C2×C4⋊C4—15832no—
482C2×C4⋊C4—1588no—
483C2×C4⋊C4—1584no—
484C2×C4⋊C4—1584no—
485C2×C4⋊C4C22×D7914yes—
486C2×C4⋊C4C22×D7914yes—
487C2×C22⋊C4—44no—
488C2×C22⋊C4—3164no—
489C2×C22⋊C4—3164no—
490C2×C22⋊C4—3164no—
491C2×C22⋊C4—798no—
492C2×C22⋊C4—798no—
493C2×C22⋊C4—798no—
494C2×C22⋊C4—798no—
495C2×C22⋊C4—1588no—
496C2×C22⋊C4C22×D7918yes—
497C2×C42—798no—
498C2×C42—1588no—
499#95—798no—
500#95—798no—
501#95—798no—
502#95C22×D7918yes—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—792no—
510C24—794no—
511C24—794no—
512C24—794no—
513C24—792no—
514C24—794no—
515C24—1582no—
516C24—1582no—
517C24—1582no—
518C24—1582no—
519C24—1582no—
520C24—1582no—
521C24—1582no—
522C24—1582no—
523C24—1582no—
524C24—1582no—
525C24C2×C4×D7914yes—
526C24C23×D7912yes—
527C24C23×D7911yescharacteristic
528#41—158256no—
529C2×Q8—7916no—
530C2×Q8—15832no—
531C2×Q8—1588no—
532C2×Q8—1588no—
533C2×D4—7916no—
534C2×D4—7916no—
535C2×D4—7916no—
536C2×D4—15832no—
537C2×D4—1588no—
538C2×D4—1588no—
539C2×D4—15832no—
540C2×D4—1588no—
541C2×D4—1588no—
542C2×D4—15832no—
543C2×D4—1588no—
544C2×D4—1588no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—232no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—3168no—
557C22×C4—3168no—
558C22×C4—31632no—
559C22×C4—792no—
560C22×C4—794no—
561C22×C4—794no—
562C22×C4—794no—
563C22×C4—7964no—
564C22×C4—7916no—
565C22×C4—7916no—
566C22×C4—7916no—
567C22×C4—792no—
568C22×C4—794no—
569C22×C4—7916no—
570C22×C4—794no—
571C22×C4—794no—
572C22×C4—15816no—
573C22×C4—1584no—
574C22×C4—1584no—
575C22×C4—1584no—
576C22×C4—1584no—
577C22×C4—1584no—
578C22×C4—1584no—
579C22×C4—1582no—
580C22×C4—1582no—
581C22×C4—15832no—
582C22×C4—1588no—
583C22×C4—1588no—
584C22×C4C2×C4×D7914yes—
585C22×C4C2×C4×D7914yes—
586C22×C4C2×C4×D79116yescomplemented
587C22×C4D4×D7914yes—
588C22×C4D4×D7914yes—
589C22×C4C23×D7914yes—
590C22×C4C23×D7914yes—
591C22×C4C23×D7912yes—
592C22×C4C23×D7912yes—
593C4⋊C4—28no—
594C4⋊C4—28no—
595C4⋊C4—15816no—
596C4⋊C4—1588no—
597C4⋊C4—1588no—
598C22⋊C4—48no—
599C22⋊C4—3168no—
600C22⋊C4—3168no—
601C22⋊C4—3168no—
602C22⋊C4—15816no—
603C42—15816no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—28no—
609C23—28no—
610C23—28no—
611C23—22no—
612C23—22no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—3164no—
618C23—3164no—
619C23—3164no—
620C23—3164no—
621C23—7916no—
622C23—794no—
623C23—794no—
624C23—794no—
625C23—794no—
626C23—1582no—
627C23—1582no—
628C23—1582no—
629C23—1582no—
630C23—1588no—
631C23—1588no—
632C23—1588no—
633C23—1582no—
634C23—1582no—
635C23—1588no—
636C23—1582no—
637C23—1582no—
638C23—1582no—
639C23—1582no—
640C23—1588no—
641C23—1588no—
642C23—1588no—
643C23—1588no—
644C23—1588no—
645C23C22×C4×D7914yes—
646C23C22×C4×D7912yes—
647C23C2×D4×D7912yes—
648C23C2×D4×D7912yes—
649C23#1457920612yes—
650C23#1457920712yes—
651C23#1457920812yes—
652C23#1457920912yes—
653C23C24×D7911yescharacteristic
654Q8—15832no—
655D4—15832no—
656D4—15832no—
657D4—15832no—
658C2×C4—28no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—232no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—48no—
669C2×C4—48no—
670C2×C4—31632no—
671C2×C4—3168no—
672C2×C4—3168no—
673C2×C4—7916no—
674C2×C4—794no—
675C2×C4—794no—
676C2×C4—794no—
677C2×C4—7964no—
678C2×C4—794no—
679C2×C4—1584no—
680C2×C4—1584no—
681C2×C4—1584no—
682C2×C4—1584no—
683C2×C4—1584no—
684C2×C4—1584no—
685C2×C4—1588no—
686C2×C4—1582no—
687C2×C4—1582no—
688C2×C4—15832no—
689C2×C4C22⋊C4×D79116yes—
690C2×C4C22×C4×D7914yes—
691C2×C4C22×C4×D7914yes—
692C2×C4C2×D4×D7914yes—
693C2×C4C2×D4×D7914yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—416no—
702C22—3162no—
703C22—3162no—
704C22—3162no—
705C22—3162no—
706C22—31616no—
707C22—798no—
708C22—1584no—
709C22—1584no—
710C22—1584no—
711C22—1584no—
712C22—1584no—
713C22—1584no—
714C22—1584no—
715C22—1584no—
716C22—1584no—
717C22—15832no—
718C22C2×C22⋊C4×D7914yes—
719C22#1909904314yes—
720C22#1909904414yes—
721C22#1909912914yes—
722C22#1909913614yes—
723C22#1909914214yes—
724C22#1909914314yes—
725C22C23×C4×D7911yescharacteristic
726C22C22×D4×D7911yescharacteristic
727C22C22×D4×D7911yescharacteristic
728C22C2×#1457920611yescharacteristic
729C22C2×#1457920711yescharacteristic
730C22C2×#1457920811yescharacteristic
731C22C2×#1457920911yescharacteristic
732C4—24no—
733C4—44no—
734C4—44no—
735C4—3164no—
736C4—3164no—
737C4—798no—
738C4—1584no—
739C4C2×C22⋊C4×D7918yes—
740C2—44no—
741C2—3164no—
742C2—1588no—
743C2#2376598918yesdirect product factor
744C2C22×C22⋊C4×D7911yescharacteristic
745C2C2×#1909904311yescharacteristic
746C2C2×#1909904411yescharacteristic
747C2C2×#1909912911yescharacteristic
748C2C2×#1909913611yescharacteristic
749C2C2×#1909914211yescharacteristic
750C2C2×#1909914311yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#380×C79C2
socleC24×C79C24
prime radicalC23×#11929624C2
cosocleC23×C79C25
hypercenterC2×#380D79
hypocenterC79C2×#2311
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#14579119C2semidirect
3. C22×C4⋊C4×D79C2semidirect
4. #23765989C2direct (N × H)
5. C2×#19098467C2semidirect
6. C2×#19098463C2semidirect
7. C2×#19098441C2semidirect
8. C2×#19098439C2semidirect
9. C2×#19098423C2semidirect
10. C2×#19098420C2semidirect
11. C2×#19098420C2semidirect
12. C2×#380×C79C2semidirect
15. C22×#11929624C4semidirect
25. C2×#14579119C22semidirect
30. C2×C4⋊C4×D79C22semidirect
36. #19098467C22semidirect
37. #19098463C22semidirect
38. #19098441C22semidirect
39. #19098439C22semidirect
40. #19098423C22semidirect
41. #19098420C22semidirect
42. #19098420C22semidirect
50. #380×C79C22semidirect
57. C2×#11929624C2×C4semidirect
60. C22×Dic158C2×C4semidirect
71. C22×C22⋊D79C2×C4semidirect
84. C22×C4×D79C2×C4semidirect
114. C23×C4×C79C2×C4semidirect
147. C2×Dic158C22×C4semidirect
159. C2×C22⋊D79C22×C4semidirect
183. C2×C4×D79C22⋊C4semidirect
185. C2×C4×D79C22×C4semidirect
218. C22×C4×C79C22×C4semidirect
316. C4×D79C2×C22⋊C4semidirect
366. C2×C79#2311semidirect
387. C2×#380D79semidirect
388. C79C2×#2311semidirect
423. #380C2×D79semidirect
469. C23×C4C4×D79semidirect
586. C22×C4C2×C4×D79semidirect
743. C2#23765989direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#119296242
C22×#145791192
C22×C4⋊C4×D792
#237659892
C2×#190984672
C2×#190984632
C2×#190984412
C2×#190984392
C2×#190984232
C2×#190984202
C2×#380×C792
C2×#231179