Finite Group Databasebeta

← C2×#23768122 #34457464

Subgroups — C2×#23768122 #34457464

Order 20224.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23768122C2116yesmaximal, direct product factor
2C2×#19098499C211yesmaximal, characteristic
3C2×#19098497C211yesmaximal, characteristic, complemented
4C2×#19098493C211yesmaximal, characteristic, complemented
5C2×#19098486C211yesmaximal, characteristic
6C2×#19098462C211yesmaximal, characteristic, complemented
7C2×#19098460C211yesmaximal, characteristic, complemented
8C2×#19098457C211yesmaximal, characteristic
9C2×#19098457C211yesmaximal, characteristic
10C2×#19098449C211yesmaximal, characteristic, complemented
11C2×#19098448C211yesmaximal, characteristic, complemented
12C2×#19098444C211yesmaximal, characteristic, complemented
13C2×#19098423C211yesmaximal, characteristic
14C2×#19098414C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic79C211yesmaximal, characteristic
16C2×#385×C79C211yesmaximal, characteristic
17C22×C4⋊Dic79C2211yescharacteristic
18C22×C4⋊Dic79C2211yescharacteristic
19C22×C4⋊Dic79C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21C22×Dic79⋊C4C2211yescharacteristic
22C22×Dic79⋊C4C2211yescharacteristic
23C22×Dic79⋊C4C2211yescharacteristic
24C22×Dic79⋊C4C2211yescharacteristic
25C22×Dic79⋊C4C2211yescharacteristic
26C22×Dic79⋊C4C2211yescharacteristic
27C22×C22⋊Dic79C2211yescharacteristic
28C22×C22⋊Dic79C2211yescharacteristic
29C22×C22⋊Dic79C2211yescharacteristic
30C22×C22⋊Dic79C2211yescharacteristic
31C22×C4×Dic79C2211yescharacteristic
32C22×C4×Dic79C2211yescharacteristic
33C22×C4×Dic79C2211yescharacteristic
34C22×C4×Dic79C2211yescharacteristic
35#19098499C2218yes—
36#19098497C2218yescomplemented
37#19098493C2218yescomplemented
38#19098486C2218yes—
39#19098462C2218yescomplemented
40#19098460C2218yescomplemented
41#19098457C2218yes—
42#19098457C2218yes—
43#19098449C2218yescomplemented
44#19098448C2218yescomplemented
45#19098444C2218yescomplemented
46#19098423C2218yes—
47#19098414C2218yescomplemented
48C4×C22⋊Dic79C2218yes—
49C2×C79⋊#95C2211yescharacteristic
50C2×C79⋊#95C2211yescharacteristic
51C2×C79⋊#95C2211yescharacteristic
52C2×C79⋊#95C2211yescharacteristic
53C2×C79⋊#95C2211yescharacteristic
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C24×C4×C79C2211yescharacteristic
60C22×C4⋊C4×C79C2211yescharacteristic
61C22×C4⋊C4×C79C2211yescharacteristic
62C22×C22⋊C4×C79C2211yescharacteristic
63C22×C22⋊C4×C79C2211yescharacteristic
64#385×C79C2218yes—
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C23×Dic79C2311yescharacteristic
68C23×Dic79C2311yescharacteristic
69C23×Dic79C2311yescharacteristic
70C23×Dic79C2311yescharacteristic
71C23×Dic79C2311yescharacteristic
72C23×Dic79C2311yescharacteristic
73C23×Dic79C2311yescharacteristic
74C23×Dic79C2311yescharacteristic
75C2×C4⋊Dic79—24no—
76C2×C4⋊Dic79—42no—
77C2×C4⋊Dic79—42no—
78C2×C4⋊Dic79—42no—
79C2×C4⋊Dic79C2314yes—
80C2×C4⋊Dic79C2314yes—
81C2×C4⋊Dic79C2314yes—
82C2×C4⋊Dic79C2314yes—
83C2×Dic79⋊C4—24no—
84C2×Dic79⋊C4—24no—
85C2×Dic79⋊C4—24no—
86C2×Dic79⋊C4—24no—
87C2×Dic79⋊C4—42no—
88C2×Dic79⋊C4—42no—
89C2×Dic79⋊C4C2314yes—
90C2×Dic79⋊C4C2314yes—
91C2×Dic79⋊C4C2314yes—
92C2×Dic79⋊C4C2314yes—
93C2×Dic79⋊C4C2314yes—
94C2×Dic79⋊C4C2314yes—
95C2×C22⋊Dic79—24no—
96C2×C22⋊Dic79—42no—
97C2×C22⋊Dic79—42no—
98C2×C22⋊Dic79Q818yes—
99C2×C22⋊Dic79C2314yes—
100C2×C22⋊Dic79C2314yes—
101C2×C22⋊Dic79C2314yes—
102C2×C22⋊Dic79C2314yes—
103C2×C4×Dic79—24no—
104C2×C4×Dic79—42no—
105C2×C4×Dic79—42no—
106C2×C4×Dic79—42no—
107C2×C4×Dic79C2314yes—
108C2×C4×Dic79C2314yes—
109C2×C4×Dic79C2314yes—
110C2×C4×Dic79C2314yes—
111C79⋊#95C2314yes—
112C79⋊#95C2314yes—
113C79⋊#95C2314yes—
114C79⋊#95C2314yes—
115C79⋊#95C2314yes—
116C79⋊#95C2314yes—
117C79⋊#95C2314yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C25×C79C2311yescharacteristic
122C23×C4×C79—24no—
123C23×C4×C79—24no—
124C23×C4×C79—42no—
125C23×C4×C79C2311yescharacteristic
126C23×C4×C79C2311yescharacteristic
127C23×C4×C79C2311yescharacteristic
128C23×C4×C79C2314yes—
129C23×C4×C79C2311yescharacteristic
130C23×C4×C79C2311yescharacteristic
131C23×C4×C79C2311yescharacteristic
132C2×C4⋊C4×C79—24no—
133C2×C4⋊C4×C79—24no—
134C2×C4⋊C4×C79C2314yes—
135C2×C4⋊C4×C79C2314yes—
136C2×C22⋊C4×C79—24no—
137C2×C22⋊C4×C79—42no—
138C2×C22⋊C4×C79C2314yes—
139C2×C22⋊C4×C79C2314yes—
140#95×C79C2314yes—
141#95×C79C2314yes—
142C22×Dic79—22no—
143C22×Dic79—22no—
144C22×Dic79—22no—
145C22×Dic79—22no—
146C22×Dic79—22no—
147C22×Dic79—22no—
148C22×Dic79—22no—
149C22×Dic79—22no—
150C22×Dic79—22no—
151C22×Dic79—22no—
152C22×Dic79—22no—
153C22×Dic79—22no—
154C22×Dic79—22no—
155C22×Dic79—22no—
156C22×Dic79—22no—
157C22×Dic79—22no—
158C22×Dic79—22no—
159C22×Dic79—22no—
160C22×Dic79—22no—
161C22×Dic79—22no—
162C22×Dic79—22no—
163C22×Dic79C2×Q814yes—
164C22×Dic79C2×Q814yes—
165C22×Dic79#4114yes—
166C22×Dic79C2412yes—
167C22×Dic79C2412yes—
168C22×Dic79C2412yes—
169C22×Dic79C2412yes—
170C22×Dic79C2412yes—
171C22×Dic79C2412yes—
172C22×Dic79C2412yes—
173C22×Dic79C2412yes—
174C4⋊Dic79—28no—
175C4⋊Dic79—44no—
176C4⋊Dic79—44no—
177C4⋊Dic79—44no—
178Dic79⋊C4—28no—
179Dic79⋊C4—28no—
180Dic79⋊C4—28no—
181Dic79⋊C4—28no—
182Dic79⋊C4—44no—
183Dic79⋊C4—44no—
184C22⋊Dic79—28no—
185C22⋊Dic79—44no—
186C22⋊Dic79—44no—
187C22⋊Dic79C2×Q8116yes—
188C4×Dic79—28no—
189C4×Dic79—44no—
190C4×Dic79—44no—
191C4×Dic79—44no—
192C24×C79—22no—
193C24×C79—22no—
194C24×C79—22no—
195C24×C79—22no—
196C24×C79—22no—
197C24×C79—22no—
198C24×C79C2×Q814yes—
199C24×C79C2412yes—
200C24×C79C2411yescharacteristic
201C22×C4×C79—22no—
202C22×C4×C79—22no—
203C22×C4×C79—22no—
204C22×C4×C79—22no—
205C22×C4×C79—22no—
206C22×C4×C79—22no—
207C22×C4×C79—22no—
208C22×C4×C79—22no—
209C22×C4×C79—22no—
210C22×C4×C79—22no—
211C22×C4×C79—22no—
212C22×C4×C79—22no—
213C22×C4×C79—22no—
214C22×C4×C79—22no—
215C22×C4×C79—22no—
216C22×C4×C79—28no—
217C22×C4×C79—28no—
218C22×C4×C79—44no—
219C22×C4×C79—416no—
220C22×C4×C79#4114yes—
221C22×C4×C79#4114yes—
222C22×C4×C79#4114yes—
223C22×C4×C79C2412yes—
224C22×C4×C79C2412yes—
225C22×C4×C79C2412yes—
226C22×C4×C79C2412yes—
227C22×C4×C79C2412yes—
228C22×C4×C79C2412yes—
229C4⋊C4×C79—28no—
230C4⋊C4×C79—28no—
231C22⋊C4×C79—28no—
232C22⋊C4×C79—44no—
233C23×C79—28no—
234C23×C79—28no—
235C23×C79—28no—
236C23×C79—22no—
237C23×C79—22no—
238C23×C79—22no—
239C23×C79—22no—
240C23×C79—22no—
241C23×C79—22no—
242C23×C79—44no—
243C23×C79—44no—
244C23×C79—44no—
245C23×C79—44no—
246C23×C79C22×Q814yes—
247C23×C79C22×Q812yes—
248C23×C79C2×#4112yes—
249C23×C79C2×#4112yes—
250C23×C79C2×#4112yes—
251C23×C79C2×#4112yes—
252C23×C79H(5,𝔽2)12yes—
253C23×C79H(5,𝔽2)12yes—
254C23×C79C2511yescharacteristic
255C2×C4×C79—28no—
256C2×C4×C79—28no—
257C2×C4×C79—28no—
258C2×C4×C79—22no—
259C2×C4×C79—22no—
260C2×C4×C79—22no—
261C2×C4×C79—22no—
262C2×C4×C79—22no—
263C2×C4×C79—22no—
264C2×C4×C79—22no—
265C2×C4×C79—22no—
266C2×C4×C79—22no—
267C2×C4×C79—22no—
268C2×C4×C79—22no—
269C2×C4×C79—22no—
270C2×C4×C79—22no—
271C2×C4×C79—22no—
272C2×C4×C79—22no—
273C2×C4×C79—416no—
274C2×C4×C79—44no—
275C2×C4×C79—44no—
276C2×C4×C79—44no—
277C2×C4×C79C2×#4114yes—
278C2×C4×C79C2×#4114yes—
279C2×C4×C79C2×#4114yes—
280C2×Dic79—28no—
281C2×Dic79—28no—
282C2×Dic79—28no—
283C2×Dic79—22no—
284C2×Dic79—22no—
285C2×Dic79—22no—
286C2×Dic79—22no—
287C2×Dic79—22no—
288C2×Dic79—22no—
289C2×Dic79—22no—
290C2×Dic79—22no—
291C2×Dic79—22no—
292C2×Dic79—22no—
293C2×Dic79—22no—
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—44no—
305C2×Dic79—44no—
306C2×Dic79—44no—
307C2×Dic79—44no—
308C2×Dic79—44no—
309C2×Dic79C22×Q814yes—
310C2×Dic79C22×Q814yes—
311C2×Dic79C2×#4114yes—
312C22×C79—24no—
313C22×C79—24no—
314C22×C79—24no—
315C22×C79—42no—
316C22×C79—42no—
317C22×C79—42no—
318C22×C79—42no—
319C22×C79—416no—
320C22×C79#52914yes—
321C22×C79#53314yes—
322C22×C79#54014yes—
323C22×C79#55114yes—
324C22×C79#55314yes—
325C22×C79#55414yes—
326C22×C79#55414yes—
327C22×C79C23×Q811yescharacteristic
328C22×C79C22×#4111yescharacteristic
329C22×C79C22×#4111yescharacteristic
330C22×C79C22×#4111yescharacteristic
331C22×C79C22×#4111yescharacteristic
332C22×C79C2×H(5,𝔽2)11yescharacteristic
333C22×C79C2×H(5,𝔽2)11yescharacteristic
334C4×C79—24no—
335C4×C79—24no—
336C4×C79—24no—
337C4×C79—42no—
338C4×C79—42no—
339C4×C79—42no—
340Dic79—24no—
341Dic79—24no—
342Dic79—24no—
343Dic79—42no—
344Dic79—42no—
345Dic79—42no—
346Dic79—42no—
347Dic79—42no—
348C2×#2522—791nomaximal, Sylow
349C2×C79—44no—
350C2×C79#252218yescomplemented
351C2×C79C2×#52911yescharacteristic
352C2×C79C2×#53311yescharacteristic
353C2×C79C2×#54011yescharacteristic
354C2×C79C2×#55111yescharacteristic
355C2×C79C2×#55311yescharacteristic
356C2×C79C2×#55411yescharacteristic
357C2×C79C2×#55411yescharacteristic
358#2522—7916no—
359C2×#399—791no—
360C2×#398—791no—
361C2×#398—791no—
362C2×#396—791no—
363C2×#389—791no—
364C2×#389—791no—
365C2×#388—791no—
366C2×#388—791no—
367C2×#387—791no—
368C2×#387—791no—
369C2×#387—791no—
370C2×#385D7911yescharacteristic
371C2×#380—791no—
372C2×C4×C4⋊C4—791no—
373C2×C4×C22⋊C4—791no—
374C79C2×#252211yescharacteristic, complemented, Sylow
375C24×C4C2×D7911yescharacteristic
376C22×C4⋊C4—791no—
377C22×C4⋊C4—791no—
378C22×C4⋊C4—791no—
379C22×C4⋊C4—791no—
380C22×C4⋊C4—791no—
381C22×C4⋊C4—791no—
382C22×C4⋊C4—791no—
383C22×C4⋊C4—791no—
384C22×C4⋊C4—791no—
385C22×C4⋊C4—791no—
386C22×C4⋊C4C2×D7911yescharacteristic
387C22×C4⋊C4C2×D7911yescharacteristic
388C22×C22⋊C4—791no—
389C22×C22⋊C4—791no—
390C22×C22⋊C4—791no—
391C22×C22⋊C4—791no—
392C22×C22⋊C4C2×D7911yescharacteristic
393C22×C22⋊C4C2×D7911yescharacteristic
394C22×C42—791no—
395C22×C42—791no—
396C22×C42—791no—
397C22×C42—791no—
398#399—798no—
399#398—798no—
400#398—798no—
401#396—798no—
402#389—798no—
403#389—798no—
404#388—798no—
405#388—798no—
406#387—798no—
407#387—798no—
408#387—798no—
409#385C2×D7918yes—
410#380—798no—
411C4×C4⋊C4—798no—
412C4×C22⋊C4—798no—
413C2×#95—791no—
414C2×#95—791no—
415C2×#95—791no—
416C2×#95—791no—
417C2×#95—791no—
418C2×#95—791no—
419C2×#95—791no—
420C2×#95—791no—
421C2×#95—791no—
422C2×#95—791no—
423C2×#95C2×D7911yescharacteristic
424C2×#95C2×D7911yescharacteristic
425C25C22×D7911yescharacteristic
426C23×C4—24no—
427C23×C4—24no—
428C23×C4—42no—
429C23×C4—791no—
430C23×C4—791no—
431C23×C4—791no—
432C23×C4—791no—
433C23×C4—791no—
434C23×C4—791no—
435C23×C4—791no—
436C23×C4—791no—
437C23×C4C22×D7911yescharacteristic
438C23×C4C22×D7911yescharacteristic
439C23×C4C22×D7911yescharacteristic
440C23×C4C22×D7914yes—
441C23×C4C22×D7911yescharacteristic
442C23×C4C22×D7911yescharacteristic
443C23×C4C22×D7911yescharacteristic
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—3162no—
447C2×C4⋊C4—3162no—
448C2×C4⋊C4—3162no—
449C2×C4⋊C4—3162no—
450C2×C4⋊C4—3162no—
451C2×C4⋊C4—794no—
452C2×C4⋊C4—794no—
453C2×C4⋊C4—794no—
454C2×C4⋊C4—794no—
455C2×C4⋊C4—794no—
456C2×C4⋊C4—794no—
457C2×C4⋊C4—794no—
458C2×C4⋊C4—794no—
459C2×C4⋊C4—794no—
460C2×C4⋊C4—794no—
461C2×C4⋊C4—1584no—
462C2×C4⋊C4—1584no—
463C2×C4⋊C4—1584no—
464C2×C4⋊C4—1584no—
465C2×C4⋊C4—1584no—
466C2×C4⋊C4C22×D7914yes—
467C2×C4⋊C4C22×D7914yes—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—3162no—
471C2×C22⋊C4—3162no—
472C2×C22⋊C4—794no—
473C2×C22⋊C4—794no—
474C2×C22⋊C4—798no—
475C2×C22⋊C4—794no—
476C2×C22⋊C4—794no—
477C2×C22⋊C4—1584no—
478C2×C22⋊C4C22×D7914yes—
479C2×C22⋊C4C22×D7914yes—
480C2×C42—3162no—
481C2×C42—3162no—
482C2×C42—3162no—
483C2×C42—794no—
484C2×C42—794no—
485C2×C42—794no—
486C2×C42—794no—
487C2×C42—1584no—
488#95—794no—
489#95—794no—
490#95—794no—
491#95—794no—
492#95—794no—
493#95—794no—
494#95—794no—
495#95—794no—
496#95—794no—
497#95—794no—
498#95C22×D7914yes—
499#95C22×D7914yes—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24Q8×D7914yes—
507C24C23×D7912yes—
508C24C23×D7911yescharacteristic
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—44no—
527C22×C4—416no—
528C22×C4—794no—
529C22×C4—794no—
530C22×C4—794no—
531C22×C4—792no—
532C22×C4—792no—
533C22×C4—792no—
534C22×C4—792no—
535C22×C4—792no—
536C22×C4—792no—
537C22×C4—792no—
538C22×C4—792no—
539C22×C4—1582no—
540C22×C4—1582no—
541C22×C4—1582no—
542C22×C4—1582no—
543C22×C4—1582no—
544C22×C4—1582no—
545C22×C4—1582no—
546C22×C4—1582no—
547C22×C4—1582no—
548C22×C4—1582no—
549C22×C4—1582no—
550C22×C4—1582no—
551C22×C4—1582no—
552C22×C4—1582no—
553C22×C4—1582no—
554C22×C4—1582no—
555C22×C4—1582no—
556C22×C4—1582no—
557C22×C4—1582no—
558C22×C4—1582no—
559C22×C4—1582no—
560C22×C4#1192962314yes—
561C22×C4#1192962314yes—
562C22×C4#1192962414yes—
563C22×C4C23×D7912yes—
564C22×C4C23×D7912yes—
565C22×C4C23×D7912yes—
566C22×C4C23×D7912yes—
567C22×C4C23×D7912yes—
568C22×C4C23×D7912yes—
569C4⋊C4—28no—
570C4⋊C4—28no—
571C4⋊C4—3164no—
572C4⋊C4—3164no—
573C4⋊C4—3164no—
574C4⋊C4—3164no—
575C4⋊C4—3164no—
576C4⋊C4—1588no—
577C4⋊C4—1588no—
578C4⋊C4—1588no—
579C4⋊C4—1588no—
580C4⋊C4—1588no—
581C22⋊C4—28no—
582C22⋊C4—44no—
583C22⋊C4—3164no—
584C22⋊C4—3164no—
585C22⋊C4—7916no—
586C22⋊C4—1588no—
587C42—3164no—
588C42—3164no—
589C42—3164no—
590C42—1588no—
591C23—22no—
592C23—22no—
593C23—28no—
594C23—28no—
595C23—28no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23C2×Q8×D7914yes—
605C23C2×Q8×D7912yes—
606C23#41×D7912yes—
607C23C2×#1192962312yes—
608C23C2×#1192962312yes—
609C23C2×#1192962412yes—
610C23#1457920612yes—
611C23#1457920712yes—
612C23C24×D7911yescharacteristic
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—28no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—416no—
632C2×C4—44no—
633C2×C4—44no—
634C2×C4—44no—
635C2×C4—3164no—
636C2×C4—3164no—
637C2×C4—3164no—
638C2×C4—3164no—
639C2×C4—3164no—
640C2×C4—794no—
641C2×C4—794no—
642C2×C4—794no—
643C2×C4—1582no—
644C2×C4—1582no—
645C2×C4—1582no—
646C2×C4—1582no—
647C2×C4—1582no—
648C2×C4—1582no—
649C2×C4—1582no—
650C2×C4—1582no—
651C2×C4—1582no—
652C2×C4—1582no—
653C2×C4—1582no—
654C2×C4—1582no—
655C2×C4—1582no—
656C2×C4—1582no—
657C2×C4—1582no—
658C2×C4—1582no—
659C2×C4—1582no—
660C2×C4—1588no—
661C2×C4—1588no—
662C2×C4—1588no—
663C2×C4—1582no—
664C2×C4—1582no—
665C2×C4—1582no—
666C2×C4—1582no—
667C2×C4C2×#1192962314yes—
668C2×C4C2×#1192962314yes—
669C2×C4C2×#1192962414yes—
670C22—24no—
671C22—24no—
672C22—24no—
673C22—416no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22#1909909514yes—
679C22#1909911514yes—
680C22#1909916514yes—
681C22#1909924414yes—
682C22#1909925914yes—
683C22#1909926814yes—
684C22#1909927114yes—
685C22C22×Q8×D7911yescharacteristic
686C22C2×#41×D7911yescharacteristic
687C22C22×#1192962311yescharacteristic
688C22C22×#1192962311yescharacteristic
689C22C22×#1192962411yescharacteristic
690C22C2×#1457920611yescharacteristic
691C22C2×#1457920711yescharacteristic
692C4—24no—
693C4—24no—
694C4—24no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—3162no—
699C4—3162no—
700C4—3162no—
701C4—3162no—
702C4—3162no—
703C4—1584no—
704C4—1584no—
705C4—1584no—
706C2—44no—
707C2#2376812218yesdirect product factor
708C2C2×#1909909511yescharacteristic
709C2C2×#1909911511yescharacteristic
710C2C2×#1909916511yescharacteristic
711C2C2×#1909924411yescharacteristic
712C2C2×#1909925911yescharacteristic
713C2C2×#1909926811yescharacteristic
714C2C2×#1909927111yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#385×C79C2
socleC24×C79C24
prime radicalC25×C79C23
hypercenterC2×#385D79
hypocenterC79C2×#2522
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. #23768122C2direct (N × H)
3. C2×#19098497C2semidirect
4. C2×#19098493C2semidirect
6. C2×#19098462C2semidirect
7. C2×#19098460C2semidirect
10. C2×#19098449C2semidirect
11. C2×#19098448C2semidirect
12. C2×#19098444C2semidirect
14. C2×#19098414C2semidirect
36. #19098497C22semidirect
37. #19098493C22semidirect
39. #19098462C22semidirect
40. #19098460C22semidirect
43. #19098449C22semidirect
44. #19098448C22semidirect
45. #19098444C22semidirect
47. #19098414C22semidirect
350. C2×C79#2522semidirect
374. C79C2×#2522semidirect
707. C2#23768122direct (N × H)

Maximal subgroups

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

subgroupindex
#237681222
C2×#190984992
C2×#190984972
C2×#190984932
C2×#190984862
C2×#190984622
C2×#190984602
C2×#190984572
C2×#190984492
C2×#190984482
C2×#190984442
C2×#190984232
C2×#190984142
C2×C4×C22⋊Dic792
C2×#385×C792
C2×#252279