Finite Group Databasebeta

← C2×#23768851 #34458564

Subgroups — C2×#23768851 #34458564

Order 20224.

2334 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23768851C2116yesmaximal, direct product factor
2C2×#19098501C211yesmaximal, characteristic, complemented
3C2×#19098498C211yesmaximal, characteristic
4C2×#19098497C211yesmaximal, characteristic, complemented
5C2×#19098476C211yesmaximal, characteristic
6C2×#19098469C211yesmaximal, characteristic, complemented
7C2×#19098467C211yesmaximal, characteristic, complemented
8C2×#19098458C211yesmaximal, characteristic, complemented
9C2×#19098454C211yesmaximal, characteristic
10C2×#19098454C211yesmaximal, characteristic
11C2×#19098447C211yesmaximal, characteristic, complemented
12C2×#19098447C211yesmaximal, characteristic, complemented
13C2×#19098437C211yesmaximal, characteristic
14C2×#19098434C211yesmaximal, characteristic
15C2×C4×(C2×D79)⋊C4C211yesmaximal, characteristic
16C2×C4×C4⋊C4×C79C211yesmaximal, characteristic, complemented
17C23×Dic158C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C22×C4⋊Dic79C2211yescharacteristic
20C22×Dic79⋊C4C2211yescharacteristic
21C22×Dic79⋊C4C2211yescharacteristic
22C22×Dic79⋊C4C2211yescharacteristic
23C22×Dic79⋊C4C2211yescharacteristic
24C22×Dic79⋊C4C2211yescharacteristic
25C22×Dic79⋊C4C2211yescharacteristic
26C22×(C2×D79)⋊C4C2211yescharacteristic
27C22×(C2×D79)⋊C4C2211yescharacteristic
28C22×(C2×D79)⋊C4C2211yescharacteristic
29C22×(C2×D79)⋊C4C2211yescharacteristic
30C22×(C2×D79)⋊C4C2211yescharacteristic
31C22×(C2×D79)⋊C4C2211yescharacteristic
32C22×C4×Dic79C2211yescharacteristic
33#19098501C2218yescomplemented
34#19098498C2218yes—
35#19098497C2218yescomplemented
36#19098476C2218yes—
37#19098469C2218yescomplemented
38#19098467C2218yescomplemented
39#19098458C2218yescomplemented
40#19098454C2218yes—
41#19098454C2218yes—
42#19098447C2218yescomplemented
43#19098447C2218yescomplemented
44#19098437C2218yes—
45#19098434C2218yes—
46C4×(C2×D79)⋊C4C2218yes—
47C2×C79⋊#95C2211yescharacteristic
48C2×C79⋊#95C2211yescharacteristic
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
59C22×C4⋊C4×C79C2211yescharacteristic
60C22×C4⋊C4×C79C2211yescharacteristic
61C22×C42×C79C2211yescharacteristic
62C22×C42×C79C2211yescharacteristic
63C22×C42×C79C2211yescharacteristic
64C4×C4⋊C4×C79C2218yescomplemented
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C24×D79C2311yescharacteristic
68C22×Dic158—24no—
69C22×Dic158—24no—
70C22×Dic158—42no—
71C22×Dic158C2314yes—
72C23×Dic79C2311yescharacteristic
73C23×Dic79C2311yescharacteristic
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C22×C4×D79—24no—
80C22×C4×D79—42no—
81C22×C4×D79—42no—
82C22×C4×D79C2314yes—
83C2×C4⋊Dic79—42no—
84C2×C4⋊Dic79C2314yes—
85C2×Dic79⋊C4—24no—
86C2×Dic79⋊C4—24no—
87C2×Dic79⋊C4—24no—
88C2×Dic79⋊C4—42no—
89C2×Dic79⋊C4—42no—
90C2×Dic79⋊C4—42no—
91C2×Dic79⋊C4C2314yes—
92C2×Dic79⋊C4C2314yes—
93C2×Dic79⋊C4C2314yes—
94C2×Dic79⋊C4C2314yes—
95C2×Dic79⋊C4C2314yes—
96C2×Dic79⋊C4C2314yes—
97C2×(C2×D79)⋊C4—24no—
98C2×(C2×D79)⋊C4—24no—
99C2×(C2×D79)⋊C4—24no—
100C2×(C2×D79)⋊C4—42no—
101C2×(C2×D79)⋊C4—42no—
102C2×(C2×D79)⋊C4Q818yescomplemented
103C2×(C2×D79)⋊C4C2314yes—
104C2×(C2×D79)⋊C4C2314yes—
105C2×(C2×D79)⋊C4C2314yes—
106C2×(C2×D79)⋊C4C2314yes—
107C2×(C2×D79)⋊C4C2314yes—
108C2×(C2×D79)⋊C4C2314yes—
109C2×C4×Dic79—42no—
110C2×C4×Dic79C2314yes—
111C79⋊#95C2314yes—
112C79⋊#95C2314yes—
113C79⋊#95C2314yes—
114C79⋊#95C2314yes—
115C79⋊#95C2314yes—
116C79⋊#95C2314yes—
117C79⋊#95C2314yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C79⋊#95C2314yes—
122C79⋊#95C2314yes—
123C23×C4×C79C2311yescharacteristic
124C23×C4×C79C2311yescharacteristic
125C23×C4×C79C2311yescharacteristic
126C23×C4×C79C2311yescharacteristic
127C23×C4×C79C2311yescharacteristic
128C23×C4×C79C2311yescharacteristic
129C23×C4×C79C2311yescharacteristic
130C2×C4⋊C4×C79—24no—
131C2×C4⋊C4×C79—24no—
132C2×C4⋊C4×C79C2314yes—
133C2×C4⋊C4×C79C2314yes—
134C2×C42×C79—24no—
135C2×C42×C79—42no—
136C2×C42×C79—42no—
137C2×C42×C79C2314yes—
138C2×C42×C79C2314yes—
139C2×C42×C79C2314yes—
140#95×C79C2314yes—
141#95×C79C2314yes—
142C23×D79—22no—
143C23×D79—22no—
144C23×D79—22no—
145C23×D79—22no—
146C23×D79—22no—
147C23×D79—22no—
148C23×D79C2×Q814yes—
149C23×D79C2412yes—
150C2×Dic158—28no—
151C2×Dic158—28no—
152C2×Dic158—44no—
153C2×Dic158—416no—
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×Dic79—22no—
164C22×Dic79—22no—
165C22×Dic79—22no—
166C22×Dic79—22no—
167C22×Dic79—22no—
168C22×Dic79—22no—
169C22×Dic79—22no—
170C22×Dic79—22no—
171C22×Dic79—22no—
172C22×Dic79—22no—
173C22×Dic79C2×Q814yes—
174C22×Dic79#4114yes—
175C22×Dic79C2412yes—
176C22×Dic79C2412yes—
177C22×Dic79C2412yes—
178C22×Dic79C2412yes—
179C22×Dic79C2412yes—
180C22×Dic79C2412yes—
181C22×Dic79C2412yes—
182C2×C4×D79—28no—
183C2×C4×D79—44no—
184C2×C4×D79—44no—
185C2×C4×D79—416no—
186C4⋊Dic79—44no—
187Dic79⋊C4—28no—
188Dic79⋊C4—28no—
189Dic79⋊C4—28no—
190Dic79⋊C4—44no—
191Dic79⋊C4—44no—
192Dic79⋊C4—44no—
193(C2×D79)⋊C4—28no—
194(C2×D79)⋊C4—28no—
195(C2×D79)⋊C4—28no—
196(C2×D79)⋊C4—44no—
197(C2×D79)⋊C4—44no—
198(C2×D79)⋊C4C2×Q8116yescomplemented
199C4×Dic79—44no—
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—22no—
217C22×C4×C79—22no—
218C22×C4×C79C2×Q814yes—
219C22×C4×C79#4114yes—
220C22×C4×C79#4114yes—
221C22×C4×C79#4114yes—
222C22×C4×C79C2412yes—
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—
231C42×C79—28no—
232C42×C79—44no—
233C42×C79—44no—
234C23×C79C22×Q812yes—
235C23×C79C2×#4112yes—
236C23×C79C2×#4112yes—
237C23×C79C2×#4112yes—
238C23×C79C2×#4112yes—
239C23×C79H(5,𝔽2)12yes—
240C23×C79H(5,𝔽2)12yes—
241C23×C79C2511yescharacteristic
242C22×D79—28no—
243C22×D79—28no—
244C22×D79—28no—
245C22×D79—22no—
246C22×D79—22no—
247C22×D79—22no—
248C22×D79—22no—
249C22×D79—22no—
250C22×D79—22no—
251C22×D79—44no—
252C22×D79—44no—
253C22×D79—44no—
254C22×D79—44no—
255C22×D79C22×Q814yes—
256C2×C4×C79—28no—
257C2×C4×C79—28no—
258C2×C4×C79—28no—
259C2×C4×C79—28no—
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—22no—
274C2×C4×C79—22no—
275C2×C4×C79—22no—
276C2×C4×C79—22no—
277C2×C4×C79—44no—
278C2×C4×C79—44no—
279C2×C4×C79—44no—
280C2×C4×C79C22×Q814yes—
281C2×C4×C79C2×#4114yes—
282C2×C4×C79C2×#4114yes—
283C2×C4×C79C2×#4114yes—
284C2×Dic79—28no—
285C2×Dic79—28no—
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—22no—
305C2×Dic79—44no—
306C2×Dic79—44no—
307C2×Dic79—44no—
308C2×Dic79—44no—
309C2×Dic79—44no—
310C2×Dic79C22×Q814yes—
311C2×Dic79C2×#4114yes—
312C4×D79—416no—
313Dic158—416no—
314C22×C79#52914yes—
315C22×C79#53314yes—
316C22×C79#53814yes—
317C22×C79#55114yes—
318C22×C79#55414yes—
319C22×C79#55414yes—
320C22×C79#55914yes—
321C22×C79C23×Q811yescharacteristic
322C22×C79C22×#4111yescharacteristic
323C22×C79C22×#4111yescharacteristic
324C22×C79C22×#4111yescharacteristic
325C22×C79C22×#4111yescharacteristic
326C22×C79C2×H(5,𝔽2)11yescharacteristic
327C22×C79C2×H(5,𝔽2)11yescharacteristic
328C2×D79—24no—
329C2×D79—24no—
330C2×D79—24no—
331C2×D79—416no—
332C2×D79—42no—
333C2×D79—42no—
334C2×D79—42no—
335C2×D79—42no—
336C4×C79—24no—
337C4×C79—24no—
338C4×C79—24no—
339C4×C79—24no—
340C4×C79—42no—
341C4×C79—42no—
342C4×C79—42no—
343Dic79—24no—
344Dic79—24no—
345Dic79—42no—
346Dic79—42no—
347Dic79—42no—
348Dic79—42no—
349Dic79—42no—
350C2×#2589—791nomaximal, Sylow
351C2×C79#258918yescomplemented
352C2×C79C2×#52911yescharacteristic
353C2×C79C2×#53311yescharacteristic
354C2×C79C2×#53811yescharacteristic
355C2×C79C2×#55111yescharacteristic
356C2×C79C2×#55411yescharacteristic
357C2×C79C2×#55411yescharacteristic
358C2×C79C2×#55911yescharacteristic
359D79—44no—
360#2589—7916no—
361C2×#400—791no—
362C2×#399—791no—
363C2×#398—791no—
364C2×#393—791no—
365C2×#391—791no—
366C2×#391—791no—
367C2×#389—791no—
368C2×#388—791no—
369C2×#388—791no—
370C2×#387—791no—
371C2×#387—791no—
372C2×#385—791no—
373C2×#385—791no—
374C2×C4×C4⋊C4D7911yescharacteristic, complemented
375C2×C4×C22⋊C4—791no—
376C79C2×#258911yescharacteristic, complemented, Sylow
377C23×Q8—791no—
378C24×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⋊C4—791no—
393C22×C22⋊C4—791no—
394C22×C42—791no—
395C22×C42C2×D7911yescharacteristic
396C22×C42C2×D7911yescharacteristic
397C22×C42C2×D7911yescharacteristic
398#400—798no—
399#399—798no—
400#398—798no—
401#393—798no—
402#391—798no—
403#391—798no—
404#389—798no—
405#388—798no—
406#388—798no—
407#387—798no—
408#387—798no—
409#385—798no—
410#385—798no—
411C4×C4⋊C4C2×D7918yescomplemented
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×#95—791no—
424C2×#95—791no—
425C2×#95C2×D7911yescharacteristic
426C2×#95C2×D7911yescharacteristic
427C25—791no—
428C22×Q8—3162no—
429C22×Q8—794no—
430C22×Q8—1584no—
431C22×Q8—1584no—
432C23×C4—3162no—
433C23×C4—3162no—
434C23×C4—794no—
435C23×C4—791no—
436C23×C4—791no—
437C23×C4—791no—
438C23×C4—791no—
439C23×C4—791no—
440C23×C4—791no—
441C23×C4—791no—
442C23×C4—1584no—
443C23×C4C22×D7911yescharacteristic
444C23×C4C22×D7911yescharacteristic
445C23×C4C22×D7911yescharacteristic
446C23×C4C22×D7911yescharacteristic
447C23×C4C22×D7911yescharacteristic
448C23×C4C22×D7911yescharacteristic
449C23×C4C22×D7911yescharacteristic
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—3162no—
453C2×C4⋊C4—3162no—
454C2×C4⋊C4—3162no—
455C2×C4⋊C4—3162no—
456C2×C4⋊C4—794no—
457C2×C4⋊C4—794no—
458C2×C4⋊C4—794no—
459C2×C4⋊C4—794no—
460C2×C4⋊C4—794no—
461C2×C4⋊C4—794no—
462C2×C4⋊C4—794no—
463C2×C4⋊C4—1584no—
464C2×C4⋊C4—1584no—
465C2×C4⋊C4—1584no—
466C2×C4⋊C4C22×D7914yes—
467C2×C4⋊C4C22×D7914yes—
468C2×C22⋊C4—3162no—
469C2×C22⋊C4—3162no—
470C2×C22⋊C4—794no—
471C2×C22⋊C4—794no—
472C2×C22⋊C4—798no—
473C2×C22⋊C4—794no—
474C2×C22⋊C4—794no—
475C2×C22⋊C4—794no—
476C2×C22⋊C4—794no—
477C2×C22⋊C4—1584no—
478C2×C22⋊C4—1584no—
479C2×C22⋊C4—1584no—
480C2×C42—24no—
481C2×C42—42no—
482C2×C42—42no—
483C2×C42—3162no—
484C2×C42—794no—
485C2×C42C22×D7914yes—
486C2×C42C22×D7914yes—
487C2×C42C22×D7914yes—
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#95—794no—
499#95—794no—
500#95C22×D7914yes—
501#95C22×D7914yes—
502C24—794no—
503C24—792no—
504C24—1582no—
505C24—1582no—
506C24—1582no—
507C24—1582no—
508C24—1582no—
509C24—1582no—
510C24C23×D7911yescharacteristic
511C2×Q8—31616no—
512C2×Q8—3164no—
513C2×Q8—1588no—
514C2×Q8—1588no—
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—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—31616no—
533C22×C4—3164no—
534C22×C4—3164no—
535C22×C4—794no—
536C22×C4—794no—
537C22×C4—792no—
538C22×C4—792no—
539C22×C4—792no—
540C22×C4—792no—
541C22×C4—792no—
542C22×C4—792no—
543C22×C4—792no—
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—1588no—
560C22×C4—1582no—
561C22×C4—1582no—
562C22×C4—1582no—
563C22×C4—1582no—
564C22×C4Q8×D7914yes—
565C22×C4#1192962414yes—
566C22×C4#1192962414yes—
567C22×C4#1192962414yes—
568C22×C4C23×D7912yes—
569C22×C4C23×D7912yes—
570C22×C4C23×D7912yes—
571C22×C4C23×D7912yes—
572C22×C4C23×D7912yes—
573C22×C4C23×D7912yes—
574C22×C4C23×D7912yes—
575C4⋊C4—28no—
576C4⋊C4—28no—
577C4⋊C4—3164no—
578C4⋊C4—3164no—
579C4⋊C4—3164no—
580C4⋊C4—3164no—
581C4⋊C4—1588no—
582C4⋊C4—1588no—
583C4⋊C4—1588no—
584C22⋊C4—3164no—
585C22⋊C4—3164no—
586C22⋊C4—7916no—
587C22⋊C4—1588no—
588C22⋊C4—1588no—
589C22⋊C4—1588no—
590C42—28no—
591C42—44no—
592C42—44no—
593C42—3164no—
594C23—3164no—
595C23—3164no—
596C23—3164no—
597C23—3164no—
598C23—794no—
599C23—1582no—
600C23—1582no—
601C23—1588no—
602C23—1588no—
603C23—1588no—
604C23—1582no—
605C23—1582no—
606C23—1582no—
607C23—1582no—
608C23C2×Q8×D7912yes—
609C23#41×D7912yes—
610C23C2×#1192962412yes—
611C23C2×#1192962412yes—
612C23C2×#1192962412yes—
613C23#1457920612yes—
614C23#1457920712yes—
615C23C24×D7911yescharacteristic
616Q8—31616no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—31616no—
642C2×C4—3164no—
643C2×C4—3164no—
644C2×C4—3164no—
645C2×C4—3164no—
646C2×C4—3164no—
647C2×C4—794no—
648C2×C4—794no—
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—1582no—
661C2×C4—1582no—
662C2×C4—1582no—
663C2×C4—1582no—
664C2×C4—1582no—
665C2×C4—1582no—
666C2×C4—1588no—
667C2×C4—1588no—
668C2×C4—1582no—
669C2×C4—1582no—
670C2×C4C2×Q8×D7914yes—
671C2×C4C2×#1192962414yes—
672C2×C4C2×#1192962414yes—
673C2×C4C2×#1192962414yes—
674C22—31616no—
675C22—3162no—
676C22—3162no—
677C22—3162no—
678C22—3162no—
679C22—1584no—
680C22—1584no—
681C22—1584no—
682C22#1909909714yes—
683C22#1909911714yes—
684C22#1909914614yes—
685C22#1909923714yes—
686C22#1909926814yes—
687C22#1909927314yes—
688C22#1909929614yes—
689C22C22×Q8×D7911yescharacteristic
690C22C2×#41×D7911yescharacteristic
691C22C22×#1192962411yescharacteristic
692C22C22×#1192962411yescharacteristic
693C22C22×#1192962411yescharacteristic
694C22C2×#1457920611yescharacteristic
695C22C2×#1457920711yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—3162no—
704C4—3162no—
705C4—3162no—
706C4—3162no—
707C4—3162no—
708C4—1584no—
709C4—1584no—
710C2—3164no—
711C2#2376885118yesdirect product factor
712C2C2×#1909909711yescharacteristic
713C2C2×#1909911711yescharacteristic
714C2C2×#1909914611yescharacteristic
715C2C2×#1909923711yescharacteristic
716C2C2×#1909926811yescharacteristic
717C2C2×#1909927311yescharacteristic
718C2C2×#1909929611yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×C4×C4⋊C4×C79C2
socleC24×C79C24
prime radicalC24×D79C23
hypercenterC2×C4×C4⋊C4D79
hypocenterC79C2×#2589
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #23768851C2direct (N × H)
2. C2×#19098501C2semidirect
4. C2×#19098497C2semidirect
6. C2×#19098469C2semidirect
7. C2×#19098467C2semidirect
8. C2×#19098458C2semidirect
11. C2×#19098447C2semidirect
12. C2×#19098447C2semidirect
16. C2×C4×C4⋊C4×C79C2semidirect
33. #19098501C22semidirect
35. #19098497C22semidirect
37. #19098469C22semidirect
38. #19098467C22semidirect
39. #19098458C22semidirect
42. #19098447C22semidirect
43. #19098447C22semidirect
64. C4×C4⋊C4×C79C22semidirect
102. C2×(C2×D79)⋊C4Q8semidirect
198. (C2×D79)⋊C4C2×Q8semidirect
351. C2×C79#2589semidirect
374. C2×C4×C4⋊C4D79semidirect
376. C79C2×#2589semidirect
411. C4×C4⋊C4C2×D79semidirect
711. C2#23768851direct (N × H)

Maximal subgroups

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

subgroupindex
#237688512
C2×#190985012
C2×#190984982
C2×#190984972
C2×#190984762
C2×#190984692
C2×#190984672
C2×#190984582
C2×#190984542
C2×#190984472
C2×#190984372
C2×#190984342
C2×C4×(C2×D79)⋊C42
C2×C4×C4⋊C4×C792
C2×#258979