Finite Group Databasebeta

← C2×#23768741 #34458735

Subgroups — C2×#23768741 #34458735

Order 20224.

2550 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23768741C2116yesmaximal, direct product factor
2C2×#19098505C211yesmaximal, characteristic, complemented
3C2×#19098489C211yesmaximal, characteristic, complemented
4C2×#19098489C211yesmaximal, characteristic, complemented
5C2×#19098481C211yesmaximal, characteristic
6C2×#19098454C211yesmaximal, characteristic, complemented
7C2×#19098453C211yesmaximal, characteristic, complemented
8C2×#19098445C211yesmaximal, characteristic, complemented
9C2×#19098441C211yesmaximal, characteristic
10C2×#19098441C211yesmaximal, characteristic
11C2×#19098437C211yesmaximal, characteristic, complemented
12C2×#19098430C211yesmaximal, characteristic, complemented
13C2×#19098420C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
15C2×#19098410C211yesmaximal, characteristic, complemented
16C2×#387×C79C211yesmaximal, characteristic, complemented
17C23×D316C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21C22×Dic79⋊C4C2211yescharacteristic
22C22×Dic79⋊C4C2211yescharacteristic
23C22×(C2×D79)⋊C4C2211yescharacteristic
24C22×(C2×D79)⋊C4C2211yescharacteristic
25C22×(C2×D79)⋊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×(C2×D79)⋊C4C2211yescharacteristic
33C22×C4×Dic79C2211yescharacteristic
34C22×C4×Dic79C2211yescharacteristic
35#19098505C2218yescomplemented
36#19098489C2218yescomplemented
37#19098489C2218yescomplemented
38#19098481C2218yes—
39#19098454C2218yescomplemented
40#19098453C2218yescomplemented
41#19098445C2218yescomplemented
42#19098441C2218yes—
43#19098441C2218yes—
44#19098437C2218yescomplemented
45#19098430C2218yescomplemented
46#19098420C2218yescomplemented
47C4×(C2×D79)⋊C4C2218yescomplemented
48#19098410C2218yescomplemented
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
62#387×C79C2218yescomplemented
63C2×#95×C79C2211yescharacteristic
64C2×#95×C79C2211yescharacteristic
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C24×D79C2311yescharacteristic
68C24×D79C2311yescharacteristic
69C22×D316—24no—
70C22×D316—24no—
71C22×D316—42no—
72C22×D316C2314yes—
73C23×Dic79C2311yescharacteristic
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C22×C4×D79—24no—
80C22×C4×D79—24no—
81C22×C4×D79—24no—
82C22×C4×D79—42no—
83C22×C4×D79—42no—
84C22×C4×D79—42no—
85C22×C4×D79C2314yes—
86C22×C4×D79C2314yes—
87C2×C4⋊Dic79—42no—
88C2×C4⋊Dic79C2314yes—
89C2×Dic79⋊C4—24no—
90C2×Dic79⋊C4—42no—
91C2×Dic79⋊C4C2314yes—
92C2×Dic79⋊C4C2314yes—
93C2×(C2×D79)⋊C4—24no—
94C2×(C2×D79)⋊C4—24no—
95C2×(C2×D79)⋊C4—24no—
96C2×(C2×D79)⋊C4—24no—
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)⋊C4—42no—
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×(C2×D79)⋊C4C2314yes—
110C2×(C2×D79)⋊C4C2314yes—
111C2×(C2×D79)⋊C4C2314yes—
112C2×(C2×D79)⋊C4C2314yes—
113C2×C4×Dic79—24no—
114C2×C4×Dic79—42no—
115C2×C4×Dic79C2314yes—
116C2×C4×Dic79C2314yes—
117C79⋊#95C2314yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C79⋊#95C2314yes—
122C79⋊#95C2314yes—
123C79⋊#95C2314yes—
124C79⋊#95C2314yes—
125C79⋊#95C2314yes—
126C79⋊#95C2314yes—
127C23×C4×C79C2311yescharacteristic
128C23×C4×C79C2311yescharacteristic
129C23×C4×C79C2311yescharacteristic
130C23×C4×C79C2311yescharacteristic
131C23×C4×C79C2311yescharacteristic
132C23×C4×C79C2311yescharacteristic
133C23×C4×C79C2311yescharacteristic
134C2×C4⋊C4×C79—24no—
135C2×C4⋊C4×C79—42no—
136C2×C4⋊C4×C79C2314yes—
137C2×C4⋊C4×C79C2314yes—
138C2×C42×C79—42no—
139C2×C42×C79C2314yes—
140#95×C79C2314yes—
141#95×C79C2314yes—
142#95×C79C2314yes—
143#95×C79C2314yes—
144C23×D79—22no—
145C23×D79—22no—
146C23×D79—22no—
147C23×D79—22no—
148C23×D79—22no—
149C23×D79—22no—
150C23×D79—22no—
151C23×D79—22no—
152C23×D79—22no—
153C23×D79—22no—
154C23×D79—22no—
155C23×D79—22no—
156C23×D79#4114yes—
157C23×D79#4114yes—
158C23×D79C2412yes—
159C23×D79C2412yes—
160C2×D316—28no—
161C2×D316—28no—
162C2×D316—44no—
163C2×D316—416no—
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×Dic79—22no—
174C22×Dic79—22no—
175C22×Dic79—22no—
176C22×Dic79—22no—
177C22×Dic79—22no—
178C22×Dic79—22no—
179C22×Dic79—22no—
180C22×Dic79—22no—
181C22×Dic79#4114yes—
182C22×Dic79C2412yes—
183C22×Dic79C2412yes—
184C22×Dic79C2412yes—
185C22×Dic79C2412yes—
186C22×Dic79C2412yes—
187C22×Dic79C2412yes—
188C2×C4×D79—28no—
189C2×C4×D79—28no—
190C2×C4×D79—28no—
191C2×C4×D79—44no—
192C2×C4×D79—44no—
193C2×C4×D79—44no—
194C2×C4×D79—416no—
195C2×C4×D79—416no—
196C4⋊Dic79—44no—
197Dic79⋊C4—28no—
198Dic79⋊C4—44no—
199(C2×D79)⋊C4—28no—
200(C2×D79)⋊C4—28no—
201(C2×D79)⋊C4—28no—
202(C2×D79)⋊C4—28no—
203(C2×D79)⋊C4—28no—
204(C2×D79)⋊C4—28no—
205(C2×D79)⋊C4—28no—
206(C2×D79)⋊C4—44no—
207(C2×D79)⋊C4—44no—
208(C2×D79)⋊C4—44no—
209C4×Dic79—28no—
210C4×Dic79—44no—
211C24×C79C2411yescharacteristic
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×C79—22no—
219C22×C4×C79—22no—
220C22×C4×C79—22no—
221C22×C4×C79—22no—
222C22×C4×C79—22no—
223C22×C4×C79—22no—
224C22×C4×C79—22no—
225C22×C4×C79—22no—
226C22×C4×C79—22no—
227C22×C4×C79—22no—
228C22×C4×C79—22no—
229C22×C4×C79—22no—
230C22×C4×C79—22no—
231C22×C4×C79#4114yes—
232C22×C4×C79#4114yes—
233C22×C4×C79C2412yes—
234C22×C4×C79C2412yes—
235C22×C4×C79C2412yes—
236C22×C4×C79C2412yes—
237C22×C4×C79C2412yes—
238C22×C4×C79C2412yes—
239C22×C4×C79C2412yes—
240C4⋊C4×C79—28no—
241C4⋊C4×C79—44no—
242C42×C79—44no—
243C23×C79C2×#4112yes—
244C23×C79C2×#4112yes—
245C23×C79C2×#4112yes—
246C23×C79C2×#4112yes—
247C23×C79C2×#4112yes—
248C23×C79H(5,𝔽2)12yes—
249C23×C79H(5,𝔽2)12yes—
250C23×C79C2511yescharacteristic
251C22×D79—28no—
252C22×D79—28no—
253C22×D79—28no—
254C22×D79—28no—
255C22×D79—28no—
256C22×D79—28no—
257C22×D79—22no—
258C22×D79—22no—
259C22×D79—22no—
260C22×D79—22no—
261C22×D79—22no—
262C22×D79—22no—
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×D79—44no—
274C22×D79—44no—
275C22×D79—44no—
276C22×D79—44no—
277C22×D79C2×#4114yes—
278C22×D79C2×#4114yes—
279C2×C4×C79—28no—
280C2×C4×C79—28no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
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—22no—
300C2×C4×C79—44no—
301C2×C4×C79—44no—
302C2×C4×C79—44no—
303C2×C4×C79—44no—
304C2×C4×C79—44no—
305C2×C4×C79C2×#4114yes—
306C2×C4×C79C2×#4114yes—
307C2×Dic79—28no—
308C2×Dic79—22no—
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—22no—
318C2×Dic79—22no—
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×Dic79—44no—
328C2×Dic79—44no—
329C2×Dic79—44no—
330C2×Dic79C2×#4114yes—
331D316—416no—
332C4×D79—416no—
333C4×D79—416no—
334C22×C79#52914yes—
335C22×C79#52914yes—
336C22×C79#53814yes—
337C22×C79#55114yes—
338C22×C79#55114yes—
339C22×C79#55314yes—
340C22×C79#55314yes—
341C22×C79C22×#4111yescharacteristic
342C22×C79C22×#4111yescharacteristic
343C22×C79C22×#4111yescharacteristic
344C22×C79C22×#4111yescharacteristic
345C22×C79C22×#4111yescharacteristic
346C22×C79C2×H(5,𝔽2)11yescharacteristic
347C22×C79C2×H(5,𝔽2)11yescharacteristic
348C2×D79—24no—
349C2×D79—24no—
350C2×D79—24no—
351C2×D79—24no—
352C2×D79—24no—
353C2×D79—24no—
354C2×D79—416no—
355C2×D79—416no—
356C2×D79—42no—
357C2×D79—42no—
358C2×D79—42no—
359C2×D79—42no—
360C2×D79—42no—
361C2×D79—42no—
362C2×D79—42no—
363C2×D79—42no—
364C4×C79—24no—
365C4×C79—24no—
366C4×C79—42no—
367C4×C79—42no—
368C4×C79—42no—
369C4×C79—42no—
370C4×C79—42no—
371Dic79—24no—
372Dic79—42no—
373Dic79—42no—
374Dic79—42no—
375Dic79—42no—
376Dic79—42no—
377C2×#2578—791nomaximal, Sylow
378C2×C79#257818yescomplemented
379C2×C79C2×#52911yescharacteristic
380C2×C79C2×#52911yescharacteristic
381C2×C79C2×#53811yescharacteristic
382C2×C79C2×#55111yescharacteristic
383C2×C79C2×#55111yescharacteristic
384C2×C79C2×#55311yescharacteristic
385C2×C79C2×#55311yescharacteristic
386D79—44no—
387D79—44no—
388#2578—7916no—
389C2×#400—791no—
390C2×#397—791no—
391C2×#397—791no—
392C2×#394—791no—
393C2×#388—791no—
394C2×#388—791no—
395C2×#387—791no—
396C2×#387D7911yescharacteristic, complemented
397C2×#386—791no—
398C2×#386—791no—
399C2×#385—791no—
400C2×#383—791no—
401C2×#380—791no—
402C2×C4×C22⋊C4—791no—
403C2×C4×C22⋊C4—791no—
404C79C2×#257811yescharacteristic, complemented, Sylow
405C23×D4—791no—
406C24×C4—791no—
407C24×C4—791no—
408C22×C4⋊C4—791no—
409C22×C4⋊C4—791no—
410C22×C4⋊C4—791no—
411C22×C4⋊C4C2×D7911yescharacteristic
412C22×C4⋊C4C2×D7911yescharacteristic
413C22×C22⋊C4—791no—
414C22×C22⋊C4—791no—
415C22×C22⋊C4—791no—
416C22×C22⋊C4—791no—
417C22×C22⋊C4—791no—
418C22×C22⋊C4—791no—
419C22×C22⋊C4—791no—
420C22×C22⋊C4—791no—
421C22×C22⋊C4—791no—
422C22×C22⋊C4—791no—
423C22×C42—791no—
424C22×C42—791no—
425C22×C42C2×D7911yescharacteristic
426#400—798no—
427#397—798no—
428#397—798no—
429#394—798no—
430#388—798no—
431#388—798no—
432#387—798no—
433#387C2×D7918yescomplemented
434#386—798no—
435#386—798no—
436#385—798no—
437#383—798no—
438#380—798no—
439C4×C22⋊C4—798no—
440C4×C22⋊C4—798no—
441C2×#95—791no—
442C2×#95—791no—
443C2×#95—791no—
444C2×#95—791no—
445C2×#95—791no—
446C2×#95—791no—
447C2×#95—791no—
448C2×#95—791no—
449C2×#95—791no—
450C2×#95—791no—
451C2×#95C2×D7911yescharacteristic
452C2×#95C2×D7911yescharacteristic
453C2×#95C2×D7911yescharacteristic
454C2×#95C2×D7911yescharacteristic
455C25—791no—
456C25—791no—
457C22×D4—3162no—
458C22×D4—794no—
459C22×D4—1584no—
460C22×D4—1584no—
461C23×C4—3162no—
462C23×C4—3162no—
463C23×C4—3162no—
464C23×C4—794no—
465C23×C4—794no—
466C23×C4—791no—
467C23×C4—791no—
468C23×C4—791no—
469C23×C4—791no—
470C23×C4—791no—
471C23×C4—791no—
472C23×C4—1584no—
473C23×C4—1584no—
474C23×C4—1584no—
475C23×C4C22×D7911yescharacteristic
476C23×C4C22×D7911yescharacteristic
477C23×C4C22×D7911yescharacteristic
478C23×C4C22×D7911yescharacteristic
479C23×C4C22×D7911yescharacteristic
480C23×C4C22×D7911yescharacteristic
481C23×C4C22×D7911yescharacteristic
482C2×C4⋊C4—24no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—3162no—
485C2×C4⋊C4—3162no—
486C2×C4⋊C4—794no—
487C2×C4⋊C4—794no—
488C2×C4⋊C4—794no—
489C2×C4⋊C4—1584no—
490C2×C4⋊C4C22×D7914yes—
491C2×C4⋊C4C22×D7914yes—
492C2×C22⋊C4—3162no—
493C2×C22⋊C4—3162no—
494C2×C22⋊C4—3162no—
495C2×C22⋊C4—794no—
496C2×C22⋊C4—794no—
497C2×C22⋊C4—794no—
498C2×C22⋊C4—794no—
499C2×C22⋊C4—794no—
500C2×C22⋊C4—794no—
501C2×C22⋊C4—794no—
502C2×C22⋊C4—794no—
503C2×C22⋊C4—794no—
504C2×C22⋊C4—794no—
505C2×C22⋊C4—1584no—
506C2×C22⋊C4—1584no—
507C2×C22⋊C4—1584no—
508C2×C22⋊C4—1584no—
509C2×C22⋊C4—1584no—
510C2×C22⋊C4—1584no—
511C2×C22⋊C4—1584no—
512C2×C42—42no—
513C2×C42—3162no—
514C2×C42—794no—
515C2×C42—794no—
516C2×C42—1584no—
517C2×C42C22×D7914yes—
518#95—794no—
519#95—794no—
520#95—794no—
521#95—794no—
522#95—794no—
523#95—794no—
524#95—794no—
525#95—794no—
526#95—794no—
527#95—794no—
528#95C22×D7914yes—
529#95C22×D7914yes—
530#95C22×D7914yes—
531#95C22×D7914yes—
532C24—794no—
533C24—794no—
534C24—792no—
535C24—792no—
536C24—1582no—
537C24—1582no—
538C24—1582no—
539C24—1582no—
540C24—1582no—
541C24—1582no—
542C24—1582no—
543C24—1582no—
544C24—1582no—
545C24—1582no—
546C24—1582no—
547C24—1582no—
548C24C23×D7911yescharacteristic
549C2×D4—3164no—
550C2×D4—31616no—
551C2×D4—1588no—
552C2×D4—1588no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—31616no—
573C22×C4—31616no—
574C22×C4—3164no—
575C22×C4—3164no—
576C22×C4—3164no—
577C22×C4—794no—
578C22×C4—792no—
579C22×C4—792no—
580C22×C4—792no—
581C22×C4—792no—
582C22×C4—792no—
583C22×C4—792no—
584C22×C4—1588no—
585C22×C4—1582no—
586C22×C4—1582no—
587C22×C4—1582no—
588C22×C4—1582no—
589C22×C4—1582no—
590C22×C4—1582no—
591C22×C4—1582no—
592C22×C4—1582no—
593C22×C4—1582no—
594C22×C4—1582no—
595C22×C4—1582no—
596C22×C4—1582no—
597C22×C4—1582no—
598C22×C4—1582no—
599C22×C4—1582no—
600C22×C4—1588no—
601C22×C4—1588no—
602C22×C4—1582no—
603C22×C4—1582no—
604C22×C4#1192962414yes—
605C22×C4#1192962514yes—
606C22×C4C23×D7912yes—
607C22×C4C23×D7912yes—
608C22×C4C23×D7912yes—
609C22×C4C23×D7912yes—
610C22×C4C23×D7912yes—
611C22×C4C23×D7912yes—
612C22×C4C23×D7912yes—
613C4⋊C4—28no—
614C4⋊C4—44no—
615C4⋊C4—3164no—
616C4⋊C4—3164no—
617C4⋊C4—1588no—
618C22⋊C4—3164no—
619C22⋊C4—3164no—
620C22⋊C4—3164no—
621C22⋊C4—1588no—
622C22⋊C4—1588no—
623C22⋊C4—1588no—
624C22⋊C4—1588no—
625C22⋊C4—1588no—
626C22⋊C4—1588no—
627C22⋊C4—1588no—
628C42—44no—
629C42—3164no—
630C42—1588no—
631C23—3164no—
632C23—3164no—
633C23—3164no—
634C23—3164no—
635C23—3164no—
636C23—3164no—
637C23—3164no—
638C23—3164no—
639C23—794no—
640C23—794no—
641C23—1582no—
642C23—1582no—
643C23—1582no—
644C23—1582no—
645C23—1588no—
646C23—1588no—
647C23—1588no—
648C23—1588no—
649C23—1588no—
650C23—1588no—
651C23—1582no—
652C23—1582no—
653C23—1582no—
654C23—1582no—
655C23—1582no—
656C23—1582no—
657C23—1582no—
658C23—1582no—
659C23#41×D7912yes—
660C23#41×D7912yes—
661C23#41×D7912yes—
662C23C2×#1192962412yes—
663C23C2×#1192962512yes—
664C23#1457920612yes—
665C23#1457920712yes—
666C23C24×D7911yescharacteristic
667D4—31616no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—28no—
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—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—31616no—
695C2×C4—31616no—
696C2×C4—3164no—
697C2×C4—3164no—
698C2×C4—3164no—
699C2×C4—3164no—
700C2×C4—3164no—
701C2×C4—794no—
702C2×C4—1582no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4—1582no—
708C2×C4—1582no—
709C2×C4—1582no—
710C2×C4—1582no—
711C2×C4—1582no—
712C2×C4—1582no—
713C2×C4—1582no—
714C2×C4—1582no—
715C2×C4—1582no—
716C2×C4—1582no—
717C2×C4—1582no—
718C2×C4—1588no—
719C2×C4—1582no—
720C2×C4C2×#1192962414yes—
721C2×C4C2×#1192962514yes—
722C22—3162no—
723C22—3162no—
724C22—3162no—
725C22—3162no—
726C22—3162no—
727C22—3162no—
728C22—31616no—
729C22—31616no—
730C22—3162no—
731C22—3162no—
732C22—1584no—
733C22—1584no—
734C22—1584no—
735C22—1584no—
736C22—1584no—
737C22—1584no—
738C22#1909909814yes—
739C22#1909910014yes—
740C22#1909915314yes—
741C22#1909923714yes—
742C22#1909923814yes—
743C22#1909925814yes—
744C22#1909926314yes—
745C22C2×#41×D7911yescharacteristic
746C22C2×#41×D7911yescharacteristic
747C22C2×#41×D7911yescharacteristic
748C22C22×#1192962411yescharacteristic
749C22C22×#1192962511yescharacteristic
750C22C2×#1457920611yescharacteristic
751C22C2×#1457920711yescharacteristic
752C4—24no—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—3162no—
760C4—3162no—
761C4—3162no—
762C4—3162no—
763C4—3162no—
764C4—1584no—
765C2—3164no—
766C2—3164no—
767C2#2376874118yesdirect product factor
768C2C2×#1909909811yescharacteristic
769C2C2×#1909910011yescharacteristic
770C2C2×#1909915311yescharacteristic
771C2C2×#1909923711yescharacteristic
772C2C2×#1909923811yescharacteristic
773C2C2×#1909925811yescharacteristic
774C2C2×#1909926311yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#387×C79C2
socleC24×C79C24
prime radicalC23×D316C22
hypercenterC2×#387D79
hypocenterC79C2×#2578
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #23768741C2direct (N × H)
2. C2×#19098505C2semidirect
3. C2×#19098489C2semidirect
4. C2×#19098489C2semidirect
6. C2×#19098454C2semidirect
7. C2×#19098453C2semidirect
8. C2×#19098445C2semidirect
11. C2×#19098437C2semidirect
12. C2×#19098430C2semidirect
13. C2×#19098420C2semidirect
14. C2×C4×(C2×D79)⋊C4C2semidirect
15. C2×#19098410C2semidirect
16. C2×#387×C79C2semidirect
35. #19098505C22semidirect
36. #19098489C22semidirect
37. #19098489C22semidirect
39. #19098454C22semidirect
40. #19098453C22semidirect
41. #19098445C22semidirect
44. #19098437C22semidirect
45. #19098430C22semidirect
46. #19098420C22semidirect
47. C4×(C2×D79)⋊C4C22semidirect
48. #19098410C22semidirect
62. #387×C79C22semidirect
378. C2×C79#2578semidirect
396. C2×#387D79semidirect
404. C79C2×#2578semidirect
433. #387C2×D79semidirect
767. C2#23768741direct (N × H)

Maximal subgroups

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

subgroupindex
#237687412
C2×#190985052
C2×#190984892
C2×#190984812
C2×#190984542
C2×#190984532
C2×#190984452
C2×#190984412
C2×#190984372
C2×#190984302
C2×#190984202
C2×C4×(C2×D79)⋊C42
C2×#190984102
C2×#387×C792
C2×#257879