Finite Group Databasebeta

← C2×#23771545 #34494652

Subgroups — C2×#23771545 #34494652

Order 20224.

2174 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
1#23771545C2116yesmaximal, direct product factor
2C2×#19098495C211yesmaximal, characteristic, complemented
3C2×#19098492C211yesmaximal, characteristic, complemented
4C2×#19098492C211yesmaximal, characteristic, complemented
5C2×#19098491C211yesmaximal, characteristic, complemented
6C2×#19098486C211yesmaximal, characteristic, complemented
7C2×#19098485C211yesmaximal, characteristic, complemented
8C2×#19098483C211yesmaximal, characteristic, complemented
9C2×#19098479C211yesmaximal, characteristic
10C2×#19098479C211yesmaximal, characteristic
11C2×#19098476C211yesmaximal, characteristic, complemented
12C2×#19098475C211yesmaximal, characteristic, complemented
13C2×#19098463C211yesmaximal, characteristic
14C2×#19098448C211yesmaximal, characteristic, complemented
15C2×#19098446C211yesmaximal, characteristic, complemented
16C2×#397×C79C211yesmaximal, characteristic, complemented
17C23×Dic158C2211yescharacteristic
18C23×C22⋊D79C2211yescharacteristic
19C22×C4⋊Dic79C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21C22×C4⋊Dic79C2211yescharacteristic
22C22×Dic79⋊C4C2211yescharacteristic
23C22×Dic79⋊C4C2211yescharacteristic
24C22×Dic79⋊C4C2211yescharacteristic
25C22×Dic79⋊C4C2211yescharacteristic
26C22×C22⋊Dic79C2211yescharacteristic
27C22×C22⋊Dic79C2211yescharacteristic
28C22×C22⋊Dic79C2211yescharacteristic
29C22×(C2×D79)⋊C4C2211yescharacteristic
30C22×(C2×D79)⋊C4C2211yescharacteristic
31C22×(C2×D79)⋊C4C2211yescharacteristic
32C22×(C2×D79)⋊C4C2211yescharacteristic
33C22×(C2×D79)⋊C4C2211yescharacteristic
34C22×(C2×D79)⋊C4C2211yescharacteristic
35C22×C4×Dic79C2211yescharacteristic
36#19098495C2218yescomplemented
37#19098492C2218yescomplemented
38#19098492C2218yescomplemented
39#19098491C2218yescomplemented
40#19098486C2218yescomplemented
41#19098485C2218yescomplemented
42#19098483C2218yescomplemented
43#19098479C2218yes—
44#19098479C2218yes—
45#19098476C2218yescomplemented
46#19098475C2218yescomplemented
47#19098463C2218yes—
48#19098448C2218yescomplemented
49#19098446C2218yescomplemented
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×C22⋊C4×C79C2211yescharacteristic
61C22×C22⋊C4×C79C2211yescharacteristic
62C22×C22⋊C4×C79C2211yescharacteristic
63#397×C79C2218yescomplemented
64C2×#95×C79C2211yescharacteristic
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C24×D79C2311yescharacteristic
68C22×Dic158—42no—
69C22×Dic158—42no—
70C22×Dic158—42no—
71C22×Dic158C2314yes—
72C22×C22⋊D79—24no—
73C22×C22⋊D79—42no—
74C22×C22⋊D79—42no—
75C22×C22⋊D79C2314yes—
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2311yescharacteristic
80C23×Dic79C2311yescharacteristic
81C23×Dic79C2311yescharacteristic
82C23×Dic79C2311yescharacteristic
83C2×C4⋊Dic79—24no—
84C2×C4⋊Dic79—24no—
85C2×C4⋊Dic79—42no—
86C2×C4⋊Dic79C2314yes—
87C2×C4⋊Dic79C2314yes—
88C2×C4⋊Dic79C2314yes—
89C2×Dic79⋊C4—42no—
90C2×Dic79⋊C4—42no—
91C2×Dic79⋊C4—42no—
92C2×Dic79⋊C4—42no—
93C2×Dic79⋊C4C2314yes—
94C2×Dic79⋊C4C2314yes—
95C2×Dic79⋊C4C2314yes—
96C2×Dic79⋊C4C2314yes—
97C2×C22⋊Dic79—42no—
98C2×C22⋊Dic79—42no—
99C2×C22⋊Dic79—42no—
100C2×C22⋊Dic79C2314yes—
101C2×C22⋊Dic79C2314yes—
102C2×C22⋊Dic79C2314yes—
103C2×(C2×D79)⋊C4—42no—
104C2×(C2×D79)⋊C4—42no—
105C2×(C2×D79)⋊C4—42no—
106C2×(C2×D79)⋊C4—42no—
107C2×(C2×D79)⋊C4—42no—
108C2×(C2×D79)⋊C4—42no—
109C2×(C2×D79)⋊C4C2314yes—
110C2×(C2×D79)⋊C4C2314yes—
111C2×(C2×D79)⋊C4C2314yes—
112C2×(C2×D79)⋊C4C2314yes—
113C2×(C2×D79)⋊C4C2314yes—
114C2×(C2×D79)⋊C4C2314yes—
115C2×C4×Dic79—42no—
116C2×C4×Dic79C2314yes—
117C79⋊#95C2314yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C79⋊#95C2314yes—
122C79⋊#95C2314yes—
123C79⋊#95C2314yes—
124C79⋊#95C2314yes—
125C79⋊#95C2314yes—
126C25×C79C2311yescharacteristic
127C23×C4×C79C2311yescharacteristic
128C23×C4×C79C2311yescharacteristic
129C23×C4×C79C2311yescharacteristic
130C23×C4×C79C2311yescharacteristic
131C23×C4×C79C2311yescharacteristic
132C23×C4×C79C2311yescharacteristic
133C2×C4⋊C4×C79—42no—
134C2×C4⋊C4×C79C2314yes—
135C2×C22⋊C4×C79—42no—
136C2×C22⋊C4×C79—42no—
137C2×C22⋊C4×C79—42no—
138C2×C22⋊C4×C79C2314yes—
139C2×C22⋊C4×C79C2314yes—
140C2×C22⋊C4×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×D79C2412yes—
152C2×Dic158—44no—
153C2×Dic158—44no—
154C2×Dic158—44no—
155C2×Dic158—416no—
156C2×C22⋊D79—28no—
157C2×C22⋊D79—44no—
158C2×C22⋊D79—44no—
159C2×C22⋊D79—416no—
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×Dic79—22no—
174C22×Dic79—22no—
175C22×Dic79—22no—
176C22×Dic79—22no—
177C22×Dic79—22no—
178C22×Dic79—22no—
179C22×Dic79—22no—
180C22×Dic79#4114yes—
181C22×Dic79C2412yes—
182C22×Dic79C2412yes—
183C22×Dic79C2412yes—
184C22×Dic79C2412yes—
185C22×Dic79C2412yes—
186C22×Dic79C2412yes—
187C22×Dic79C2412yes—
188C4⋊Dic79—28no—
189C4⋊Dic79—28no—
190C4⋊Dic79—44no—
191Dic79⋊C4—44no—
192Dic79⋊C4—44no—
193Dic79⋊C4—44no—
194Dic79⋊C4—44no—
195C22⋊Dic79—44no—
196C22⋊Dic79—44no—
197C22⋊Dic79—44no—
198(C2×D79)⋊C4—44no—
199(C2×D79)⋊C4—44no—
200(C2×D79)⋊C4—44no—
201(C2×D79)⋊C4—44no—
202(C2×D79)⋊C4—44no—
203(C2×D79)⋊C4—44no—
204C4×Dic79—44no—
205C24×C79—22no—
206C24×C79—22no—
207C24×C79—22no—
208C24×C79—22no—
209C24×C79—22no—
210C24×C79—22no—
211C24×C79—22no—
212C24×C79C2412yes—
213C24×C79C2411yescharacteristic
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—22no—
232C22×C4×C79C2412yes—
233C22×C4×C79C2412yes—
234C22×C4×C79C2412yes—
235C22×C4×C79C2412yes—
236C22×C4×C79C2412yes—
237C22×C4×C79C2412yes—
238C4⋊C4×C79—44no—
239C22⋊C4×C79—44no—
240C22⋊C4×C79—44no—
241C22⋊C4×C79—44no—
242C23×C79—22no—
243C23×C79—22no—
244C23×C79—22no—
245C23×C79—22no—
246C23×C79—22no—
247C23×C79—22no—
248C23×C79—22no—
249C23×C79—44no—
250C23×C79—44no—
251C23×C79—44no—
252C23×C79—44no—
253C23×C79—44no—
254C23×C79—44no—
255C23×C79—44no—
256C23×C79C2×#4112yes—
257C23×C79H(5,𝔽2)12yes—
258C23×C79H(5,𝔽2)12yes—
259C23×C79H(5,𝔽2)12yes—
260C23×C79H(5,𝔽2)12yes—
261C23×C792−1+412yes—
262C23×C792−1+412yes—
263C23×C79C2511yescharacteristic
264C22×D79—22no—
265C22×D79—22no—
266C22×D79—22no—
267C22×D79—22no—
268C22×D79—22no—
269C22×D79—22no—
270C22×D79—22no—
271C22×D79—44no—
272C22×D79—44no—
273C22×D79—44no—
274C22×D79—44no—
275C22×D79—44no—
276C22×D79—44no—
277C22×D79—44no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
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—44no—
297C2×C4×C79—44no—
298C2×C4×C79—44no—
299C2×C4×C79—44no—
300C2×C4×C79—44no—
301C2×C4×C79—44no—
302C22⋊D79—416no—
303C2×Dic79—28no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
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—44no—
325C2×Dic79—44no—
326C2×Dic79—44no—
327C2×Dic79—44no—
328C2×Dic79—44no—
329C2×Dic79—44no—
330C2×Dic79C2×#4114yes—
331Dic158—416no—
332C22×C79—42no—
333C22×C79—42no—
334C22×C79—42no—
335C22×C79—42no—
336C22×C79—42no—
337C22×C79—42no—
338C22×C79—42no—
339C22×C79—88no—
340C22×C79#53814yes—
341C22×C79#54214yes—
342C22×C79#54214yes—
343C22×C79#56014yes—
344C22×C79#56214yes—
345C22×C79#56214yes—
346C22×C79#56314yes—
347C22×C79C22×#4111yescharacteristic
348C22×C79C2×H(5,𝔽2)11yescharacteristic
349C22×C79C2×H(5,𝔽2)11yescharacteristic
350C22×C79C2×H(5,𝔽2)11yescharacteristic
351C22×C79C2×H(5,𝔽2)11yescharacteristic
352C22×C79C2×2−1+411yescharacteristic
353C22×C79C2×2−1+411yescharacteristic
354C2×D79—42no—
355C2×D79—42no—
356C2×D79—42no—
357C2×D79—42no—
358C2×D79—42no—
359C2×D79—42no—
360C2×D79—42no—
361C2×D79—88no—
362C4×C79—42no—
363C4×C79—42no—
364C4×C79—42no—
365C4×C79—42no—
366C4×C79—42no—
367C4×C79—42no—
368Dic79—24no—
369Dic79—42no—
370Dic79—42no—
371Dic79—42no—
372Dic79—42no—
373Dic79—42no—
374Dic79—42no—
375C2×#2830—791nomaximal, Sylow
376C2×C79—82no—
377C2×C79#283018yescomplemented
378C2×C79C2×#53811yescharacteristic
379C2×C79C2×#54211yescharacteristic
380C2×C79C2×#54211yescharacteristic
381C2×C79C2×#56011yescharacteristic
382C2×C79C2×#56211yescharacteristic
383C2×C79C2×#56211yescharacteristic
384C2×C79C2×#56311yescharacteristic
385D79—82no—
386#2830—7916no—
387C2×#398—791no—
388C2×#397—791no—
389C2×#397—791no—
390C2×#397—791no—
391C2×#397D7911yescharacteristic, complemented
392C2×#396—791no—
393C2×#396—791no—
394C2×#395—791no—
395C2×#394—791no—
396C2×#394—791no—
397C2×#393—791no—
398C2×#393—791no—
399C2×#390—791no—
400C2×#387—791no—
401C2×#387—791no—
402C79C2×#283011yescharacteristic, complemented, Sylow
403C23×Q8—791no—
404C23×D4—791no—
405C22×C4⋊C4—791no—
406C22×C4⋊C4—791no—
407C22×C4⋊C4—791no—
408C22×C4⋊C4—791no—
409C22×C4⋊C4—791no—
410C22×C4⋊C4—791no—
411C22×C4⋊C4—791no—
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⋊C4C2×D7911yescharacteristic
423C22×C22⋊C4C2×D7911yescharacteristic
424C22×C22⋊C4C2×D7911yescharacteristic
425C22×C42—791no—
426#398—798no—
427#397—798no—
428#397—798no—
429#397—798no—
430#397C2×D7918yescomplemented
431#396—798no—
432#396—798no—
433#395—798no—
434#394—798no—
435#394—798no—
436#393—798no—
437#393—798no—
438#390—798no—
439#387—798no—
440#387—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×#95C2×D7911yescharacteristic
451C2×#95C2×D7911yescharacteristic
452C2×#95C2×D7911yescharacteristic
453C25—791no—
454C25C22×D7911yescharacteristic
455C22×Q8—3162no—
456C22×Q8—3162no—
457C22×Q8—3162no—
458C22×Q8—794no—
459C22×D4—3162no—
460C22×D4—3162no—
461C22×D4—794no—
462C22×D4—1584no—
463C23×C4—791no—
464C23×C4—791no—
465C23×C4—791no—
466C23×C4—791no—
467C23×C4—791no—
468C23×C4—791no—
469C23×C4—791no—
470C23×C4C22×D7911yescharacteristic
471C23×C4C22×D7911yescharacteristic
472C23×C4C22×D7911yescharacteristic
473C23×C4C22×D7911yescharacteristic
474C23×C4C22×D7911yescharacteristic
475C23×C4C22×D7911yescharacteristic
476C2×C4⋊C4—42no—
477C2×C4⋊C4—3162no—
478C2×C4⋊C4—3162no—
479C2×C4⋊C4—3162no—
480C2×C4⋊C4—3162no—
481C2×C4⋊C4—3162no—
482C2×C4⋊C4—794no—
483C2×C4⋊C4—794no—
484C2×C4⋊C4—794no—
485C2×C4⋊C4—794no—
486C2×C4⋊C4—794no—
487C2×C4⋊C4—794no—
488C2×C4⋊C4—794no—
489C2×C4⋊C4—1584no—
490C2×C4⋊C4—1584no—
491C2×C4⋊C4C22×D7914yes—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—3162no—
496C2×C22⋊C4—3162no—
497C2×C22⋊C4—3162no—
498C2×C22⋊C4—3162no—
499C2×C22⋊C4—3162no—
500C2×C22⋊C4—3162no—
501C2×C22⋊C4—3162no—
502C2×C22⋊C4—3162no—
503C2×C22⋊C4—3162no—
504C2×C22⋊C4—794no—
505C2×C22⋊C4—794no—
506C2×C22⋊C4—794no—
507C2×C22⋊C4—794no—
508C2×C22⋊C4—794no—
509C2×C22⋊C4—794no—
510C2×C22⋊C4—794no—
511C2×C22⋊C4—794no—
512C2×C22⋊C4—794no—
513C2×C22⋊C4C22×D7914yes—
514C2×C22⋊C4C22×D7914yes—
515C2×C22⋊C4C22×D7914yes—
516C2×C42—3162no—
517C2×C42—794no—
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#95C22×D7914yes—
528#95C22×D7914yes—
529#95C22×D7914yes—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—792no—
538C24—1582no—
539C24—1582no—
540C24—1582no—
541C24—1582no—
542C24—1582no—
543C24—1582no—
544C24—1582no—
545C24C23×D7912yes—
546C24C23×D7911yescharacteristic
547C2×Q8—3164no—
548C2×Q8—3164no—
549C2×Q8—3164no—
550C2×Q8—31616no—
551C2×D4—3164no—
552C2×D4—3164no—
553C2×D4—31616no—
554C2×D4—1588no—
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—22no—
573C22×C4—794no—
574C22×C4—792no—
575C22×C4—792no—
576C22×C4—792no—
577C22×C4—792no—
578C22×C4—792no—
579C22×C4—792no—
580C22×C4—792no—
581C22×C4—1582no—
582C22×C4—1582no—
583C22×C4—1582no—
584C22×C4—1582no—
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—1582no—
601C22×C4C23×D7912yes—
602C22×C4C23×D7912yes—
603C22×C4C23×D7912yes—
604C22×C4C23×D7912yes—
605C22×C4C23×D7912yes—
606C22×C4C23×D7912yes—
607C4⋊C4—44no—
608C4⋊C4—3164no—
609C4⋊C4—3164no—
610C4⋊C4—3164no—
611C4⋊C4—3164no—
612C4⋊C4—3164no—
613C4⋊C4—1588no—
614C4⋊C4—1588no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—3164no—
619C22⋊C4—3164no—
620C22⋊C4—3164no—
621C22⋊C4—3164no—
622C22⋊C4—3164no—
623C22⋊C4—3164no—
624C22⋊C4—3164no—
625C22⋊C4—3164no—
626C22⋊C4—3164no—
627C42—3164no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—3164no—
643C23—3164no—
644C23—3164no—
645C23—3164no—
646C23—3164no—
647C23—3164no—
648C23—3164no—
649C23—1582no—
650C23—1582no—
651C23—1582no—
652C23—1582no—
653C23—1582no—
654C23—1582no—
655C23—1582no—
656C23#41×D7912yes—
657C23#1457920612yes—
658C23#1457920612yes—
659C23#1457920712yes—
660C23#1457920712yes—
661C23#1457920812yes—
662C23#1457920812yes—
663C23C24×D7911yescharacteristic
664Q8—31616no—
665D4—31616no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
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—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—3164no—
691C2×C4—3164no—
692C2×C4—3164no—
693C2×C4—3164no—
694C2×C4—3164no—
695C2×C4—3164no—
696C2×C4—794no—
697C2×C4—1582no—
698C2×C4—1582no—
699C2×C4—1582no—
700C2×C4—1582no—
701C2×C4—1582no—
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—1588no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—88no—
726C22—3162no—
727C22—3162no—
728C22—3162no—
729C22—3162no—
730C22—3162no—
731C22—3162no—
732C22—3162no—
733C22—6328no—
734C22#1909915214yes—
735C22#1909917714yes—
736C22#1909918114yes—
737C22#1909930114yes—
738C22#1909931014yes—
739C22#1909931014yes—
740C22#1909931514yes—
741C22C2×#41×D7911yescharacteristic
742C22C2×#1457920611yescharacteristic
743C22C2×#1457920611yescharacteristic
744C22C2×#1457920711yescharacteristic
745C22C2×#1457920711yescharacteristic
746C22C2×#1457920811yescharacteristic
747C22C2×#1457920811yescharacteristic
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—3162no—
755C4—3162no—
756C4—3162no—
757C4—3162no—
758C4—3162no—
759C4—3162no—
760C4—1584no—
761C2—82no—
762C2—6322no—
763C2#2377154518yesdirect product factor
764C2C2×#1909915211yescharacteristic
765C2C2×#1909917711yescharacteristic
766C2C2×#1909918111yescharacteristic
767C2C2×#1909930111yescharacteristic
768C2C2×#1909931011yescharacteristic
769C2C2×#1909931011yescharacteristic
770C2C2×#1909931511yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#397×C79C2
socleC24×C79C24
prime radicalC23×C22⋊D79C22
hypercenterC2×#397D79
hypocenterC79C2×#2830
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. #23771545C2direct (N × H)
2. C2×#19098495C2semidirect
3. C2×#19098492C2semidirect
4. C2×#19098492C2semidirect
5. C2×#19098491C2semidirect
6. C2×#19098486C2semidirect
7. C2×#19098485C2semidirect
8. C2×#19098483C2semidirect
11. C2×#19098476C2semidirect
12. C2×#19098475C2semidirect
14. C2×#19098448C2semidirect
15. C2×#19098446C2semidirect
16. C2×#397×C79C2semidirect
36. #19098495C22semidirect
37. #19098492C22semidirect
38. #19098492C22semidirect
39. #19098491C22semidirect
40. #19098486C22semidirect
41. #19098485C22semidirect
42. #19098483C22semidirect
45. #19098476C22semidirect
46. #19098475C22semidirect
48. #19098448C22semidirect
49. #19098446C22semidirect
63. #397×C79C22semidirect
377. C2×C79#2830semidirect
391. C2×#397D79semidirect
402. C79C2×#2830semidirect
430. #397C2×D79semidirect
763. C2#23771545direct (N × H)

Maximal subgroups

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

subgroupindex
#237715452
C2×#190984952
C2×#190984922
C2×#190984912
C2×#190984862
C2×#190984852
C2×#190984832
C2×#190984792
C2×#190984762
C2×#190984752
C2×#190984632
C2×#190984482
C2×#190984462
C2×#397×C792
C2×#283079