Finite Group Databasebeta

← C2×#23766562 #34450872

Subgroups — C2×#23766562 #34450872

Order 20224.

2566 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579139C211yesmaximal, characteristic
2#23766562C2116yesmaximal, direct product factor
3C2×#19098468C211yesmaximal, characteristic, complemented
4C2×#19098467C211yesmaximal, characteristic, complemented
5C2×#19098460C211yesmaximal, characteristic, complemented
6C2×#19098454C211yesmaximal, characteristic
7C2×#19098453C211yesmaximal, characteristic
8C2×#19098453C211yesmaximal, characteristic
9C2×#19098452C211yesmaximal, characteristic
10C2×#19098449C211yesmaximal, characteristic, complemented
11C2×#19098447C211yesmaximal, characteristic, complemented
12C2×#19098444C211yesmaximal, characteristic, complemented
13C2×#19098444C211yesmaximal, characteristic, complemented
14C2×#19098425C211yesmaximal, characteristic
15C2×#19098420C211yesmaximal, characteristic
16C2×#389×C79C211yesmaximal, characteristic, complemented
17C23×Dic158C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C2×#14579139C4116yescomplemented
20C2×#14579139C2218yes—
21C22×C4⋊Dic79C2211yescharacteristic
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
33C22×C4×Dic79C2211yescharacteristic
34C22×C4×Dic79C2211yescharacteristic
35#19098468C2218yescomplemented
36#19098467C2218yescomplemented
37#19098460C2218yescomplemented
38#19098454C2218yes—
39#19098453C2218yes—
40#19098453C2218yes—
41#19098452C2218yes—
42#19098449C2218yescomplemented
43#19098447C2218yescomplemented
44#19098444C2218yescomplemented
45#19098444C2218yescomplemented
46#19098425C2218yes—
47#19098420C2218yes—
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
59C2×C79⋊#95C2211yescharacteristic
60C22×C4⋊C4×C79C2211yescharacteristic
61C22×C4⋊C4×C79C2211yescharacteristic
62C22×C4⋊C4×C79C2211yescharacteristic
63C22×C4⋊C4×C79C2211yescharacteristic
64C22×C42×C79C2211yescharacteristic
65#389×C79C2218yescomplemented
66C2×#95×C79C2211yescharacteristic
67C2×#95×C79C2211yescharacteristic
68C24×D79C2311yescharacteristic
69C22×Dic158—42no—
70C22×Dic158—42no—
71C22×Dic158C2×C418yes—
72C22×Dic158C2314yes—
73C23×Dic79C2311yescharacteristic
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2311yescharacteristic
80C22×C4×D79—42no—
81C22×C4×D79—42no—
82C22×C4×D79C2×C418yes—
83C22×C4×D79C2314yes—
84#14579139C2×C4164yescomplemented
85C2×C4⋊Dic79—42no—
86C2×C4⋊Dic79C2314yes—
87C2×Dic79⋊C4—42no—
88C2×Dic79⋊C4—42no—
89C2×Dic79⋊C4C2×C418yes—
90C2×Dic79⋊C4C2×C418yes—
91C2×Dic79⋊C4C2314yes—
92C2×Dic79⋊C4C2314yes—
93C2×Dic79⋊C4C2314yes—
94C2×Dic79⋊C4C2314yes—
95C2×(C2×D79)⋊C4—42no—
96C2×(C2×D79)⋊C4—42no—
97C2×(C2×D79)⋊C4—42no—
98C2×(C2×D79)⋊C4—42no—
99C2×(C2×D79)⋊C4C2×C418yes—
100C2×(C2×D79)⋊C4C2×C418yes—
101C2×(C2×D79)⋊C4C2314yes—
102C2×(C2×D79)⋊C4C2314yes—
103C2×(C2×D79)⋊C4C2314yes—
104C2×(C2×D79)⋊C4C2314yes—
105C2×(C2×D79)⋊C4C2314yes—
106C2×(C2×D79)⋊C4C2314yes—
107C2×C4×Dic79—42no—
108C2×C4×Dic79—42no—
109C2×C4×Dic79—42no—
110C2×C4×Dic79C2314yes—
111C2×C4×Dic79C2314yes—
112C2×C4×Dic79C2314yes—
113C79⋊#95C2314yes—
114C79⋊#95C2314yes—
115C79⋊#95C2314yes—
116C79⋊#95C2314yes—
117C79⋊#95C2314yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C79⋊#95C2314yes—
122C79⋊#95C2314yes—
123C79⋊#95C2314yes—
124C79⋊#95C2314yes—
125C23×C4×C79C2311yescharacteristic
126C23×C4×C79C2311yescharacteristic
127C23×C4×C79C2311yescharacteristic
128C23×C4×C79C2311yescharacteristic
129C23×C4×C79C2311yescharacteristic
130C23×C4×C79C2311yescharacteristic
131C23×C4×C79C2311yescharacteristic
132C2×C4⋊C4×C79—42no—
133C2×C4⋊C4×C79—42no—
134C2×C4⋊C4×C79—42no—
135C2×C4⋊C4×C79C2×C418yes—
136C2×C4⋊C4×C79C2314yes—
137C2×C4⋊C4×C79C2314yes—
138C2×C4⋊C4×C79C2314yes—
139C2×C4⋊C4×C79C2314yes—
140C2×C42×C79—42no—
141C2×C42×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×D79C22×C414yes—
151C23×D79C2412yes—
152C2×Dic158—416no—
153C2×Dic158—44no—
154C2×Dic158—44no—
155C2×Dic158C22×C4116yes—
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×Dic79—22no—
174C22×Dic79C22×C414yes—
175C22×Dic79C22×C414yes—
176C22×Dic79C22×C414yes—
177C22×Dic79C2412yes—
178C22×Dic79C2412yes—
179C22×Dic79C2412yes—
180C22×Dic79C2412yes—
181C22×Dic79C2412yes—
182C22×Dic79C2412yes—
183C22×Dic79C2412yes—
184C2×C4×D79—416no—
185C2×C4×D79—44no—
186C2×C4×D79—44no—
187C2×C4×D79C22×C4116yes—
188C4⋊Dic79—44no—
189Dic79⋊C4—44no—
190Dic79⋊C4—44no—
191Dic79⋊C4C22×C4116yes—
192Dic79⋊C4C22×C4116yes—
193(C2×D79)⋊C4—44no—
194(C2×D79)⋊C4—44no—
195(C2×D79)⋊C4—44no—
196(C2×D79)⋊C4—44no—
197(C2×D79)⋊C4C22×C4116yes—
198(C2×D79)⋊C4C22×C4116yes—
199C4×Dic79—44no—
200C4×Dic79—44no—
201C4×Dic79—44no—
202C24×C79C2411yescharacteristic
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×C79—22no—
219C22×C4×C79—22no—
220C22×C4×C79—22no—
221C22×C4×C79C22×C414yes—
222C22×C4×C79C22×C414yes—
223C22×C4×C79C22×C414yes—
224C22×C4×C79C2412yes—
225C22×C4×C79C2412yes—
226C22×C4×C79C2412yes—
227C22×C4×C79C2412yes—
228C22×C4×C79C2412yes—
229C22×C4×C79C2412yes—
230C22×C4×C79C2412yes—
231C4⋊C4×C79—44no—
232C4⋊C4×C79—44no—
233C4⋊C4×C79—44no—
234C4⋊C4×C79C22×C4116yes—
235C42×C79—44no—
236C23×C79C23×C412yes—
237C23×C79H(5,𝔽2)12yes—
238C23×C79H(5,𝔽2)12yes—
239C23×C79H(5,𝔽2)12yes—
240C23×C792−1+412yes—
241C23×C792−1+412yes—
242C23×C792−1+412yes—
243C23×C79C2511yescharacteristic
244C22×D79—28no—
245C22×D79—28no—
246C22×D79—28no—
247C22×D79—22no—
248C22×D79—22no—
249C22×D79—22no—
250C22×D79—22no—
251C22×D79—22no—
252C22×D79—22no—
253C22×D79—44no—
254C22×D79—44no—
255C22×D79—44no—
256C22×D79—44no—
257C22×D79C23×C414yes—
258C2×C4×C79—28no—
259C2×C4×C79—28no—
260C2×C4×C79—28no—
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—22no—
278C2×C4×C79—22no—
279C2×C4×C79—44no—
280C2×C4×C79—44no—
281C2×C4×C79—44no—
282C2×C4×C79—44no—
283C2×C4×C79C23×C414yes—
284C2×C4×C79C23×C414yes—
285C2×C4×C79C23×C414yes—
286C2×Dic79—28no—
287C2×Dic79—28no—
288C2×Dic79—28no—
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—22no—
306C2×Dic79—22no—
307C2×Dic79—44no—
308C2×Dic79—44no—
309C2×Dic79—44no—
310C2×Dic79—44no—
311C2×Dic79C23×C414yes—
312C2×Dic79C23×C414yes—
313C2×Dic79C23×C414yes—
314C4×D79—416no—
315Dic158—416no—
316C22×C79#51814yes—
317C22×C79#51914yes—
318C22×C79#52014yes—
319C22×C79#56214yes—
320C22×C79#56214yes—
321C22×C79#56314yes—
322C22×C79#56314yes—
323C22×C79C24×C411yescharacteristic
324C22×C79C2×H(5,𝔽2)11yescharacteristic
325C22×C79C2×H(5,𝔽2)11yescharacteristic
326C22×C79C2×H(5,𝔽2)11yescharacteristic
327C22×C79C2×2−1+411yescharacteristic
328C22×C79C2×2−1+411yescharacteristic
329C22×C79C2×2−1+411yescharacteristic
330C2×D79—24no—
331C2×D79—24no—
332C2×D79—24no—
333C2×D79—416no—
334C2×D79—42no—
335C2×D79—42no—
336C2×D79—42no—
337C2×D79—42no—
338C4×C79—24no—
339C4×C79—24no—
340C4×C79—24no—
341C4×C79—42no—
342C4×C79—42no—
343C4×C79—42no—
344C4×C79—42no—
345Dic79—24no—
346Dic79—24no—
347Dic79—24no—
348Dic79—42no—
349Dic79—42no—
350Dic79—42no—
351Dic79—42no—
352C2×#2378—791nomaximal, Sylow
353C2×C79#237818yescomplemented
354C2×C79C2×#51811yescharacteristic
355C2×C79C2×#51911yescharacteristic
356C2×C79C2×#52011yescharacteristic
357C2×C79C2×#56211yescharacteristic
358C2×C79C2×#56211yescharacteristic
359C2×C79C2×#56311yescharacteristic
360C2×C79C2×#56311yescharacteristic
361D79—44no—
362C22×C22⋊Q8—791no—
363#2378—7916no—
364C2×#391—791no—
365C2×#391—791no—
366C2×#389—791no—
367C2×#389D7911yescharacteristic, complemented
368C2×#388—791no—
369C2×#388—791no—
370C2×#388—791no—
371C2×#388—791no—
372C2×#387—791no—
373C2×#387—791no—
374C2×#387—791no—
375C2×#387—791no—
376C2×#381—791no—
377C2×#380—791no—
378C79C2×#237811yescharacteristic, complemented, Sylow
379C23×Q8—791no—
380C24×C4—791no—
381C2×C22⋊Q8—798no—
382C2×C22⋊Q8—7916no—
383C22×C4⋊C4—791no—
384C22×C4⋊C4—791no—
385C22×C4⋊C4—791no—
386C22×C4⋊C4—791no—
387C22×C4⋊C4—791no—
388C22×C4⋊C4C2×D7911yescharacteristic
389C22×C4⋊C4C2×D7911yescharacteristic
390C22×C4⋊C4C2×D7911yescharacteristic
391C22×C4⋊C4C2×D7911yescharacteristic
392C22×C22⋊C4—791no—
393C22×C22⋊C4—791no—
394C22×C22⋊C4—791no—
395C22×C22⋊C4—791no—
396C22×C22⋊C4—791no—
397C22×C22⋊C4—791no—
398C22×C42—791no—
399C22×C42—791no—
400C22×C42—791no—
401C22×C42C2×D7911yescharacteristic
402#391—798no—
403#391—798no—
404#389—798no—
405#389C2×D7918yescomplemented
406#388—798no—
407#388—798no—
408#388—798no—
409#388—798no—
410#387—798no—
411#387—798no—
412#387—798no—
413#387—798no—
414#381—798no—
415#380—798no—
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×#95—791no—
426C2×#95—791no—
427C2×#95—791no—
428C2×#95C2×D7911yescharacteristic
429C2×#95C2×D7911yescharacteristic
430C25—791no—
431C22×Q8—3162no—
432C22×Q8—3162no—
433C22×Q8—798no—
434C22×Q8—794no—
435C23×C4—3162no—
436C23×C4—3162no—
437C23×C4—798no—
438C23×C4—794no—
439C23×C4—791no—
440C23×C4—791no—
441C23×C4—791no—
442C23×C4—791no—
443C23×C4—791no—
444C23×C4—791no—
445C23×C4—791no—
446C23×C4C22×D7911yescharacteristic
447C23×C4C22×D7911yescharacteristic
448C23×C4C22×D7911yescharacteristic
449C23×C4C22×D7911yescharacteristic
450C23×C4C22×D7911yescharacteristic
451C23×C4C22×D7911yescharacteristic
452C23×C4C22×D7911yescharacteristic
453C22⋊Q8—7964no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—3162no—
458C2×C4⋊C4—3162no—
459C2×C4⋊C4—3162no—
460C2×C4⋊C4—794no—
461C2×C4⋊C4—794no—
462C2×C4⋊C4—794no—
463C2×C4⋊C4—798no—
464C2×C4⋊C4—798no—
465C2×C4⋊C4—794no—
466C2×C4⋊C4—794no—
467C2×C4⋊C4C4×D7918yes—
468C2×C4⋊C4C22×D7914yes—
469C2×C4⋊C4C22×D7914yes—
470C2×C4⋊C4C22×D7914yes—
471C2×C4⋊C4C22×D7914yes—
472C2×C22⋊C4—3162no—
473C2×C22⋊C4—3162no—
474C2×C22⋊C4—3162no—
475C2×C22⋊C4—3162no—
476C2×C22⋊C4—794no—
477C2×C22⋊C4—794no—
478C2×C22⋊C4—794no—
479C2×C22⋊C4—794no—
480C2×C22⋊C4—798no—
481C2×C22⋊C4—798no—
482C2×C22⋊C4—794no—
483C2×C22⋊C4—794no—
484C2×C42—42no—
485C2×C42—3162no—
486C2×C42—3162no—
487C2×C42—3162no—
488C2×C42—794no—
489C2×C42—794no—
490C2×C42—794no—
491C2×C42C22×D7914yes—
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#95—794no—
501#95—794no—
502#95—794no—
503#95—794no—
504#95C22×D7914yes—
505#95C22×D7914yes—
506C24—792no—
507C24—794no—
508C24—1582no—
509C24—1582no—
510C24—1582no—
511C24—1582no—
512C24—1582no—
513C24—1582no—
514C24C23×D7911yescharacteristic
515C2×Q8—3164no—
516C2×Q8—3164no—
517C2×Q8—31616no—
518C2×Q8—7916no—
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—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—3164no—
538C22×C4—3164no—
539C22×C4—31616no—
540C22×C4—7916no—
541C22×C4—792no—
542C22×C4—792no—
543C22×C4—792no—
544C22×C4—794no—
545C22×C4—794no—
546C22×C4—794no—
547C22×C4—792no—
548C22×C4—792no—
549C22×C4—792no—
550C22×C4—792no—
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—1582no—
561C22×C4—1582no—
562C22×C4—1582no—
563C22×C4—1582no—
564C22×C4—1582no—
565C22×C4—1582no—
566C22×C4—1582no—
567C22×C4—1582no—
568C22×C4—1582no—
569C22×C4C2×C4×D7914yes—
570C22×C4C2×C4×D7914yes—
571C22×C4C2×C4×D7914yes—
572C22×C4C23×D7912yes—
573C22×C4C23×D7912yes—
574C22×C4C23×D7912yes—
575C22×C4C23×D7912yes—
576C22×C4C23×D7912yes—
577C22×C4C23×D7912yes—
578C22×C4C23×D7912yes—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—3164no—
583C4⋊C4—3164no—
584C4⋊C4—3164no—
585C4⋊C4—7916no—
586C4⋊C4—7916no—
587C4⋊C4C2×C4×D79116yes—
588C22⋊C4—3164no—
589C22⋊C4—3164no—
590C22⋊C4—3164no—
591C22⋊C4—3164no—
592C22⋊C4—7916no—
593C22⋊C4—7916no—
594C42—44no—
595C42—3164no—
596C42—3164no—
597C42—3164no—
598C23—3164no—
599C23—3164no—
600C23—3164no—
601C23—3164no—
602C23—794no—
603C23—1582no—
604C23—1582no—
605C23—1582no—
606C23—1582no—
607C23—1582no—
608C23—1582no—
609C23—1588no—
610C23—1588no—
611C23—1588no—
612C23C22×C4×D7912yes—
613C23#1457920612yes—
614C23#1457920612yes—
615C23#1457920712yes—
616C23#1457920812yes—
617C23#1457920912yes—
618C23#1457920912yes—
619C23C24×D7911yescharacteristic
620Q8—31616no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—28no—
628C2×C4—28no—
629C2×C4—28no—
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—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—31616no—
647C2×C4—3164no—
648C2×C4—3164no—
649C2×C4—3164no—
650C2×C4—3164no—
651C2×C4—794no—
652C2×C4—794no—
653C2×C4—794no—
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—1582no—
667C2×C4—1582no—
668C2×C4—1582no—
669C2×C4—1582no—
670C2×C4—1582no—
671C2×C4—1582no—
672C2×C4—1588no—
673C2×C4—1588no—
674C2×C4—1588no—
675C2×C4C22×C4×D7914yes—
676C2×C4C22×C4×D7914yes—
677C2×C4C22×C4×D7914yes—
678C22—31616no—
679C22—3162no—
680C22—3162no—
681C22—3162no—
682C22—3162no—
683C22—1584no—
684C22—1584no—
685C22—1584no—
686C22#1909903514yes—
687C22#1909903914yes—
688C22#1909904414yes—
689C22#1909930814yes—
690C22#1909930914yes—
691C22#1909931214yes—
692C22#1909931714yes—
693C22C23×C4×D7911yescharacteristic
694C22C2×#1457920611yescharacteristic
695C22C2×#1457920611yescharacteristic
696C22C2×#1457920711yescharacteristic
697C22C2×#1457920811yescharacteristic
698C22C2×#1457920911yescharacteristic
699C22C2×#1457920911yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—3162no—
708C4—3162no—
709C4—3162no—
710C4—3162no—
711C4—1584no—
712C4—1584no—
713C4—1584no—
714C2—3164no—
715C2#2376656218yesdirect product factor
716C2C2×#1909903511yescharacteristic
717C2C2×#1909903911yescharacteristic
718C2C2×#1909904411yescharacteristic
719C2C2×#1909930811yescharacteristic
720C2C2×#1909930911yescharacteristic
721C2C2×#1909931211yescharacteristic
722C2C2×#1909931711yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#389×C79C2
socleC24×C79C24
prime radicalC24×D79C23
cosocleC23×C79C25
hypercenterC2×#389D79
hypocenterC79C2×#2378
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. #23766562C2direct (N × H)
3. C2×#19098468C2semidirect
4. C2×#19098467C2semidirect
5. C2×#19098460C2semidirect
10. C2×#19098449C2semidirect
11. C2×#19098447C2semidirect
12. C2×#19098444C2semidirect
13. C2×#19098444C2semidirect
16. C2×#389×C79C2semidirect
19. C2×#14579139C4semidirect
35. #19098468C22semidirect
36. #19098467C22semidirect
37. #19098460C22semidirect
42. #19098449C22semidirect
43. #19098447C22semidirect
44. #19098444C22semidirect
45. #19098444C22semidirect
65. #389×C79C22semidirect
84. #14579139C2×C4semidirect
353. C2×C79#2378semidirect
367. C2×#389D79semidirect
378. C79C2×#2378semidirect
405. #389C2×D79semidirect
715. C2#23766562direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791392
#237665622
C2×#190984682
C2×#190984672
C2×#190984602
C2×#190984542
C2×#190984532
C2×#190984522
C2×#190984492
C2×#190984472
C2×#190984442
C2×#190984252
C2×#190984202
C2×#389×C792
C2×#237879