Finite Group Databasebeta

← C2×#23768618 #34458649

Subgroups — C2×#23768618 #34458649

Order 20224.

2486 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
1#23768618C2116yesmaximal, direct product factor
2C2×#19098505C211yesmaximal, characteristic, complemented
3C2×#19098502C211yesmaximal, characteristic, complemented
4C2×#19098495C211yesmaximal, characteristic, complemented
5C2×#19098449C211yesmaximal, characteristic, complemented
6C2×#19098449C211yesmaximal, characteristic, complemented
7C2×#19098448C211yesmaximal, characteristic, complemented
8C2×#19098444C211yesmaximal, characteristic, complemented
9C2×#19098437C211yesmaximal, characteristic
10C2×#19098434C211yesmaximal, characteristic
11C2×#19098420C211yesmaximal, characteristic
12C2×#19098420C211yesmaximal, characteristic
13C2×#19098420C211yesmaximal, characteristic
14C2×#19098410C211yesmaximal, characteristic
15C2×#95×D79C211yesmaximal, characteristic
16C2×#398×C79C211yesmaximal, characteristic, complemented
17C23×C4×D79C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21C22×C4⋊Dic79C2211yescharacteristic
22C22×C4⋊Dic79C2211yescharacteristic
23C22×C4⋊Dic79C2211yescharacteristic
24C22×Dic79⋊C4C2211yescharacteristic
25C22×Dic79⋊C4C2211yescharacteristic
26C22×(C2×D79)⋊C4C2211yescharacteristic
27C22×(C2×D79)⋊C4C2211yescharacteristic
28C22×(C2×D79)⋊C4C2211yescharacteristic
29C22×(C2×D79)⋊C4C2211yescharacteristic
30C22×C4×Dic79C2211yescharacteristic
31C22×C4×Dic79C2211yescharacteristic
32#19098505C2218yescomplemented
33#19098502C2218yescomplemented
34#19098495C2218yescomplemented
35#19098449C2218yescomplemented
36#19098449C2218yescomplemented
37#19098448C2218yescomplemented
38#19098444C2218yescomplemented
39#19098437C2218yes—
40#19098434C2218yes—
41#19098420C2218yes—
42#19098420C2218yes—
43#19098420C2218yes—
44#19098410C2218yes—
45C2×C79⋊#95C2211yescharacteristic
46C2×C79⋊#95C2211yescharacteristic
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
58#95×D79C2218yes—
59C22×C4⋊C4×C79C2211yescharacteristic
60C22×C4⋊C4×C79C2211yescharacteristic
61C22×C4⋊C4×C79C2211yescharacteristic
62C22×C4⋊C4×C79C2211yescharacteristic
63#398×C79C2218yescomplemented
64C2×#95×C79C2211yescharacteristic
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C24×D79C2311yescharacteristic
68C23×Dic79C2311yescharacteristic
69C23×Dic79C2311yescharacteristic
70C23×Dic79C2311yescharacteristic
71C23×Dic79C2311yescharacteristic
72C23×Dic79C2311yescharacteristic
73C23×Dic79C2311yescharacteristic
74C23×Dic79C2311yescharacteristic
75C22×C4×D79—24no—
76C22×C4×D79—24no—
77C22×C4×D79—24no—
78C22×C4×D79—24no—
79C22×C4×D79—42no—
80C22×C4×D79—42no—
81C22×C4×D79—42no—
82C22×C4×D79—42no—
83C22×C4×D79Q818yes—
84C22×C4×D79C2314yes—
85C22×C4×D79C2314yes—
86C22×C4×D79C2314yes—
87C2×C4⋊Dic79—24no—
88C2×C4⋊Dic79—42no—
89C2×C4⋊Dic79—42no—
90C2×C4⋊Dic79—42no—
91C2×C4⋊Dic79C2314yes—
92C2×C4⋊Dic79C2314yes—
93C2×C4⋊Dic79C2314yes—
94C2×C4⋊Dic79C2314yes—
95C2×Dic79⋊C4—24no—
96C2×Dic79⋊C4—42no—
97C2×Dic79⋊C4C2314yes—
98C2×Dic79⋊C4C2314yes—
99C2×(C2×D79)⋊C4—24no—
100C2×(C2×D79)⋊C4—24no—
101C2×(C2×D79)⋊C4—24no—
102C2×(C2×D79)⋊C4—24no—
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×Dic79C2314yes—
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—
123C79⋊#95C2314yes—
124C23×C4×C79C2311yescharacteristic
125C23×C4×C79C2311yescharacteristic
126C23×C4×C79C2311yescharacteristic
127C23×C4×C79C2311yescharacteristic
128C23×C4×C79C2311yescharacteristic
129C23×C4×C79C2311yescharacteristic
130C23×C4×C79C2311yescharacteristic
131C2×C4⋊C4×C79—24no—
132C2×C4⋊C4×C79—24no—
133C2×C4⋊C4×C79—42no—
134C2×C4⋊C4×C79—42no—
135C2×C4⋊C4×C79C2314yes—
136C2×C4⋊C4×C79C2314yes—
137C2×C4⋊C4×C79C2314yes—
138C2×C4⋊C4×C79C2314yes—
139#95×C79C2314yes—
140#95×C79C2314yes—
141#95×C79C2314yes—
142C23×D79—22no—
143C23×D79—22no—
144C23×D79—22no—
145C23×D79—22no—
146C23×D79C2×Q814yes—
147C23×D79#4114yes—
148C23×D79#4114yes—
149C23×D79C2412yes—
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×Dic79—22no—
164C22×Dic79—22no—
165C22×Dic79—22no—
166C22×Dic79—22no—
167C22×Dic79—22no—
168C22×Dic79—22no—
169C22×Dic79—22no—
170C22×Dic79C2×Q814yes—
171C22×Dic79C2412yes—
172C22×Dic79C2412yes—
173C22×Dic79C2412yes—
174C22×Dic79C2412yes—
175C22×Dic79C2412yes—
176C22×Dic79C2412yes—
177C22×Dic79C2412yes—
178C2×C4×D79—28no—
179C2×C4×D79—28no—
180C2×C4×D79—28no—
181C2×C4×D79—28no—
182C2×C4×D79—416no—
183C2×C4×D79—44no—
184C2×C4×D79—44no—
185C2×C4×D79—44no—
186C2×C4×D79—44no—
187C2×C4×D79—416no—
188C2×C4×D79—416no—
189C2×C4×D79C2×Q8116yes—
190C4⋊Dic79—28no—
191C4⋊Dic79—44no—
192C4⋊Dic79—44no—
193C4⋊Dic79—44no—
194Dic79⋊C4—28no—
195Dic79⋊C4—44no—
196(C2×D79)⋊C4—28no—
197(C2×D79)⋊C4—28no—
198(C2×D79)⋊C4—28no—
199(C2×D79)⋊C4—28no—
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×C79C2×Q814yes—
222C22×C4×C79#4114yes—
223C22×C4×C79#4114yes—
224C22×C4×C79C2412yes—
225C22×C4×C79C2412yes—
226C22×C4×C79C2412yes—
227C22×C4×C79C2412yes—
228C22×C4×C79C2412yes—
229C22×C4×C79C2412yes—
230C22×C4×C79C2412yes—
231C4⋊C4×C79—28no—
232C4⋊C4×C79—28no—
233C4⋊C4×C79—44no—
234C4⋊C4×C79—44no—
235C23×C79C22×Q812yes—
236C23×C79C2×#4112yes—
237C23×C79C2×#4112yes—
238C23×C79C2×#4112yes—
239C23×C79C2×#4112yes—
240C23×C79H(5,𝔽2)12yes—
241C23×C79H(5,𝔽2)12yes—
242C23×C79C2511yescharacteristic
243C22×D79—28no—
244C22×D79—28no—
245C22×D79—28no—
246C22×D79—28no—
247C22×D79—28no—
248C22×D79—28no—
249C22×D79—22no—
250C22×D79—22no—
251C22×D79—22no—
252C22×D79—22no—
253C22×D79#125116yes—
254C22×D79C22×Q814yes—
255C22×D79C2×#4114yes—
256C22×D79C2×#4114yes—
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—22no—
278C2×C4×C79—44no—
279C2×C4×C79—44no—
280C2×C4×C79—44no—
281C2×C4×C79—44no—
282C2×C4×C79C22×Q814yes—
283C2×C4×C79C2×#4114yes—
284C2×C4×C79C2×#4114yes—
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—22no—
306C2×Dic79—44no—
307C2×Dic79—44no—
308C2×Dic79—44no—
309C2×Dic79—44no—
310C2×Dic79—44no—
311C2×Dic79—44no—
312C2×Dic79C22×Q814yes—
313C4×D79—416no—
314C4×D79—416no—
315C4×D79—416no—
316C22×C79C2×#12514yes—
317C22×C79#53314yes—
318C22×C79#54314yes—
319C22×C79#55114yes—
320C22×C79#55114yes—
321C22×C79#55314yes—
322C22×C79#55314yes—
323C22×C79C23×Q811yescharacteristic
324C22×C79C22×#4111yescharacteristic
325C22×C79C22×#4111yescharacteristic
326C22×C79C22×#4111yescharacteristic
327C22×C79C22×#4111yescharacteristic
328C22×C79C2×H(5,𝔽2)11yescharacteristic
329C22×C79C2×H(5,𝔽2)11yescharacteristic
330C2×D79—232no—
331C2×D79—24no—
332C2×D79—24no—
333C2×D79—24no—
334C2×D79—24no—
335C2×D79—24no—
336C2×D79—24no—
337C2×D79C2×#12518yes—
338C4×C79—24no—
339C4×C79—24no—
340C4×C79—24no—
341C4×C79—42no—
342C4×C79—42no—
343C4×C79—42no—
344C4×C79—42no—
345Dic79—24no—
346Dic79—42no—
347Dic79—42no—
348Dic79—42no—
349Dic79—42no—
350Dic79—42no—
351Dic79—42no—
352C2×#2569—791nomaximal, Sylow
353C2×C79#256918yescomplemented
354C2×C79C22×#12511yescharacteristic
355C2×C79C2×#53311yescharacteristic
356C2×C79C2×#54311yescharacteristic
357C2×C79C2×#55111yescharacteristic
358C2×C79C2×#55111yescharacteristic
359C2×C79C2×#55311yescharacteristic
360C2×C79C2×#55311yescharacteristic
361D79—28no—
362#2569—7916no—
363C2×#400—791no—
364C2×#400—791no—
365C2×#398—791no—
366C2×#398D7911yescharacteristic, complemented
367C2×#387—791no—
368C2×#387—791no—
369C2×#387—791no—
370C2×#387—791no—
371C2×#385—791no—
372C2×#385—791no—
373C2×#380—791no—
374C2×#380—791no—
375C2×#380—791no—
376C2×C4×C22⋊C4—791no—
377C22×#95—791no—
378C79C2×#256911yescharacteristic, complemented, Sylow
379C24×C4—791no—
380C24×C4—791no—
381C24×C4—791no—
382C22×C4⋊C4—791no—
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×C42—791no—
397C22×C42—791no—
398#400—798no—
399#400—798no—
400#398—798no—
401#398C2×D7918yescomplemented
402#387—798no—
403#387—798no—
404#387—798no—
405#387—798no—
406#385—798no—
407#385—798no—
408#380—798no—
409#380—798no—
410#380—798no—
411C4×C22⋊C4—798no—
412C2×#95—791no—
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×#95—798no—
426C2×#95C2×D7911yescharacteristic
427C2×#95C2×D7911yescharacteristic
428C2×#95C2×D7911yescharacteristic
429C25—791no—
430C23×C4—3162no—
431C23×C4—3162no—
432C23×C4—3162no—
433C23×C4—3162no—
434C23×C4—798no—
435C23×C4—794no—
436C23×C4—794no—
437C23×C4—794no—
438C23×C4—791no—
439C23×C4—791no—
440C23×C4—791no—
441C23×C4—791no—
442C23×C4—791no—
443C23×C4—791no—
444C23×C4—791no—
445C23×C4—1584no—
446C23×C4—1584no—
447C23×C4—1584no—
448C23×C4—1584no—
449C23×C4C22×D7911yescharacteristic
450C23×C4C22×D7911yescharacteristic
451C23×C4C22×D7911yescharacteristic
452C23×C4C22×D7911yescharacteristic
453C23×C4C22×D7911yescharacteristic
454C23×C4C22×D7911yescharacteristic
455C23×C4C22×D7911yescharacteristic
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—3162no—
461C2×C4⋊C4—3162no—
462C2×C4⋊C4—3162no—
463C2×C4⋊C4—3162no—
464C2×C4⋊C4—794no—
465C2×C4⋊C4—794no—
466C2×C4⋊C4—794no—
467C2×C4⋊C4—794no—
468C2×C4⋊C4—794no—
469C2×C4⋊C4—794no—
470C2×C4⋊C4—1584no—
471C2×C4⋊C4—1584no—
472C2×C4⋊C4C22×D7914yes—
473C2×C4⋊C4C22×D7914yes—
474C2×C4⋊C4C22×D7914yes—
475C2×C4⋊C4C22×D7914yes—
476C2×C22⋊C4—794no—
477C2×C22⋊C4—794no—
478C2×C22⋊C4—794no—
479C2×C22⋊C4—794no—
480C2×C22⋊C4—1584no—
481C2×C22⋊C4—1584no—
482C2×C22⋊C4—1584no—
483C2×C22⋊C4—1584no—
484C2×C42—3162no—
485C2×C42—3162no—
486C2×C42—794no—
487C2×C42—794no—
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#95—794no—
501#95C22×D7914yes—
502#95C22×D7914yes—
503#95C22×D7914yes—
504C24—794no—
505C24—794no—
506C24—794no—
507C24—792no—
508C24—1582no—
509C24—1582no—
510C24—1582no—
511C24—1582no—
512C24C23×D7911yescharacteristic
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—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—31616no—
532C22×C4—31616no—
533C22×C4—3164no—
534C22×C4—3164no—
535C22×C4—3164no—
536C22×C4—3164no—
537C22×C4—31616no—
538C22×C4—7916no—
539C22×C4—794no—
540C22×C4—792no—
541C22×C4—792no—
542C22×C4—792no—
543C22×C4—792no—
544C22×C4—792no—
545C22×C4—792no—
546C22×C4—792no—
547C22×C4—1588no—
548C22×C4—1588no—
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—1582no—
561C22×C4—1582no—
562C22×C4—1582no—
563C22×C4—1582no—
564C22×C4—1582no—
565C22×C4—1582no—
566C22×C4—1582no—
567C22×C4—1588no—
568C22×C4—1588no—
569C22×C4—1582no—
570C22×C4—1582no—
571C22×C4Q8×D7914yes—
572C22×C4#1192962314yes—
573C22×C4#1192962514yes—
574C22×C4C23×D7912yes—
575C22×C4C23×D7912yes—
576C22×C4C23×D7912yes—
577C22×C4C23×D7912yes—
578C22×C4C23×D7912yes—
579C22×C4C23×D7912yes—
580C22×C4C23×D7912yes—
581C4⋊C4—28no—
582C4⋊C4—28no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—3164no—
586C4⋊C4—3164no—
587C4⋊C4—3164no—
588C4⋊C4—3164no—
589C4⋊C4—1588no—
590C4⋊C4—1588no—
591C22⋊C4—1588no—
592C22⋊C4—1588no—
593C22⋊C4—1588no—
594C22⋊C4—1588no—
595C42—3164no—
596C42—3164no—
597C23—7916no—
598C23—794no—
599C23—794no—
600C23—794no—
601C23—1582no—
602C23—1582no—
603C23—1588no—
604C23—1588no—
605C23—1588no—
606C23—1588no—
607C23—1588no—
608C23—1588no—
609C23—1582no—
610C23—1582no—
611C23C2×Q8×D7912yes—
612C23#41×D7912yes—
613C23#41×D7912yes—
614C23C2×#1192962312yes—
615C23C2×#1192962512yes—
616C23#1457920612yes—
617C23#1457920712yes—
618C23C24×D7911yescharacteristic
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—28no—
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—22no—
639C2×C4—22no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—31616no—
645C2×C4—31616no—
646C2×C4—31616no—
647C2×C4—3164no—
648C2×C4—3164no—
649C2×C4—3164no—
650C2×C4—3164no—
651C2×C4—3164no—
652C2×C4—3164no—
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—1582no—
673C2×C4—1582no—
674C2×C4—1588no—
675C2×C4C2×Q8×D7914yes—
676C2×C4C2×#1192962314yes—
677C2×C4C2×#1192962514yes—
678C22—798no—
679C22—1584no—
680C22—15832no—
681C22—1584no—
682C22—1584no—
683C22—1584no—
684C22—1584no—
685C22—1584no—
686C22#125×D7914yes—
687C22#1909911814yes—
688C22#1909918814yes—
689C22#1909923614yes—
690C22#1909924014yes—
691C22#1909926014yes—
692C22#1909926614yes—
693C22C22×Q8×D7911yescharacteristic
694C22C2×#41×D7911yescharacteristic
695C22C2×#41×D7911yescharacteristic
696C22C22×#1192962311yescharacteristic
697C22C22×#1192962511yescharacteristic
698C22C2×#1457920611yescharacteristic
699C22C2×#1457920711yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—3162no—
708C4—3162no—
709C4—3162no—
710C4—3162no—
711C4—3162no—
712C4—3162no—
713C4—1584no—
714C2—1588no—
715C2#2376861818yesdirect product factor
716C2C2×#125×D7911yescharacteristic
717C2C2×#1909911811yescharacteristic
718C2C2×#1909918811yescharacteristic
719C2C2×#1909923611yescharacteristic
720C2C2×#1909924011yescharacteristic
721C2C2×#1909926011yescharacteristic
722C2C2×#1909926611yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#398×C79C2
socleC24×C79C24
prime radicalC24×D79C23
hypercenterC2×#398D79
hypocenterC79C2×#2569
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #23768618C2direct (N × H)
2. C2×#19098505C2semidirect
3. C2×#19098502C2semidirect
4. C2×#19098495C2semidirect
5. C2×#19098449C2semidirect
6. C2×#19098449C2semidirect
7. C2×#19098448C2semidirect
8. C2×#19098444C2semidirect
16. C2×#398×C79C2semidirect
32. #19098505C22semidirect
33. #19098502C22semidirect
34. #19098495C22semidirect
35. #19098449C22semidirect
36. #19098449C22semidirect
37. #19098448C22semidirect
38. #19098444C22semidirect
63. #398×C79C22semidirect
353. C2×C79#2569semidirect
366. C2×#398D79semidirect
378. C79C2×#2569semidirect
401. #398C2×D79semidirect
715. C2#23768618direct (N × H)

Maximal subgroups

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

subgroupindex
#237686182
C2×#190985052
C2×#190985022
C2×#190984952
C2×#190984492
C2×#190984482
C2×#190984442
C2×#190984372
C2×#190984342
C2×#190984202
C2×#190984102
C2×#95×D792
C2×#398×C792
C2×#256979