Finite Group Databasebeta

← C2×#23775766 #35166702

Subgroups — C2×#23775766 #35166702

Order 20224.

1866 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099255C211yesmaximal, characteristic
2C2×#19099248C211yesmaximal, characteristic
3#23775766C2116yesmaximal, direct product factor
4C2×#19098963C211yesmaximal, characteristic, complemented
5C2×#19098907C211yesmaximal, characteristic, complemented
6C2×#19098902C211yesmaximal, characteristic, complemented
7C2×#19098894C211yesmaximal, characteristic, complemented
8C2×#19098873C211yesmaximal, characteristic, complemented
9C2×#19098868C211yesmaximal, characteristic, complemented
10C2×#19098803C211yesmaximal, characteristic, complemented
11C2×#19098802C211yesmaximal, characteristic, complemented
12C2×#19098655C211yesmaximal, characteristic, complemented
13C2×(C22⋊D79)⋊C8C211yesmaximal, characteristic
14C2×#19098598C211yesmaximal, characteristic, complemented
15C22×#14579094C211yesmaximal, characteristic, complemented
16C2×#483×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C23×C79⋊C8C2211yescharacteristic
19C22×C8×D79C2211yescharacteristic
20#19099255—24no—
21#19099255C2218yes—
22#19099248—24no—
23#19099248C2218yes—
24C2×#14579156—21no—
25C2×#14579156—21no—
26C2×#14579152—21no—
27C2×#14579152C2211yescharacteristic
28C2×#14579152C2211yescharacteristic
29C2×#14579151—21no—
30C2×#14579145—21no—
31C2×#14579144—21no—
32C2×#14579141C2211yescharacteristic
33C2×#14579140C2211yescharacteristic
34C2×#14579137C2211yescharacteristic
35C2×Q8×Dic79C2211yescharacteristic
36C2×#14579126C2211yescharacteristic
37C2×C4×C22⋊D79C2211yescharacteristic
38C2×#14579120—21no—
39C2×#14579119C2211yescharacteristic
40C2×#14579119C2211yescharacteristic
41C2×#14579117—21no—
42C22×C4⋊Dic79C2211yescharacteristic
43#19098963C2218yescomplemented
44#19098907C2218yescomplemented
45#19098902C2218yescomplemented
46#19098894C2218yescomplemented
47#19098873C2218yescomplemented
48#19098868C2218yescomplemented
49#19098803C2218yescomplemented
50#19098802C2218yescomplemented
51#19098655C2218yescomplemented
52(C22⋊D79)⋊C8C2218yes—
53#19098598C2218yescomplemented
54C2×#14579094C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
58C2×#14579094C2211yescharacteristic
59C2×#14579094C2218yescomplemented
60C2×#14579093C2211yescharacteristic
61C2×#14579093C2211yescharacteristic
62C2×Dic79⋊C8C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579086C2211yescharacteristic
65C2×#14579085C2211yescharacteristic
66C2×#14579084C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C2×C22⋊Q8×C79C2211yescharacteristic
70C22×C4⋊C4×C79C2211yescharacteristic
71#483×C79C2218yescomplemented
72C2×#106×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic
77C22×Dic158C2311yescharacteristic
78C22×C22⋊D79D411yescharacteristic
79C23×Dic79—21no—
80C22×C4×D79C2311yescharacteristic
81C2×#11929614—24no—
82C2×#11929614C2314yes—
83C22×C79⋊C8—24no—
84C22×C79⋊C8C2314yes—
85C22×C79⋊C8C2311yescharacteristic
86C22×C79⋊C8C2311yescharacteristic
87C2×C8×D79—24no—
88C2×C8×D79C2314yes—
89#14579156—28no—
90#14579156—28no—
91#14579152—28no—
92#14579152—22no—
93#14579152—22no—
94#14579152C2314yes—
95#14579152C2314yes—
96#14579151—28no—
97#14579145—28no—
98#14579144—28no—
99#14579141—22no—
100#14579141C2314yes—
101#14579140—22no—
102#14579140C2314yes—
103#14579137—22no—
104#14579137C2314yes—
105Q8×Dic79—22no—
106Q8×Dic79C2314yes—
107#14579126—22no—
108#14579126C2314yes—
109C4×C22⋊D79D414yes—
110C4×C22⋊D79C2314yes—
111#14579120—28no—
112#14579119—22no—
113#14579119—22no—
114#14579119C2314yes—
115#14579119C2314yes—
116#14579117—28no—
117C2×C4⋊Dic79—22no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79C2314yes—
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4D411yescharacteristic
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79D411yescharacteristic
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4D411yescharacteristic
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79C2311yescharacteristic
145#14579094C2314yes—
146#14579094C2314yes—
147#14579094C2314yes—
148#14579094C2314yes—
149#14579094C2314yes—
150#14579093C2314yes—
151#14579093C2314yes—
152Dic79⋊C8C2314yes—
153#14579086C2314yes—
154#14579086C2314yes—
155#14579085C2314yes—
156#14579084C2314yes—
157(C2×D79)⋊C8C2314yes—
158C8×Dic79C2314yes—
159C22×Q8×C79C2311yescharacteristic
160C23×C4×C79—21no—
161C23×C4×C79C2311yescharacteristic
162C22×C8×C79C2311yescharacteristic
163C22×C8×C79C2311yescharacteristic
164C22⋊Q8×C79—22no—
165C22⋊Q8×C79C2314yes—
166C2×C4⋊C4×C79—22no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2314yes—
173C2×C22⋊C4×C79—21no—
174#106×C79C2314yes—
175#106×C79C2314yes—
176#103×C79C2314yes—
177#103×C79C2314yes—
178C22⋊C8×C79C2314yes—
179C23×D79C2×D411yescharacteristic
180C2×Dic158—21no—
181C2×Dic158—22no—
182C2×Dic158—22no—
183C2×Dic158C2412yes—
184C2×C22⋊D79—24no—
185C2×C22⋊D79C2×D414yes—
186C22×Dic79—21no—
187C22×Dic79—21no—
188C22×Dic79—21no—
189C22×Dic79—21no—
190C22×Dic79—24no—
191C22×Dic79—44no—
192C22×Dic79C2×D411yescharacteristic
193C22×Dic79C2×D411yescharacteristic
194C22×Dic79C2×D411yescharacteristic
195C2×C4×D79—22no—
196C2×C4×D79—22no—
197C2×C4×D79C2×D412yes—
198C2×C4×D79C2412yes—
199#11929614—28no—
200C2×C79⋊C8—28no—
201C2×C79⋊C8—22no—
202C2×C79⋊C8#4114yes—
203C2×C79⋊C8C2412yes—
204C2×C79⋊C8C2412yes—
205C8×D79—28no—
206C4⋊Dic79—24no—
207C4⋊Dic79—24no—
208C4⋊Dic79—24no—
209C4⋊Dic79—24no—
210C4⋊Dic79—21no—
211C4⋊Dic79—21no—
212C4⋊Dic79—24no—
213C4⋊Dic79—21no—
214C4⋊Dic79C2412yes—
215C4⋊Dic79C2412yes—
216C4⋊Dic79C2412yes—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4C2×D414yes—
223C22⋊Dic79—24no—
224C22⋊Dic79C2×D414yes—
225(C2×D79)⋊C4—24no—
226(C2×D79)⋊C4—24no—
227(C2×D79)⋊C4—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4C2×D414yes—
230C4×Dic79—24no—
231C4×Dic79—24no—
232C4×Dic79—24no—
233C4×Dic79—24no—
234C4×Dic79C2×D412yes—
235C4×Dic79C2412yes—
236C24×C79C2×D411yescharacteristic
237C2×Q8×C79—21no—
238C2×Q8×C79—22no—
239C2×Q8×C79—22no—
240C2×Q8×C79C2412yes—
241C22×C4×C79—22no—
242C22×C4×C79—22no—
243C22×C4×C79—21no—
244C22×C4×C79—21no—
245C22×C4×C79—21no—
246C22×C4×C79—21no—
247C22×C4×C79—24no—
248C22×C4×C79—44no—
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2×D412yes—
251C22×C4×C79C2412yes—
252C22×C4×C79C2411yescharacteristic
253C2×C8×C79—22no—
254C2×C8×C79—22no—
255C2×C8×C79C2412yes—
256C2×C8×C79C2412yes—
257C4⋊C4×C79—21no—
258C4⋊C4×C79—21no—
259C4⋊C4×C79—24no—
260C4⋊C4×C79—24no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79C2412yes—
263C4⋊C4×C79C2412yes—
264C4⋊C4×C79C2412yes—
265C22⋊C4×C79—24no—
266C23×C79—22no—
267C23×C79—22no—
268C23×C79#13514yes—
269C23×C79C22×D412yes—
270C23×C79C22×D411yescharacteristic
271C22×D79—22no—
272C22×D79—22no—
273C22×D79—22no—
274C22×D79C22×D412yes—
275Q8×C79—22no—
276Q8×C79—22no—
277Q8×C79—42no—
278C2×C4×C79—22no—
279C2×C4×C79—24no—
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—42no—
287C2×C4×C79—48no—
288C2×C4×C79—42no—
289C2×C4×C79—42no—
290C2×C4×C79—42no—
291C2×C4×C79C22×D412yes—
292C2×C4×C79C22×D411yescharacteristic
293C2×C4×C79C2×#4112yes—
294C2×C4×C792−1+412yes—
295C2×C4×C79C2511yescharacteristic
296C22⋊D79—28no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—42no—
305C2×Dic79—48no—
306C2×Dic79—42no—
307C2×Dic79—42no—
308C2×Dic79—42no—
309C2×Dic79C22×D412yes—
310C2×Dic79C22×D412yes—
311C2×Dic79C22×D412yes—
312C4×D79—24no—
313C4×D79—22no—
314C4×D79—22no—
315Dic158—22no—
316Dic158—22no—
317Dic158—42no—
318C8×C79—22no—
319C8×C79—22no—
320C79⋊C8—22no—
321C79⋊C8C2×#4114yes—
322C22×C79—28no—
323C22×C79—22no—
324C22×C79—22no—
325C22×C79#54712yes—
326C22×C79C2×#13514yes—
327C22×C79C2×#13512yes—
328C22×C79#57812yes—
329C22×C79C23×D411yescharacteristic
330C2×D79—22no—
331C2×D79—22no—
332C2×D79—22no—
333C2×D79—44no—
334C4×C79—22no—
335C4×C79—42no—
336C4×C79—42no—
337C4×C79—42no—
338C4×C79—42no—
339C4×C79#54712yes—
340C4×C79C22×#4111yescharacteristic
341C4×C79C2×2−1+411yescharacteristic
342Dic79—22no—
343Dic79—22no—
344Dic79—22no—
345Dic79—42no—
346Dic79—42no—
347Dic79—42no—
348Dic79—42no—
349C2×#3336—791nomaximal, Sylow
350C2×C79—24no—
351C2×C79#333614yescomplemented
352C2×C79C2×#54711yescharacteristic
353C2×C79C22×#13511yescharacteristic
354C2×C79C2×#57811yescharacteristic
355D79—42no—
356C2×#552—791no—
357C2×#552—791no—
358#3336—7916no—
359C2×#499—791no—
360C2×#485—791no—
361C2×#485—791no—
362C2×#483—791no—
363C2×#483D7911yescharacteristic, complemented
364C2×#479—791no—
365C2×#479—791no—
366C2×#467—791no—
367C2×#467—791no—
368C2×C4×Q16—791no—
369C2×C8×D4—791no—
370C2×#427—791no—
371C22×#107—791no—
372C79C2×#333611yescharacteristic, complemented, Sylow
373C22×Q16—791no—
374C23×C8—791no—
375C23×C8—791no—
376#552—798no—
377#552—798no—
378#552—1584no—
379#552—1584no—
380C2×#126—1581no—
381C2×#126—1581no—
382C2×#125—791no—
383C2×#125—791no—
384C2×#125—1581no—
385C2×#125—1581no—
386C2×#123—1581no—
387C2×#123—1581no—
388C2×C22⋊Q8—791no—
389C2×C22⋊Q8—791no—
390C2×C22⋊Q8—791no—
391C2×C22⋊Q8C2×D7911yescharacteristic
392C2×C4×Q8—791no—
393C2×C4×Q8—791no—
394C2×C4×D4—791no—
395C2×#117—791no—
396C2×#117—791no—
397C2×#117—1581no—
398C2×#117—1581no—
399C22×C4⋊C4—791no—
400C22×C4⋊C4C2×D7911yescharacteristic
401#499—798no—
402#485—798no—
403#485—798no—
404#483—798no—
405#483C2×D7918yescomplemented
406#479—798no—
407#479—798no—
408#467—798no—
409#467—798no—
410C4×Q16—798no—
411C8×D4—798no—
412#427—798no—
413C2×#107—791no—
414C2×#107—791no—
415C2×#107—798no—
416C2×#107—791no—
417C2×#107—791no—
418C2×#107—791no—
419C2×#106—791no—
420C2×#106—791no—
421C2×#106C2×D7911yescharacteristic
422C2×#106C2×D7911yescharacteristic
423C2×C4⋊C8—791no—
424C2×#103—791no—
425C2×#103—791no—
426C2×#103—791no—
427C2×#103—791no—
428C2×#103C2×D7911yescharacteristic
429C2×#103C2×D7911yescharacteristic
430C2×C22⋊C8—791no—
431C2×C22⋊C8C2×D7911yescharacteristic
432C2×C4×C8—791no—
433C22×Q8—791no—
434C22×Q8C22×D7911yescharacteristic
435C22×D4—791no—
436C23×C4—21no—
437C23×C4—791no—
438C23×C4—1581no—
439C23×C4C22×D7911yescharacteristic
440C2×Q16—794no—
441C2×Q16—1584no—
442C22×C8—791no—
443C22×C8—791no—
444C22×C8—794no—
445C22×C8—794no—
446C22×C8—1584no—
447C22×C8—1584no—
448C22×C8C22×D7911yescharacteristic
449C22×C8C22×D7911yescharacteristic
450#126—1588no—
451#126—1588no—
452#125—794no—
453#125—794no—
454#125—1582no—
455#125—1582no—
456#125—1588no—
457#125—1588no—
458#123—1588no—
459#123—1588no—
460C22⋊Q8—22no—
461C22⋊Q8—794no—
462C22⋊Q8—794no—
463C22⋊Q8—794no—
464C22⋊Q8—1582no—
465C22⋊Q8—1582no—
466C22⋊Q8—1582no—
467C22⋊Q8C22×D7914yes—
468C4×Q8—794no—
469C4×Q8—794no—
470C4×Q8—1582no—
471C4×Q8—1582no—
472C4×D4—794no—
473C4×D4—794no—
474#117—794no—
475#117—794no—
476#117—1588no—
477#117—1588no—
478#117—1582no—
479#117—1582no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—791no—
484C2×C4⋊C4—791no—
485C2×C4⋊C4—791no—
486C2×C4⋊C4—794no—
487C2×C4⋊C4—791no—
488C2×C4⋊C4—1581no—
489C2×C4⋊C4—1581no—
490C2×C4⋊C4—1581no—
491C2×C4⋊C4—1581no—
492C2×C4⋊C4—1581no—
493C2×C4⋊C4—1581no—
494C2×C4⋊C4—1581no—
495C2×C4⋊C4—1581no—
496C2×C4⋊C4—1581no—
497C2×C4⋊C4—1582no—
498C2×C4⋊C4—1581no—
499C2×C4⋊C4C22×D7911yescharacteristic
500C2×C4⋊C4C22×D7911yescharacteristic
501C2×C4⋊C4C22×D7914yes—
502C2×C4⋊C4C22×D7911yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—791no—
505C2×C22⋊C4—791no—
506C2×C22⋊C4—1581no—
507C2×C22⋊C4—1581no—
508C2×C22⋊C4—1581no—
509C2×C22⋊C4—1581no—
510C2×C22⋊C4—1581no—
511C2×C42—791no—
512C2×C42—1581no—
513C2×C42—1581no—
514C2×C42—1581no—
515C2×C42—1581no—
516#107—794no—
517#107—794no—
518#107—794no—
519#107—794no—
520#107—794no—
521#106—794no—
522#106—794no—
523#106C22×D7914yes—
524#106C22×D7914yes—
525C4⋊C8—794no—
526#103—794no—
527#103—794no—
528#103—794no—
529#103—794no—
530#103C22×D7914yes—
531#103C22×D7914yes—
532C22⋊C8—794no—
533C22⋊C8C22×D7914yes—
534C4×C8—794no—
535C24—791no—
536C24D4×D7911yescharacteristic
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—792no—
541C2×Q8—1582no—
542C2×Q8—1582no—
543C2×Q8—1581no—
544C2×Q8C23×D7912yes—
545C2×D4—794no—
546C2×D4—1584no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—44no—
555C22×C4—3164no—
556C22×C4—791no—
557C22×C4—791no—
558C22×C4—791no—
559C22×C4—792no—
560C22×C4—792no—
561C22×C4—1584no—
562C22×C4—1581no—
563C22×C4—1581no—
564C22×C4—1581no—
565C22×C4—1581no—
566C22×C4—1582no—
567C22×C4—1582no—
568C22×C4D4×D7912yes—
569C22×C4D4×D7911yescharacteristic
570C22×C4C23×D7912yes—
571C22×C4C23×D7911yescharacteristic
572Q16—1588no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—794no—
576C2×C8—792no—
577C2×C8—792no—
578C2×C8—1588no—
579C2×C8—1588no—
580C2×C8—1582no—
581C2×C8C23×D7912yes—
582C2×C8C23×D7912yes—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—794no—
589C4⋊C4—792no—
590C4⋊C4—792no—
591C4⋊C4—792no—
592C4⋊C4—1584no—
593C4⋊C4—1584no—
594C4⋊C4—1584no—
595C4⋊C4—1584no—
596C4⋊C4—1584no—
597C4⋊C4—1584no—
598C4⋊C4—1584no—
599C4⋊C4—1584no—
600C4⋊C4—1584no—
601C4⋊C4—1581no—
602C4⋊C4—1581no—
603C4⋊C4—1584no—
604C4⋊C4—1581no—
605C4⋊C4C23×D7912yes—
606C4⋊C4C23×D7912yes—
607C4⋊C4C23×D7912yes—
608C22⋊C4—24no—
609C22⋊C4—794no—
610C22⋊C4—794no—
611C22⋊C4—1584no—
612C22⋊C4—1584no—
613C22⋊C4—1584no—
614C22⋊C4—1584no—
615C22⋊C4—1584no—
616C42—792no—
617C42—792no—
618C42—1584no—
619C42—1584no—
620C42—1584no—
621C42—1584no—
622C23—22no—
623C23—22no—
624C23—792no—
625C23—1582no—
626C23—1582no—
627C23—1582no—
628C23#1457918214yes—
629C23C2×D4×D7912yes—
630C23C2×D4×D7911yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—3162no—
635Q8—1582no—
636Q8—1582no—
637D4—1588no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—48no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—3162no—
652C2×C4—3168no—
653C2×C4—3162no—
654C2×C4—3162no—
655C2×C4—3162no—
656C2×C4—792no—
657C2×C4—792no—
658C2×C4—792no—
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—1584no—
668C2×C4—1582no—
669C2×C4C2×D4×D7912yes—
670C2×C4C2×D4×D7911yescharacteristic
671C2×C4#41×D7912yes—
672C2×C4#1457920812yes—
673C2×C4C24×D7911yescharacteristic
674C8—22no—
675C8—22no—
676C8—794no—
677C8—1582no—
678C22—28no—
679C22—22no—
680C22—22no—
681C22—3164no—
682C22—1582no—
683C22—1582no—
684C22—1582no—
685C22#1909921112yes—
686C22C2×#1457918214yes—
687C22C2×#1457918212yes—
688C22#1909937912yes—
689C22C22×D4×D7911yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—3162no—
696C4—3162no—
697C4—3162no—
698C4—3162no—
699C4—1582no—
700C4—1582no—
701C4—1582no—
702C4#1909921112yes—
703C4C2×#41×D7911yescharacteristic
704C4C2×#1457920811yescharacteristic
705C2—24no—
706C2—3162no—
707C2#2377576614yesdirect product factor
708C2C2×#1909921111yescharacteristic
709C2C22×#1457918211yescharacteristic
710C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#483×C79C2
socleC23×C79C22×D4
prime radicalC22×C22⋊D79D4
hypercenterC2×#483D79
hypocenterC79C2×#3336
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. #23775766C2direct (N × H)
4. C2×#19098963C2semidirect
5. C2×#19098907C2semidirect
6. C2×#19098902C2semidirect
7. C2×#19098894C2semidirect
8. C2×#19098873C2semidirect
9. C2×#19098868C2semidirect
10. C2×#19098803C2semidirect
11. C2×#19098802C2semidirect
12. C2×#19098655C2semidirect
14. C2×#19098598C2semidirect
15. C22×#14579094C2semidirect
16. C2×#483×C79C2semidirect
43. #19098963C22semidirect
44. #19098907C22semidirect
45. #19098902C22semidirect
46. #19098894C22semidirect
47. #19098873C22semidirect
48. #19098868C22semidirect
49. #19098803C22semidirect
50. #19098802C22semidirect
51. #19098655C22semidirect
53. #19098598C22semidirect
59. C2×#14579094C22semidirect
71. #483×C79C22semidirect
351. C2×C79#3336semidirect
363. C2×#483D79semidirect
372. C79C2×#3336semidirect
405. #483C2×D79semidirect
707. C2#23775766direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992552
C2×#190992482
#237757662
C2×#190989632
C2×#190989072
C2×#190989022
C2×#190988942
C2×#190988732
C2×#190988682
C2×#190988032
C2×#190988022
C2×#190986552
C2×(C22⋊D79)⋊C82
C2×#190985982
C22×#145790942
C2×#483×C792
C2×#333679