Finite Group Databasebeta

← C2×#23775970 #35166958

Subgroups — C2×#23775970 #35166958

Order 20224.

1834 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×#19099247C211yesmaximal, characteristic
3#23775970C2116yesmaximal, direct product factor
4C2×#19098963C211yesmaximal, characteristic, complemented
5C2×#19098897C211yesmaximal, characteristic, complemented
6C2×#19098896C211yesmaximal, characteristic, complemented
7C2×#19098902C211yesmaximal, characteristic, complemented
8C2×#19098901C211yesmaximal, characteristic, complemented
9C2×#19098872C211yesmaximal, characteristic, complemented
10C2×#19098868C211yesmaximal, characteristic, complemented
11C2×#19098818C211yesmaximal, characteristic, complemented
12C2×Q16×Dic79C211yesmaximal, characteristic, complemented
13C2×#19098639C211yesmaximal, characteristic
14C2×#19098605C211yesmaximal, characteristic, complemented
15C2×#19098602C211yesmaximal, characteristic, complemented
16C2×#470×C79C211yesmaximal, characteristic, complemented
17C22×#11929607C2211yescharacteristic
18#19099255—24no—
19#19099255C2218yes—
20#19099247—24no—
21#19099247C2218yes—
22C2×#14579156—21no—
23C2×#14579154—21no—
24C2×#14579152—21no—
25C2×#14579152C2211yescharacteristic
26C2×#14579152C2211yescharacteristic
27C2×#14579151—21no—
28C2×#14579145—21no—
29C2×#14579143—21no—
30C2×#14579137C2211yescharacteristic
31C2×#14579137C2211yescharacteristic
32C2×Q8×Dic79C2211yescharacteristic
33C2×Q8×Dic79C2211yescharacteristic
34C2×C4×C22⋊D79C2211yescharacteristic
35C2×#14579120C2211yescharacteristic
36C2×#14579119—21no—
37C2×#14579119C2211yescharacteristic
38C2×#14579117—21no—
39C22×C4⋊Dic79C2211yescharacteristic
40C2×C4⋊C4×D79C2211yescharacteristic
41#19098963C2218yescomplemented
42#19098902C2218yescomplemented
43#19098901C2218yescomplemented
44#19098897C2218yescomplemented
45#19098896C2218yescomplemented
46#19098872C2218yescomplemented
47#19098868C2218yescomplemented
48#19098818C2218yescomplemented
49Q16×Dic79C2218yescomplemented
50#19098639C2218yes—
51#19098605C2218yescomplemented
52#19098602C2218yescomplemented
53C2×#14579095C2211yescharacteristic
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
58C2×#14579093C2211yescharacteristic
59C2×#14579093C2211yescharacteristic
60C2×#14579092C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579085C2211yescharacteristic
65C2×#14579085C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×Q16×C79C2211yescharacteristic
70C22×M16×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×C22⋊Q8×C79C2211yescharacteristic
73#470×C79C2218yescomplemented
74C2×#106×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C22×C22⋊D79D411yescharacteristic
78C23×Dic79—21no—
79C22×C4×D79—21no—
80C22×C4×D79C2311yescharacteristic
81C2×#11929607—24no—
82C2×#11929607C2314yes—
83C22×C79⋊C8C2311yescharacteristic
84C22×C79⋊C8C2311yescharacteristic
85#14579156—28no—
86#14579154—28no—
87#14579152—28no—
88#14579152—22no—
89#14579152—22no—
90#14579152C2314yes—
91#14579152C2314yes—
92#14579151—28no—
93#14579145—28no—
94#14579143—28no—
95#14579137—22no—
96#14579137—22no—
97#14579137C2314yes—
98#14579137C2314yes—
99Q8×Dic79—22no—
100Q8×Dic79—22no—
101Q8×Dic79C2314yes—
102Q8×Dic79C2314yes—
103C4×C22⋊D79D414yes—
104C4×C22⋊D79C2314yes—
105#14579120—22no—
106#14579120C2314yes—
107#14579119—22no—
108#14579119—28no—
109#14579119C2314yes—
110#14579117—28no—
111C2×C4⋊Dic79—22no—
112C2×C4⋊Dic79—21no—
113C2×C4⋊Dic79—21no—
114C2×C4⋊Dic79—21no—
115C2×C4⋊Dic79—21no—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79C2314yes—
118C2×C4⋊Dic79C2311yescharacteristic
119C2×C4⋊Dic79C2311yescharacteristic
120C2×C4⋊Dic79C2311yescharacteristic
121C2×C4⋊Dic79C2311yescharacteristic
122C2×Dic79⋊C4—21no—
123C2×Dic79⋊C4—21no—
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4D411yescharacteristic
128C4⋊C4×D79—22no—
129C4⋊C4×D79C2314yes—
130C2×C22⋊Dic79—21no—
131C2×C22⋊Dic79D411yescharacteristic
132C2×(C2×D79)⋊C4—21no—
133C2×(C2×D79)⋊C4—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4D411yescharacteristic
136C2×C4×Dic79—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79C2311yescharacteristic
141#14579095C2314yes—
142#14579095C2314yes—
143#14579094C2314yes—
144#14579094C2314yes—
145#14579094C2314yes—
146#14579093C2314yes—
147#14579093C2314yes—
148#14579092C2314yes—
149Dic79⋊C8C2314yes—
150#14579085C2314yes—
151#14579085C2314yes—
152#14579085C2314yes—
153#14579085C2314yes—
154C22⋊(C79⋊C8)C2314yes—
155(C2×D79)⋊C8C2314yes—
156C8×Dic79C2314yes—
157C22×Q8×C79C2311yescharacteristic
158C22×Q8×C79C2311yescharacteristic
159C23×C4×C79C2311yescharacteristic
160C2×Q16×C79—24no—
161C2×Q16×C79C2314yes—
162C2×M16×C79—24no—
163C2×M16×C79C2314yes—
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166C22⋊Q8×C79—22no—
167C22⋊Q8×C79—22no—
168C22⋊Q8×C79C2314yes—
169C22⋊Q8×C79C2314yes—
170C2×C4⋊C4×C79—21no—
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176#106×C79C2314yes—
177#103×C79C2314yes—
178#103×C79C2314yes—
179C23×D79C2×D411yescharacteristic
180C2×C22⋊D79—42no—
181C2×C22⋊D79C2×D414yes—
182C22×Dic79—21no—
183C22×Dic79—21no—
184C22×Dic79—21no—
185C22×Dic79—21no—
186C22×Dic79—24no—
187C22×Dic79—44no—
188C22×Dic79C2×D411yescharacteristic
189C22×Dic79C2×D411yescharacteristic
190C22×Dic79C2×D411yescharacteristic
191C2×C4×D79—24no—
192C2×C4×D79—22no—
193C2×C4×D79—22no—
194C2×C4×D79—44no—
195C2×C4×D79C2×D412yes—
196C2×C4×D79C2412yes—
197#11929607—28no—
198C2×C79⋊C8—22no—
199C2×C79⋊C8—22no—
200C2×C79⋊C8C2412yes—
201C2×C79⋊C8C2412yes—
202C4⋊Dic79—24no—
203C4⋊Dic79—24no—
204C4⋊Dic79—24no—
205C4⋊Dic79—24no—
206C4⋊Dic79—21no—
207C4⋊Dic79—21no—
208C4⋊Dic79—21no—
209C4⋊Dic79—24no—
210C4⋊Dic79—21no—
211C4⋊Dic79C2412yes—
212C4⋊Dic79C2412yes—
213C4⋊Dic79C2412yes—
214C4⋊Dic79C2412yes—
215Dic79⋊C4—24no—
216Dic79⋊C4—24no—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4C2×D414yes—
221C22⋊Dic79—24no—
222C22⋊Dic79C2×D414yes—
223(C2×D79)⋊C4—24no—
224(C2×D79)⋊C4—24no—
225(C2×D79)⋊C4—24no—
226(C2×D79)⋊C4C2×D414yes—
227C4×Dic79—24no—
228C4×Dic79—24no—
229C4×Dic79—24no—
230C4×Dic79—24no—
231C4×Dic79C2×D412yes—
232C4×Dic79C2412yes—
233C24×C79C2×D411yescharacteristic
234C2×Q8×C79—21no—
235C2×Q8×C79—21no—
236C2×Q8×C79—22no—
237C2×Q8×C79—22no—
238C2×Q8×C79—22no—
239C2×Q8×C79—22no—
240C2×Q8×C79C2412yes—
241C2×Q8×C79C2412yes—
242C22×C4×C79—22no—
243C22×C4×C79—22no—
244C22×C4×C79—21no—
245C22×C4×C79—21no—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79C2×D411yescharacteristic
249C22×C4×C79C2×D412yes—
250C22×C4×C79C2412yes—
251C22×C4×C79C2411yescharacteristic
252Q16×C79—28no—
253M16×C79—28no—
254C2×C8×C79—22no—
255C2×C8×C79#4114yes—
256C2×C8×C79C2412yes—
257C2×C8×C79C2412yes—
258C4⋊C4×C79—24no—
259C4⋊C4×C79—24no—
260C4⋊C4×C79—21no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79C2412yes—
263C4⋊C4×C79C2412yes—
264C22⋊C4×C79—24no—
265C22⋊C4×C79—24no—
266C23×C79—22no—
267C23×C79—22no—
268C23×C79—22no—
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—22no—
278Q8×C79—22no—
279Q8×C79—42no—
280Q8×C79—42no—
281C2×C4×C79—22no—
282C2×C4×C79—24no—
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—42no—
290C2×C4×C79—42no—
291C2×C4×C79—42no—
292C2×C4×C79—42no—
293C2×C4×C79C22×D412yes—
294C2×C4×C79C22×D411yescharacteristic
295C2×C4×C79C2×#4112yes—
296C2×C4×C792−1+412yes—
297C2×C4×C79C2511yescharacteristic
298C22⋊D79—44no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—48no—
307C2×Dic79—42no—
308C2×Dic79—42no—
309C2×Dic79—42no—
310C2×Dic79—42no—
311C2×Dic79C22×D412yes—
312C2×Dic79C22×D412yes—
313C2×Dic79C22×D412yes—
314C4×D79—24no—
315C4×D79—22no—
316C4×D79—22no—
317C4×D79—48no—
318C8×C79—22no—
319C8×C79C2×#4114yes—
320C79⋊C8—22no—
321C79⋊C8—22no—
322C22×C79—22no—
323C22×C79—22no—
324C22×C79—22no—
325C22×C79—44no—
326C22×C79#54712yes—
327C22×C79#57512yes—
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×#3352—791nomaximal, Sylow
350C2×C79—42no—
351C2×C79#335214yescomplemented
352C2×C79C2×#54711yescharacteristic
353C2×C79C2×#57511yescharacteristic
354C2×C79C2×#57811yescharacteristic
355D79—42no—
356C2×#552—791no—
357C2×#552—791no—
358#3352—7916no—
359C2×#499—791no—
360C2×#484—791no—
361C2×#484—791no—
362C2×#485—791no—
363C2×#485—791no—
364C2×#479—791no—
365C2×#479—791no—
366C2×#470—791no—
367C2×#470D7911yescharacteristic, complemented
368C2×C4×Q16—791no—
369C2×#436—791no—
370C2×#428—791no—
371C2×#428—791no—
372C79C2×#335211yescharacteristic, complemented, Sylow
373C22×Q16C2×D7911yescharacteristic
374C22×M16—791no—
375C22×M16C2×D7911yescharacteristic
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⋊Q8C2×D7911yescharacteristic
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⋊C4—791no—
401#499—798no—
402#485—798no—
403#485—798no—
404#484—798no—
405#484—798no—
406#479—798no—
407#479—798no—
408#470—798no—
409#470C2×D7918yescomplemented
410C4×Q16—798no—
411#436—798no—
412#428—798no—
413#428—798no—
414C2×#107—791no—
415C2×#107—791no—
416C2×#107—791no—
417C2×#107—791no—
418C2×#107—791no—
419C2×#106—791no—
420C2×#106—791no—
421C2×#106—791no—
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⋊C8—791no—
432C2×C4×C8—791no—
433C22×Q8C22×D7911yescharacteristic
434C22×Q8C22×D7911yescharacteristic
435C22×D4—791no—
436C23×C4—791no—
437C23×C4—1581no—
438C23×C4—1581no—
439C23×C4C22×D7911yescharacteristic
440C2×Q16—24no—
441C2×Q16C22×D7914yes—
442C2×M16—24no—
443C2×M16—794no—
444C2×M16—1584no—
445C2×M16C22×D7914yes—
446C22×C8—791no—
447C22×C8—791no—
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—22no—
462C22⋊Q8—794no—
463C22⋊Q8—794no—
464C22⋊Q8—1582no—
465C22⋊Q8—1582no—
466C22⋊Q8C22×D7914yes—
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—21no—
482C2×C4⋊C4—791no—
483C2×C4⋊C4—791no—
484C2×C4⋊C4—791no—
485C2×C4⋊C4—791no—
486C2×C4⋊C4—794no—
487C2×C4⋊C4—791no—
488C2×C4⋊C4—794no—
489C2×C4⋊C4—1582no—
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—1581no—
498C2×C4⋊C4—1581no—
499C2×C4⋊C4—1581no—
500C2×C4⋊C4—1582no—
501C2×C4⋊C4C22×D7911yescharacteristic
502C2×C4⋊C4C22×D7911yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—791no—
506C2×C22⋊C4—791no—
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#106—794no—
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⋊C8—794no—
534C4×C8—794no—
535C24—791no—
536C24D4×D7911yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8C23×D7912yes—
544C2×Q8C23×D7912yes—
545C2×D4—3162no—
546C2×D4—794no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—3164no—
554C22×C4—3164no—
555C22×C4—791no—
556C22×C4—791no—
557C22×C4—791no—
558C22×C4—792no—
559C22×C4—792no—
560C22×C4—1584no—
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—28no—
573M16—28no—
574M16—1588no—
575C2×C8—22no—
576C2×C8—792no—
577C2×C8—792no—
578C2×C8—1582no—
579C2×C8—1582no—
580C2×C8#1192962314yes—
581C2×C8C23×D7912yes—
582C2×C8C23×D7912yes—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—794no—
588C4⋊C4—792no—
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—1581no—
604C4⋊C4—1584no—
605C4⋊C4—1581no—
606C4⋊C4C23×D7912yes—
607C4⋊C4C23×D7912yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—794no—
611C22⋊C4—794no—
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—22no—
625C23—792no—
626C23—1582no—
627C23—1582no—
628C23—1582no—
629C23C2×D4×D7912yes—
630C23C2×D4×D7911yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—22no—
635Q8—42no—
636Q8—42no—
637D4—3164no—
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—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—3168no—
651C2×C4—3168no—
652C2×C4—3162no—
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×C4C2×#1192962312yes—
672C2×C4#1457920812yes—
673C2×C4C24×D7911yescharacteristic
674C8—22no—
675C8—1582no—
676C8—1582no—
677C8C2×#1192962314yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—44no—
682C22—3164no—
683C22—1582no—
684C22—1582no—
685C22—1582no—
686C22#1909921312yes—
687C22#1909936212yes—
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#1909921312yes—
703C4C22×#1192962311yescharacteristic
704C4C2×#1457920811yescharacteristic
705C2—42no—
706C2—3162no—
707C2#2377597014yesdirect product factor
708C2C2×#1909921311yescharacteristic
709C2C2×#1909936211yescharacteristic
710C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#470×C79C2
socleC23×C79C22×D4
prime radicalC22×C22⋊D79D4
hypercenterC2×#470D79
hypocenterC79C2×#3352
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
3. #23775970C2direct (N × H)
4. C2×#19098963C2semidirect
5. C2×#19098897C2semidirect
6. C2×#19098896C2semidirect
7. C2×#19098902C2semidirect
8. C2×#19098901C2semidirect
9. C2×#19098872C2semidirect
10. C2×#19098868C2semidirect
11. C2×#19098818C2semidirect
12. C2×Q16×Dic79C2semidirect
14. C2×#19098605C2semidirect
15. C2×#19098602C2semidirect
16. C2×#470×C79C2semidirect
41. #19098963C22semidirect
42. #19098902C22semidirect
43. #19098901C22semidirect
44. #19098897C22semidirect
45. #19098896C22semidirect
46. #19098872C22semidirect
47. #19098868C22semidirect
48. #19098818C22semidirect
49. Q16×Dic79C22semidirect
51. #19098605C22semidirect
52. #19098602C22semidirect
73. #470×C79C22semidirect
351. C2×C79#3352semidirect
367. C2×#470D79semidirect
372. C79C2×#3352semidirect
409. #470C2×D79semidirect
707. C2#23775970direct (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×#190992472
#237759702
C2×#190989632
C2×#190988972
C2×#190988962
C2×#190989022
C2×#190989012
C2×#190988722
C2×#190988682
C2×#190988182
C2×Q16×Dic792
C2×#190986392
C2×#190986052
C2×#190986022
C2×#470×C792
C2×#335279