Finite Group Databasebeta

← C2×#23775931 #35166897

Subgroups — C2×#23775931 #35166897

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×#19099281C211yesmaximal, characteristic
2C2×#19099248C211yesmaximal, characteristic
3#23775931C2116yesmaximal, direct product factor
4C2×#19098971C211yesmaximal, characteristic, complemented
5C2×#19098898C211yesmaximal, characteristic, complemented
6C2×#19098907C211yesmaximal, characteristic, complemented
7C2×#19098906C211yesmaximal, characteristic, complemented
8C2×#19098904C211yesmaximal, characteristic, complemented
9C2×#19098873C211yesmaximal, characteristic, complemented
10C2×#19098857C211yesmaximal, characteristic, complemented
11C2×#19098821C211yesmaximal, characteristic, complemented
12C2×#19098805C211yesmaximal, characteristic, complemented
13C2×#19098669C211yesmaximal, characteristic, complemented
14C2×#19098632C211yesmaximal, characteristic
15C2×#19098598C211yesmaximal, characteristic, complemented
16C2×#428×C79C211yesmaximal, characteristic, complemented
17C22×Dic316C2211yescharacteristic
18C22×C8×D79C2211yescharacteristic
19#19099281—24no—
20#19099281C2218yes—
21#19099248—24no—
22#19099248C2218yes—
23C2×#14579160C2211yescharacteristic
24C2×#14579156—21no—
25C2×#14579155—21no—
26C2×#14579154—21no—
27C2×#14579152C2211yescharacteristic
28C2×#14579151—21no—
29C2×#14579147—21no—
30C2×#14579144—21no—
31C2×#14579141C2211yescharacteristic
32C2×#14579141C2211yescharacteristic
33C2×#14579140C2211yescharacteristic
34C2×#14579140C2211yescharacteristic
35C2×C4×Dic158—21no—
36C2×#14579126C2211yescharacteristic
37C2×#14579126C2211yescharacteristic
38C2×C4×C22⋊D79C2211yescharacteristic
39C2×#14579120—21no—
40C2×#14579119C2211yescharacteristic
41C2×#14579119C2211yescharacteristic
42#19098971C2218yescomplemented
43#19098907C2218yescomplemented
44#19098906C2218yescomplemented
45#19098904C2218yescomplemented
46#19098898C2218yescomplemented
47#19098873C2218yescomplemented
48#19098857C2218yescomplemented
49#19098821C2218yescomplemented
50#19098805C2218yescomplemented
51#19098669C2218yescomplemented
52#19098632C2218yes—
53#19098598C2218yescomplemented
54C2×#14579094C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579093C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579084C2211yescharacteristic
63C2×#14579084C2211yescharacteristic
64C2×#14579084C2211yescharacteristic
65C2×#14579084C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×#14579071C2211yescharacteristic
69C22×M16×C79C2211yescharacteristic
70C2×#117×C79C2211yescharacteristic
71C22×C4⋊C4×C79C2211yescharacteristic
72#428×C79C2218yescomplemented
73C2×#107×C79C2211yescharacteristic
74C2×#107×C79C2211yescharacteristic
75C2×#106×C79C2211yescharacteristic
76C2×#106×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×Dic158C2311yescharacteristic
80C22×C22⋊D79D411yescharacteristic
81C22×C4×D79C2311yescharacteristic
82C2×Dic316—24no—
83C2×Dic316C2314yes—
84C22×C79⋊C8C2311yescharacteristic
85C22×C79⋊C8C2311yescharacteristic
86C2×C8×D79—24no—
87C2×C8×D79C2314yes—
88#14579160—22no—
89#14579160C2314yes—
90#14579156—28no—
91#14579155—28no—
92#14579154—28no—
93#14579152—22no—
94#14579152C2314yes—
95#14579151—28no—
96#14579147—28no—
97#14579144—28no—
98#14579141—22no—
99#14579141—22no—
100#14579141C2314yes—
101#14579141C2314yes—
102#14579140—22no—
103#14579140—22no—
104#14579140C2314yes—
105#14579140C2314yes—
106C4×Dic158—28no—
107#14579126—22no—
108#14579126—22no—
109#14579126C2314yes—
110#14579126C2314yes—
111C4×C22⋊D79D414yes—
112C4×C22⋊D79C2314yes—
113#14579120—28no—
114#14579119—22no—
115#14579119—22no—
116#14579119C2314yes—
117#14579119C2314yes—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79C2311yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×Dic79⋊C4—21no—
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4D411yescharacteristic
130C2×C22⋊Dic79—21no—
131C2×C22⋊Dic79—21no—
132C2×C22⋊Dic79D411yescharacteristic
133C2×(C2×D79)⋊C4—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4D411yescharacteristic
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79C2311yescharacteristic
143#14579094C2314yes—
144#14579094C2314yes—
145#14579094C2314yes—
146#14579093C2314yes—
147#14579092C2314yes—
148Dic79⋊C8C2314yes—
149#14579086C2314yes—
150#14579086C2314yes—
151#14579084C2314yes—
152#14579084C2314yes—
153#14579084C2314yes—
154#14579084C2314yes—
155C22⋊(C79⋊C8)C2314yes—
156(C2×D79)⋊C8C2314yes—
157#14579071C2314yes—
158C23×C4×C79—21no—
159C23×C4×C79C2311yescharacteristic
160C2×M16×C79—24no—
161C2×M16×C79C2314yes—
162C22×C8×C79C2311yescharacteristic
163C22×C8×C79C2311yescharacteristic
164#117×C79—22no—
165#117×C79C2314yes—
166C2×C4⋊C4×C79—22no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79C2311yescharacteristic
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2314yes—
173C2×C22⋊C4×C79—21no—
174C2×C42×C79—21no—
175#107×C79C2314yes—
176#107×C79C2314yes—
177#106×C79C2314yes—
178#106×C79C2314yes—
179C23×D79C2×D411yescharacteristic
180C2×Dic158—24no—
181C2×Dic158—21no—
182C2×Dic158—21no—
183C2×Dic158—22no—
184C2×Dic158—22no—
185C2×Dic158—22no—
186C2×Dic158—22no—
187C2×Dic158—44no—
188C2×Dic158C2412yes—
189C2×Dic158C2412yes—
190C2×C22⋊D79—42no—
191C2×C22⋊D79C2×D414yes—
192C22×Dic79—21no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79C2×D411yescharacteristic
197C22×Dic79C2×D411yescharacteristic
198C22×Dic79C2×D411yescharacteristic
199C2×C4×D79—22no—
200C2×C4×D79—22no—
201C2×C4×D79C2×D412yes—
202C2×C4×D79C2412yes—
203Dic316—28no—
204C2×C79⋊C8—22no—
205C2×C79⋊C8—22no—
206C2×C79⋊C8C2412yes—
207C2×C79⋊C8C2412yes—
208C8×D79—28no—
209C4⋊Dic79—24no—
210C4⋊Dic79—24no—
211C4⋊Dic79—24no—
212C4⋊Dic79—21no—
213C4⋊Dic79—21no—
214C4⋊Dic79C2412yes—
215C4⋊Dic79C2412yes—
216Dic79⋊C4—24no—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4C2×D414yes—
223C22⋊Dic79—24no—
224C22⋊Dic79—24no—
225C22⋊Dic79C2×D414yes—
226(C2×D79)⋊C4—24no—
227(C2×D79)⋊C4—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4C2×D414yes—
231C4×Dic79—24no—
232C4×Dic79—24no—
233C4×Dic79—24no—
234C4×Dic79—24no—
235C4×Dic79C2×D412yes—
236C4×Dic79C2412yes—
237C24×C79C2×D411yescharacteristic
238C22×C4×C79—22no—
239C22×C4×C79—22no—
240C22×C4×C79—21no—
241C22×C4×C79—21no—
242C22×C4×C79—21no—
243C22×C4×C79—21no—
244C22×C4×C79—24no—
245C22×C4×C79—44no—
246C22×C4×C79C2×D411yescharacteristic
247C22×C4×C79C2×D412yes—
248C22×C4×C79C2412yes—
249C22×C4×C79C2411yescharacteristic
250M16×C79—28no—
251C2×C8×C79—22no—
252C2×C8×C79#4114yes—
253C2×C8×C79C2412yes—
254C2×C8×C79C2412yes—
255C4⋊C4×C79—21no—
256C4⋊C4×C79—21no—
257C4⋊C4×C79—24no—
258C4⋊C4×C79—21no—
259C4⋊C4×C79—21no—
260C4⋊C4×C79C2412yes—
261C4⋊C4×C79C2412yes—
262C4⋊C4×C79C2412yes—
263C4⋊C4×C79C2412yes—
264C22⋊C4×C79—24no—
265C42×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—
275C2×C4×C79—22no—
276C2×C4×C79—24no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—48no—
284C2×C4×C79—42no—
285C2×C4×C79—42no—
286C2×C4×C79—42no—
287C2×C4×C79—42no—
288C2×C4×C79C22×D412yes—
289C2×C4×C79C22×D411yescharacteristic
290C2×C4×C79C2×#4112yes—
291C2×C4×C792−1+412yes—
292C2×C4×C79C2511yescharacteristic
293C22⋊D79—44no—
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—42no—
302C2×Dic79—42no—
303C2×Dic79—42no—
304C2×Dic79—42no—
305C2×Dic79C22×D412yes—
306C2×Dic79C22×D412yes—
307C2×Dic79C22×D412yes—
308C4×D79—24no—
309C4×D79—22no—
310C4×D79—22no—
311Dic158—22no—
312Dic158—22no—
313Dic158—22no—
314Dic158—22no—
315Dic158—48no—
316Dic158—42no—
317Dic158—42no—
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×#3349—791nomaximal, Sylow
350C2×C79—42no—
351C2×C79#334914yescomplemented
352C2×C79C2×#54711yescharacteristic
353C2×C79C2×#57511yescharacteristic
354C2×C79C2×#57811yescharacteristic
355D79—42no—
356C2×#556—791no—
357C2×#552—791no—
358#3349—7916no—
359C2×#501—791no—
360C2×#484—791no—
361C2×#485—791no—
362C2×#485—791no—
363C2×#485—791no—
364C2×#479—791no—
365C2×#477—791no—
366C2×#470—791no—
367C2×#467—791no—
368C2×#441—791no—
369C2×#435—791no—
370C2×#428D7911yescharacteristic, complemented
371C2×#427—791no—
372C79C2×#334911yescharacteristic, complemented, Sylow
373C22×Q16—791no—
374C22×M16C2×D7911yescharacteristic
375C23×C8—791no—
376#556—798no—
377#556—1584no—
378#552—798no—
379#552—1584no—
380C2×C4⋊Q8—791no—
381C2×#126—1581no—
382C2×#126—1581no—
383C2×#126—1581no—
384C2×#125—791no—
385C2×#125—1581no—
386C2×#124—1581no—
387C2×#123—1581no—
388C2×C22⋊Q8—791no—
389C2×C22⋊Q8—791no—
390C2×C22⋊Q8—791no—
391C2×C22⋊Q8—791no—
392C2×C4×Q8—791no—
393C2×C4×Q8—791no—
394C2×C4×Q8—1581no—
395C2×C4×D4—791no—
396C2×#117—791no—
397C2×#117—791no—
398C2×#117—1581no—
399C2×#117C2×D7911yescharacteristic
400C22×C4⋊C4C2×D7911yescharacteristic
401#501—798no—
402#485—798no—
403#485—798no—
404#485—798no—
405#484—798no—
406#479—798no—
407#477—798no—
408#470—798no—
409#467—798no—
410#441—798no—
411#435—798no—
412#428C2×D7918yescomplemented
413#427—798no—
414C2×#107—791no—
415C2×#107—791no—
416C2×#107—791no—
417C2×#107C2×D7911yescharacteristic
418C2×#107C2×D7911yescharacteristic
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×#103—791no—
429C2×#103—791no—
430C2×C22⋊C8—791no—
431C2×C22⋊C8—791no—
432C2×#97—791no—
433C22×Q8—791no—
434C22×Q8—791no—
435C22×Q8—1581no—
436C22×D4—791no—
437C23×C4—21no—
438C23×C4—791no—
439C23×C4C22×D7911yescharacteristic
440C2×Q16—794no—
441C2×Q16—1584no—
442C2×M16—24no—
443C2×M16C22×D7914yes—
444C22×C8—791no—
445C22×C8—791no—
446C22×C8—794no—
447C22×C8—1584no—
448C22×C8C22×D7911yescharacteristic
449C22×C8C22×D7911yescharacteristic
450C4⋊Q8—794no—
451C4⋊Q8—1582no—
452#126—1588no—
453#126—1588no—
454#126—1588no—
455#125—794no—
456#125—1582no—
457#125—1588no—
458#124—1588no—
459#123—1588no—
460C22⋊Q8—794no—
461C22⋊Q8—794no—
462C22⋊Q8—794no—
463C22⋊Q8—794no—
464C22⋊Q8—1582no—
465C22⋊Q8—1582no—
466C22⋊Q8—1582no—
467C22⋊Q8—1582no—
468C4×Q8—794no—
469C4×Q8—794no—
470C4×Q8—1588no—
471C4×Q8—1582no—
472C4×Q8—1582no—
473C4×D4—794no—
474C4×D4—794no—
475#117—22no—
476#117—794no—
477#117—794no—
478#117—1588no—
479#117—1582no—
480#117—1582no—
481#117C22×D7914yes—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—791no—
485C2×C4⋊C4—791no—
486C2×C4⋊C4—791no—
487C2×C4⋊C4—1581no—
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⋊C4C22×D7911yescharacteristic
497C2×C4⋊C4C22×D7911yescharacteristic
498C2×C4⋊C4C22×D7914yes—
499C2×C4⋊C4C22×D7911yescharacteristic
500C2×C4⋊C4C22×D7911yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—791no—
503C2×C22⋊C4—791no—
504C2×C22⋊C4—1581no—
505C2×C22⋊C4—1581no—
506C2×C22⋊C4—1581no—
507C2×C22⋊C4—1581no—
508C2×C22⋊C4—1581no—
509C2×C22⋊C4—1581no—
510C2×C42—21no—
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#107C22×D7914yes—
520#107C22×D7914yes—
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#103—794no—
531#103—794no—
532C22⋊C8—794no—
533C22⋊C8—794no—
534#97—794no—
535C24—791no—
536C24D4×D7911yescharacteristic
537C2×Q8—3164no—
538C2×Q8—792no—
539C2×Q8—792no—
540C2×Q8—1584no—
541C2×Q8—1582no—
542C2×Q8—1582no—
543C2×Q8—1582no—
544C2×Q8—1582no—
545C2×Q8—1581no—
546C2×Q8—1581no—
547C2×D4—3162no—
548C2×D4—794no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—44no—
557C22×C4—791no—
558C22×C4—791no—
559C22×C4—791no—
560C22×C4—792no—
561C22×C4—792no—
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—
573M16—28no—
574C2×C8—22no—
575C2×C8—792no—
576C2×C8—792no—
577C2×C8—1582no—
578C2×C8—1582no—
579C2×C8—1588no—
580C2×C8#1192962414yes—
581C2×C8C23×D7912yes—
582C2×C8C23×D7912yes—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—794no—
589C4⋊C4—792no—
590C4⋊C4—792no—
591C4⋊C4—1584no—
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—1581no—
601C4⋊C4—1581no—
602C4⋊C4C23×D7912yes—
603C4⋊C4C23×D7912yes—
604C4⋊C4C23×D7912yes—
605C4⋊C4C23×D7912yes—
606C22⋊C4—24no—
607C22⋊C4—794no—
608C22⋊C4—794no—
609C22⋊C4—1584no—
610C22⋊C4—1584no—
611C22⋊C4—1584no—
612C22⋊C4—1584no—
613C22⋊C4—1584no—
614C22⋊C4—1584no—
615C42—24no—
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—3168no—
632Q8—3162no—
633Q8—3162no—
634Q8—1582no—
635Q8—1582no—
636Q8—1582no—
637Q8—1582no—
638D4—3164no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—48no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
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×#1192962412yes—
672C2×C4#1457920912yes—
673C2×C4C24×D7911yescharacteristic
674C8—22no—
675C8—1582no—
676C8—1582no—
677C8C2×#1192962414yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—44no—
682C22—3164no—
683C22—1582no—
684C22—1582no—
685C22—1582no—
686C22#1909921412yes—
687C22#1909935912yes—
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#1909921412yes—
703C4C22×#1192962411yescharacteristic
704C4C2×#1457920911yescharacteristic
705C2—42no—
706C2—3162no—
707C2#2377593114yesdirect product factor
708C2C2×#1909921411yescharacteristic
709C2C2×#1909935911yescharacteristic
710C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#428×C79C2
socleC23×C79C22×D4
prime radicalC22×C22⋊D79D4
hypercenterC2×#428D79
hypocenterC79C2×#3349
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
3. #23775931C2direct (N × H)
4. C2×#19098971C2semidirect
5. C2×#19098898C2semidirect
6. C2×#19098907C2semidirect
7. C2×#19098906C2semidirect
8. C2×#19098904C2semidirect
9. C2×#19098873C2semidirect
10. C2×#19098857C2semidirect
11. C2×#19098821C2semidirect
12. C2×#19098805C2semidirect
13. C2×#19098669C2semidirect
15. C2×#19098598C2semidirect
16. C2×#428×C79C2semidirect
42. #19098971C22semidirect
43. #19098907C22semidirect
44. #19098906C22semidirect
45. #19098904C22semidirect
46. #19098898C22semidirect
47. #19098873C22semidirect
48. #19098857C22semidirect
49. #19098821C22semidirect
50. #19098805C22semidirect
51. #19098669C22semidirect
53. #19098598C22semidirect
72. #428×C79C22semidirect
351. C2×C79#3349semidirect
370. C2×#428D79semidirect
372. C79C2×#3349semidirect
412. #428C2×D79semidirect
707. C2#23775931direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992812
C2×#190992482
#237759312
C2×#190989712
C2×#190988982
C2×#190989072
C2×#190989062
C2×#190989042
C2×#190988732
C2×#190988572
C2×#190988212
C2×#190988052
C2×#190986692
C2×#190986322
C2×#190985982
C2×#428×C792
C2×#334979