Finite Group Databasebeta

← C2×#23777512 #35196554

Subgroups — C2×#23777512 #35196554

Order 20224.

7226 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
1#23777512C2132yesmaximal, direct product factor
2C2×#19099298C213yesmaximal, complemented
3C2×#19099279C213yesmaximal, complemented
4C2×#19099266C213yesmaximal, complemented
5C2×#19099251C213yesmaximal, complemented
6C2×#19099235C211yesmaximal, characteristic, complemented
7C2×#19099225C211yesmaximal, characteristic, complemented
8C2×#19099225C211yesmaximal, characteristic, complemented
9C2×#19099187C213yesmaximal, complemented
10C2×#19099169C213yesmaximal, complemented
11C2×#19099100C213yesmaximal, complemented
12C2×#19099098C213yesmaximal, complemented
13C2×#19099045C211yesmaximal, characteristic, complemented
14C2×#19099039C211yesmaximal, characteristic, complemented
15C2×C4×#11929625C211yesmaximal, characteristic, complemented
16C2×#557×C79C211yesmaximal, characteristic, complemented
17C22×#11929625C2211yescharacteristic
18C22×#11929625C2211yescharacteristic
19C22×Q8×D79C2211yescharacteristic
20#19099298C22148yescomplemented
21#19099279C22148yescomplemented
22#19099266C22148yescomplemented
23#19099251C22148yescomplemented
24#19099235C22116yescomplemented
25#19099225C22116yescomplemented
26#19099225C22116yescomplemented
27#19099187C22148yescomplemented
28#19099169C22148yescomplemented
29C2×#14579158C2213yes—
30#19099100C22148yescomplemented
31#19099098C22148yescomplemented
32C2×#14579156C2216yes—
33C2×#14579156C2213yes—
34C2×#14579156C2211yescharacteristic
35C2×#14579152C2213yes—
36C2×#14579150C2216yes—
37C2×#14579150C2213yes—
38C2×#14579149C2213yes—
39C2×#14579149C2213yes—
40C2×#14579146C2216yes—
41C2×#14579146C2216yes—
42C2×#14579146C2213yes—
43C2×#14579146C2213yes—
44C2×#14579141C2213yes—
45C2×#14579141C2213yes—
46C2×#14579137C2213yes—
47C2×#14579136C2213yes—
48C2×#14579136C2213yes—
49C2×#14579136C2213yes—
50C2×#14579136C2213yes—
51C2×#14579136C2213yes—
52C2×#14579136C2216yes—
53#19099045C22116yescomplemented
54#19099039C22116yescomplemented
55C4×#11929625C22116yescomplemented
56C2×Q8×Dic79C2211yescharacteristic
57C2×C4×Dic158C2213yes—
58C2×#14579126C2213yes—
59C2×C4×D316C2213yes—
60C2×C4×D316C2213yes—
61C2×C4×D316C2213yes—
62C2×C4×D316C2213yes—
63C2×C4×D316C2213yes—
64C2×#14579123C2213yes—
65C2×#14579123C2213yes—
66C2×#14579123C2216yes—
67C2×#14579119C2213yes—
68C2×#14579119C2213yes—
69C2×#14579119C2216yes—
70C2×#14579118C2213yes—
71C2×#14579118C2213yes—
72C2×C4⋊C4×D79C2213yes—
73C2×C42×D79C2213yes—
74#557×C79C22116yescomplemented
75C2×C4⋊Q8×C79C2213yes—
76C2×#125×C79C2213yes—
77C2×#125×C79C2213yes—
78C2×C4×Q8×C79C2211yescharacteristic
79C2×C4×Q8×C79C2211yescharacteristic
80C2×C4×Q8×C79C2211yescharacteristic
81C2×C4×Q8×C79C2213yes—
82C2×#11929625—28no—
83C2×#11929625—28no—
84C2×#11929625C2318yes—
85C2×#11929625C2318yes—
86C22×Dic158C2313yes—
87C2×Q8×D79—28no—
88C2×Q8×D79C2318yes—
89C22×D316C2313yes—
90C22×D316C2313yes—
91C22×D316C2316yes—
92C22×D316C2313yes—
93C22×D316C2313yes—
94C22×D316C2313yes—
95C22×C4×D79C2313yes—
96C22×C4×D79C2313yes—
97C22×C4×D79C2313yes—
98C22×C4×D79C2313yes—
99C22×C4×D79C2313yes—
100C22×C4×D79C2316yes—
101#14579158C23124yes—
102#14579156C23148yes—
103#14579156C23124yes—
104#14579156C2318yes—
105#14579152C23124yes—
106#14579150C23148yes—
107#14579150C23124yes—
108#14579149C23124yes—
109#14579149C23124yes—
110#14579146C23148yes—
111#14579146C23148yes—
112#14579146C23124yes—
113#14579146C23124yes—
114#14579141C23124yes—
115#14579141C23124yes—
116#14579137C23124yes—
117#14579136C23124yes—
118#14579136C23124yes—
119#14579136C23124yes—
120#14579136C23148yes—
121#14579136C23124yes—
122#14579136C23124yes—
123Q8×Dic79C2318yes—
124C4×Dic158C23124yes—
125#14579126C23124yes—
126C4×D316C23124yes—
127C4×D316C23124yes—
128C4×D316C23124yes—
129C4×D316C23124yes—
130C4×D316C23124yes—
131#14579123C23124yes—
132#14579123C23124yes—
133#14579123C23148yes—
134#14579119C23124yes—
135#14579119C23148yes—
136#14579119C23124yes—
137#14579118C23124yes—
138#14579118C23124yes—
139C2×C4⋊Dic79C2313yes—
140C2×C4⋊Dic79C2313yes—
141C2×C4⋊Dic79C2311yescharacteristic
142C2×C4⋊Dic79C2313yes—
143C2×Dic79⋊C4C2313yes—
144C2×Dic79⋊C4C2311yescharacteristic
145C2×Dic79⋊C4C2313yes—
146C2×Dic79⋊C4C2313yes—
147C4⋊C4×D79C23124yes—
148C2×(C2×D79)⋊C4C2311yescharacteristic
149C2×(C2×D79)⋊C4C2313yes—
150C2×(C2×D79)⋊C4C2313yes—
151C2×(C2×D79)⋊C4C2313yes—
152C2×(C2×D79)⋊C4C2313yes—
153C2×(C2×D79)⋊C4C2316yes—
154C2×(C2×D79)⋊C4C2316yes—
155C2×(C2×D79)⋊C4C2313yes—
156C2×(C2×D79)⋊C4C2316yes—
157C2×(C2×D79)⋊C4C2311yescharacteristic
158C2×(C2×D79)⋊C4C2311yescharacteristic
159C2×(C2×D79)⋊C4C2313yes—
160C2×(C2×D79)⋊C4C2313yes—
161C2×C4×Dic79C2311yescharacteristic
162C2×C4×Dic79C2313yes—
163C2×C4×Dic79C2313yes—
164C2×C4×Dic79C2316yes—
165C42×D79C23124yes—
166C22×Q8×C79C2313yes—
167C22×Q8×C79C2311yescharacteristic
168C4⋊Q8×C79C23124yes—
169#125×C79C23124yes—
170#125×C79C23124yes—
171C4×Q8×C79C2318yes—
172C4×Q8×C79C2318yes—
173C4×Q8×C79C2318yes—
174C4×Q8×C79C23124yes—
175C2×C4⋊C4×C79C2311yescharacteristic
176C2×C4⋊C4×C79C2313yes—
177C2×C4⋊C4×C79C2313yes—
178C2×C4⋊C4×C79C2313yes—
179C2×C4⋊C4×C79C2313yes—
180C2×C4⋊C4×C79C2313yes—
181C2×C4⋊C4×C79C2316yes—
182C2×C42×C79C2313yes—
183C2×C42×C79C2313yes—
184C2×C42×C79C2313yes—
185C23×D79C2411yescharacteristic
186C23×D79C2413yes—
187C23×D79C2413yes—
188#11929625—232no—
189#11929625—232no—
190C2×Dic158—212no—
191C2×Dic158C24112yes—
192Q8×D79—232no—
193C2×D316—212no—
194C2×D316—212no—
195C2×D316—46no—
196C2×D316—46no—
197C2×D316—46no—
198C2×D316—412no—
199C2×D316C24112yes—
200C2×D316C24112yes—
201C2×D316C24124yes—
202C2×D316C24112yes—
203C2×D316C24112yes—
204C2×D316C24112yes—
205C22×Dic79C2413yes—
206C22×Dic79C2411yescharacteristic
207C22×Dic79C2413yes—
208C22×Dic79C2411yescharacteristic
209C22×Dic79C2411yescharacteristic
210C2×C4×D79—212no—
211C2×C4×D79—212no—
212C2×C4×D79—212no—
213C2×C4×D79—46no—
214C2×C4×D79—412no—
215C2×C4×D79—46no—
216C2×C4×D79C24112yes—
217C2×C4×D79C24112yes—
218C2×C4×D79C24112yes—
219C2×C4×D79C24112yes—
220C2×C4×D79C24112yes—
221C2×C4×D79C24124yes—
222C4⋊Dic79C24112yes—
223C4⋊Dic79C24112yes—
224C4⋊Dic79C2414yes—
225C4⋊Dic79C24112yes—
226Dic79⋊C4C24112yes—
227Dic79⋊C4C2414yes—
228Dic79⋊C4C24112yes—
229Dic79⋊C4C24112yes—
230(C2×D79)⋊C4C2414yes—
231(C2×D79)⋊C4C24112yes—
232(C2×D79)⋊C4C24112yes—
233(C2×D79)⋊C4C24112yes—
234(C2×D79)⋊C4C24112yes—
235(C2×D79)⋊C4C24124yes—
236(C2×D79)⋊C4C24124yes—
237(C2×D79)⋊C4C24112yes—
238(C2×D79)⋊C4C24124yes—
239(C2×D79)⋊C4C2414yes—
240(C2×D79)⋊C4C2414yes—
241(C2×D79)⋊C4C24112yes—
242(C2×D79)⋊C4C24112yes—
243C4×Dic79C2414yes—
244C4×Dic79C24112yes—
245C4×Dic79C24112yes—
246C4×Dic79C24124yes—
247C2×Q8×C79—46no—
248C2×Q8×C79#4118yes—
249C2×Q8×C79C24112yes—
250C2×Q8×C79C2414yes—
251C22×C4×C79C2411yescharacteristic
252C22×C4×C79C2411yescharacteristic
253C22×C4×C79C2411yescharacteristic
254C22×C4×C79C2413yes—
255C22×C4×C79C2413yes—
256C22×C4×C79C2413yes—
257C22×C4×C79C2413yes—
258C4⋊C4×C79C2414yes—
259C4⋊C4×C79C24112yes—
260C4⋊C4×C79C24112yes—
261C4⋊C4×C79C24112yes—
262C4⋊C4×C79C24112yes—
263C4⋊C4×C79C24112yes—
264C4⋊C4×C79C24124yes—
265C42×C79C24112yes—
266C42×C79C24112yes—
267C42×C79C24112yes—
268C23×C79C2511yescharacteristic
269C22×D79—22no—
270C22×D79—26no—
271C22×D79—26no—
272C22×D79—26no—
273C22×D79—26no—
274C22×D79—26no—
275C22×D79—22no—
276C22×D79—26no—
277C22×D79—22no—
278C22×D79C2512yes—
279C22×D79C2516yes—
280C22×D79C2516yes—
281Q8×C79—412no—
282Q8×C79C2×#41116yes—
283C2×C4×C79—22no—
284C2×C4×C79—26no—
285C2×C4×C79—26no—
286C2×C4×C79—22no—
287C2×C4×C79—26no—
288C2×C4×C79—22no—
289C2×C4×C79C2×#41112yes—
290C2×C4×C79C2516yes—
291C2×C4×C79C2516yes—
292C2×C4×C79C2512yes—
293C2×C4×C79C2512yes—
294C2×C4×C79C2516yes—
295C2×C4×C79C2512yes—
296C2×C4×C79C2516yes—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—26no—
300C2×Dic79—22no—
301C2×Dic79—26no—
302C2×Dic79C2512yes—
303C2×Dic79C2516yes—
304C2×Dic79C2512yes—
305C2×Dic79C2516yes—
306C2×Dic79C2512yes—
307D316—224no—
308D316—224no—
309D316—412no—
310D316—424no—
311D316—412no—
312D316—412no—
313C4×D79—224no—
314C4×D79—224no—
315C4×D79—224no—
316C4×D79—412no—
317C4×D79—412no—
318C4×D79—424no—
319Dic158—224no—
320C22×C79C22×#4112yes—
321C22×C79#58512yes—
322C22×C79#58512yes—
323C22×C79C2611yescharacteristic
324C2×D79—22no—
325C2×D79—26no—
326C2×D79—26no—
327C2×D79—26no—
328C2×D79—26no—
329C2×D79—26no—
330C2×D79—22no—
331C2×D79—26no—
332C2×D79—22no—
333C2×D79—44no—
334C2×D79—412no—
335C2×D79—412no—
336C4×C79—22no—
337C4×C79—26no—
338C4×C79—26no—
339C4×C79—22no—
340C4×C79—26no—
341C4×C79—22no—
342C4×C79C22×#41112yes—
343Dic79—26no—
344Dic79—22no—
345Dic79—22no—
346Dic79—22no—
347Dic79—26no—
348C2×#3524—791nomaximal, Sylow
349C2×C79#352414yescomplemented
350C2×C79C23×#4111yescharacteristic
351C2×C79C2×#58511yescharacteristic
352C2×C79C2×#58511yescharacteristic
353D79—42no—
354D79—46no—
355D79—46no—
356#3524—7932no—
357C2×#559—793no—
358C2×#557D7911yescharacteristic, complemented
359C2×#555—793no—
360C2×#553—793no—
361C2×#552—793no—
362C2×#550—791no—
363C2×#548—791no—
364C2×#548—791no—
365C2×#542—793no—
366C2×#540—793no—
367C2×#529—793no—
368C2×#529—793no—
369C2×#520—791no—
370C2×#519—791no—
371C2×C4×#41—791no—
372C79C2×#352411yescharacteristic, complemented, Sylow
373C22×#41—791no—
374C22×#41—791no—
375C23×Q8—791no—
376#559—7948no—
377#557C2×D79116yescomplemented
378#555—7948no—
379#553—7948no—
380#552—7948no—
381#550—7916no—
382#548—7916no—
383#548—7916no—
384#542—7948no—
385#540—7948no—
386C2×C4⋊Q8C2×D7913yes—
387C2×#127—793no—
388#529—7948no—
389#529—7948no—
390C2×#126—791no—
391C2×#126—793no—
392C2×#126—796no—
393C2×#125—793no—
394C2×#125C2×D7913yes—
395C2×#125C2×D7913yes—
396C2×#124—793no—
397C2×#124—796no—
398C2×#124—793no—
399C2×#124—793no—
400C2×#123—796no—
401C2×#123—793no—
402C2×#123—793no—
403C2×#123—796no—
404C2×C22⋊Q8—793no—
405C2×C22⋊Q8—793no—
406C2×C22⋊Q8—793no—
407C2×#121—793no—
408C2×#121—793no—
409C2×#121—793no—
410C2×#121—793no—
411C2×#121—796no—
412C2×#121—793no—
413#520—7916no—
414#519—7916no—
415C4×#41—7916no—
416C2×C4×Q8—791no—
417C2×C4×Q8—793no—
418C2×C4×Q8—793no—
419C2×C4×Q8C2×D7911yescharacteristic
420C2×C4×Q8C2×D7911yescharacteristic
421C2×C4×Q8C2×D7911yescharacteristic
422C2×C4×Q8C2×D7913yes—
423C2×C4×D4—793no—
424C2×C4×D4—793no—
425C2×C4×D4—796no—
426C2×C4×D4—793no—
427C2×C4×D4—793no—
428C2×C4×D4—793no—
429C2×C4×D4—793no—
430C2×C4×D4—793no—
431C2×#117—793no—
432C2×#117—793no—
433C2×#117—796no—
434C2×#117—793no—
435C2×#117—793no—
436C22×C4⋊C4—793no—
437C22×C42—793no—
438C2×#41—798no—
439C2×#41—798no—
440C2×#41—1588no—
441C2×#41—1588no—
442C22×Q8—798no—
443C22×Q8—793no—
444C22×Q8—1588no—
445C22×Q8C22×D7913yes—
446C22×Q8C22×D7911yescharacteristic
447C22×D4—793no—
448C22×D4—793no—
449C22×D4—796no—
450C22×D4—793no—
451C22×D4—793no—
452C22×D4—793no—
453C23×C4—796no—
454C23×C4—793no—
455C23×C4—793no—
456C23×C4—793no—
457C23×C4—793no—
458C23×C4—793no—
459C4⋊Q8C22×D79124yes—
460#127—7924no—
461#126—798no—
462#126—7924no—
463#126—7948no—
464#125—7924no—
465#125C22×D79124yes—
466#125C22×D79124yes—
467#124—7924no—
468#124—7948no—
469#124—7924no—
470#124—7924no—
471#123—7948no—
472#123—7924no—
473#123—7924no—
474#123—7948no—
475C22⋊Q8—7924no—
476C22⋊Q8—7924no—
477C22⋊Q8—7924no—
478#121—7924no—
479#121—7924no—
480#121—7924no—
481#121—7924no—
482#121—7948no—
483#121—7924no—
484C4×Q8—798no—
485C4×Q8—7924no—
486C4×Q8—7924no—
487C4×Q8C22×D7918yes—
488C4×Q8C22×D7918yes—
489C4×Q8C22×D7918yes—
490C4×Q8C22×D79124yes—
491C4×D4—7924no—
492C4×D4—7924no—
493C4×D4—7948no—
494C4×D4—7924no—
495C4×D4—7924no—
496C4×D4—7924no—
497C4×D4—7924no—
498C4×D4—7924no—
499#117—7924no—
500#117—7924no—
501#117—7948no—
502#117—7924no—
503#117—7924no—
504C2×C4⋊C4—793no—
505C2×C4⋊C4—793no—
506C2×C4⋊C4—791no—
507C2×C4⋊C4—793no—
508C2×C4⋊C4—793no—
509C2×C4⋊C4—793no—
510C2×C4⋊C4—791no—
511C2×C4⋊C4—793no—
512C2×C4⋊C4—7924no—
513C2×C4⋊C4C22×D7913yes—
514C2×C4⋊C4C22×D7913yes—
515C2×C4⋊C4C22×D7913yes—
516C2×C4⋊C4C22×D7916yes—
517C2×C4⋊C4C22×D7913yes—
518C2×C4⋊C4C22×D7911yescharacteristic
519C2×C4⋊C4C22×D7913yes—
520C2×C22⋊C4—791no—
521C2×C22⋊C4—793no—
522C2×C22⋊C4—793no—
523C2×C22⋊C4—793no—
524C2×C22⋊C4—796no—
525C2×C22⋊C4—793no—
526C2×C22⋊C4—796no—
527C2×C22⋊C4—791no—
528C2×C22⋊C4—793no—
529C2×C22⋊C4—791no—
530C2×C22⋊C4—793no—
531C2×C22⋊C4—796no—
532C2×C22⋊C4—793no—
533C2×C42—793no—
534C2×C42—793no—
535C2×C42—796no—
536C2×C42—791no—
537C2×C42—7924no—
538C2×C42C22×D7913yes—
539C2×C42C22×D7913yes—
540C2×C42C22×D7913yes—
541C24—793no—
542C24—793no—
543C24—791no—
544#41—15832no—
545#41—15832no—
546C2×Q8—46no—
547C2×Q8—7912no—
548C2×Q8—15832no—
549C2×Q8—15812no—
550C2×Q8#1192962518yes—
551C2×Q8C23×D79112yes—
552C2×Q8C23×D7914yes—
553C2×D4—3166no—
554C2×D4—31612no—
555C2×D4—3166no—
556C2×D4—3166no—
557C2×D4—7912no—
558C2×D4—7912no—
559C2×D4—7924no—
560C2×D4—7912no—
561C2×D4—7912no—
562C2×D4—7912no—
563C2×D4—15812no—
564C2×D4—15812no—
565C22×C4—3166no—
566C22×C4—3166no—
567C22×C4—31612no—
568C22×C4—7912no—
569C22×C4—7912no—
570C22×C4—7924no—
571C22×C4—791no—
572C22×C4—793no—
573C22×C4—791no—
574C22×C4—793no—
575C22×C4—791no—
576C22×C4—7912no—
577C22×C4—7912no—
578C22×C4—7912no—
579C22×C4—15812no—
580C22×C4—15812no—
581C22×C4—15812no—
582C22×C4C23×D7913yes—
583C22×C4C23×D7911yescharacteristic
584C22×C4C23×D7913yes—
585C22×C4C23×D7911yescharacteristic
586C22×C4C23×D7911yescharacteristic
587C22×C4C23×D7913yes—
588C22×C4C23×D7913yes—
589C4⋊C4—7912no—
590C4⋊C4—794no—
591C4⋊C4—7912no—
592C4⋊C4—7912no—
593C4⋊C4—7912no—
594C4⋊C4—7912no—
595C4⋊C4—794no—
596C4⋊C4—7912no—
597C4⋊C4C23×D79112yes—
598C4⋊C4C23×D79112yes—
599C4⋊C4C23×D79112yes—
600C4⋊C4C23×D79124yes—
601C4⋊C4C23×D79112yes—
602C4⋊C4C23×D7914yes—
603C4⋊C4C23×D79112yes—
604C22⋊C4—794no—
605C22⋊C4—7912no—
606C22⋊C4—7912no—
607C22⋊C4—7912no—
608C22⋊C4—7924no—
609C22⋊C4—7912no—
610C22⋊C4—7924no—
611C22⋊C4—794no—
612C22⋊C4—7912no—
613C22⋊C4—794no—
614C22⋊C4—7912no—
615C22⋊C4—7924no—
616C22⋊C4—7912no—
617C42—794no—
618C42—7912no—
619C42—7912no—
620C42—7924no—
621C42C23×D79112yes—
622C42C23×D79112yes—
623C42C23×D79112yes—
624C23—792no—
625C23—796no—
626C23—796no—
627C23—1586no—
628C23—1586no—
629C23—1582no—
630C23—1586no—
631C23—1586no—
632C23—1582no—
633C23—1582no—
634C23—1586no—
635C23—1586no—
636C23C24×D7911yescharacteristic
637Q8—412no—
638Q8—15824no—
639Q8C2×#11929625116yes—
640D4—31612no—
641D4—31624no—
642D4—31612no—
643D4—31612no—
644D4—15824no—
645D4—15824no—
646C2×C4—26no—
647C2×C4—26no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—26no—
651C2×C4—22no—
652C2×C4—31612no—
653C2×C4—31612no—
654C2×C4—31624no—
655C2×C4—792no—
656C2×C4—792no—
657C2×C4—796no—
658C2×C4—796no—
659C2×C4—792no—
660C2×C4—1582no—
661C2×C4—1586no—
662C2×C4—1582no—
663C2×C4—1582no—
664C2×C4—1586no—
665C2×C4—15824no—
666C2×C4—15824no—
667C2×C4—15824no—
668C2×C4C2×#11929625112yes—
669C2×C4C24×D7916yes—
670C2×C4C24×D7912yes—
671C2×C4C24×D7916yes—
672C2×C4C24×D7912yes—
673C2×C4C24×D7912yes—
674C2×C4C24×D7916yes—
675C2×C4C24×D7916yes—
676C22—31612no—
677C22—31612no—
678C22—3164no—
679C22—1582no—
680C22—1586no—
681C22—1586no—
682C22—1586no—
683C22—1582no—
684C22—1586no—
685C22—1586no—
686C22—1586no—
687C22—1582no—
688C22C22×#1192962512yes—
689C22#1909939912yes—
690C22#1909940012yes—
691C22C25×D7911yescharacteristic
692C4—26no—
693C4—26no—
694C4—22no—
695C4—22no—
696C4—26no—
697C4—22no—
698C4—1582no—
699C4—1582no—
700C4—1586no—
701C4—1582no—
702C4—1586no—
703C4C22×#11929625112yes—
704C2—3162no—
705C2—3166no—
706C2—3166no—
707C2#2377751214yesdirect product factor
708C2C23×#1192962511yescharacteristic
709C2C2×#1909939911yescharacteristic
710C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#557×C79C2
socleC23×C79C25
hypercenterC2×#557D79
hypocenterC79C2×#3524
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #23777512C2direct (N × H)
2. C2×#19099298C2semidirect
3. C2×#19099279C2semidirect
4. C2×#19099266C2semidirect
5. C2×#19099251C2semidirect
6. C2×#19099235C2semidirect
7. C2×#19099225C2semidirect
8. C2×#19099225C2semidirect
9. C2×#19099187C2semidirect
10. C2×#19099169C2semidirect
11. C2×#19099100C2semidirect
12. C2×#19099098C2semidirect
13. C2×#19099045C2semidirect
14. C2×#19099039C2semidirect
15. C2×C4×#11929625C2semidirect
16. C2×#557×C79C2semidirect
20. #19099298C22semidirect
21. #19099279C22semidirect
22. #19099266C22semidirect
23. #19099251C22semidirect
24. #19099235C22semidirect
25. #19099225C22semidirect
26. #19099225C22semidirect
27. #19099187C22semidirect
28. #19099169C22semidirect
30. #19099100C22semidirect
31. #19099098C22semidirect
53. #19099045C22semidirect
54. #19099039C22semidirect
55. C4×#11929625C22semidirect
74. #557×C79C22semidirect
349. C2×C79#3524semidirect
358. C2×#557D79semidirect
372. C79C2×#3524semidirect
377. #557C2×D79semidirect
707. C2#23777512direct (N × H)

Maximal subgroups

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

subgroupindex
#237775122
C2×#190992982
C2×#190992792
C2×#190992662
C2×#190992512
C2×#190992352
C2×#190992252
C2×#190991872
C2×#190991692
C2×#190991002
C2×#190990982
C2×#190990452
C2×#190990392
C2×C4×#119296252
C2×#557×C792
C2×#352479