Finite Group Databasebeta

← C2×#23777510 #35196556

Subgroups — C2×#23777510 #35196556

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#23777510C2132yesmaximal, direct product factor
2C2×#19099295C213yesmaximal, complemented
3C2×#19099292C211yesmaximal, characteristic, complemented
4C2×#19099278C213yesmaximal, complemented
5C2×#19099260C213yesmaximal, complemented
6C2×#19099247C213yesmaximal, complemented
7C2×#19099232C211yesmaximal, characteristic, complemented
8C2×#19099224C211yesmaximal, characteristic, complemented
9C2×#19099182C213yesmaximal, complemented
10C2×#19099166C213yesmaximal, complemented
11C2×#19099099C213yesmaximal, complemented
12C2×#19099093C213yesmaximal, complemented
13C2×#19099045C211yesmaximal, characteristic, complemented
14C2×#19099041C211yesmaximal, characteristic, complemented
15C2×#41×Dic79C211yesmaximal, characteristic, complemented
16C2×#548×C79C211yesmaximal, characteristic, complemented
17C22×#11929625C2211yescharacteristic
18#19099295C22148yescomplemented
19#19099292C22116yescomplemented
20#19099278C22148yescomplemented
21#19099260C22148yescomplemented
22#19099247C22148yescomplemented
23#19099232C22116yescomplemented
24#19099224C22116yescomplemented
25#19099182C22148yescomplemented
26#19099166C22148yescomplemented
27C2×#14579161C2213yes—
28C2×#14579157C2213yes—
29#19099099C22148yescomplemented
30#19099093C22148yescomplemented
31C2×#14579156C2213yes—
32C2×#14579154C2216yes—
33C2×#14579154C2211yescharacteristic
34C2×#14579152C2213yes—
35C2×#14579152C2213yes—
36C2×#14579151C2213yes—
37C2×#14579150C2213yes—
38C2×#14579147C2216yes—
39C2×#14579147C2213yes—
40C2×#14579145C2216yes—
41C2×#14579145C2213yes—
42C2×#14579143C2216yes—
43C2×#14579142C2213yes—
44C2×#14579138C2213yes—
45C2×#14579137C2213yes—
46C2×#14579135C2213yes—
47C2×#14579135C2213yes—
48C2×#14579133C2213yes—
49C2×#14579132C2213yes—
50C2×#14579132C2216yes—
51#19099045C22116yescomplemented
52#19099041C22116yescomplemented
53#41×Dic79C22116yescomplemented
54C2×Q8×Dic79C2213yes—
55C2×Q8×Dic79C2211yescharacteristic
56C2×Q8×Dic79C2211yescharacteristic
57C2×Q8×Dic79C2211yescharacteristic
58C2×Q8×Dic79C2213yes—
59C2×C4×Dic158C2213yes—
60C2×C4×D316C2213yes—
61C2×D4×Dic79C2213yes—
62C2×D4×Dic79C2213yes—
63C2×#14579123C2213yes—
64C2×C4×C22⋊D79C2213yes—
65C2×C4×C22⋊D79C2213yes—
66C2×(C22⋊D79)⋊C4C2216yes—
67C2×#14579120C2213yes—
68C2×#14579120C2213yes—
69C2×#14579120C2213yes—
70C2×#14579119C2216yes—
71C2×#14579118C2213yes—
72C2×C4⋊C4×D79C2213yes—
73C22×C4×Dic79C2213yes—
74C22×#41×C79C2211yescharacteristic
75C23×Q8×C79C2211yescharacteristic
76#548×C79C22116yescomplemented
77C2×#124×C79C2213yes—
78C2×C22⋊Q8×C79C2213yes—
79C2×#121×C79C2213yes—
80C2×C4×Q8×C79C2211yescharacteristic
81C2×C4×D4×C79C2213yes—
82C2×#11929625—28no—
83C2×#11929625C2318yes—
84C22×Dic158C2313yes—
85C22×D316C2313yes—
86C22×C22⋊D79C2316yes—
87C22×C22⋊D79C2313yes—
88C22×C22⋊D79C2313yes—
89C23×Dic79C2313yes—
90C23×Dic79C2313yes—
91C22×C4×D79C2313yes—
92C22×C4×D79C2316yes—
93#14579161C23124yes—
94#14579157C23124yes—
95#14579156C23124yes—
96#14579154C23148yes—
97#14579154C2318yes—
98#14579152C23124yes—
99#14579152C23124yes—
100#14579151C23124yes—
101#14579150C23124yes—
102#14579147C23148yes—
103#14579147C23124yes—
104#14579145C23148yes—
105#14579145C23124yes—
106#14579143C23148yes—
107#14579142C23124yes—
108#14579138C23124yes—
109#14579137C23124yes—
110#14579135C23124yes—
111#14579135C23124yes—
112#14579133C23124yes—
113#14579132C23148yes—
114#14579132C23124yes—
115Q8×Dic79C23124yes—
116Q8×Dic79C2318yes—
117Q8×Dic79C2318yes—
118Q8×Dic79C23124yes—
119Q8×Dic79C2318yes—
120C4×Dic158C23124yes—
121C4×D316C23124yes—
122D4×Dic79C23124yes—
123D4×Dic79C23124yes—
124#14579123C23124yes—
125C4×C22⋊D79C23124yes—
126C4×C22⋊D79C23124yes—
127(C22⋊D79)⋊C4C23148yes—
128#14579120C23124yes—
129#14579120C23124yes—
130#14579120C23124yes—
131#14579119C23148yes—
132#14579118C23124yes—
133C2×C4⋊Dic79C2313yes—
134C2×C4⋊Dic79C2316yes—
135C2×C4⋊Dic79C2313yes—
136C2×C4⋊Dic79C2313yes—
137C2×C4⋊Dic79C2313yes—
138C2×C4⋊Dic79C2313yes—
139C2×C4⋊Dic79C2311yescharacteristic
140C2×Dic79⋊C4C2313yes—
141C2×Dic79⋊C4C2311yescharacteristic
142C2×Dic79⋊C4C2313yes—
143C2×Dic79⋊C4C2311yescharacteristic
144C2×Dic79⋊C4C2313yes—
145C2×Dic79⋊C4C2313yes—
146C4⋊C4×D79C23124yes—
147C2×C22⋊Dic79C2313yes—
148C2×C22⋊Dic79C2311yescharacteristic
149C2×C22⋊Dic79C2316yes—
150C2×C22⋊Dic79C2311yescharacteristic
151C2×C22⋊Dic79C2313yes—
152C2×(C2×D79)⋊C4C2313yes—
153C2×(C2×D79)⋊C4C2313yes—
154C2×(C2×D79)⋊C4C2313yes—
155C2×(C2×D79)⋊C4C2316yes—
156C2×(C2×D79)⋊C4C2313yes—
157C2×C4×Dic79C2311yescharacteristic
158C2×C4×Dic79C2313yes—
159C2×C4×Dic79C2313yes—
160C2×C4×Dic79C2313yes—
161C2×C4×Dic79C23124yes—
162C2×C4×Dic79C2316yes—
163C2×C4×Dic79C2313yes—
164C2×#41×C79—28no—
165C2×#41×C79C2318yes—
166C22×Q8×C79—28no—
167C22×Q8×C79C2318yes—
168C22×Q8×C79C2313yes—
169C22×Q8×C79C2311yescharacteristic
170C22×D4×C79C2313yes—
171C22×D4×C79C2313yes—
172C23×C4×C79C2313yes—
173C23×C4×C79C2313yes—
174#124×C79C23124yes—
175C22⋊Q8×C79C23124yes—
176#121×C79C23124yes—
177C4×Q8×C79C2318yes—
178C4×D4×C79C23124yes—
179C2×C4⋊C4×C79C2313yes—
180C2×C4⋊C4×C79C2313yes—
181C2×C22⋊C4×C79C2311yescharacteristic
182C2×C22⋊C4×C79C2313yes—
183C2×C22⋊C4×C79C2316yes—
184C2×C42×C79C2313yes—
185C23×D79C2413yes—
186#11929625—232no—
187C2×Dic158—46no—
188C2×Dic158C24112yes—
189C2×D316—212no—
190C2×D316C24112yes—
191C2×C22⋊D79—46no—
192C2×C22⋊D79—412no—
193C2×C22⋊D79—46no—
194C2×C22⋊D79C24124yes—
195C2×C22⋊D79C24112yes—
196C2×C22⋊D79C24112yes—
197C22×Dic79—46no—
198C22×Dic79—46no—
199C22×Dic79C2413yes—
200C22×Dic79C2413yes—
201C22×Dic79C2411yescharacteristic
202C22×Dic79C2411yescharacteristic
203C22×Dic79C2413yes—
204C22×Dic79C2411yescharacteristic
205C22×Dic79C2411yescharacteristic
206C22×Dic79C24112yes—
207C22×Dic79C24112yes—
208C2×C4×D79—212no—
209C2×C4×D79—412no—
210C2×C4×D79C24112yes—
211C2×C4×D79C24124yes—
212C4⋊Dic79C24112yes—
213C4⋊Dic79C24124yes—
214C4⋊Dic79C24112yes—
215C4⋊Dic79C24112yes—
216C4⋊Dic79C24112yes—
217C4⋊Dic79C24112yes—
218C4⋊Dic79C2414yes—
219Dic79⋊C4C24112yes—
220Dic79⋊C4C2414yes—
221Dic79⋊C4C24112yes—
222Dic79⋊C4C2414yes—
223Dic79⋊C4C24112yes—
224Dic79⋊C4C24112yes—
225C22⋊Dic79C24112yes—
226C22⋊Dic79C2414yes—
227C22⋊Dic79C24124yes—
228C22⋊Dic79C2414yes—
229C22⋊Dic79C24112yes—
230(C2×D79)⋊C4C24112yes—
231(C2×D79)⋊C4C24112yes—
232(C2×D79)⋊C4C24112yes—
233(C2×D79)⋊C4C24124yes—
234(C2×D79)⋊C4C24112yes—
235C4×Dic79C2414yes—
236C4×Dic79C24112yes—
237C4×Dic79C24112yes—
238C4×Dic79C24112yes—
239C4×Dic79C24124yes—
240C4×Dic79C24112yes—
241C24×C79C2413yes—
242C24×C79C2411yescharacteristic
243#41×C79—232no—
244C2×Q8×C79—232no—
245C2×Q8×C79—212no—
246C2×Q8×C79#4118yes—
247C2×Q8×C79C24112yes—
248C2×Q8×C79C2414yes—
249C2×D4×C79—212no—
250C2×D4×C79—46no—
251C2×D4×C79C24112yes—
252C2×D4×C79C24112yes—
253C22×C4×C79—212no—
254C22×C4×C79—212no—
255C22×C4×C79C2411yescharacteristic
256C22×C4×C79C2413yes—
257C22×C4×C79C2413yes—
258C22×C4×C79C2411yescharacteristic
259C22×C4×C79C24112yes—
260C22×C4×C79C24112yes—
261C22×C4×C79C2413yes—
262C4⋊C4×C79C24112yes—
263C4⋊C4×C79C24112yes—
264C22⋊C4×C79C2414yes—
265C22⋊C4×C79C24112yes—
266C22⋊C4×C79C24124yes—
267C42×C79C24112yes—
268C23×C79—22no—
269C23×C79—26no—
270C23×C79—26no—
271C23×C79—26no—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79C2512yes—
275C23×C79C2516yes—
276C23×C79C2511yescharacteristic
277C22×D79—26no—
278C22×D79—26no—
279C22×D79—26no—
280C22×D79C2516yes—
281Q8×C79—224no—
282Q8×C79C2×#41116yes—
283D4×C79—224no—
284D4×C79—412no—
285C2×C4×C79—22no—
286C2×C4×C79—26no—
287C2×C4×C79—26no—
288C2×C4×C79—22no—
289C2×C4×C79—224no—
290C2×C4×C79—224no—
291C2×C4×C79C2×#41112yes—
292C2×C4×C79C2512yes—
293C2×C4×C79C2516yes—
294C2×C4×C79C2512yes—
295C2×C4×C79C2516yes—
296C2×C4×C79C2516yes—
297C22⋊D79—412no—
298C22⋊D79—424no—
299C22⋊D79—412no—
300C2×Dic79—22no—
301C2×Dic79—26no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—26no—
305C2×Dic79—22no—
306C2×Dic79—26no—
307C2×Dic79—412no—
308C2×Dic79—412no—
309C2×Dic79C2512yes—
310C2×Dic79C2512yes—
311C2×Dic79C2516yes—
312C2×Dic79C2516yes—
313C2×Dic79C2512yes—
314C2×Dic79C2516yes—
315C2×Dic79C2512yes—
316D316—224no—
317C4×D79—224no—
318C4×D79—424no—
319Dic158—412no—
320C22×C79—22no—
321C22×C79—26no—
322C22×C79—22no—
323C22×C79—26no—
324C22×C79—26no—
325C22×C79—22no—
326C22×C79—44no—
327C22×C79—412no—
328C22×C79C22×#4112yes—
329C22×C79#58512yes—
330C22×C79#58512yes—
331C22×C79C2611yescharacteristic
332C2×D79—26no—
333C2×D79—26no—
334C2×D79—26no—
335C2×D79—412no—
336C4×C79—22no—
337C4×C79—26no—
338C4×C79—26no—
339C4×C79—22no—
340C4×C79C22×#41112yes—
341Dic79—22no—
342Dic79—22no—
343Dic79—26no—
344Dic79—26no—
345Dic79—26no—
346Dic79—22no—
347Dic79—22no—
348C2×#3524—791nomaximal, Sylow
349C2×C79—42no—
350C2×C79—46no—
351C2×C79#352414yescomplemented
352C2×C79C23×#4111yescharacteristic
353C2×C79C2×#58511yescharacteristic
354C2×C79C2×#58511yescharacteristic
355D79—46no—
356#3524—7932no—
357C2×#559—793no—
358C2×#557—791no—
359C2×#555—793no—
360C2×#553—793no—
361C2×#552—793no—
362C2×#550—791no—
363C2×#548—791no—
364C2×#548D7911yescharacteristic, complemented
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×#41C2×D7911yescharacteristic
375C23×Q8C2×D7911yescharacteristic
376#559—7948no—
377#557—7916no—
378#555—7948no—
379#553—7948no—
380#552—7948no—
381#550—7916no—
382#548—7916no—
383#548C2×D79116yescomplemented
384#542—7948no—
385#540—7948no—
386C2×C4⋊Q8—793no—
387C2×#127—793no—
388#529—7948no—
389#529—7948no—
390C2×#126—793no—
391C2×#126—791no—
392C2×#126—796no—
393C2×#125—793no—
394C2×#125—793no—
395C2×#125—793no—
396C2×#124—793no—
397C2×#124—793no—
398C2×#124—796no—
399C2×#124C2×D7913yes—
400C2×#123—793no—
401C2×#123—796no—
402C2×#123—793no—
403C2×#123—796no—
404C2×C22⋊Q8—793no—
405C2×C22⋊Q8—793no—
406C2×C22⋊Q8C2×D7913yes—
407C2×#121—793no—
408C2×#121—796no—
409C2×#121—793no—
410C2×#121—793no—
411C2×#121—793no—
412C2×#121C2×D7913yes—
413#520—7916no—
414#519—7916no—
415C4×#41—7916no—
416C2×C4×Q8—791no—
417C2×C4×Q8—791no—
418C2×C4×Q8—793no—
419C2×C4×Q8—791no—
420C2×C4×Q8—793no—
421C2×C4×Q8—793no—
422C2×C4×Q8C2×D7911yescharacteristic
423C2×C4×D4—793no—
424C2×C4×D4—793no—
425C2×C4×D4—793no—
426C2×C4×D4—793no—
427C2×C4×D4—793no—
428C2×C4×D4—796no—
429C2×C4×D4—793no—
430C2×C4×D4C2×D7913yes—
431C2×#117—793no—
432C2×#117—793no—
433C2×#117—793no—
434C2×#117—796no—
435C2×#117—793no—
436C22×C4⋊C4—793no—
437C22×C42—793no—
438C2×#41—28no—
439C2×#41—798no—
440C2×#41—1588no—
441C2×#41C22×D7918yes—
442C22×Q8—28no—
443C22×Q8—793no—
444C22×Q8C22×D7913yes—
445C22×Q8C22×D7918yes—
446C22×Q8C22×D7911yescharacteristic
447C22×D4—793no—
448C22×D4—796no—
449C22×D4—793no—
450C22×D4—793no—
451C22×D4C22×D7913yes—
452C22×D4C22×D7913yes—
453C23×C4—793no—
454C23×C4—793no—
455C23×C4—796no—
456C23×C4—793no—
457C23×C4C22×D7913yes—
458C23×C4C22×D7913yes—
459C4⋊Q8—7924no—
460#127—7924no—
461#126—7924no—
462#126—798no—
463#126—7948no—
464#125—7924no—
465#125—7924no—
466#125—7924no—
467#124—7924no—
468#124—7924no—
469#124—7948no—
470#124C22×D79124yes—
471#123—7924no—
472#123—7948no—
473#123—7924no—
474#123—7948no—
475C22⋊Q8—7924no—
476C22⋊Q8—7924no—
477C22⋊Q8C22×D79124yes—
478#121—7924no—
479#121—7948no—
480#121—7924no—
481#121—7924no—
482#121—7924no—
483#121C22×D79124yes—
484C4×Q8—798no—
485C4×Q8—798no—
486C4×Q8—7924no—
487C4×Q8—798no—
488C4×Q8—7924no—
489C4×Q8—7924no—
490C4×Q8C22×D7918yes—
491C4×D4—7924no—
492C4×D4—7924no—
493C4×D4—7924no—
494C4×D4—7924no—
495C4×D4—7924no—
496C4×D4—7948no—
497C4×D4—7924no—
498C4×D4C22×D79124yes—
499#117—7924no—
500#117—7924no—
501#117—7924no—
502#117—7948no—
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—793no—
511C2×C4⋊C4—796no—
512C2×C4⋊C4—791no—
513C2×C4⋊C4—793no—
514C2×C4⋊C4—793no—
515C2×C4⋊C4—791no—
516C2×C4⋊C4—793no—
517C2×C4⋊C4—7924no—
518C2×C4⋊C4C22×D7913yes—
519C2×C4⋊C4C22×D7913yes—
520C2×C22⋊C4—791no—
521C2×C22⋊C4—793no—
522C2×C22⋊C4—796no—
523C2×C22⋊C4—791no—
524C2×C22⋊C4—793no—
525C2×C22⋊C4—793no—
526C2×C22⋊C4—793no—
527C2×C22⋊C4—793no—
528C2×C22⋊C4—796no—
529C2×C22⋊C4—793no—
530C2×C22⋊C4C22×D7916yes—
531C2×C22⋊C4C22×D7911yescharacteristic
532C2×C22⋊C4C22×D7913yes—
533C2×C42—793no—
534C2×C42—793no—
535C2×C42—796no—
536C2×C42—793no—
537C2×C42—793no—
538C2×C42—7924no—
539C2×C42—791no—
540C2×C42C22×D7913yes—
541C24—793no—
542C24C23×D7911yescharacteristic
543C24C23×D7913yes—
544#41—232no—
545#41—15832no—
546C2×Q8—232no—
547C2×Q8—212no—
548C2×Q8—3166no—
549C2×Q8—7912no—
550C2×Q8#1192962318yes—
551C2×Q8C23×D79112yes—
552C2×Q8C23×D7914yes—
553C2×D4—212no—
554C2×D4—46no—
555C2×D4—3166no—
556C2×D4—3166no—
557C2×D4—31612no—
558C2×D4—7912no—
559C2×D4—7924no—
560C2×D4—7912no—
561C2×D4—7912no—
562C2×D4—15812no—
563C2×D4C23×D79112yes—
564C2×D4C23×D79112yes—
565C22×C4—212no—
566C22×C4—212no—
567C22×C4—31612no—
568C22×C4—3166no—
569C22×C4—3166no—
570C22×C4—7912no—
571C22×C4—7912no—
572C22×C4—7924no—
573C22×C4—791no—
574C22×C4—793no—
575C22×C4—791no—
576C22×C4—793no—
577C22×C4—791no—
578C22×C4—793no—
579C22×C4—791no—
580C22×C4—7912no—
581C22×C4—15812no—
582C22×C4C23×D79112yes—
583C22×C4C23×D79112yes—
584C22×C4C23×D7911yescharacteristic
585C22×C4C23×D7913yes—
586C22×C4C23×D7911yescharacteristic
587C22×C4C23×D7913yes—
588C22×C4C23×D7913yes—
589C4⋊C4—7912no—
590C4⋊C4—794no—
591C4⋊C4—794no—
592C4⋊C4—7912no—
593C4⋊C4—7912no—
594C4⋊C4—7912no—
595C4⋊C4—7912no—
596C4⋊C4—7912no—
597C4⋊C4—7912no—
598C4⋊C4—7912no—
599C4⋊C4—7912no—
600C4⋊C4—7924no—
601C4⋊C4—794no—
602C4⋊C4C23×D79112yes—
603C4⋊C4C23×D79112yes—
604C22⋊C4—794no—
605C22⋊C4—7912no—
606C22⋊C4—7924no—
607C22⋊C4—794no—
608C22⋊C4—7912no—
609C22⋊C4—7912no—
610C22⋊C4—7912no—
611C22⋊C4—7912no—
612C22⋊C4—7924no—
613C22⋊C4—7912no—
614C22⋊C4C23×D79124yes—
615C22⋊C4C23×D7914yes—
616C22⋊C4C23×D79112yes—
617C42—794no—
618C42—7912no—
619C42—7912no—
620C42—7912no—
621C42—7924no—
622C42—7912no—
623C42C23×D79112yes—
624C23—26no—
625C23—22no—
626C23—26no—
627C23—22no—
628C23—22no—
629C23—26no—
630C23—796no—
631C23—1586no—
632C23—1586no—
633C23—1586no—
634C23C24×D7912yes—
635C23C24×D7916yes—
636C23C24×D7911yescharacteristic
637Q8—224no—
638Q8—31612no—
639Q8C2×#11929623116yes—
640D4—224no—
641D4—412no—
642D4—31612no—
643D4—31612no—
644D4—31624no—
645D4—15824no—
646C2×C4—26no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—26no—
650C2×C4—224no—
651C2×C4—224no—
652C2×C4—31624no—
653C2×C4—31612no—
654C2×C4—31612no—
655C2×C4—792no—
656C2×C4—796no—
657C2×C4—792no—
658C2×C4—796no—
659C2×C4—792no—
660C2×C4—796no—
661C2×C4—792no—
662C2×C4—1586no—
663C2×C4—1582no—
664C2×C4—1582no—
665C2×C4—1582no—
666C2×C4—1586no—
667C2×C4—1586no—
668C2×C4—1582no—
669C2×C4—15824no—
670C2×C4C2×#11929623112yes—
671C2×C4C24×D7912yes—
672C2×C4C24×D7916yes—
673C2×C4C24×D7912yes—
674C2×C4C24×D7916yes—
675C2×C4C24×D7916yes—
676C22—22no—
677C22—26no—
678C22—26no—
679C22—22no—
680C22—26no—
681C22—22no—
682C22—412no—
683C22—44no—
684C22—31612no—
685C22—1586no—
686C22—1586no—
687C22—1586no—
688C22C22×#1192962312yes—
689C22#1909939912yes—
690C22#1909940012yes—
691C22C25×D7911yescharacteristic
692C4—22no—
693C4—26no—
694C4—26no—
695C4—22no—
696C4—1582no—
697C4—1586no—
698C4—1582no—
699C4—1582no—
700C4—1582no—
701C4—1586no—
702C4—1586no—
703C4C22×#11929623112yes—
704C2—42no—
705C2—46no—
706C2—3166no—
707C2#2377751014yesdirect product factor
708C2C23×#1192962311yescharacteristic
709C2C2×#1909939911yescharacteristic
710C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#548×C79C2
socleC23×C79C25
hypercenterC2×#548D79
hypocenterC79C2×#3524
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #23777510C2direct (N × H)
2. C2×#19099295C2semidirect
3. C2×#19099292C2semidirect
4. C2×#19099278C2semidirect
5. C2×#19099260C2semidirect
6. C2×#19099247C2semidirect
7. C2×#19099232C2semidirect
8. C2×#19099224C2semidirect
9. C2×#19099182C2semidirect
10. C2×#19099166C2semidirect
11. C2×#19099099C2semidirect
12. C2×#19099093C2semidirect
13. C2×#19099045C2semidirect
14. C2×#19099041C2semidirect
15. C2×#41×Dic79C2semidirect
16. C2×#548×C79C2semidirect
18. #19099295C22semidirect
19. #19099292C22semidirect
20. #19099278C22semidirect
21. #19099260C22semidirect
22. #19099247C22semidirect
23. #19099232C22semidirect
24. #19099224C22semidirect
25. #19099182C22semidirect
26. #19099166C22semidirect
29. #19099099C22semidirect
30. #19099093C22semidirect
51. #19099045C22semidirect
52. #19099041C22semidirect
53. #41×Dic79C22semidirect
76. #548×C79C22semidirect
351. C2×C79#3524semidirect
364. C2×#548D79semidirect
372. C79C2×#3524semidirect
383. #548C2×D79semidirect
707. C2#23777510direct (N × H)

Maximal subgroups

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

subgroupindex
#237775102
C2×#190992952
C2×#190992922
C2×#190992782
C2×#190992602
C2×#190992472
C2×#190992322
C2×#190992242
C2×#190991822
C2×#190991662
C2×#190990992
C2×#190990932
C2×#190990452
C2×#190990412
C2×#41×Dic792
C2×#548×C792
C2×#352479