Finite Group Databasebeta

← C2×#23777385 #35196460

Subgroups — C2×#23777385 #35196460

Order 20224.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777385C2132yesmaximal, direct product factor
2C2×#19099289C211yesmaximal, characteristic, complemented
3C2×#19099283C213yesmaximal, complemented
4C2×#19099268C213yesmaximal, complemented
5C2×#19099263C213yesmaximal, complemented
6C2×#19099248C213yesmaximal, complemented
7C2×Q8×D316C211yesmaximal, characteristic, complemented
8C2×#19099220C211yesmaximal, characteristic, complemented
9C2×#19099220C211yesmaximal, characteristic, complemented
10C2×#19099178C213yesmaximal, complemented
11C2×#19099175C213yesmaximal, complemented
12C2×#19099095C213yesmaximal, complemented
13C2×#19099091C213yesmaximal, complemented
14C2×#19099039C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
16C2×#520×C79C211yesmaximal, characteristic, complemented
17C22×Q8×D79C2211yescharacteristic
18C22×Q8×D79C2211yescharacteristic
19#19099289C22116yescomplemented
20#19099283C22148yescomplemented
21#19099268C22148yescomplemented
22#19099263C22148yescomplemented
23#19099248C22148yescomplemented
24Q8×D316C22116yescomplemented
25#19099220C22116yescomplemented
26#19099220C22116yescomplemented
27#19099178C22148yescomplemented
28#19099175C22148yescomplemented
29C2×#14579161C2213yes—
30C2×#14579160C2213yes—
31#19099095C22148yescomplemented
32#19099091C22148yescomplemented
33C2×#14579156C2213yes—
34C2×#14579154C2216yes—
35C2×#14579154C2216yes—
36C2×#14579154C2213yes—
37C2×#14579153C2213yes—
38C2×#14579152C2213yes—
39C2×#14579151C2213yes—
40C2×#14579151C2216yes—
41C2×#14579148C2213yes—
42C2×#14579148C2213yes—
43C2×#14579147C2213yes—
44C2×#14579146C2211yescharacteristic
45C2×#14579144C2216yes—
46C2×#14579143C2213yes—
47C2×#14579141C2213yes—
48C2×#14579141C2213yes—
49C2×#14579140C2213yes—
50C2×#14579140C2213yes—
51C2×#14579140C2216yes—
52C2×#14579139C2213yes—
53C2×#14579134C2213yes—
54C2×#14579132C2213yes—
55C2×#14579132C2213yes—
56#19099039C22116yescomplemented
57C2×Q8×Dic79C2211yescharacteristic
58C2×Q8×Dic79C2211yescharacteristic
59C2×C4×Dic158C2213yes—
60C2×C4×Dic158C2213yes—
61C2×C4×Dic158C2213yes—
62C2×#14579126C2213yes—
63C2×#14579126C2213yes—
64C4×Q8×D79C22116yescomplemented
65C2×C4×D316C2213yes—
66C2×C4×C22⋊D79C2213yes—
67C2×C4×C22⋊D79C2213yes—
68C2×C4×C22⋊D79C2216yes—
69C2×#14579120C2216yes—
70C2×#14579119C2213yes—
71C2×#14579118C2213yes—
72C2×C4⋊C4×D79C2213yes—
73C2×C42×D79C2213yes—
74C22×#41×C79C2211yescharacteristic
75#520×C79C22116yescomplemented
76C2×C4×Q8×C79C2211yescharacteristic
77C2×C4×Q8×C79C2211yescharacteristic
78C2×C4×D4×C79C2213yes—
79C2×C4×D4×C79C2213yes—
80C2×#117×C79C2213yes—
81C22×C4⋊C4×C79C2213yes—
82C22×Dic158C2313yes—
83C22×Dic158C2313yes—
84C22×Dic158C2313yes—
85C2×Q8×D79—28no—
86C2×Q8×D79—28no—
87C2×Q8×D79C2318yes—
88C2×Q8×D79C2318yes—
89C22×D316C2311yescharacteristic
90C22×C22⋊D79C2313yes—
91C22×C22⋊D79C2313yes—
92C22×C4×D79C2311yescharacteristic
93C22×C4×D79C2313yes—
94C22×C4×D79C2313yes—
95C22×C4×D79C2313yes—
96#14579161C23124yes—
97#14579160C23124yes—
98#14579156C23124yes—
99#14579154C23148yes—
100#14579154C23148yes—
101#14579154C23124yes—
102#14579153C23124yes—
103#14579152C23124yes—
104#14579151C23124yes—
105#14579151C23148yes—
106#14579148C23124yes—
107#14579148C23124yes—
108#14579147C23124yes—
109#14579146C2318yes—
110#14579144C23148yes—
111#14579143C23124yes—
112#14579141C23124yes—
113#14579141C23124yes—
114#14579140C23124yes—
115#14579140C23124yes—
116#14579140C23148yes—
117#14579139C23124yes—
118#14579134C23124yes—
119#14579132C23124yes—
120#14579132C23124yes—
121Q8×Dic79C2318yes—
122Q8×Dic79C2318yes—
123C4×Dic158C23124yes—
124C4×Dic158C23124yes—
125C4×Dic158C23124yes—
126#14579126C23124yes—
127#14579126C23124yes—
128C4×D316C23124yes—
129C4×C22⋊D79C23124yes—
130C4×C22⋊D79C23124yes—
131C4×C22⋊D79C23148yes—
132#14579120C23148yes—
133#14579119C23124yes—
134#14579118C23124yes—
135C2×C4⋊Dic79C2313yes—
136C2×C4⋊Dic79C2313yes—
137C2×C4⋊Dic79C2313yes—
138C2×C4⋊Dic79C2316yes—
139C2×C4⋊Dic79C2313yes—
140C2×Dic79⋊C4C2316yes—
141C2×Dic79⋊C4C2313yes—
142C2×Dic79⋊C4C2313yes—
143C2×Dic79⋊C4C2313yes—
144C2×Dic79⋊C4C2313yes—
145C2×Dic79⋊C4C2316yes—
146C2×Dic79⋊C4C2311yescharacteristic
147C2×Dic79⋊C4C2313yes—
148C4⋊C4×D79C23124yes—
149C2×C22⋊Dic79C2313yes—
150C2×C22⋊Dic79C2316yes—
151C2×C22⋊Dic79C2316yes—
152C2×C22⋊Dic79C2313yes—
153C2×(C2×D79)⋊C4C2311yescharacteristic
154C2×(C2×D79)⋊C4C2313yes—
155C2×(C2×D79)⋊C4C2311yescharacteristic
156C2×(C2×D79)⋊C4C2311yescharacteristic
157C2×(C2×D79)⋊C4C2313yes—
158C2×(C2×D79)⋊C4C2313yes—
159C2×C4×Dic79C2313yes—
160C2×C4×Dic79C2313yes—
161C2×C4×Dic79C2313yes—
162C2×C4×Dic79C2313yes—
163C2×C4×Dic79C2316yes—
164C42×D79C23124yes—
165C2×#41×C79—28no—
166C2×#41×C79C2318yes—
167C22×Q8×C79C2311yescharacteristic
168C22×D4×C79C2313yes—
169C23×C4×C79C2313yes—
170C23×C4×C79C2316yes—
171C4×Q8×C79C2318yes—
172C4×Q8×C79C2318yes—
173C4×D4×C79C23124yes—
174C4×D4×C79C23124yes—
175#117×C79C23124yes—
176C2×C4⋊C4×C79C2313yes—
177C2×C4⋊C4×C79C2313yes—
178C2×C4⋊C4×C79C2313yes—
179C2×C4⋊C4×C79C23124yes—
180C2×C4⋊C4×C79C2311yescharacteristic
181C2×C22⋊C4×C79C2313yes—
182C2×C22⋊C4×C79C2313yes—
183C2×C42×C79C2313yes—
184C2×C42×C79C2313yes—
185C23×D79C2411yescharacteristic
186C23×D79C2411yescharacteristic
187C2×Dic158—212no—
188C2×Dic158—212no—
189C2×Dic158—46no—
190C2×Dic158C24112yes—
191C2×Dic158C24112yes—
192C2×Dic158C24112yes—
193Q8×D79—232no—
194Q8×D79—232no—
195C2×D316—24no—
196C2×D316C2414yes—
197C2×C22⋊D79—212no—
198C2×C22⋊D79—46no—
199C2×C22⋊D79C24112yes—
200C2×C22⋊D79C24112yes—
201C22×Dic79C2411yescharacteristic
202C22×Dic79C2413yes—
203C22×Dic79C2413yes—
204C22×Dic79C2413yes—
205C22×Dic79C2411yescharacteristic
206C22×Dic79C2413yes—
207C2×C4×D79—24no—
208C2×C4×D79—212no—
209C2×C4×D79—212no—
210C2×C4×D79—46no—
211C2×C4×D79C24112yes—
212C2×C4×D79C24112yes—
213C2×C4×D79C2414yes—
214C2×C4×D79C24112yes—
215C4⋊Dic79C24112yes—
216C4⋊Dic79C24112yes—
217C4⋊Dic79C24112yes—
218C4⋊Dic79C24124yes—
219C4⋊Dic79C24112yes—
220Dic79⋊C4C24124yes—
221Dic79⋊C4C24112yes—
222Dic79⋊C4C24112yes—
223Dic79⋊C4C24112yes—
224Dic79⋊C4C24112yes—
225Dic79⋊C4C24124yes—
226Dic79⋊C4C2414yes—
227Dic79⋊C4C24112yes—
228C22⋊Dic79C24112yes—
229C22⋊Dic79C24124yes—
230C22⋊Dic79C24124yes—
231C22⋊Dic79C24112yes—
232(C2×D79)⋊C4C2414yes—
233(C2×D79)⋊C4C24112yes—
234(C2×D79)⋊C4C2414yes—
235(C2×D79)⋊C4C2414yes—
236(C2×D79)⋊C4C24112yes—
237(C2×D79)⋊C4C24112yes—
238C4×Dic79C24112yes—
239C4×Dic79C24112yes—
240C4×Dic79C24112yes—
241C4×Dic79C24112yes—
242C4×Dic79C24124yes—
243C24×C79C2413yes—
244#41×C79—232no—
245C2×Q8×C79#4118yes—
246C2×Q8×C79C2414yes—
247C2×D4×C79—212no—
248C2×D4×C79C24112yes—
249C22×C4×C79—212no—
250C22×C4×C79—412no—
251C22×C4×C79C2413yes—
252C22×C4×C79C2411yescharacteristic
253C22×C4×C79C2411yescharacteristic
254C22×C4×C79C2413yes—
255C22×C4×C79C2411yescharacteristic
256C22×C4×C79C24112yes—
257C22×C4×C79C24124yes—
258C22×C4×C79C2413yes—
259C4⋊C4×C79C24112yes—
260C4⋊C4×C79C24112yes—
261C4⋊C4×C79C24112yes—
262C4⋊C4×C79C2414yes—
263C22⋊C4×C79C24112yes—
264C22⋊C4×C79C24112yes—
265C42×C79C24112yes—
266C42×C79C24112yes—
267C23×C79—26no—
268C23×C79—26no—
269C23×C79—26no—
270C23×C79C2516yes—
271C23×C79C2511yescharacteristic
272C22×D79—22no—
273C22×D79—22no—
274C22×D79—22no—
275C22×D79—22no—
276C22×D79—22no—
277C22×D792−1+414yes—
278C22×D79C2512yes—
279C22×D79C2512yes—
280Q8×C79C2×#41116yes—
281D4×C79—224no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—26no—
286C2×C4×C79—26no—
287C2×C4×C79—224no—
288C2×C4×C79—424no—
289C2×C4×C79C2×#41112yes—
290C2×C4×C79C2512yes—
291C2×C4×C79C2516yes—
292C2×C4×C79C2512yes—
293C2×C4×C79C2516yes—
294C2×C4×C79C2512yes—
295C2×C4×C79C2516yes—
296C22⋊D79—224no—
297C22⋊D79—412no—
298C2×Dic79—26no—
299C2×Dic79—26no—
300C2×Dic79—22no—
301C2×Dic79—26no—
302C2×Dic79—26no—
303C2×Dic79—22no—
304C2×Dic79C2512yes—
305C2×Dic79C2512yes—
306C2×Dic79C2516yes—
307C2×Dic79C2516yes—
308C2×Dic79C2516yes—
309C2×Dic79C2516yes—
310D316—28no—
311C4×D79—28no—
312C4×D79—224no—
313C4×D79—224no—
314C4×D79—412no—
315Dic158—224no—
316Dic158—224no—
317Dic158—412no—
318C22×C79—26no—
319C22×C79—26no—
320C22×C79—26no—
321C22×C79—412no—
322C22×C79C22×#4112yes—
323C22×C79C2×2−1+412yes—
324C22×C79#58512yes—
325C22×C79C2611yescharacteristic
326C2×D79—22no—
327C2×D79—22no—
328C2×D79—28no—
329C2×D79—22no—
330C2×D79—22no—
331C2×D79—22no—
332C2×D79—44no—
333C2×D79C2×2−1+414yes—
334C4×C79—22no—
335C4×C79—22no—
336C4×C79—22no—
337C4×C79—26no—
338C4×C79—26no—
339C4×C79C22×#41112yes—
340Dic79—26no—
341Dic79—26no—
342Dic79—26no—
343Dic79—22no—
344Dic79—26no—
345Dic79—22no—
346C2×#3516—791nomaximal, Sylow
347C2×C79—46no—
348C2×C79#351614yescomplemented
349C2×C79C23×#4111yescharacteristic
350C2×C79C22×2−1+411yescharacteristic
351C2×C79C2×#58511yescharacteristic
352D79—24no—
353D79—42no—
354#3516—7932no—
355C2×#557—791no—
356C2×#556—793no—
357C2×#554—793no—
358C2×#553—793no—
359C2×#552—793no—
360C2×D4×Q8—791no—
361C2×#548—791no—
362C2×#548—791no—
363C2×#542—793no—
364C2×#541—793no—
365C2×#529—793no—
366C2×#529—793no—
367C2×#520D7911yescharacteristic, complemented
368C2×#519—791no—
369C22×C4×Q8—791no—
370C79C2×#351611yescharacteristic, complemented, Sylow
371C22×#41C2×D7911yescharacteristic
372C23×Q8—791no—
373C23×Q8—791no—
374#557—7916no—
375#556—7948no—
376#554—7948no—
377#553—7948no—
378#552—7948no—
379D4×Q8—7916no—
380#548—7916no—
381#548—7916no—
382#542—7948no—
383#541—7948no—
384C2×C4⋊Q8—793no—
385C2×C4⋊Q8—793no—
386#529—7948no—
387#529—7948no—
388C2×#126—793no—
389C2×#126—796no—
390C2×#126—793no—
391C2×#126—796no—
392C2×#125—793no—
393C2×#125—793no—
394C2×#125—796no—
395C2×#125—793no—
396C2×#124—793no—
397C2×#124—793no—
398C2×#124—793no—
399C2×#123—796no—
400C2×#123—791no—
401C2×#123—793no—
402C2×C22⋊Q8—793no—
403C2×C22⋊Q8—793no—
404C2×C22⋊Q8—796no—
405C2×C22⋊Q8—793no—
406C2×C22⋊Q8—793no—
407C2×C22⋊Q8—793no—
408C2×#121—793no—
409C2×#121—793no—
410C2×#121—793no—
411#520C2×D79116yescomplemented
412#519—7916no—
413C2×C4×Q8—791no—
414C2×C4×Q8—791no—
415C2×C4×Q8—7916no—
416C2×C4×Q8—793no—
417C2×C4×Q8—793no—
418C2×C4×Q8—793no—
419C2×C4×Q8—793no—
420C2×C4×Q8—793no—
421C2×C4×Q8C2×D7911yescharacteristic
422C2×C4×Q8C2×D7911yescharacteristic
423C2×C4×D4—793no—
424C2×C4×D4—793no—
425C2×C4×D4—796no—
426C2×C4×D4—793no—
427C2×C4×D4C2×D7913yes—
428C2×C4×D4C2×D7913yes—
429C2×#117—796no—
430C2×#117—793no—
431C2×#117—793no—
432C2×#117C2×D7913yes—
433C22×C4⋊C4—793no—
434C22×C4⋊C4C2×D7913yes—
435C22×C42—793no—
436C2×#41—28no—
437C2×#41C22×D7918yes—
438C22×Q8—798no—
439C22×Q8—798no—
440C22×Q8—793no—
441C22×Q8—793no—
442C22×Q8—793no—
443C22×Q8—1588no—
444C22×Q8—1588no—
445C22×Q8C22×D7911yescharacteristic
446C22×D4—793no—
447C22×D4—793no—
448C22×D4—791no—
449C22×D4C22×D7913yes—
450C23×C4—793no—
451C23×C4—793no—
452C23×C4—793no—
453C23×C4—791no—
454C23×C4C22×D7913yes—
455C23×C4C22×D7916yes—
456C4⋊Q8—7924no—
457C4⋊Q8—7924no—
458#126—7924no—
459#126—7948no—
460#126—7924no—
461#126—7948no—
462#125—7924no—
463#125—7924no—
464#125—7948no—
465#125—7924no—
466#124—7924no—
467#124—7924no—
468#124—7924no—
469#123—7948no—
470#123—798no—
471#123—7924no—
472C22⋊Q8—7924no—
473C22⋊Q8—7924no—
474C22⋊Q8—7948no—
475C22⋊Q8—7924no—
476C22⋊Q8—7924no—
477C22⋊Q8—7924no—
478#121—7924no—
479#121—7924no—
480#121—7924no—
481C4×Q8—798no—
482C4×Q8—798no—
483C4×Q8—7924no—
484C4×Q8—7924no—
485C4×Q8—7924no—
486C4×Q8—7924no—
487C4×Q8—7924no—
488C4×Q8C22×D7918yes—
489C4×Q8C22×D7918yes—
490C4×D4—7924no—
491C4×D4—7924no—
492C4×D4—7948no—
493C4×D4—7924no—
494C4×D4C22×D79124yes—
495C4×D4C22×D79124yes—
496#117—7948no—
497#117—7924no—
498#117—7924no—
499#117C22×D79124yes—
500C2×C4⋊C4—793no—
501C2×C4⋊C4—796no—
502C2×C4⋊C4—793no—
503C2×C4⋊C4—793no—
504C2×C4⋊C4—793no—
505C2×C4⋊C4—793no—
506C2×C4⋊C4—796no—
507C2×C4⋊C4—793no—
508C2×C4⋊C4—793no—
509C2×C4⋊C4—796no—
510C2×C4⋊C4—793no—
511C2×C4⋊C4—791no—
512C2×C4⋊C4—793no—
513C2×C4⋊C4—7924no—
514C2×C4⋊C4C22×D7913yes—
515C2×C4⋊C4C22×D7913yes—
516C2×C4⋊C4C22×D7913yes—
517C2×C4⋊C4C22×D79124yes—
518C2×C4⋊C4C22×D7911yescharacteristic
519C2×C22⋊C4—793no—
520C2×C22⋊C4—796no—
521C2×C22⋊C4—796no—
522C2×C22⋊C4—793no—
523C2×C22⋊C4—793no—
524C2×C22⋊C4—791no—
525C2×C22⋊C4—791no—
526C2×C22⋊C4—793no—
527C2×C22⋊C4—791no—
528C2×C22⋊C4—793no—
529C2×C22⋊C4C22×D7913yes—
530C2×C22⋊C4C22×D7913yes—
531C2×C42—796no—
532C2×C42—793no—
533C2×C42—793no—
534C2×C42—793no—
535C2×C42—793no—
536C2×C42—7924no—
537C2×C42C22×D7913yes—
538C2×C42C22×D7913yes—
539C24—791no—
540C24—791no—
541C24C23×D7913yes—
542#41—232no—
543C2×Q8—3166no—
544C2×Q8—7912no—
545C2×Q8—7912no—
546C2×Q8—7912no—
547C2×Q8—15832no—
548C2×Q8—15832no—
549C2×Q8—15812no—
550C2×Q8—15812no—
551C2×Q8#1192962418yes—
552C2×Q8C23×D7914yes—
553C2×D4—212no—
554C2×D4—3166no—
555C2×D4—7912no—
556C2×D4—7912no—
557C2×D4—794no—
558C2×D4—1584no—
559C2×D4—15812no—
560C2×D4C23×D79112yes—
561C22×C4—212no—
562C22×C4—412no—
563C22×C4—3166no—
564C22×C4—7912no—
565C22×C4—791no—
566C22×C4—791no—
567C22×C4—793no—
568C22×C4—793no—
569C22×C4—793no—
570C22×C4—793no—
571C22×C4—794no—
572C22×C4—7912no—
573C22×C4—7912no—
574C22×C4—1584no—
575C22×C4—15812no—
576C22×C4—15812no—
577C22×C4C23×D79112yes—
578C22×C4C23×D7911yescharacteristic
579C22×C4C23×D7913yes—
580C22×C4C23×D7911yescharacteristic
581C22×C4C23×D7913yes—
582C22×C4C23×D7911yescharacteristic
583C22×C4C23×D79124yes—
584C22×C4C23×D7913yes—
585C4⋊C4—7924no—
586C4⋊C4—7912no—
587C4⋊C4—7912no—
588C4⋊C4—7912no—
589C4⋊C4—7912no—
590C4⋊C4—7924no—
591C4⋊C4—794no—
592C4⋊C4—7912no—
593C4⋊C4—7912no—
594C4⋊C4—7912no—
595C4⋊C4—7912no—
596C4⋊C4—7924no—
597C4⋊C4—7912no—
598C4⋊C4C23×D79112yes—
599C4⋊C4C23×D79112yes—
600C4⋊C4C23×D79112yes—
601C4⋊C4C23×D7914yes—
602C22⋊C4—7912no—
603C22⋊C4—7924no—
604C22⋊C4—7924no—
605C22⋊C4—7912no—
606C22⋊C4—7912no—
607C22⋊C4—794no—
608C22⋊C4—794no—
609C22⋊C4—7912no—
610C22⋊C4—794no—
611C22⋊C4—7912no—
612C22⋊C4C23×D79112yes—
613C22⋊C4C23×D79112yes—
614C42—7912no—
615C42—7912no—
616C42—7912no—
617C42—7924no—
618C42—7912no—
619C42C23×D79112yes—
620C42C23×D79112yes—
621C23—26no—
622C23—26no—
623C23—26no—
624C23—794no—
625C23—792no—
626C23—792no—
627C23—1582no—
628C23—1582no—
629C23—1582no—
630C23—1582no—
631C23—1582no—
632C23C24×D7916yes—
633C23C24×D7911yescharacteristic
634Q8—31612no—
635Q8—15824no—
636Q8—15824no—
637Q8C2×#11929624116yes—
638D4—224no—
639D4—31612no—
640D4—1588no—
641D4—15824no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—26no—
645C2×C4—26no—
646C2×C4—22no—
647C2×C4—224no—
648C2×C4—424no—
649C2×C4—31612no—
650C2×C4—792no—
651C2×C4—792no—
652C2×C4—796no—
653C2×C4—796no—
654C2×C4—796no—
655C2×C4—796no—
656C2×C4—1588no—
657C2×C4—1582no—
658C2×C4—1586no—
659C2×C4—1586no—
660C2×C4—1582no—
661C2×C4—1586no—
662C2×C4—1586no—
663C2×C4—15824no—
664C2×C4—15824no—
665C2×C4C2×#11929624112yes—
666C2×C4C24×D7912yes—
667C2×C4C24×D7916yes—
668C2×C4C24×D7912yes—
669C2×C4C24×D7916yes—
670C2×C4C24×D7912yes—
671C2×C4C24×D7916yes—
672C22—26no—
673C22—26no—
674C22—26no—
675C22—412no—
676C22—3164no—
677C22—794no—
678C22—1582no—
679C22—1582no—
680C22—1582no—
681C22—1588no—
682C22—1582no—
683C22—1582no—
684C22C22×#1192962412yes—
685C222−1+4×D7912yes—
686C22#1909939812yes—
687C22C25×D7911yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—26no—
692C4—26no—
693C4—1586no—
694C4—1586no—
695C4—1582no—
696C4—1586no—
697C4—1586no—
698C4—1582no—
699C4C22×#11929624112yes—
700C2—46no—
701C2—3162no—
702C2—1584no—
703C2#2377738514yesdirect product factor
704C2C23×#1192962411yescharacteristic
705C2C2×2−1+4×D7911yescharacteristic
706C2C2×#1909939811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#520×C79C2
socleC23×C79C25
hypercenterC2×#520D79
hypocenterC79C2×#3516
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #23777385C2direct (N × H)
2. C2×#19099289C2semidirect
3. C2×#19099283C2semidirect
4. C2×#19099268C2semidirect
5. C2×#19099263C2semidirect
6. C2×#19099248C2semidirect
7. C2×Q8×D316C2semidirect
8. C2×#19099220C2semidirect
9. C2×#19099220C2semidirect
10. C2×#19099178C2semidirect
11. C2×#19099175C2semidirect
12. C2×#19099095C2semidirect
13. C2×#19099091C2semidirect
14. C2×#19099039C2semidirect
15. C2×C4×Q8×D79C2semidirect
16. C2×#520×C79C2semidirect
19. #19099289C22semidirect
20. #19099283C22semidirect
21. #19099268C22semidirect
22. #19099263C22semidirect
23. #19099248C22semidirect
24. Q8×D316C22semidirect
25. #19099220C22semidirect
26. #19099220C22semidirect
27. #19099178C22semidirect
28. #19099175C22semidirect
31. #19099095C22semidirect
32. #19099091C22semidirect
56. #19099039C22semidirect
64. C4×Q8×D79C22semidirect
75. #520×C79C22semidirect
348. C2×C79#3516semidirect
367. C2×#520D79semidirect
370. C79C2×#3516semidirect
411. #520C2×D79semidirect
703. C2#23777385direct (N × H)

Maximal subgroups

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

subgroupindex
#237773852
C2×#190992892
C2×#190992832
C2×#190992682
C2×#190992632
C2×#190992482
C2×Q8×D3162
C2×#190992202
C2×#190991782
C2×#190991752
C2×#190990952
C2×#190990912
C2×#190990392
C2×C4×Q8×D792
C2×#520×C792
C2×#351679