Finite Group Databasebeta

← C2×#23777476 #35196477

Subgroups — C2×#23777476 #35196477

Order 20224.

7758 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777476C2132yesmaximal, direct product factor
2C2×#19099295C213yesmaximal, complemented
3C2×Q8×Dic158C211yesmaximal, characteristic, complemented
4C2×#19099271C213yesmaximal, complemented
5C2×#19099232C211yesmaximal, characteristic, complemented
6C2×#19099224C211yesmaximal, characteristic, complemented
7C2×#19099217C213yesmaximal, complemented
8C2×#19099213C213yesmaximal, complemented
9C2×#19099186C213yesmaximal, complemented
10C2×#19099182C213yesmaximal, complemented
11C2×#19099108C213yesmaximal, complemented
12C2×#19099093C213yesmaximal, complemented
13C2×#19099046C211yesmaximal, characteristic, complemented
14C2×#19099045C211yesmaximal, characteristic, complemented
15C22×Q8×Dic79C211yesmaximal, characteristic, complemented
16C2×#548×C79C211yesmaximal, characteristic, complemented
17C22×#11929625C2211yescharacteristic
18C22×#11929623C2216yes—
19#19099295C22148yescomplemented
20Q8×Dic158C22116yescomplemented
21#19099271C22148yescomplemented
22#19099232C22116yescomplemented
23#19099224C22116yescomplemented
24#19099217C22148yescomplemented
25#19099213C22148yescomplemented
26#19099186C22148yescomplemented
27#19099182C22148yescomplemented
28#19099108C22148yescomplemented
29C2×#14579161C2213yes—
30C2×#14579160C2213yes—
31C2×#14579160C2213yes—
32C2×#14579157C2213yes—
33#19099093C22148yescomplemented
34C2×#14579156C2213yes—
35C2×#14579154C2213yes—
36C2×#14579151C2213yes—
37C2×#14579150C2213yes—
38C2×#14579147C2216yes—
39C2×#14579147C2213yes—
40C2×#14579145C2216yes—
41C2×#14579145C2213yes—
42C2×#14579143C2216yes—
43C2×#14579142C2213yes—
44C2×#14579141C2216yes—
45C2×#14579138C2216yes—
46C2×#14579138C2211yescharacteristic
47C2×#14579137C2213yes—
48C2×#14579135C2213yes—
49C2×#14579135C2213yes—
50C2×#14579133C2213yes—
51C2×#14579132C2213yes—
52#19099046C22116yescomplemented
53#19099045C22116yescomplemented
54C2×Q8×Dic79C2213yes—
55C2×Q8×Dic79C2211yescharacteristic
56C2×Q8×Dic79C2211yescharacteristic
57C2×Q8×Dic79C2213yes—
58C2×Q8×Dic79C2211yescharacteristic
59C2×Q8×Dic79C22116yescomplemented
60C2×C4×Dic158C2213yes—
61C2×C4×D316C2213yes—
62C2×D4×Dic79C2213yes—
63C2×D4×Dic79C2213yes—
64C2×#14579123C2213yes—
65C2×C4×C22⋊D79C2213yes—
66C2×C4×C22⋊D79C2213yes—
67C2×(C22⋊D79)⋊C4C2216yes—
68C2×#14579120C2213yes—
69C2×#14579118C2213yes—
70C22×C4⋊Dic79C2213yes—
71C22×C4⋊Dic79C2213yes—
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—
84C2×#11929623—424no—
85C2×#11929623C23148yes—
86C22×Dic158C2311yescharacteristic
87C22×Dic158C2316yes—
88C22×D316C2313yes—
89C22×C22⋊D79C2313yes—
90C22×C22⋊D79C2313yes—
91C22×C22⋊D79C2316yes—
92C23×Dic79C2311yescharacteristic
93C23×Dic79C2313yes—
94C23×Dic79C2316yes—
95C22×C4×D79C2313yes—
96C22×C4×D79C2316yes—
97#14579161C23124yes—
98#14579160C23124yes—
99#14579160C23124yes—
100#14579157C23124yes—
101#14579156C23124yes—
102#14579154C23124yes—
103#14579151C23124yes—
104#14579150C23124yes—
105#14579147C23148yes—
106#14579147C23124yes—
107#14579145C23148yes—
108#14579145C23124yes—
109#14579143C23148yes—
110#14579142C23124yes—
111#14579141C23148yes—
112#14579138C23148yes—
113#14579138C2318yes—
114#14579137C23124yes—
115#14579135C23124yes—
116#14579135C23124yes—
117#14579133C23124yes—
118#14579132C23124yes—
119Q8×Dic79C23124yes—
120Q8×Dic79C2318yes—
121Q8×Dic79C2318yes—
122Q8×Dic79C23124yes—
123Q8×Dic79C2318yes—
124C4×Dic158C23124yes—
125C4×D316C23124yes—
126D4×Dic79C23124yes—
127D4×Dic79C23124yes—
128#14579123C23124yes—
129C4×C22⋊D79C23124yes—
130C4×C22⋊D79C23124yes—
131(C22⋊D79)⋊C4C23148yes—
132#14579120C23124yes—
133#14579118C23124yes—
134C2×C4⋊Dic79C23124yes—
135C2×C4⋊Dic79C23124yes—
136C2×C4⋊Dic79C2313yes—
137C2×C4⋊Dic79C2313yes—
138C2×C4⋊Dic79C2313yes—
139C2×C4⋊Dic79C2313yes—
140C2×C4⋊Dic79C2316yes—
141C2×C4⋊Dic79C2311yescharacteristic
142C2×C4⋊Dic79C2313yes—
143C2×Dic79⋊C4C2313yes—
144C2×Dic79⋊C4C2311yescharacteristic
145C2×Dic79⋊C4C2313yes—
146C2×Dic79⋊C4C2311yescharacteristic
147C2×Dic79⋊C4C2313yes—
148C2×Dic79⋊C4C2313yes—
149C4⋊C4×D79C23124yes—
150C2×C22⋊Dic79C2313yes—
151C2×C22⋊Dic79C2313yes—
152C2×C22⋊Dic79C2311yescharacteristic
153C2×C22⋊Dic79C2313yes—
154C2×(C2×D79)⋊C4C2313yes—
155C2×(C2×D79)⋊C4C2313yes—
156C2×(C2×D79)⋊C4C2316yes—
157C2×(C2×D79)⋊C4C2313yes—
158C2×(C2×D79)⋊C4C2313yes—
159C2×C4×Dic79C2313yes—
160C2×C4×Dic79C2313yes—
161C2×C4×Dic79C2313yes—
162C2×C4×Dic79C2313yes—
163C2×C4×Dic79C23124yes—
164C2×C4×Dic79C2313yes—
165C2×#41×C79—28no—
166C2×#41×C79C2318yes—
167C22×Q8×C79—28no—
168C22×Q8×C79C2318yes—
169C22×Q8×C79C2313yes—
170C22×Q8×C79C2311yescharacteristic
171C22×D4×C79C2313yes—
172C22×D4×C79C2313yes—
173C23×C4×C79C2313yes—
174C23×C4×C79C2313yes—
175#124×C79C23124yes—
176C22⋊Q8×C79C23124yes—
177#121×C79C23124yes—
178C4×Q8×C79C2318yes—
179C4×D4×C79C23124yes—
180C2×C4⋊C4×C79C2313yes—
181C2×C4⋊C4×C79C2313yes—
182C2×C22⋊C4×C79C2311yescharacteristic
183C2×C22⋊C4×C79C2313yes—
184C2×C22⋊C4×C79C2316yes—
185C2×C42×C79C2313yes—
186C23×D79C2413yes—
187#11929625—232no—
188#11929623—496no—
189C2×Dic158—24no—
190C2×Dic158—412no—
191C2×Dic158C2414yes—
192C2×Dic158C24124yes—
193C2×D316—212no—
194C2×D316C24112yes—
195C2×C22⋊D79—212no—
196C2×C22⋊D79—212no—
197C2×C22⋊D79—412no—
198C2×C22⋊D79C24112yes—
199C2×C22⋊D79C24112yes—
200C2×C22⋊D79C24124yes—
201C22×Dic79—24no—
202C22×Dic79—212no—
203C22×Dic79—412no—
204C22×Dic79C2413yes—
205C22×Dic79C2413yes—
206C22×Dic79C2411yescharacteristic
207C22×Dic79C24112yes—
208C22×Dic79C2411yescharacteristic
209C22×Dic79C2414yes—
210C22×Dic79C2413yes—
211C22×Dic79C2411yescharacteristic
212C22×Dic79C24124yes—
213C22×Dic79C2411yescharacteristic
214C2×C4×D79—212no—
215C2×C4×D79—412no—
216C2×C4×D79C24112yes—
217C2×C4×D79C24124yes—
218C4⋊Dic79C24112yes—
219C4⋊Dic79C24112yes—
220C4⋊Dic79C24112yes—
221C4⋊Dic79C24112yes—
222C4⋊Dic79C24124yes—
223C4⋊Dic79C2414yes—
224C4⋊Dic79C24112yes—
225Dic79⋊C4C24112yes—
226Dic79⋊C4C2414yes—
227Dic79⋊C4C24112yes—
228Dic79⋊C4C2414yes—
229Dic79⋊C4C24112yes—
230Dic79⋊C4C24112yes—
231C22⋊Dic79C24112yes—
232C22⋊Dic79C24112yes—
233C22⋊Dic79C2414yes—
234C22⋊Dic79C24112yes—
235(C2×D79)⋊C4C24112yes—
236(C2×D79)⋊C4C24112yes—
237(C2×D79)⋊C4C24124yes—
238(C2×D79)⋊C4C24112yes—
239(C2×D79)⋊C4C24112yes—
240C4×Dic79C24112yes—
241C4×Dic79C24112yes—
242C4×Dic79C24112yes—
243C4×Dic79C24112yes—
244C4×Dic79C24112yes—
245C24×C79C2413yes—
246C24×C79C2411yescharacteristic
247#41×C79—232no—
248C2×Q8×C79—232no—
249C2×Q8×C79—212no—
250C2×Q8×C79#4118yescomplemented
251C2×Q8×C79C24112yes—
252C2×Q8×C79C2414yes—
253C2×D4×C79—212no—
254C2×D4×C79—212no—
255C2×D4×C79C24112yes—
256C2×D4×C79C24112yes—
257C22×C4×C79—212no—
258C22×C4×C79—212no—
259C22×C4×C79C2413yes—
260C22×C4×C79C2411yescharacteristic
261C22×C4×C79C2413yes—
262C22×C4×C79C2411yescharacteristic
263C22×C4×C79C24112yes—
264C22×C4×C79C24112yes—
265C22×C4×C79C2413yes—
266C4⋊C4×C79C24112yes—
267C4⋊C4×C79C24112yes—
268C22⋊C4×C79C2414yes—
269C22⋊C4×C79C24112yes—
270C22⋊C4×C79C24124yes—
271C42×C79C24112yes—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79—26no—
275C23×C79—26no—
276C23×C79—26no—
277C23×C79H(5,𝔽2)14yes—
278C23×C79C2516yes—
279C23×C79C2512yes—
280C23×C79C2511yescharacteristic
281C22×D79—26no—
282C22×D79—26no—
283C22×D79—26no—
284C22×D79C2516yes—
285Q8×C79—224no—
286Q8×C79C2×#41116yescomplemented
287D4×C79—224no—
288D4×C79—224no—
289C2×C4×C79—22no—
290C2×C4×C79—26no—
291C2×C4×C79—26no—
292C2×C4×C79—22no—
293C2×C4×C79—224no—
294C2×C4×C79—224no—
295C2×C4×C79C2×#41112yes—
296C2×C4×C79C2516yes—
297C2×C4×C79C2512yes—
298C2×C4×C79C2512yes—
299C2×C4×C79C2516yes—
300C2×C4×C79C2516yes—
301C22⋊D79—224no—
302C22⋊D79—224no—
303C22⋊D79—424no—
304C2×Dic79—22no—
305C2×Dic79—26no—
306C2×Dic79—26no—
307C2×Dic79—224no—
308C2×Dic79—26no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—28no—
312C2×Dic79—424no—
313C2×Dic792−1+414yes—
314C2×Dic79C2512yes—
315C2×Dic79C2512yes—
316C2×Dic79C2516yes—
317C2×Dic79C2516yes—
318C2×Dic79C2516yes—
319C2×Dic79C2512yes—
320C2×Dic79C2512yes—
321D316—224no—
322C4×D79—224no—
323C4×D79—424no—
324Dic158—28no—
325Dic158—424no—
326C22×C79—22no—
327C22×C79—22no—
328C22×C79—28no—
329C22×C79—26no—
330C22×C79—26no—
331C22×C79—26no—
332C22×C79—412no—
333C22×C79C22×#4112yes—
334C22×C79C2×H(5,𝔽2)14yes—
335C22×C79C2×H(5,𝔽2)12yes—
336C22×C79C2×2−1+412yes—
337C22×C79C2611yescharacteristic
338C2×D79—26no—
339C2×D79—26no—
340C2×D79—26no—
341C2×D79—412no—
342C4×C79—22no—
343C4×C79—26no—
344C4×C79—26no—
345C4×C79—22no—
346C4×C79C22×#41112yes—
347Dic79—22no—
348Dic79—26no—
349Dic79—26no—
350Dic79—26no—
351Dic79—22no—
352Dic79—22no—
353Dic79C2×2−1+414yes—
354C2×#3522—791nomaximal, Sylow
355C2×C79—24no—
356C2×C79—46no—
357C2×C79#352214yescomplemented
358C2×C79C23×#4111yescharacteristic
359C2×C79C22×H(5,𝔽2)11yescharacteristic
360C2×C79C22×2−1+411yescharacteristic
361D79—46no—
362#3522—7932no—
363C2×#559—793no—
364C2×Q82—791no—
365C2×#554—793no—
366C2×#550—791no—
367C2×#548—791no—
368C2×#548D7911yescharacteristic, complemented
369C2×#547—793no—
370C2×#547—793no—
371C2×#542—793no—
372C2×#542—793no—
373C2×#532—793no—
374C2×#529—793no—
375C2×#520—791no—
376C2×#520—791no—
377C22×C4×Q8—791no—
378C79C2×#352211yescharacteristic, complemented, Sylow
379C22×#41—791no—
380C22×#41—796no—
381C22×#41C2×D7911yescharacteristic
382C23×Q8C2×D7911yescharacteristic
383#559—7948no—
384Q82—7916no—
385#554—7948no—
386#550—7916no—
387#548—7916no—
388#548C2×D79116yescomplemented
389#547—7948no—
390#547—7948no—
391#542—7948no—
392#542—7948no—
393#532—7948no—
394C2×C4⋊Q8—793no—
395C2×C4⋊Q8—793no—
396C2×C4⋊Q8—793no—
397C2×#127—793no—
398#529—7948no—
399C2×#126—793no—
400C2×#126—793no—
401C2×#125—793no—
402C2×#124—793no—
403C2×#124—793no—
404C2×#124—796no—
405C2×#124C2×D7913yes—
406C2×#123—793no—
407C2×#123—793no—
408C2×#123—796no—
409C2×#123—796no—
410C2×C22⋊Q8—793no—
411C2×C22⋊Q8—796no—
412C2×C22⋊Q8—791no—
413C2×C22⋊Q8—796no—
414C2×C22⋊Q8C2×D7913yes—
415C2×#121—793no—
416C2×#121—793no—
417C2×#121—793no—
418C2×#121—793no—
419C2×#121C2×D7913yes—
420#520—7916no—
421#520—7916no—
422C2×C4×Q8—791no—
423C2×C4×Q8—793no—
424C2×C4×Q8—791no—
425C2×C4×Q8—793no—
426C2×C4×Q8—7916no—
427C2×C4×Q8—791no—
428C2×C4×Q8—793no—
429C2×C4×Q8C2×D7911yescharacteristic
430C2×C4×D4—793no—
431C2×C4×D4—793no—
432C2×C4×D4—793no—
433C2×C4×D4—793no—
434C2×C4×D4—793no—
435C2×C4×D4—796no—
436C2×C4×D4—793no—
437C2×C4×D4C2×D7913yes—
438C2×#117—793no—
439C2×#117—793no—
440C22×C4⋊C4—793no—
441C22×C4⋊C4—793no—
442C22×C4⋊C4—793no—
443C22×C42—793no—
444C2×#41—28no—
445C2×#41—31624no—
446C2×#41—798no—
447C2×#41—7948no—
448C2×#41—1588no—
449C2×#41C22×D7918yes—
450C22×Q8—28no—
451C22×Q8—796no—
452C22×Q8—791no—
453C22×Q8C22×D7913yes—
454C22×Q8C22×D7918yes—
455C22×Q8C22×D7911yescharacteristic
456C22×D4—796no—
457C22×D4—793no—
458C22×D4—793no—
459C22×D4—793no—
460C22×D4C22×D7913yes—
461C22×D4C22×D7913yes—
462C23×C4—796no—
463C23×C4—796no—
464C23×C4—793no—
465C23×C4—791no—
466C23×C4—793no—
467C23×C4C22×D7913yes—
468C23×C4C22×D7913yes—
469C4⋊Q8—7924no—
470C4⋊Q8—7924no—
471C4⋊Q8—7924no—
472#127—7924no—
473#126—7924no—
474#126—7924no—
475#125—7924no—
476#124—7924no—
477#124—7924no—
478#124—7948no—
479#124C22×D79124yes—
480#123—7924no—
481#123—7924no—
482#123—7948no—
483#123—7948no—
484C22⋊Q8—7924no—
485C22⋊Q8—7948no—
486C22⋊Q8—798no—
487C22⋊Q8—7948no—
488C22⋊Q8C22×D79124yes—
489#121—7924no—
490#121—7924no—
491#121—7924no—
492#121—7924no—
493#121C22×D79124yes—
494C4×Q8—798no—
495C4×Q8—7924no—
496C4×Q8—798no—
497C4×Q8—7924no—
498C4×Q8—798no—
499C4×Q8—7924no—
500C4×Q8C22×D7918yes—
501C4×D4—7924no—
502C4×D4—7924no—
503C4×D4—7924no—
504C4×D4—7924no—
505C4×D4—7924no—
506C4×D4—7948no—
507C4×D4—7924no—
508C4×D4C22×D79124yes—
509#117—7924no—
510#117—7924no—
511C2×C4⋊C4—793no—
512C2×C4⋊C4—793no—
513C2×C4⋊C4—793no—
514C2×C4⋊C4—793no—
515C2×C4⋊C4—793no—
516C2×C4⋊C4—796no—
517C2×C4⋊C4—7924no—
518C2×C4⋊C4—7924no—
519C2×C4⋊C4—791no—
520C2×C4⋊C4—791no—
521C2×C4⋊C4—791no—
522C2×C4⋊C4—793no—
523C2×C4⋊C4—793no—
524C2×C4⋊C4—793no—
525C2×C4⋊C4—793no—
526C2×C4⋊C4—7924no—
527C2×C4⋊C4C22×D7913yes—
528C2×C4⋊C4C22×D7913yes—
529C2×C22⋊C4—793no—
530C2×C22⋊C4—793no—
531C2×C22⋊C4—791no—
532C2×C22⋊C4—793no—
533C2×C22⋊C4—793no—
534C2×C22⋊C4—793no—
535C2×C22⋊C4—793no—
536C2×C22⋊C4—796no—
537C2×C22⋊C4—793no—
538C2×C22⋊C4C22×D7916yes—
539C2×C22⋊C4C22×D7911yescharacteristic
540C2×C22⋊C4C22×D7913yes—
541C2×C42—793no—
542C2×C42—793no—
543C2×C42—793no—
544C2×C42—793no—
545C2×C42—793no—
546C2×C42—7924no—
547C2×C42C22×D7913yes—
548C24—793no—
549C24C23×D7913yes—
550C24C23×D7911yescharacteristic
551#41—232no—
552#41—31696no—
553#41—15832no—
554C2×Q8—232no—
555C2×Q8—212no—
556C2×Q8—31612no—
557C2×Q8—7924no—
558C2×Q8—794no—
559C2×Q8—1584no—
560C2×Q8#1192962318yescomplemented
561C2×Q8C23×D79112yes—
562C2×Q8C23×D7914yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—31612no—
566C2×D4—7924no—
567C2×D4—7912no—
568C2×D4—7912no—
569C2×D4—7912no—
570C2×D4—15812no—
571C2×D4—15812no—
572C2×D4—15812no—
573C2×D4C23×D79112yes—
574C2×D4C23×D79112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—31612no—
578C22×C4—31612no—
579C22×C4—7924no—
580C22×C4—7924no—
581C22×C4—791no—
582C22×C4—794no—
583C22×C4—7912no—
584C22×C4—791no—
585C22×C4—791no—
586C22×C4—793no—
587C22×C4—793no—
588C22×C4—793no—
589C22×C4—791no—
590C22×C4—7912no—
591C22×C4—1584no—
592C22×C4—15812no—
593C22×C4—15812no—
594C22×C4C23×D79112yes—
595C22×C4C23×D79112yes—
596C22×C4C23×D7913yes—
597C22×C4C23×D7911yescharacteristic
598C22×C4C23×D7913yes—
599C22×C4C23×D7911yescharacteristic
600C22×C4C23×D7913yes—
601C4⋊C4—7912no—
602C4⋊C4—794no—
603C4⋊C4—794no—
604C4⋊C4—7912no—
605C4⋊C4—7912no—
606C4⋊C4—7912no—
607C4⋊C4—7912no—
608C4⋊C4—7912no—
609C4⋊C4—7912no—
610C4⋊C4—7912no—
611C4⋊C4—7924no—
612C4⋊C4—794no—
613C4⋊C4—7912no—
614C4⋊C4C23×D79112yes—
615C4⋊C4C23×D79112yes—
616C22⋊C4—7912no—
617C22⋊C4—7912no—
618C22⋊C4—794no—
619C22⋊C4—7912no—
620C22⋊C4—7912no—
621C22⋊C4—7912no—
622C22⋊C4—7912no—
623C22⋊C4—7924no—
624C22⋊C4—7912no—
625C22⋊C4C23×D79124yes—
626C22⋊C4C23×D7914yes—
627C22⋊C4C23×D79112yes—
628C42—7912no—
629C42—7912no—
630C42—7912no—
631C42—7912no—
632C42—7912no—
633C42C23×D79112yes—
634C23—22no—
635C23—22no—
636C23—26no—
637C23—26no—
638C23—26no—
639C23—796no—
640C23—1586no—
641C23—1586no—
642C23—1586no—
643C23#1457920714yes—
644C23C24×D7916yes—
645C23C24×D7912yes—
646C23C24×D7911yescharacteristic
647Q8—224no—
648Q8—31624no—
649Q8—1588no—
650Q8C2×#11929623116yescomplemented
651D4—224no—
652D4—224no—
653D4—31624no—
654D4—15824no—
655D4—15824no—
656D4—15824no—
657C2×C4—26no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—26no—
661C2×C4—224no—
662C2×C4—224no—
663C2×C4—31624no—
664C2×C4—31624no—
665C2×C4—794no—
666C2×C4—792no—
667C2×C4—792no—
668C2×C4—792no—
669C2×C4—796no—
670C2×C4—796no—
671C2×C4—796no—
672C2×C4—792no—
673C2×C4—1588no—
674C2×C4—1586no—
675C2×C4—1586no—
676C2×C4—1586no—
677C2×C4—15824no—
678C2×C4—1582no—
679C2×C4—1582no—
680C2×C4—1582no—
681C2×C4—15824no—
682C2×C4C2×#11929623112yes—
683C2×C4C24×D7916yes—
684C2×C4C24×D7912yes—
685C2×C4C24×D7916yes—
686C2×C4C24×D7912yes—
687C2×C4C24×D7916yes—
688C22—22no—
689C22—22no—
690C22—28no—
691C22—26no—
692C22—26no—
693C22—26no—
694C22—412no—
695C22—31612no—
696C22—1586no—
697C22—1586no—
698C22—1586no—
699C22C22×#1192962312yes—
700C22C2×#1457920714yes—
701C22C2×#1457920712yes—
702C222−1+4×D7912yes—
703C22C25×D7911yescharacteristic
704C4—22no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—794no—
709C4—1582no—
710C4—1586no—
711C4—1586no—
712C4—1586no—
713C4—1582no—
714C4—1582no—
715C4C22×#11929623112yes—
716C2—24no—
717C2—46no—
718C2—3166no—
719C2#2377747614yesdirect product factor
720C2C23×#1192962311yescharacteristic
721C2C22×#1457920711yescharacteristic
722C2C2×2−1+4×D7911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#548×C79C2
socleC23×C79C25
hypercenterC2×#548D79
hypocenterC79C2×#3522
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #23777476C2direct (N × H)
2. C2×#19099295C2semidirect
3. C2×Q8×Dic158C2semidirect
4. C2×#19099271C2semidirect
5. C2×#19099232C2semidirect
6. C2×#19099224C2semidirect
7. C2×#19099217C2semidirect
8. C2×#19099213C2semidirect
9. C2×#19099186C2semidirect
10. C2×#19099182C2semidirect
11. C2×#19099108C2semidirect
12. C2×#19099093C2semidirect
13. C2×#19099046C2semidirect
14. C2×#19099045C2semidirect
15. C22×Q8×Dic79C2semidirect
16. C2×#548×C79C2semidirect
19. #19099295C22semidirect
20. Q8×Dic158C22semidirect
21. #19099271C22semidirect
22. #19099232C22semidirect
23. #19099224C22semidirect
24. #19099217C22semidirect
25. #19099213C22semidirect
26. #19099186C22semidirect
27. #19099182C22semidirect
28. #19099108C22semidirect
33. #19099093C22semidirect
52. #19099046C22semidirect
53. #19099045C22semidirect
59. C2×Q8×Dic79C22semidirect
76. #548×C79C22semidirect
250. C2×Q8×C79#41semidirect
286. Q8×C79C2×#41semidirect
357. C2×C79#3522semidirect
368. C2×#548D79semidirect
378. C79C2×#3522semidirect
388. #548C2×D79semidirect
560. C2×Q8#11929623semidirect
650. Q8C2×#11929623semidirect
719. C2#23777476direct (N × H)

Maximal subgroups

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

subgroupindex
#237774762
C2×#190992952
C2×Q8×Dic1582
C2×#190992712
C2×#190992322
C2×#190992242
C2×#190992172
C2×#190992132
C2×#190991862
C2×#190991822
C2×#190991082
C2×#190990932
C2×#190990462
C2×#190990452
C22×Q8×Dic792
C2×#548×C792
C2×#352279