Finite Group Databasebeta

← C2×#23777487 #35196489

Subgroups — C2×#23777487 #35196489

Order 20224.

7022 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777487C2132yesmaximal, direct product factor
2C2×#19099289C211yesmaximal, characteristic, complemented
3C2×#19099288C213yesmaximal, complemented
4C2×#19099284C213yesmaximal, complemented
5C2×#19099255C213yesmaximal, complemented
6C2×#19099253C213yesmaximal, complemented
7C2×Q8×C22⋊D79C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D79C211yesmaximal, characteristic, complemented
9C2×#19099174C213yesmaximal, complemented
10C2×#19099173C213yesmaximal, complemented
11C2×#19099115C213yesmaximal, complemented
12C2×#19099093C213yesmaximal
13C2×#19099041C211yesmaximal, characteristic, complemented
14C2×#19099039C211yesmaximal, characteristic, complemented
15C22×Q8×Dic79C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C79C211yesmaximal, characteristic, complemented
17C22×Q8×D79C2211yescharacteristic
18#19099289C22116yescomplemented
19#19099288C22148yescomplemented
20#19099284C22148yescomplemented
21#19099255C22148yescomplemented
22#19099253C22148yescomplemented
23Q8×C22⋊D79C22116yescomplemented
24Q8×C22⋊D79C22116yescomplemented
25#19099174C22148yescomplemented
26#19099173C22148yescomplemented
27#19099115C22148yescomplemented
28C2×#14579160C2213yes—
29C2×#14579159C2213yes—
30C2×#14579159C2213yes—
31#19099093C22148yes—
32C2×#14579156C2216yes—
33C2×#14579156C2213yes—
34C2×#14579154C2216yes—
35C2×#14579154C2213yes—
36C2×#14579153C2213yes—
37C2×#14579152C2216yes—
38C2×#14579152C2213yes—
39C2×#14579151C2216yes—
40C2×#14579151C2213yes—
41C2×#14579151C2216yes—
42C2×#14579147C2213yes—
43C2×#14579145C2213yes—
44C2×#14579142C2213yes—
45C2×#14579140C2213yes—
46C2×#14579140C2213yes—
47C2×#14579138C2213yes—
48C2×#14579137C2213yes—
49C2×#14579137C2213yes—
50C2×#14579133C2211yescharacteristic
51#19099041C22116yescomplemented
52#19099039C22116yescomplemented
53C2×Q8×Dic79C2211yescharacteristic
54C2×Q8×Dic79C2211yescharacteristic
55C2×Q8×Dic79C2213yes—
56C2×Q8×Dic79C2213yes—
57C2×Q8×Dic79C2211yescharacteristic
58C2×Q8×Dic79C2213yes—
59C2×Q8×Dic79C2213yes—
60C2×Q8×Dic79C22116yescomplemented
61C2×C4×Dic158C2213yes—
62C2×C4×Dic158C2213yes—
63C2×#14579126C2213yes—
64C2×#14579126C2216yes—
65C2×C4×C22⋊D79C2213yes—
66C2×C4×C22⋊D79C2213yes—
67C2×#14579120C2213yes—
68C2×#14579120C2213yes—
69C2×#14579119C2213yes—
70C2×#14579118C2213yes—
71C2×#14579117C2216yes—
72C22×C4⋊Dic79C2213yes—
73C22×C4×Dic79C2213yes—
74C23×Q8×C79C2211yescharacteristic
75C23×Q8×C79C2211yescharacteristic
76D4×Q8×C79C22116yescomplemented
77C2×C4⋊Q8×C79C2213yes—
78C2×C22⋊Q8×C79C2213yes—
79C2×C22⋊Q8×C79C2213yes—
80C2×C4×Q8×C79C2211yescharacteristic
81C2×C4×D4×C79C2213yes—
82C22×Dic158C2313yes—
83C22×Dic158C2313yes—
84C2×Q8×D79—28no—
85C2×Q8×D79C2318yes—
86C22×C22⋊D79C2311yescharacteristic
87C22×C22⋊D79C2311yescharacteristic
88C23×Dic79C2311yescharacteristic
89C23×Dic79C2313yes—
90C22×C4×D79C2313yes—
91#14579160C23124yes—
92#14579159C23124yes—
93#14579159C23124yes—
94#14579156C23124yes—
95#14579156C23148yes—
96#14579154C23124yes—
97#14579154C23148yes—
98#14579153C23124yes—
99#14579152C23148yes—
100#14579152C23124yes—
101#14579151C23148yes—
102#14579151C23148yes—
103#14579151C23124yes—
104#14579147C23124yes—
105#14579145C23124yes—
106#14579142C23124yes—
107#14579140C23124yes—
108#14579140C23124yes—
109#14579138C23124yes—
110#14579137C23124yes—
111#14579137C23124yes—
112#14579133C2318yes—
113Q8×Dic79C23124yes—
114Q8×Dic79C23124yes—
115Q8×Dic79C2318yes—
116Q8×Dic79C2318yes—
117Q8×Dic79C23124yes—
118Q8×Dic79C23124yes—
119Q8×Dic79C2318yes—
120C4×Dic158C23124yes—
121C4×Dic158C23124yes—
122#14579126C23124yes—
123#14579126C23148yes—
124C4×C22⋊D79C23124yes—
125C4×C22⋊D79C23124yes—
126#14579120C23124yes—
127#14579120C23124yes—
128#14579119C23124yes—
129#14579118C23124yes—
130#14579117C23148yes—
131C2×C4⋊Dic79C23124yes—
132C2×C4⋊Dic79C2313yes—
133C2×C4⋊Dic79C2313yes—
134C2×C4⋊Dic79C2316yes—
135C2×C4⋊Dic79C2313yes—
136C2×C4⋊Dic79C2313yes—
137C2×C4⋊Dic79C2313yes—
138C2×C4⋊Dic79C2313yes—
139C2×Dic79⋊C4C2316yes—
140C2×Dic79⋊C4C2316yes—
141C2×Dic79⋊C4C2313yes—
142C2×Dic79⋊C4C2313yes—
143C2×Dic79⋊C4C2313yes—
144C2×Dic79⋊C4C2313yes—
145C2×Dic79⋊C4C2316yes—
146C2×Dic79⋊C4C2311yescharacteristic
147C2×Dic79⋊C4C2313yes—
148C2×C22⋊Dic79C2313yes—
149C2×C22⋊Dic79C2311yescharacteristic
150C2×C22⋊Dic79C2313yes—
151C2×C22⋊Dic79C2313yes—
152C2×(C2×D79)⋊C4C2311yescharacteristic
153C2×(C2×D79)⋊C4C2313yes—
154C2×(C2×D79)⋊C4C2313yes—
155C2×(C2×D79)⋊C4C2313yes—
156C2×C4×Dic79C2313yes—
157C2×C4×Dic79C2313yes—
158C2×C4×Dic79C2313yes—
159C2×C4×Dic79C2313yes—
160C2×C4×Dic79C23124yes—
161C2×C4×Dic79C2316yes—
162C2×C4×Dic79C2316yes—
163C2×C4×Dic79C2313yes—
164C22×Q8×C79—28no—
165C22×Q8×C79—28no—
166C22×Q8×C79C2318yes—
167C22×Q8×C79C2318yes—
168C22×Q8×C79C2313yes—
169C22×Q8×C79C2313yes—
170C22×Q8×C79C2311yescharacteristic
171C22×D4×C79C2311yescharacteristic
172C23×C4×C79C2313yes—
173C23×C4×C79C2313yes—
174C4⋊Q8×C79C23124yes—
175C22⋊Q8×C79C23124yes—
176C22⋊Q8×C79C23124yes—
177C4×Q8×C79C2318yes—
178C4×D4×C79C23124yes—
179C2×C4⋊C4×C79C2313yes—
180C2×C4⋊C4×C79C2313yes—
181C2×C4⋊C4×C79C2316yes—
182C2×C22⋊C4×C79C2313yes—
183C2×C22⋊C4×C79C2313yes—
184C2×C42×C79C2313yes—
185C23×D79C2411yescharacteristic
186C2×Dic158—212no—
187C2×Dic158—212no—
188C2×Dic158C24112yes—
189C2×Dic158C24112yes—
190Q8×D79—232no—
191C2×C22⋊D79—24no—
192C2×C22⋊D79—24no—
193C2×C22⋊D79C2414yes—
194C2×C22⋊D79C2414yes—
195C22×Dic79—24no—
196C22×Dic79—212no—
197C22×Dic79C2413yes—
198C22×Dic79C2413yes—
199C22×Dic79C2411yescharacteristic
200C22×Dic79C2413yes—
201C22×Dic79C2414yes—
202C22×Dic79C2411yescharacteristic
203C22×Dic79C2413yes—
204C22×Dic79C24112yes—
205C22×Dic79C2411yescharacteristic
206C2×C4×D79—212no—
207C2×C4×D79C24112yes—
208C4⋊Dic79C24112yes—
209C4⋊Dic79C24112yes—
210C4⋊Dic79C24124yes—
211C4⋊Dic79C24112yes—
212C4⋊Dic79C24112yes—
213C4⋊Dic79C24112yes—
214C4⋊Dic79C24112yes—
215Dic79⋊C4C24124yes—
216Dic79⋊C4C24124yes—
217Dic79⋊C4C24112yes—
218Dic79⋊C4C24112yes—
219Dic79⋊C4C24112yes—
220Dic79⋊C4C24112yes—
221Dic79⋊C4C24124yes—
222Dic79⋊C4C2414yes—
223Dic79⋊C4C24112yes—
224C22⋊Dic79C24112yes—
225C22⋊Dic79C2414yes—
226C22⋊Dic79C24112yes—
227C22⋊Dic79C24112yes—
228(C2×D79)⋊C4C2414yes—
229(C2×D79)⋊C4C24112yes—
230(C2×D79)⋊C4C24112yes—
231(C2×D79)⋊C4C24112yes—
232C4×Dic79C24112yes—
233C4×Dic79C24112yes—
234C4×Dic79C24112yes—
235C4×Dic79C24112yes—
236C4×Dic79C24124yes—
237C4×Dic79C24124yes—
238C4×Dic79C24112yes—
239C24×C79C2411yescharacteristic
240C24×C79C2411yescharacteristic
241C2×Q8×C79—232no—
242C2×Q8×C79—232no—
243C2×Q8×C79—212no—
244C2×Q8×C79—212no—
245C2×Q8×C79#4118yes—
246C2×Q8×C79C24112yes—
247C2×Q8×C79C24112yes—
248C2×Q8×C79C2414yes—
249C2×D4×C79—24no—
250C2×D4×C79C2414yes—
251C22×C4×C79—212no—
252C22×C4×C79—212no—
253C22×C4×C79C2413yes—
254C22×C4×C79C2411yescharacteristic
255C22×C4×C79C2413yes—
256C22×C4×C79C2413yes—
257C22×C4×C79C24112yes—
258C22×C4×C79C24112yes—
259C22×C4×C79C2413yes—
260C4⋊C4×C79C24112yes—
261C4⋊C4×C79C24112yes—
262C4⋊C4×C79C24124yes—
263C22⋊C4×C79C24112yes—
264C22⋊C4×C79C24112yes—
265C42×C79C24112yes—
266C23×C79—22no—
267C23×C79—22no—
268C23×C79—22no—
269C23×C79—22no—
270C23×C79—22no—
271C23×C792−1+414yes—
272C23×C79C2512yes—
273C23×C79C2512yes—
274C23×C79C2511yescharacteristic
275C22×D79—22no—
276C22×D79—22no—
277C22×D79—22no—
278C22×D79C2512yes—
279Q8×C79—224no—
280Q8×C79—224no—
281Q8×C79C2×#41116yes—
282D4×C79—28no—
283C2×C4×C79—26no—
284C2×C4×C79—26no—
285C2×C4×C79—26no—
286C2×C4×C79—22no—
287C2×C4×C79—224no—
288C2×C4×C79—224no—
289C2×C4×C79C2×#41112yes—
290C2×C4×C79C2516yes—
291C2×C4×C79C2516yes—
292C2×C4×C79C2516yes—
293C2×C4×C79C2512yes—
294C2×C4×C79C2516yes—
295C22⋊D79—28no—
296C22⋊D79—28no—
297C2×Dic79—26no—
298C2×Dic79—22no—
299C2×Dic79—224no—
300C2×Dic79—26no—
301C2×Dic79—26no—
302C2×Dic79—22no—
303C2×Dic79—26no—
304C2×Dic79—28no—
305C2×Dic792−1+414yes—
306C2×Dic79C2512yes—
307C2×Dic79C2516yes—
308C2×Dic79C2516yes—
309C2×Dic79C2512yes—
310C2×Dic79C2516yes—
311C2×Dic79C2516yes—
312C2×Dic79C2512yes—
313C4×D79—224no—
314Dic158—224no—
315Dic158—224no—
316C22×C79—22no—
317C22×C79—22no—
318C22×C79—28no—
319C22×C79—22no—
320C22×C79—22no—
321C22×C79—22no—
322C22×C79—44no—
323C22×C79C22×#4112yes—
324C22×C79C2×2−1+412yes—
325C22×C79C2×2−1+414yes—
326C22×C79C2×2−1+412yes—
327C22×C79C2611yescharacteristic
328C2×D79—22no—
329C2×D79—22no—
330C2×D79—22no—
331C2×D79—44no—
332C4×C79—26no—
333C4×C79—26no—
334C4×C79—22no—
335C4×C79—26no—
336C4×C79C22×#41112yes—
337Dic79—26no—
338Dic79—22no—
339Dic79—26no—
340Dic79—22no—
341Dic79—26no—
342Dic79—26no—
343Dic79C2×2−1+414yes—
344C2×#3523—791nomaximal, Sylow
345C2×C79—24no—
346C2×C79—42no—
347C2×C79#352314yescomplemented
348C2×C79C23×#4111yescharacteristic
349C2×C79C22×2−1+411yescharacteristic
350C2×C79C22×2−1+411yescharacteristic
351D79—42no—
352#3523—7932no—
353C2×#557—793no—
354C2×#557—791no—
355C2×#556—793no—
356C2×#552—793no—
357C2×#552—793no—
358C2×D4×Q8—791no—
359C2×D4×Q8—791no—
360C2×D4×Q8D7911yescharacteristic, complemented
361C2×#541—793no—
362C2×#541—793no—
363C2×#533—793no—
364C2×#529—793no—
365C2×#519—791no—
366C2×#519—791no—
367C22×C4×Q8—791no—
368C79C2×#352311yescharacteristic, complemented, Sylow
369C23×Q8—791no—
370C23×Q8C2×D7911yescharacteristic
371C23×Q8C2×D7911yescharacteristic
372#557—7948no—
373#557—7916no—
374#556—7948no—
375#552—7948no—
376#552—7948no—
377D4×Q8—7916no—
378D4×Q8—7916no—
379D4×Q8C2×D79116yescomplemented
380#541—7948no—
381#541—7948no—
382#533—7948no—
383C2×C4⋊Q8—793no—
384C2×C4⋊Q8—793no—
385C2×C4⋊Q8—793no—
386C2×C4⋊Q8C2×D7913yes—
387#529—7948no—
388C2×#126—793no—
389C2×#126—796no—
390C2×#126—793no—
391C2×#126—796no—
392C2×#125—793no—
393C2×#125—796no—
394C2×#125—796no—
395C2×#125—796no—
396C2×#125—793no—
397C2×#125—793no—
398C2×#124—793no—
399C2×#123—793no—
400C2×#123—793no—
401C2×C22⋊Q8—793no—
402C2×C22⋊Q8—793no—
403C2×C22⋊Q8—793no—
404C2×C22⋊Q8—793no—
405C2×C22⋊Q8—793no—
406C2×C22⋊Q8C2×D7913yes—
407C2×C22⋊Q8C2×D7913yes—
408C2×#121—791no—
409#519—7916no—
410#519—7916no—
411C2×C4×Q8—791no—
412C2×C4×Q8—793no—
413C2×C4×Q8—791no—
414C2×C4×Q8—793no—
415C2×C4×Q8—7916no—
416C2×C4×Q8—793no—
417C2×C4×Q8—791no—
418C2×C4×Q8—793no—
419C2×C4×Q8—793no—
420C2×C4×Q8—796no—
421C2×C4×Q8—793no—
422C2×C4×Q8—793no—
423C2×C4×Q8C2×D7911yescharacteristic
424C2×C4×D4—793no—
425C2×C4×D4—793no—
426C2×C4×D4C2×D7913yes—
427C2×#117—793no—
428C2×#117—793no—
429C2×#117—793no—
430C2×#117—796no—
431C2×#117—793no—
432C22×C4⋊C4—793no—
433C22×C42—793no—
434C22×Q8—28no—
435C22×Q8—28no—
436C22×Q8—798no—
437C22×Q8—793no—
438C22×Q8—793no—
439C22×Q8—1588no—
440C22×Q8C22×D7913yes—
441C22×Q8C22×D7913yes—
442C22×Q8C22×D7918yes—
443C22×Q8C22×D7918yes—
444C22×Q8C22×D7911yescharacteristic
445C22×D4—791no—
446C22×D4—791no—
447C22×D4C22×D7911yescharacteristic
448C23×C4—793no—
449C23×C4—791no—
450C23×C4—793no—
451C23×C4C22×D7913yes—
452C23×C4C22×D7913yes—
453C4⋊Q8—7924no—
454C4⋊Q8—7924no—
455C4⋊Q8—7924no—
456C4⋊Q8C22×D79124yes—
457#126—7924no—
458#126—7948no—
459#126—7924no—
460#126—7948no—
461#125—7924no—
462#125—7948no—
463#125—7948no—
464#125—7948no—
465#125—7924no—
466#125—7924no—
467#124—7924no—
468#123—7924no—
469#123—7924no—
470C22⋊Q8—7924no—
471C22⋊Q8—7924no—
472C22⋊Q8—7924no—
473C22⋊Q8—7924no—
474C22⋊Q8—7924no—
475C22⋊Q8C22×D79124yes—
476C22⋊Q8C22×D79124yes—
477#121—798no—
478C4×Q8—798no—
479C4×Q8—7924no—
480C4×Q8—798no—
481C4×Q8—7924no—
482C4×Q8—7924no—
483C4×Q8—798no—
484C4×Q8—7924no—
485C4×Q8—7924no—
486C4×Q8—7948no—
487C4×Q8—7924no—
488C4×Q8—7924no—
489C4×Q8C22×D7918yes—
490C4×D4—7924no—
491C4×D4—7924no—
492C4×D4C22×D79124yes—
493#117—7924no—
494#117—7924no—
495#117—7924no—
496#117—7948no—
497#117—7924no—
498C2×C4⋊C4—793no—
499C2×C4⋊C4—793no—
500C2×C4⋊C4—796no—
501C2×C4⋊C4—7924no—
502C2×C4⋊C4—793no—
503C2×C4⋊C4—793no—
504C2×C4⋊C4—793no—
505C2×C4⋊C4—793no—
506C2×C4⋊C4—793no—
507C2×C4⋊C4—796no—
508C2×C4⋊C4—796no—
509C2×C4⋊C4—793no—
510C2×C4⋊C4—793no—
511C2×C4⋊C4—791no—
512C2×C4⋊C4—796no—
513C2×C4⋊C4—793no—
514C2×C4⋊C4—793no—
515C2×C4⋊C4C22×D7913yes—
516C2×C4⋊C4C22×D7913yes—
517C2×C4⋊C4C22×D7916yes—
518C2×C22⋊C4—791no—
519C2×C22⋊C4—793no—
520C2×C22⋊C4—793no—
521C2×C22⋊C4—793no—
522C2×C22⋊C4—791no—
523C2×C22⋊C4—793no—
524C2×C22⋊C4—793no—
525C2×C22⋊C4—793no—
526C2×C22⋊C4C22×D7913yes—
527C2×C22⋊C4C22×D7913yes—
528C2×C42—793no—
529C2×C42—796no—
530C2×C42—796no—
531C2×C42—793no—
532C2×C42—793no—
533C2×C42—793no—
534C2×C42—793no—
535C2×C42—7924no—
536C2×C42C22×D7913yes—
537C24—791no—
538C24C23×D7911yescharacteristic
539C24C23×D7911yescharacteristic
540C2×Q8—232no—
541C2×Q8—232no—
542C2×Q8—212no—
543C2×Q8—212no—
544C2×Q8—7912no—
545C2×Q8—7912no—
546C2×Q8—15812no—
547C2×Q8—15832no—
548C2×Q8—15812no—
549C2×Q8#1192962318yes—
550C2×Q8C23×D79112yes—
551C2×Q8C23×D79112yes—
552C2×Q8C23×D7914yes—
553C2×D4—24no—
554C2×D4—794no—
555C2×D4—794no—
556C2×D4—1584no—
557C2×D4—1584no—
558C2×D4C23×D7914yes—
559C22×C4—212no—
560C22×C4—212no—
561C22×C4—791no—
562C22×C4—794no—
563C22×C4—7912no—
564C22×C4—791no—
565C22×C4—793no—
566C22×C4—793no—
567C22×C4—791no—
568C22×C4—793no—
569C22×C4—793no—
570C22×C4—7912no—
571C22×C4—1584no—
572C22×C4—15812no—
573C22×C4—15812no—
574C22×C4C23×D79112yes—
575C22×C4C23×D79112yes—
576C22×C4C23×D7913yes—
577C22×C4C23×D7913yes—
578C22×C4C23×D7913yes—
579C22×C4C23×D7911yescharacteristic
580C22×C4C23×D7913yes—
581C4⋊C4—7912no—
582C4⋊C4—7912no—
583C4⋊C4—7924no—
584C4⋊C4—7924no—
585C4⋊C4—7912no—
586C4⋊C4—7912no—
587C4⋊C4—794no—
588C4⋊C4—7924no—
589C4⋊C4—7912no—
590C4⋊C4—7912no—
591C4⋊C4—7912no—
592C4⋊C4—7924no—
593C4⋊C4—7912no—
594C4⋊C4—7912no—
595C4⋊C4—7912no—
596C4⋊C4—7912no—
597C4⋊C4C23×D79112yes—
598C4⋊C4C23×D79112yes—
599C4⋊C4C23×D79124yes—
600C22⋊C4—794no—
601C22⋊C4—7912no—
602C22⋊C4—7912no—
603C22⋊C4—7912no—
604C22⋊C4—794no—
605C22⋊C4—7912no—
606C22⋊C4—7912no—
607C22⋊C4—7912no—
608C22⋊C4C23×D79112yes—
609C22⋊C4C23×D79112yes—
610C42—7912no—
611C42—7912no—
612C42—7912no—
613C42—7912no—
614C42—7924no—
615C42—7924no—
616C42—7912no—
617C42C23×D79112yes—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—792no—
624C23—1582no—
625C23—1582no—
626C23—1582no—
627C23#1457920914yes—
628C23C24×D7912yes—
629C23C24×D7912yes—
630C23C24×D7911yescharacteristic
631Q8—224no—
632Q8—224no—
633Q8—15824no—
634Q8—15824no—
635Q8C2×#11929623116yes—
636D4—28no—
637D4—1588no—
638D4—1588no—
639C2×C4—26no—
640C2×C4—22no—
641C2×C4—26no—
642C2×C4—26no—
643C2×C4—224no—
644C2×C4—224no—
645C2×C4—794no—
646C2×C4—792no—
647C2×C4—792no—
648C2×C4—796no—
649C2×C4—796no—
650C2×C4—792no—
651C2×C4—796no—
652C2×C4—796no—
653C2×C4—1588no—
654C2×C4—1582no—
655C2×C4—1586no—
656C2×C4—15824no—
657C2×C4—1586no—
658C2×C4—1586no—
659C2×C4—1582no—
660C2×C4—1586no—
661C2×C4—15824no—
662C2×C4C2×#11929623112yes—
663C2×C4C24×D7916yes—
664C2×C4C24×D7916yes—
665C2×C4C24×D7916yes—
666C2×C4C24×D7912yes—
667C2×C4C24×D7916yes—
668C22—22no—
669C22—22no—
670C22—28no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—44no—
675C22—3164no—
676C22—1582no—
677C22—1582no—
678C22—1582no—
679C22C22×#1192962312yes—
680C222−1+4×D7912yes—
681C22C2×#1457920914yes—
682C22C2×#1457920912yes—
683C22C25×D7911yescharacteristic
684C4—26no—
685C4—26no—
686C4—26no—
687C4—22no—
688C4—794no—
689C4—1586no—
690C4—1582no—
691C4—1586no—
692C4—1586no—
693C4—1586no—
694C4—1582no—
695C4C22×#11929623112yes—
696C2—24no—
697C2—42no—
698C2—3162no—
699C2#2377748714yesdirect product factor
700C2C23×#1192962311yescharacteristic
701C2C2×2−1+4×D7911yescharacteristic
702C2C22×#1457920911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×D4×Q8×C79C2
socleC23×C79C25
prime radicalC2×#14579133C22
hypercenterC2×D4×Q8D79
hypocenterC79C2×#3523
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #23777487C2direct (N × H)
2. C2×#19099289C2semidirect
3. C2×#19099288C2semidirect
4. C2×#19099284C2semidirect
5. C2×#19099255C2semidirect
6. C2×#19099253C2semidirect
7. C2×Q8×C22⋊D79C2semidirect
8. C2×Q8×C22⋊D79C2semidirect
9. C2×#19099174C2semidirect
10. C2×#19099173C2semidirect
11. C2×#19099115C2semidirect
13. C2×#19099041C2semidirect
14. C2×#19099039C2semidirect
15. C22×Q8×Dic79C2semidirect
16. C2×D4×Q8×C79C2semidirect
18. #19099289C22semidirect
19. #19099288C22semidirect
20. #19099284C22semidirect
21. #19099255C22semidirect
22. #19099253C22semidirect
23. Q8×C22⋊D79C22semidirect
24. Q8×C22⋊D79C22semidirect
25. #19099174C22semidirect
26. #19099173C22semidirect
27. #19099115C22semidirect
51. #19099041C22semidirect
52. #19099039C22semidirect
60. C2×Q8×Dic79C22semidirect
76. D4×Q8×C79C22semidirect
347. C2×C79#3523semidirect
360. C2×D4×Q8D79semidirect
368. C79C2×#3523semidirect
379. D4×Q8C2×D79semidirect
699. C2#23777487direct (N × H)

Maximal subgroups

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

subgroupindex
#237774872
C2×#190992892
C2×#190992882
C2×#190992842
C2×#190992552
C2×#190992532
C2×Q8×C22⋊D792
C2×#190991742
C2×#190991732
C2×#190991152
C2×#190990932
C2×#190990412
C2×#190990392
C22×Q8×Dic792
C2×D4×Q8×C792
C2×#352379