Finite Group Databasebeta

← C2×#23777077 #35196669

Subgroups — C2×#23777077 #35196669

Order 20224.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579209C211yesmaximal, characteristic, complemented
2C23×#11929625C211yesmaximal, characteristic, complemented
3#23777077C2132yesmaximal, direct product factor
4C2×Q8×C22⋊D79C211yesmaximal, characteristic, complemented
5C2×#19099225C211yesmaximal, characteristic, complemented
6C2×#19099224C211yesmaximal, characteristic, complemented
7C2×#19099216C213yesmaximal, complemented
8C2×#19099215C213yesmaximal, complemented
9C2×#19099209C213yesmaximal, complemented
10C2×#19099204C213yesmaximal, complemented
11C2×#19099143C213yesmaximal, complemented
12C2×#19099138C213yesmaximal, complemented
13C2×#19099072C213yesmaximal, complemented
14C2×C22⋊Q8×D79C213yesmaximal, complemented
15C2×#19099045C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C79C211yesmaximal, characteristic, complemented
17C2×#14579209—216no—
18C2×#14579209C22116yescomplemented
19C22×#11929625—216no—
20C22×#11929625C2213yes—
21C22×#11929625C2211yescharacteristic
22C22×#11929625C2213yes—
23C22×#11929625C2211yescharacteristic
24C22×#11929625C22116yescomplemented
25C22×#11929625C2213yescomplemented
26C22×#11929624C2213yescomplemented
27C22×#11929624C2213yescomplemented
28C22×Q8×D79C2211yescharacteristic, complemented
29C22×Q8×D79C2213yescomplemented
30C23×D316C2213yes—
31C23×C4×D79C2213yes—
32Q8×C22⋊D79C22116yescomplemented
33#19099225C22116yescomplemented
34#19099224C22116yescomplemented
35#19099216C22148yescomplemented
36#19099215C22148yescomplemented
37#19099209C22148yescomplemented
38#19099204C22148yescomplemented
39#19099143C22148yescomplemented
40#19099138C22148yescomplemented
41C2×#14579159C2213yescomplemented
42C2×#14579150C2213yescomplemented
43C2×#14579149C2213yescomplemented
44#19099072C22148yescomplemented
45C2×#14579146C2216yescomplemented
46C2×#14579146C2216yescomplemented
47C2×#14579146C2213yescomplemented
48C2×#14579143C2213yescomplemented
49C2×#14579141C2213yescomplemented
50C2×#14579140C2213yes—
51C2×#14579139C2216yescomplemented
52C2×#14579139C2213yescomplemented
53C2×#14579138C2213yes—
54C2×#14579137C2213yescomplemented
55C2×#14579137C2213yescomplemented
56C22⋊Q8×D79C22148yescomplemented
57C2×#14579136C2216yescomplemented
58C2×#14579136C2213yescomplemented
59C2×#14579135C2213yescomplemented
60C2×#14579134C2216yescomplemented
61C2×#14579134C2213yescomplemented
62C2×#14579133C2211yescharacteristic
63C2×#14579131C2213yes—
64C2×#14579129C2213yes—
65#19099045C22116yescomplemented
66C2×Q8×Dic79C2211yescharacteristic, complemented
67C2×C4×D316C2213yescomplemented
68C2×C4×D316C2213yescomplemented
69C2×#14579123C2213yescomplemented
70C2×C4×C22⋊D79C2213yes—
71C2×C4×C22⋊D79C2213yescomplemented
72C2×#14579118C2213yescomplemented
73C2×C4⋊C4×D79C2213yescomplemented
74C2×C4⋊C4×D79C2216yescomplemented
75C2×C22⋊C4×D79C2216yes—
76C23×Q8×C79C2211yescharacteristic
77C23×Q8×C79C2211yescharacteristic, complemented
78D4×Q8×C79C22116yescomplemented
79C2×C4⋊Q8×C79C2213yescomplemented
80C2×C22⋊Q8×C79C2213yes—
81C2×C22⋊Q8×C79C2213yescomplemented
82C2×C4×Q8×C79C2211yescharacteristic, complemented
83C2×C4×D4×C79C2213yes—
84C24×D79C2313yes—
85#14579209—2128no—
86C2×#11929625—28no—
87C2×#11929625—2128no—
88C2×#11929625—224no—
89C2×#11929625—224no—
90C2×#11929625—224no—
91C2×#11929625D4116yescomplemented
92C2×#11929625C23124yes—
93C2×#11929625C23124yes—
94C2×#11929625C2318yes—
95C2×#11929625C2318yes—
96C2×#11929625C23124yescomplemented
97C2×#11929624—224no—
98C2×#11929624—224no—
99C2×#11929624C23124yescomplemented
100C2×#11929624C23124yescomplemented
101C22×Dic158C2313yes—
102C22×Dic158C2313yes—
103C2×Q8×D79—28no—
104C2×Q8×D79—224no—
105C2×Q8×D79C23124yescomplemented
106C2×Q8×D79C2318yescomplemented
107C22×D316—224no—
108C22×D316C23124yes—
109C22×D316C2313yes—
110C22×D316C2316yes—
111C22×D316C2313yes—
112C22×D316C2313yes—
113C22×D316C2313yes—
114C22×C22⋊D79C2311yescharacteristic
115C22×C22⋊D79C2313yes—
116C22×C22⋊D79C2311yescharacteristic
117C22×C22⋊D79C2313yes—
118C23×Dic79C2311yescharacteristic
119C22×C4×D79—224no—
120C22×C4×D79C2316yes—
121C22×C4×D79C2313yes—
122C22×C4×D79C2313yes—
123C22×C4×D79C2313yes—
124C22×C4×D79C2313yes—
125C22×C4×D79C23124yes—
126C22×C4×D79C2316yes—
127C22×C4×D79C2313yes—
128#14579159C23124yescomplemented
129#14579150C23124yescomplemented
130#14579149C23124yescomplemented
131#14579146C23148yescomplemented
132#14579146C23148yescomplemented
133#14579146C23124yescomplemented
134#14579143C23124yescomplemented
135#14579141C23124yescomplemented
136#14579140C23124yes—
137#14579139C23124yescomplemented
138#14579139C23148yescomplemented
139#14579138C23124yes—
140#14579137C23124yescomplemented
141#14579137C23124yescomplemented
142#14579136C23148yescomplemented
143#14579136C23124yescomplemented
144#14579135C23124yescomplemented
145#14579134C23124yescomplemented
146#14579134C23148yescomplemented
147#14579133C2318yes—
148#14579131C23124yes—
149#14579129C23124yes—
150Q8×Dic79C2318yescomplemented
151C4×D316C23124yescomplemented
152C4×D316C23124yescomplemented
153#14579123C23124yescomplemented
154C4×C22⋊D79C23124yes—
155C4×C22⋊D79C23124yescomplemented
156#14579118C23124yescomplemented
157C2×C4⋊Dic79C2313yes—
158C2×C4⋊Dic79C2313yes—
159C2×Dic79⋊C4C2313yes—
160C2×Dic79⋊C4C2313yes—
161C2×Dic79⋊C4C2316yes—
162C2×Dic79⋊C4C2311yescharacteristic
163C2×Dic79⋊C4C2313yes—
164C4⋊C4×D79C23124yescomplemented
165C4⋊C4×D79C23148yescomplemented
166C2×C22⋊Dic79C2313yes—
167C2×C22⋊Dic79C2311yescharacteristic
168C2×(C2×D79)⋊C4C2316yes—
169C2×(C2×D79)⋊C4C2316yes—
170C2×(C2×D79)⋊C4C2313yes—
171C2×(C2×D79)⋊C4C2313yes—
172C2×(C2×D79)⋊C4C2313yes—
173C2×(C2×D79)⋊C4C2313yes—
174C2×(C2×D79)⋊C4C2311yescharacteristic
175C2×(C2×D79)⋊C4C2313yes—
176C22⋊C4×D79C23148yes—
177C2×C4×Dic79C2313yes—
178C22×Q8×C79—28no—
179C22×Q8×C79—28no—
180C22×Q8×C79C2318yes—
181C22×Q8×C79C2313yes—
182C22×Q8×C79C2313yes—
183C22×Q8×C79C2311yescharacteristic
184C22×Q8×C79C2318yescomplemented
185C22×D4×C79C2311yescharacteristic
186C23×C4×C79C2313yes—
187C23×C4×C79C2313yes—
188C4⋊Q8×C79C23124yescomplemented
189C22⋊Q8×C79C23124yes—
190C22⋊Q8×C79C23124yescomplemented
191C4×Q8×C79C2318yescomplemented
192C4×D4×C79C23124yes—
193C2×C4⋊C4×C79C2313yes—
194C2×C4⋊C4×C79C2313yes—
195C2×C4⋊C4×C79C2316yes—
196C2×C22⋊C4×C79C2313yes—
197C2×C22⋊C4×C79C2313yes—
198C2×C42×C79C2313yes—
199C23×D79—212no—
200C23×D79—212no—
201C23×D79—46no—
202C23×D79C2413yes—
203C23×D79C2411yescharacteristic
204C23×D79C24112yes—
205C23×D79C2413yes—
206#11929625—296no—
207#11929625—296no—
208#11929625—296no—
209#11929625—232no—
210#11929625C2×D4164yescomplemented
211#11929624—296no—
212#11929624—296no—
213C2×Dic158—212no—
214C2×Dic158—212no—
215C2×Dic158C24112yes—
216C2×Dic158C24112yes—
217Q8×D79—296no—
218Q8×D79—232no—
219C2×D316—296no—
220C2×D316—212no—
221C2×D316—224no—
222C2×D316—212no—
223C2×D316—46no—
224C2×D316C2×D4124yes—
225C2×D316C24112yes—
226C2×D316C24124yes—
227C2×D316C24112yes—
228C2×D316C24112yes—
229C2×D316C24112yes—
230C2×C22⋊D79—24no—
231C2×C22⋊D79—24no—
232C2×C22⋊D79—212no—
233C2×C22⋊D79—46no—
234C2×C22⋊D79C24112yes—
235C2×C22⋊D79C2414yes—
236C2×C22⋊D79C2414yes—
237C2×C22⋊D79C24112yes—
238C22×Dic79—24no—
239C22×Dic79C2413yes—
240C22×Dic79C2411yescharacteristic
241C22×Dic79C2413yes—
242C22×Dic79C2411yescharacteristic
243C22×Dic79C2414yes—
244C22×Dic79C2411yescharacteristic
245C2×C4×D79—212no—
246C2×C4×D79—296no—
247C2×C4×D79—224no—
248C2×C4×D79—212no—
249C2×C4×D79—212no—
250C2×C4×D79—212no—
251C2×C4×D79—412no—
252C2×C4×D79C2×D4124yes—
253C2×C4×D79C24124yes—
254C2×C4×D79C24112yes—
255C2×C4×D79C24112yes—
256C2×C4×D79C24112yes—
257C2×C4×D79C24112yes—
258C2×C4×D79C24124yes—
259C2×C4×D79C24112yes—
260C4⋊Dic79C24112yes—
261C4⋊Dic79C24112yes—
262Dic79⋊C4C24112yes—
263Dic79⋊C4C24112yes—
264Dic79⋊C4C24124yes—
265Dic79⋊C4C2414yes—
266Dic79⋊C4C24112yes—
267C22⋊Dic79C24112yes—
268C22⋊Dic79C2414yes—
269(C2×D79)⋊C4C24124yes—
270(C2×D79)⋊C4C24124yes—
271(C2×D79)⋊C4C24112yes—
272(C2×D79)⋊C4C24112yes—
273(C2×D79)⋊C4C24112yes—
274(C2×D79)⋊C4C24112yes—
275(C2×D79)⋊C4C2414yes—
276(C2×D79)⋊C4C24112yes—
277C4×Dic79C24112yes—
278C24×C79C2411yescharacteristic
279C24×C79C2411yescharacteristic
280C2×Q8×C79—232no—
281C2×Q8×C79—232no—
282C2×Q8×C79—212no—
283C2×Q8×C79—212no—
284C2×Q8×C79C2×D418yes—
285C2×Q8×C79C24112yes—
286C2×Q8×C79C24112yes—
287C2×Q8×C79C2414yes—
288C2×D4×C79—24no—
289C2×D4×C79C2414yes—
290C22×C4×C79—212no—
291C22×C4×C79—212no—
292C22×C4×C79C2413yes—
293C22×C4×C79C24112yes—
294C22×C4×C79C2411yescharacteristic
295C22×C4×C79C2413yes—
296C22×C4×C79C2413yes—
297C22×C4×C79C24112yes—
298C22×C4×C79C2413yes—
299C4⋊C4×C79C24112yes—
300C4⋊C4×C79C24112yes—
301C4⋊C4×C79C24124yes—
302C22⋊C4×C79C24112yes—
303C22⋊C4×C79C24112yes—
304C42×C79C24112yes—
305C23×C79—22no—
306C23×C79—22no—
307C23×C79—22no—
308C23×C79—22no—
309C23×C79—22no—
310C23×C792−1+414yescomplemented
311C23×C79C2512yes—
312C23×C79C2512yes—
313C23×C79C2511yescharacteristic
314C22×D79—26no—
315C22×D79—26no—
316C22×D79—22no—
317C22×D79—26no—
318C22×D79—22no—
319C22×D79—26no—
320C22×D79—224no—
321C22×D79—26no—
322C22×D79—22no—
323C22×D79—224no—
324C22×D79—412no—
325C22×D79—448no—
326C22×D79C22×D4112yes—
327C22×D79C2516yes—
328C22×D79C2512yes—
329C22×D79C2516yes—
330Q8×C79—224no—
331Q8×C79—224no—
332Q8×C79C22×D4116yes—
333D4×C79—28no—
334C2×C4×C79—26no—
335C2×C4×C79—26no—
336C2×C4×C79—22no—
337C2×C4×C79—26no—
338C2×C4×C79—224no—
339C2×C4×C79—224no—
340C2×C4×C79C22×D4112yes—
341C2×C4×C79C2512yes—
342C2×C4×C79C2516yes—
343C2×C4×C79C2516yes—
344C2×C4×C79C2516yes—
345C2×C4×C79C2516yes—
346C22⋊D79—28no—
347C22⋊D79—224no—
348C22⋊D79—28no—
349C22⋊D79—412no—
350C2×Dic79—22no—
351C2×Dic79—26no—
352C2×Dic79—22no—
353C2×Dic79—26no—
354C2×Dic79—28no—
355C2×Dic79C22×D414yes—
356C2×Dic79C2512yes—
357C2×Dic79C2516yes—
358C2×Dic79C2516yes—
359C2×Dic79C2512yes—
360C2×Dic79C2512yes—
361D316—248no—
362D316—224no—
363D316—224no—
364D316—412no—
365D316C22×D4148yes—
366C4×D79—224no—
367C4×D79—248no—
368C4×D79—224no—
369C4×D79—224no—
370C4×D79—224no—
371C4×D79—424no—
372C4×D79C22×D4148yes—
373Dic158—224no—
374Dic158—224no—
375C22×C79—22no—
376C22×C79—22no—
377C22×C79—28no—
378C22×C79—22no—
379C22×C79—22no—
380C22×C79—22no—
381C22×C79—44no—
382C22×C79C23×D412yes—
383C22×C79C2×2−1+412yes—
384C22×C79C2×2−1+414yescomplemented
385C22×C79#58512yes—
386C22×C79C2611yescharacteristic
387C2×D79—26no—
388C2×D79—26no—
389C2×D79—224no—
390C2×D79—22no—
391C2×D79—26no—
392C2×D79—22no—
393C2×D79—26no—
394C2×D79—26no—
395C2×D79—22no—
396C2×D79—448no—
397C2×D79—44no—
398C2×D79—412no—
399C2×D79C23×D4112yes—
400C4×C79—26no—
401C4×C79—26no—
402C4×C79—22no—
403C4×C79—26no—
404C4×C79C23×D4112yes—
405Dic79—26no—
406Dic79—22no—
407Dic79—22no—
408Dic79—26no—
409Dic79C23×D414yes—
410C2×#3489—791nomaximal, Sylow
411C2×C79—24no—
412C2×C79—42no—
413C2×C79#348914yescomplemented
414C2×C79C24×D411yescharacteristic
415C2×C79C22×2−1+411yescharacteristic
416C2×C79C2×#58511yescharacteristic
417D79—212no—
418D79—42no—
419D79—46no—
420C22×2−1+4—791no—
421C23×#41—791no—
422#3489—7932no—
423C2×D4×Q8—791no—
424C2×D4×Q8D7911yescharacteristic, complemented
425C2×#548—791no—
426C2×#548—791no—
427C2×#547—793no—
428C2×#547—793no—
429C2×#546—793no—
430C2×#546—793no—
431C2×#537—793no—
432C2×#536—793no—
433C2×#525—793no—
434C22×C22⋊Q8—793no—
435C2×#520—791no—
436C79C2×#348911yescharacteristic, complemented, Sylow
437C2×2−1+4—7916no—
438C2×2−1+4—15816no—
439C22×#41—791no—
440C22×#41—793no—
441C22×#41—793no—
442C22×#41—791no—
443C22×#41—7916no—
444C22×#41—793no—
445C22×#41—793no—
446C22×#41—793no—
447C22×#41—15816no—
448C23×Q8—793no—
449C23×Q8—791no—
450C23×Q8C2×D7911yescharacteristic
451C23×Q8C2×D7911yescharacteristic, complemented
452C23×D4—793no—
453C24×C4—793no—
454D4×Q8—7916no—
455D4×Q8C2×D79116yescomplemented
456#548—7916no—
457#548—7916no—
458#547—7948no—
459#547—7948no—
460#546—7948no—
461#546—7948no—
462#537—7948no—
463#536—7948no—
464C2×C4⋊Q8—793no—
465C2×C4⋊Q8C2×D7913yescomplemented
466C2×#124—793no—
467C2×#124—793no—
468#525—7948no—
469C2×#123—793no—
470C2×#123—796no—
471C2×#123—796no—
472C2×#123—793no—
473C2×C22⋊Q8—793no—
474C2×C22⋊Q8—793no—
475C2×C22⋊Q8—793no—
476C2×C22⋊Q8—7948no—
477C2×C22⋊Q8—796no—
478C2×C22⋊Q8—793no—
479C2×C22⋊Q8—793no—
480C2×C22⋊Q8—793no—
481C2×C22⋊Q8C2×D7913yes—
482C2×C22⋊Q8C2×D7913yescomplemented
483C2×#121—791no—
484C2×#121—793no—
485C2×#121—796no—
486C2×#121—793no—
487C2×#121—793no—
488C2×#121—796no—
489C2×#120—793no—
490C2×#120—793no—
491#520—7916no—
492C2×C4×Q8—791no—
493C2×C4×Q8C2×D7911yescharacteristic, complemented
494C2×C4×D4—793no—
495C2×C4×D4—793no—
496C2×C4×D4—793no—
497C2×C4×D4—793no—
498C2×C4×D4—793no—
499C2×C4×D4C2×D7913yes—
500C2×#117—793no—
501C22×C4⋊C4—793no—
502C22×C4⋊C4—796no—
503C22×C22⋊C4—796no—
504C25—793no—
5052−1+4—158128no—
506C2×#41—7916no—
507C2×#41—798no—
508C2×#41—7924no—
509C2×#41—7924no—
510C2×#41—798no—
511C2×#41—7924no—
512C2×#41—7924no—
513C2×#41—7924no—
514C2×#41—15824no—
515C2×#41—15824no—
516C2×#41—15824no—
517C2×#41—15824no—
518C2×#41—15824no—
519C2×#41—158128no—
520C2×#41—1588no—
521C22×Q8—28no—
522C22×Q8—28no—
523C22×Q8—7924no—
524C22×Q8—798no—
525C22×Q8—793no—
526C22×Q8—793no—
527C22×Q8—15824no—
528C22×Q8—1588no—
529C22×Q8C22×D7913yes—
530C22×Q8C22×D7913yes—
531C22×Q8C22×D7918yes—
532C22×Q8C22×D7911yescharacteristic
533C22×Q8C22×D7918yescomplemented
534C22×D4—793no—
535C22×D4—791no—
536C22×D4—793no—
537C22×D4—791no—
538C22×D4—793no—
539C22×D4—793no—
540C22×D4—793no—
541C22×D4—796no—
542C22×D4—793no—
543C22×D4—7924no—
544C22×D4—15824no—
545C22×D4C22×D7911yescharacteristic
546C23×C4—796no—
547C23×C4—793no—
548C23×C4—791no—
549C23×C4—796no—
550C23×C4—793no—
551C23×C4—793no—
552C23×C4—793no—
553C23×C4—793no—
554C23×C4—7924no—
555C23×C4—15824no—
556C23×C4C22×D7913yes—
557C23×C4C22×D7913yes—
558C4⋊Q8—7924no—
559C4⋊Q8C22×D79124yescomplemented
560#124—7924no—
561#124—7924no—
562#123—7924no—
563#123—7948no—
564#123—7948no—
565#123—7924no—
566C22⋊Q8—7924no—
567C22⋊Q8—7924no—
568C22⋊Q8—7924no—
569C22⋊Q8—7948no—
570C22⋊Q8—7924no—
571C22⋊Q8—7924no—
572C22⋊Q8—7924no—
573C22⋊Q8C22×D79124yes—
574C22⋊Q8C22×D79124yescomplemented
575#121—798no—
576#121—7924no—
577#121—7948no—
578#121—7924no—
579#121—7924no—
580#121—7948no—
581#120—7924no—
582#120—7924no—
583C4×Q8—798no—
584C4×Q8C22×D7918yescomplemented
585C4×D4—7924no—
586C4×D4—7924no—
587C4×D4—7924no—
588C4×D4—7924no—
589C4×D4—7924no—
590C4×D4C22×D79124yes—
591#117—7924no—
592C2×C4⋊C4—793no—
593C2×C4⋊C4—793no—
594C2×C4⋊C4—793no—
595C2×C4⋊C4—793no—
596C2×C4⋊C4—796no—
597C2×C4⋊C4—791no—
598C2×C4⋊C4—793no—
599C2×C4⋊C4—7924no—
600C2×C4⋊C4—7948no—
601C2×C4⋊C4C22×D7913yes—
602C2×C4⋊C4C22×D7916yes—
603C2×C4⋊C4C22×D7913yes—
604C2×C22⋊C4—793no—
605C2×C22⋊C4—791no—
606C2×C22⋊C4—796no—
607C2×C22⋊C4—796no—
608C2×C22⋊C4—793no—
609C2×C22⋊C4—793no—
610C2×C22⋊C4—791no—
611C2×C22⋊C4—793no—
612C2×C22⋊C4—793no—
613C2×C22⋊C4—793no—
614C2×C22⋊C4—7948no—
615C2×C22⋊C4C22×D7913yes—
616C2×C22⋊C4C22×D7913yes—
617C2×C42—793no—
618C2×C42C22×D7913yes—
619C24—3166no—
620C24—7912no—
621C24—793no—
622C24—793no—
623C24—791no—
624C24—15812no—
625C24—15812no—
626C24C23×D7911yescharacteristic
627C24C23×D7911yescharacteristic
628#41—7964no—
629#41—15896no—
630#41—15896no—
631#41—15896no—
632#41—15896no—
633#41—15896no—
634#41—15832no—
635C2×Q8—232no—
636C2×Q8—232no—
637C2×Q8—212no—
638C2×Q8—212no—
639C2×Q8—7912no—
640C2×Q8—7912no—
641C2×Q8—15812no—
642C2×Q8—15896no—
643C2×Q8—15832no—
644C2×Q8—15812no—
645C2×Q8D4×D7918yes—
646C2×Q8C23×D79112yes—
647C2×Q8C23×D79112yes—
648C2×Q8C23×D7914yes—
649C2×D4—24no—
650C2×D4—3166no—
651C2×D4—3166no—
652C2×D4—7912no—
653C2×D4—794no—
654C2×D4—7912no—
655C2×D4—794no—
656C2×D4—7912no—
657C2×D4—7912no—
658C2×D4—7912no—
659C2×D4—7924no—
660C2×D4—7912no—
661C2×D4—7924no—
662C2×D4—15896no—
663C2×D4—15824no—
664C2×D4—15812no—
665C2×D4—1584no—
666C2×D4—15812no—
667C2×D4—1584no—
668C2×D4—15812no—
669C2×D4C23×D7914yes—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—31612no—
673C22×C4—7924no—
674C22×C4—791no—
675C22×C4—7912no—
676C22×C4—7924no—
677C22×C4—794no—
678C22×C4—791no—
679C22×C4—793no—
680C22×C4—793no—
681C22×C4—791no—
682C22×C4—7924no—
683C22×C4—7912no—
684C22×C4—7912no—
685C22×C4—7912no—
686C22×C4—7912no—
687C22×C4—15812no—
688C22×C4—15896no—
689C22×C4—15812no—
690C22×C4—15824no—
691C22×C4—1584no—
692C22×C4—15812no—
693C22×C4—15812no—
694C22×C4C23×D79112yes—
695C22×C4C23×D79112yes—
696C22×C4C23×D7911yescharacteristic
697C22×C4C23×D7913yes—
698C22×C4C23×D7913yes—
699C22×C4C23×D7913yes—
700C22×C4C23×D7913yes—
701C4⋊C4—7912no—
702C4⋊C4—7912no—
703C4⋊C4—7924no—
704C4⋊C4—794no—
705C4⋊C4—7912no—
706C4⋊C4—7912no—
707C4⋊C4—7912no—
708C4⋊C4C23×D79112yes—
709C4⋊C4C23×D79124yes—
710C4⋊C4C23×D79112yes—
711C22⋊C4—7912no—
712C22⋊C4—794no—
713C22⋊C4—7924no—
714C22⋊C4—7924no—
715C22⋊C4—7912no—
716C22⋊C4—7912no—
717C22⋊C4—794no—
718C22⋊C4—7912no—
719C22⋊C4—7912no—
720C22⋊C4—7912no—
721C22⋊C4C23×D79112yes—
722C22⋊C4C23×D79112yes—
723C42—7912no—
724C42C23×D79112yes—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—31648no—
731C23—31612no—
732C23—796no—
733C23—7912no—
734C23—796no—
735C23—792no—
736C23—15824no—
737C23—1582no—
738C23—1586no—
739C23—15824no—
740C23—1582no—
741C23—1586no—
742C23—1582no—
743C23—1586no—
744C23—1586no—
745C23—1586no—
746C23#1457920914yescomplemented
747C23C24×D7912yes—
748C23C24×D7912yes—
749C23C24×D7911yescharacteristic
750Q8—224no—
751Q8—224no—
752Q8—15824no—
753Q8—15824no—
754Q8C2×D4×D79116yes—
755D4—28no—
756D4—31612no—
757D4—31612no—
758D4—7948no—
759D4—15848no—
760D4—15824no—
761D4—1588no—
762D4—15824no—
763D4—1588no—
764D4—15824no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—26no—
768C2×C4—26no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—31624no—
772C2×C4—792no—
773C2×C4—794no—
774C2×C4—7948no—
775C2×C4—792no—
776C2×C4—796no—
777C2×C4—796no—
778C2×C4—792no—
779C2×C4—15824no—
780C2×C4—15824no—
781C2×C4—15848no—
782C2×C4—1588no—
783C2×C4—1582no—
784C2×C4—1586no—
785C2×C4—1582no—
786C2×C4—1586no—
787C2×C4—15824no—
788C2×C4—15824no—
789C2×C4C2×D4×D79112yes—
790C2×C4C24×D7912yes—
791C2×C4C24×D7916yes—
792C2×C4C24×D7916yes—
793C2×C4C24×D7916yes—
794C2×C4C24×D7916yes—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—31648no—
803C22—31612no—
804C22—3164no—
805C22—7912no—
806C22—1582no—
807C22—1586no—
808C22—1582no—
809C22—1586no—
810C22—1582no—
811C22—1586no—
812C22—15824no—
813C22—1586no—
814C22—1586no—
815C22C22×D4×D7912yes—
816C22C2×#1457920912yes—
817C22C2×#1457920914yescomplemented
818C22#1909940012yes—
819C22C25×D7911yescharacteristic
820C4—26no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—794no—
825C4—1582no—
826C4—1586no—
827C4—1582no—
828C4—1586no—
829C4C22×D4×D79112yes—
830C2—24no—
831C2—42no—
832C2—3166no—
833C2—3162no—
834C2—15812no—
835C2#2377707714yesdirect product factor
836C2C23×D4×D7911yescharacteristic
837C2C22×#1457920911yescharacteristic
838C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×D4×Q8×C79C2
socleC23×C79C25
hypercenterC2×D4×Q8D79
hypocenterC79C2×#3489
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14579209C2semidirect
2. C23×#11929625C2semidirect
3. #23777077C2direct (N × H)
4. C2×Q8×C22⋊D79C2semidirect
5. C2×#19099225C2semidirect
6. C2×#19099224C2semidirect
7. C2×#19099216C2semidirect
8. C2×#19099215C2semidirect
9. C2×#19099209C2semidirect
10. C2×#19099204C2semidirect
11. C2×#19099143C2semidirect
12. C2×#19099138C2semidirect
13. C2×#19099072C2semidirect
14. C2×C22⋊Q8×D79C2semidirect
15. C2×#19099045C2semidirect
16. C2×D4×Q8×C79C2semidirect
18. C2×#14579209C22semidirect
24. C22×#11929625C22semidirect
25. C22×#11929625C22semidirect
26. C22×#11929624C22semidirect
27. C22×#11929624C22semidirect
28. C22×Q8×D79C22semidirect
29. C22×Q8×D79C22semidirect
32. Q8×C22⋊D79C22semidirect
33. #19099225C22semidirect
34. #19099224C22semidirect
35. #19099216C22semidirect
36. #19099215C22semidirect
37. #19099209C22semidirect
38. #19099204C22semidirect
39. #19099143C22semidirect
40. #19099138C22semidirect
41. C2×#14579159C22semidirect
42. C2×#14579150C22semidirect
43. C2×#14579149C22semidirect
44. #19099072C22semidirect
45. C2×#14579146C22semidirect
46. C2×#14579146C22semidirect
47. C2×#14579146C22semidirect
48. C2×#14579143C22semidirect
49. C2×#14579141C22semidirect
51. C2×#14579139C22semidirect
52. C2×#14579139C22semidirect
54. C2×#14579137C22semidirect
55. C2×#14579137C22semidirect
56. C22⋊Q8×D79C22semidirect
57. C2×#14579136C22semidirect
58. C2×#14579136C22semidirect
59. C2×#14579135C22semidirect
60. C2×#14579134C22semidirect
61. C2×#14579134C22semidirect
65. #19099045C22semidirect
66. C2×Q8×Dic79C22semidirect
67. C2×C4×D316C22semidirect
68. C2×C4×D316C22semidirect
69. C2×#14579123C22semidirect
71. C2×C4×C22⋊D79C22semidirect
72. C2×#14579118C22semidirect
73. C2×C4⋊C4×D79C22semidirect
74. C2×C4⋊C4×D79C22semidirect
77. C23×Q8×C79C22semidirect
78. D4×Q8×C79C22semidirect
79. C2×C4⋊Q8×C79C22semidirect
81. C2×C22⋊Q8×C79C22semidirect
82. C2×C4×Q8×C79C22semidirect
91. C2×#11929625D4semidirect
96. C2×#11929625C23semidirect
99. C2×#11929624C23semidirect
100. C2×#11929624C23semidirect
105. C2×Q8×D79C23semidirect
106. C2×Q8×D79C23semidirect
128. #14579159C23semidirect
129. #14579150C23semidirect
130. #14579149C23semidirect
131. #14579146C23semidirect
132. #14579146C23semidirect
133. #14579146C23semidirect
134. #14579143C23semidirect
135. #14579141C23semidirect
137. #14579139C23semidirect
138. #14579139C23semidirect
140. #14579137C23semidirect
141. #14579137C23semidirect
142. #14579136C23semidirect
143. #14579136C23semidirect
144. #14579135C23semidirect
145. #14579134C23semidirect
146. #14579134C23semidirect
150. Q8×Dic79C23semidirect
151. C4×D316C23semidirect
152. C4×D316C23semidirect
153. #14579123C23semidirect
155. C4×C22⋊D79C23semidirect
156. #14579118C23semidirect
164. C4⋊C4×D79C23semidirect
165. C4⋊C4×D79C23semidirect
184. C22×Q8×C79C23semidirect
188. C4⋊Q8×C79C23semidirect
190. C22⋊Q8×C79C23semidirect
191. C4×Q8×C79C23semidirect
210. #11929625C2×D4semidirect
310. C23×C792−1+4semidirect
384. C22×C79C2×2−1+4semidirect
413. C2×C79#3489semidirect
424. C2×D4×Q8D79semidirect
436. C79C2×#3489semidirect
451. C23×Q8C2×D79semidirect
455. D4×Q8C2×D79semidirect
465. C2×C4⋊Q8C2×D79semidirect
482. C2×C22⋊Q8C2×D79semidirect
493. C2×C4×Q8C2×D79semidirect
533. C22×Q8C22×D79semidirect
559. C4⋊Q8C22×D79semidirect
574. C22⋊Q8C22×D79semidirect
584. C4×Q8C22×D79semidirect
746. C23#14579209semidirect
817. C22C2×#14579209semidirect
835. C2#23777077direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145792092
C23×#119296252
#237770772
C2×Q8×C22⋊D792
C2×#190992252
C2×#190992242
C2×#190992162
C2×#190992152
C2×#190992092
C2×#190992042
C2×#190991432
C2×#190991382
C2×#190990722
C2×C22⋊Q8×D792
C2×#190990452
C2×D4×Q8×C792
C2×#348979