Finite Group Databasebeta

← C2×#23777168 #35196443

Subgroups — C2×#23777168 #35196443

Order 20224.

11210 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579209C211yesmaximal, characteristic, complemented
2C22×#14579208C211yesmaximal, characteristic, complemented
3#23777168C2132yesmaximal, direct product factor
4C2×#19099232C211yesmaximal, characteristic, complemented
5C2×#19099231C213yesmaximal, complemented
6C2×Q8×C22⋊D79C211yesmaximal, characteristic, complemented
7C2×#19099226C213yesmaximal, complemented
8C2×#19099225C211yesmaximal, characteristic, complemented
9C2×#19099222C213yesmaximal, complemented
10C2×#19099221C213yesmaximal, complemented
11C2×#19099143C213yesmaximal, complemented
12C2×#19099142C213yesmaximal, complemented
13C2×#19099112C213yesmaximal, complemented
14C2×#19099110C213yesmaximal, complemented
15C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
16C2×#548×C79C211yesmaximal, characteristic, complemented
17C2×#14579209—216no—
18C2×#14579209C22116yescomplemented
19C2×#14579208—216no—
20C2×#14579208C22116yescomplemented
21C22×#11929625C2211yescharacteristic
22C22×#11929625C2213yes—
23C22×#11929624C2213yes—
24C22×#11929624C2213yes—
25C22×#11929624C2213yes—
26C22×#11929623C2213yes—
27C22×#11929623C2213yes—
28C23×Dic158C2213yes—
29C22×Q8×D79C2213yes—
30C22×Q8×D79C2211yescharacteristic
31C22×Q8×D79C2211yescharacteristic
32#19099232C22116yescomplemented
33#19099231C22148yescomplemented
34Q8×C22⋊D79C22116yescomplemented
35#19099226C22148yescomplemented
36#19099225C22116yescomplemented
37#19099222C22148yescomplemented
38#19099221C22148yescomplemented
39#19099143C22148yescomplemented
40#19099142C22148yescomplemented
41#19099112C22148yescomplemented
42#19099110C22148yescomplemented
43C2×#14579160C2213yes—
44C2×#14579159C2213yes—
45C2×#14579157C2213yes—
46C2×#14579157C2213yes—
47C2×#14579149C2213yes—
48C2×#14579147C2213yes—
49C2×#14579147C2213yes—
50C2×#14579141C2213yes—
51C2×#14579140C2213yes—
52C2×#14579139C2216yes—
53C2×#14579138C2216yes—
54C2×#14579137C2213yes—
55C2×#14579136C2213yes—
56C2×#14579136C2213yes—
57C2×#14579135C2213yes—
58C2×#14579134C2216yes—
59C2×#14579134C2211yescharacteristic
60C2×#14579134C2213yes—
61C2×#14579134C2216yes—
62C2×#14579133C2216yes—
63C2×#14579132C2213yes—
64C2×#14579132C2213yes—
65C2×Q8×Dic79C2211yescharacteristic
66C2×C4×Dic158C2213yes—
67C2×#14579126C2213yes—
68C4×Q8×D79C22116yescomplemented
69C2×C4×D316C2213yes—
70C2×C4×C22⋊D79C2213yes—
71C2×C4×C22⋊D79C2213yes—
72C2×(C22⋊D79)⋊C4C2216yes—
73C2×(C22⋊D79)⋊C4C2216yes—
74C2×C4⋊C4×D79C2213yes—
75C2×C42×D79C2213yes—
76C22×#41×C79C2211yescharacteristic
77C23×Q8×C79C2211yescharacteristic
78#548×C79C22116yescomplemented
79C2×#124×C79C2213yes—
80C2×C22⋊Q8×C79C2213yes—
81C2×#121×C79C2213yes—
82C2×C4×Q8×C79C2211yescharacteristic
83C2×C4×D4×C79C2213yes—
84#14579209—2128no—
85#14579208—2128no—
86C2×#11929625—28no—
87C2×#11929625—224no—
88C2×#11929625C23124yes—
89C2×#11929625C2318yes—
90C2×#11929624—224no—
91C2×#11929624—224no—
92C2×#11929624—224no—
93C2×#11929624C23124yes—
94C2×#11929624C23124yes—
95C2×#11929624C23124yes—
96C2×#11929623—224no—
97C2×#11929623—224no—
98C2×#11929623C23124yes—
99C2×#11929623C23124yes—
100C22×Dic158—224no—
101C22×Dic158C23124yes—
102C22×Dic158C2313yes—
103C22×Dic158C2313yes—
104C22×Dic158C2313yes—
105C22×Dic158C2313yes—
106C2×Q8×D79—28no—
107C2×Q8×D79—224no—
108C2×Q8×D79D4116yescomplemented
109C2×Q8×D79C2318yes—
110C2×Q8×D79C23124yes—
111C2×Q8×D79C2318yes—
112C22×D316C2313yes—
113C22×D316C2311yescharacteristic
114C22×D316C2313yes—
115C22×D316C2313yes—
116C22×C22⋊D79C2313yes—
117C22×C22⋊D79C2311yescharacteristic
118C22×C22⋊D79C2311yescharacteristic
119C22×C22⋊D79C2313yes—
120C22×C22⋊D79C2313yes—
121C22×C22⋊D79C2313yes—
122C22×C22⋊D79C2316yes—
123C23×Dic79C2316yes—
124C22×C4×D79C2311yescharacteristic
125C22×C4×D79C2316yes—
126C22×C4×D79C2313yes—
127C22×C4×D79C2313yes—
128C22×C4×D79C2313yes—
129C22×C4×D79C2313yes—
130#14579160C23124yes—
131#14579159C23124yes—
132#14579157C23124yes—
133#14579157C23124yes—
134#14579149C23124yes—
135#14579147C23124yes—
136#14579147C23124yes—
137#14579141C23124yes—
138#14579140C23124yes—
139#14579139C23148yes—
140#14579138C23148yes—
141#14579137C23124yes—
142#14579136C23124yes—
143#14579136C23124yes—
144#14579135C23124yes—
145#14579134C23148yes—
146#14579134C23148yes—
147#14579134C2318yes—
148#14579134C23124yes—
149#14579133C23148yes—
150#14579132C23124yes—
151#14579132C23124yes—
152Q8×Dic79C2318yes—
153C4×Dic158C23124yes—
154#14579126C23124yes—
155C4×D316C23124yes—
156C4×C22⋊D79C23124yes—
157C4×C22⋊D79C23124yes—
158(C22⋊D79)⋊C4C23148yes—
159(C22⋊D79)⋊C4C23148yes—
160C2×C4⋊Dic79C2313yes—
161C2×C4⋊Dic79C2313yes—
162C2×Dic79⋊C4C2316yes—
163C2×Dic79⋊C4C2313yes—
164C2×Dic79⋊C4C2316yes—
165C2×Dic79⋊C4C2311yescharacteristic
166C4⋊C4×D79C23124yes—
167C2×C22⋊Dic79C2313yes—
168C2×C22⋊Dic79C2313yes—
169C2×(C2×D79)⋊C4C2313yes—
170C2×(C2×D79)⋊C4C2316yes—
171C2×(C2×D79)⋊C4C2313yes—
172C2×(C2×D79)⋊C4C2313yes—
173C2×(C2×D79)⋊C4C2311yescharacteristic
174C2×C4×Dic79C2313yes—
175C2×C4×Dic79C2313yes—
176C2×C4×Dic79C2313yes—
177C42×D79C23124yes—
178C2×#41×C79—28no—
179C2×#41×C79C2318yes—
180C22×Q8×C79—28no—
181C22×Q8×C79C2318yes—
182C22×Q8×C79C2313yes—
183C22×Q8×C79C2311yescharacteristic
184C22×D4×C79C2313yes—
185C22×D4×C79C2313yes—
186C23×C4×C79C2313yes—
187C23×C4×C79C2313yes—
188#124×C79C23124yes—
189C22⋊Q8×C79C23124yes—
190#121×C79C23124yes—
191C4×Q8×C79C2318yes—
192C4×D4×C79C23124yes—
193C2×C4⋊C4×C79C2313yes—
194C2×C4⋊C4×C79C2313yes—
195C2×C22⋊C4×C79C2311yescharacteristic
196C2×C22⋊C4×C79C2313yes—
197C2×C22⋊C4×C79C2316yes—
198C2×C42×C79C2313yes—
199C23×D79C2411yescharacteristic
200C23×D79C2413yes—
201C23×D79C2411yescharacteristic
202#11929625—296no—
203#11929625—232no—
204#11929624—296no—
205#11929624—296no—
206#11929624—296no—
207#11929623—296no—
208#11929623—296no—
209C2×Dic158—212no—
210C2×Dic158—212no—
211C2×Dic158—296no—
212C2×Dic158—212no—
213C2×Dic158C2×D4124yes—
214C2×Dic158C24112yes—
215C2×Dic158C24112yes—
216C2×Dic158C24112yes—
217C2×Dic158C24112yes—
218Q8×D79—296no—
219Q8×D79—232no—
220Q8×D79C2×D4164yescomplemented
221C2×D316—24no—
222C2×D316—212no—
223C2×D316—212no—
224C2×D316—46no—
225C2×D316C2414yes—
226C2×D316C24112yes—
227C2×D316C24112yes—
228C2×D316C24112yes—
229C2×C22⋊D79—212no—
230C2×C22⋊D79—212no—
231C2×C22⋊D79—212no—
232C2×C22⋊D79—24no—
233C2×C22⋊D79—212no—
234C2×C22⋊D79—24no—
235C2×C22⋊D79—412no—
236C2×C22⋊D79C24112yes—
237C2×C22⋊D79C24112yes—
238C2×C22⋊D79C2414yes—
239C2×C22⋊D79C24112yes—
240C2×C22⋊D79C24112yes—
241C2×C22⋊D79C2414yes—
242C2×C22⋊D79C24124yes—
243C22×Dic79—224no—
244C22×Dic79C2413yes—
245C22×Dic79C2411yescharacteristic
246C22×Dic79C24124yes—
247C22×Dic79C2413yes—
248C22×Dic79C2413yes—
249C22×Dic79C2411yescharacteristic
250C2×C4×D79—224no—
251C2×C4×D79—24no—
252C2×C4×D79—212no—
253C2×C4×D79—212no—
254C2×C4×D79—46no—
255C2×C4×D79C2×D4124yes—
256C2×C4×D79C24112yes—
257C2×C4×D79C24124yes—
258C2×C4×D79C24112yes—
259C2×C4×D79C2414yes—
260C2×C4×D79C24112yes—
261C2×C4×D79C24112yes—
262C4⋊Dic79C24112yes—
263C4⋊Dic79C24112yes—
264Dic79⋊C4C24124yes—
265Dic79⋊C4C24112yes—
266Dic79⋊C4C24124yes—
267Dic79⋊C4C2414yes—
268C22⋊Dic79C24112yes—
269C22⋊Dic79C24112yes—
270(C2×D79)⋊C4C24112yes—
271(C2×D79)⋊C4C24124yes—
272(C2×D79)⋊C4C24112yes—
273(C2×D79)⋊C4C24112yes—
274(C2×D79)⋊C4C2414yes—
275C4×Dic79C24112yes—
276C4×Dic79C24112yes—
277C4×Dic79C24112yes—
278C24×C79C2413yes—
279C24×C79C2411yescharacteristic
280#41×C79—232no—
281C2×Q8×C79—232no—
282C2×Q8×C79—212no—
283C2×Q8×C79C2×D418yes—
284C2×Q8×C79C24112yes—
285C2×Q8×C79C2414yes—
286C2×D4×C79—212no—
287C2×D4×C79—46no—
288C2×D4×C79C24112yes—
289C2×D4×C79C24112yes—
290C22×C4×C79—212no—
291C22×C4×C79—212no—
292C22×C4×C79C2411yescharacteristic
293C22×C4×C79C24112yes—
294C22×C4×C79C2413yes—
295C22×C4×C79C24112yes—
296C22×C4×C79C2411yescharacteristic
297C22×C4×C79C2413yes—
298C22×C4×C79C2413yes—
299C4⋊C4×C79C24112yes—
300C4⋊C4×C79C24112yes—
301C22⋊C4×C79C2414yes—
302C22⋊C4×C79C24112yes—
303C22⋊C4×C79C24124yes—
304C42×C79C24112yes—
305C23×C79—26no—
306C23×C79—22no—
307C23×C79—26no—
308C23×C79—22no—
309C23×C79—26no—
310C23×C79—22no—
311C23×C79C2512yes—
312C23×C79C2516yes—
313C23×C79C2511yescharacteristic
314C22×D79—22no—
315C22×D79—22no—
316C22×D79—22no—
317C22×D79—26no—
318C22×D79—22no—
319C22×D79—26no—
320C22×D79—26no—
321C22×D79—22no—
322C22×D79C22×D414yes—
323C22×D79C2512yes—
324C22×D79C2516yes—
325C22×D79C2512yes—
326Q8×C79—224no—
327Q8×C79C22×D4116yes—
328D4×C79—224no—
329D4×C79—412no—
330C2×C4×C79—26no—
331C2×C4×C79—22no—
332C2×C4×C79—22no—
333C2×C4×C79—26no—
334C2×C4×C79—224no—
335C2×C4×C79—224no—
336C2×C4×C79C22×D4112yes—
337C2×C4×C79C2512yes—
338C2×C4×C79C2516yes—
339C2×C4×C79C2512yes—
340C2×C4×C79C2516yes—
341C2×C4×C79C2516yes—
342C22⋊D79—224no—
343C22⋊D79—28no—
344C22⋊D79—224no—
345C22⋊D79—224no—
346C22⋊D79—224no—
347C22⋊D79—28no—
348C22⋊D79—424no—
349C2×Dic79—22no—
350C2×Dic79—26no—
351C2×Dic79—26no—
352C2×Dic79—248no—
353C2×Dic79C22×D4112yes—
354C2×Dic792−1+414yescomplemented
355C2×Dic79C2516yes—
356C2×Dic79C2516yes—
357C2×Dic79C2512yes—
358C2×Dic79C2516yes—
359C2×Dic79C2512yes—
360D316—28no—
361D316—224no—
362D316—224no—
363D316—412no—
364C4×D79—224no—
365C4×D79—224no—
366C4×D79—248no—
367C4×D79—28no—
368C4×D79—412no—
369C4×D79C22×D4148yes—
370Dic158—224no—
371Dic158—224no—
372Dic158—224no—
373Dic158C22×D4148yes—
374C22×C79—22no—
375C22×C79—26no—
376C22×C79—22no—
377C22×C79—26no—
378C22×C79—26no—
379C22×C79—22no—
380C22×C79—412no—
381C22×C79—44no—
382C22×C79C23×D412yes—
383C22×C79C2×2−1+412yes—
384C22×C79#58512yes—
385C22×C79C2611yescharacteristic
386C2×D79—22no—
387C2×D79—22no—
388C2×D79—28no—
389C2×D79—22no—
390C2×D79—26no—
391C2×D79—22no—
392C2×D79—26no—
393C2×D79—26no—
394C2×D79—22no—
395C2×D79—44no—
396C2×D79—412no—
397C2×D79C23×D414yes—
398C4×C79—22no—
399C4×C79—26no—
400C4×C79—22no—
401C4×C79—26no—
402C4×C79C23×D4112yes—
403Dic79—22no—
404Dic79—26no—
405Dic79—26no—
406Dic79C23×D4112yes—
407Dic79C2×2−1+414yescomplemented
408C2×#3497—791nomaximal, Sylow
409C2×C79—42no—
410C2×C79—46no—
411C2×C79#349714yescomplemented
412C2×C79C24×D411yescharacteristic
413C2×C79C22×2−1+411yescharacteristic
414C2×C79C2×#58511yescharacteristic
415D79—24no—
416D79—42no—
417D79—46no—
418C22×2−1+4—791no—
419C22×2−1+4—791no—
420#3497—7932no—
421C2×#550—791no—
422C2×#550—793no—
423C2×D4×Q8—791no—
424C2×D4×Q8—793no—
425C2×#548—793no—
426C2×#548—791no—
427C2×#548—793no—
428C2×#548D7911yescharacteristic, complemented
429C2×#537—793no—
430C2×#537—793no—
431C2×#532—793no—
432C2×#532—793no—
433C22×C4×Q8—791no—
434C79C2×#349711yescharacteristic, complemented, Sylow
435C2×2−1+4—7916no—
436C2×2−1+4—7916no—
437C2×2−1+4—15816no—
438C2×2−1+4—15816no—
439C22×#41—793no—
440C22×#41—791no—
441C22×#41—793no—
442C22×#41—793no—
443C22×#41—793no—
444C22×#41—793no—
445C22×#41—793no—
446C22×#41C2×D7911yescharacteristic
447C23×Q8—791no—
448C23×Q8—793no—
449C23×Q8—791no—
450C23×Q8—793no—
451C23×Q8C2×D7911yescharacteristic
452#550—7916no—
453#550—7948no—
454D4×Q8—7916no—
455D4×Q8—7948no—
456#548—7948no—
457#548—7916no—
458#548—7948no—
459#548C2×D79116yescomplemented
460#537—7948no—
461#537—7948no—
462#532—7948no—
463#532—7948no—
464C2×C4⋊Q8—793no—
465C2×C4⋊Q8—793no—
466C2×#127—793no—
467C2×#127—793no—
468C2×#124—793no—
469C2×#124—793no—
470C2×#124—793no—
471C2×#124C2×D7913yes—
472C2×C22⋊Q8—793no—
473C2×C22⋊Q8—793no—
474C2×C22⋊Q8—796no—
475C2×C22⋊Q8—793no—
476C2×C22⋊Q8—796no—
477C2×C22⋊Q8C2×D7913yes—
478C2×#121—793no—
479C2×#121—793no—
480C2×#121—796no—
481C2×#121—793no—
482C2×#121—793no—
483C2×#121—793no—
484C2×#121—793no—
485C2×#121—791no—
486C2×#121—796no—
487C2×#121—796no—
488C2×#121C2×D7913yes—
489C2×C4×Q8—791no—
490C2×C4×Q8—7916no—
491C2×C4×Q8—793no—
492C2×C4×Q8—793no—
493C2×C4×Q8C2×D7911yescharacteristic
494C2×C4×D4—793no—
495C2×C4×D4—793no—
496C2×C4×D4—796no—
497C2×C4×D4—796no—
498C2×C4×D4—793no—
499C2×C4×D4C2×D7913yes—
500C22×C4⋊C4—793no—
501C22×C42—793no—
5022−1+4—158128no—
5032−1+4—158128no—
504C2×#41—28no—
505C2×#41—7924no—
506C2×#41—798no—
507C2×#41—7924no—
508C2×#41—7924no—
509C2×#41—7924no—
510C2×#41—7924no—
511C2×#41—7924no—
512C2×#41—15824no—
513C2×#41—15824no—
514C2×#41—15824no—
515C2×#41—15824no—
516C2×#41—15824no—
517C2×#41—15824no—
518C2×#41—1588no—
519C2×#41C22×D7918yes—
520C22×Q8—28no—
521C22×Q8—7916no—
522C22×Q8—798no—
523C22×Q8—7924no—
524C22×Q8—798no—
525C22×Q8—793no—
526C22×Q8—793no—
527C22×Q8—793no—
528C22×Q8—793no—
529C22×Q8—7924no—
530C22×Q8—15824no—
531C22×Q8—15824no—
532C22×Q8—1588no—
533C22×Q8C22×D7913yes—
534C22×Q8C22×D7918yes—
535C22×Q8C22×D7911yescharacteristic
536C22×D4—796no—
537C22×D4—791no—
538C22×D4—793no—
539C22×D4—791no—
540C22×D4—793no—
541C22×D4—793no—
542C22×D4—793no—
543C22×D4—793no—
544C22×D4—791no—
545C22×D4—793no—
546C22×D4—793no—
547C22×D4C22×D7913yes—
548C22×D4C22×D7913yes—
549C23×C4—793no—
550C23×C4—793no—
551C23×C4—796no—
552C23×C4—796no—
553C23×C4—793no—
554C23×C4—793no—
555C23×C4—791no—
556C23×C4C22×D7913yes—
557C23×C4C22×D7913yes—
558C4⋊Q8—7924no—
559C4⋊Q8—7924no—
560#127—7924no—
561#127—7924no—
562#124—7924no—
563#124—7924no—
564#124—7924no—
565#124C22×D79124yes—
566C22⋊Q8—7924no—
567C22⋊Q8—7924no—
568C22⋊Q8—7948no—
569C22⋊Q8—7924no—
570C22⋊Q8—7948no—
571C22⋊Q8C22×D79124yes—
572#121—7924no—
573#121—7924no—
574#121—7948no—
575#121—7924no—
576#121—7924no—
577#121—7924no—
578#121—7924no—
579#121—798no—
580#121—7948no—
581#121—7948no—
582#121C22×D79124yes—
583C4×Q8—798no—
584C4×Q8—7924no—
585C4×Q8—7924no—
586C4×Q8C22×D7918yes—
587C4×D4—7924no—
588C4×D4—7924no—
589C4×D4—7948no—
590C4×D4—7948no—
591C4×D4—7924no—
592C4×D4C22×D79124yes—
593C2×C4⋊C4—796no—
594C2×C4⋊C4—793no—
595C2×C4⋊C4—791no—
596C2×C4⋊C4—793no—
597C2×C4⋊C4—796no—
598C2×C4⋊C4—793no—
599C2×C4⋊C4—7924no—
600C2×C4⋊C4C22×D7913yes—
601C2×C4⋊C4C22×D7913yes—
602C2×C22⋊C4—793no—
603C2×C22⋊C4—793no—
604C2×C22⋊C4—793no—
605C2×C22⋊C4—791no—
606C2×C22⋊C4—793no—
607C2×C22⋊C4—793no—
608C2×C22⋊C4—796no—
609C2×C22⋊C4C22×D7913yes—
610C2×C22⋊C4C22×D7916yes—
611C2×C22⋊C4C22×D7911yescharacteristic
612C2×C42—793no—
613C2×C42—793no—
614C2×C42—793no—
615C2×C42—7924no—
616C2×C42C22×D7913yes—
617C24—791no—
618C24—793no—
619C24—791no—
620C24C23×D7911yescharacteristic
621C24C23×D7913yes—
622#41—232no—
623#41—15896no—
624#41—15896no—
625#41—15896no—
626#41—15896no—
627#41—15896no—
628#41—15896no—
629#41—15832no—
630C2×Q8—232no—
631C2×Q8—212no—
632C2×Q8—7964no—
633C2×Q8—7912no—
634C2×Q8—7912no—
635C2×Q8—7912no—
636C2×Q8—7912no—
637C2×Q8—7924no—
638C2×Q8—15812no—
639C2×Q8—15812no—
640C2×Q8—15896no—
641C2×Q8—15896no—
642C2×Q8—15832no—
643C2×Q8—15812no—
644C2×Q8D4×D7918yes—
645C2×Q8C23×D79112yes—
646C2×Q8C23×D7914yes—
647C2×D4—212no—
648C2×D4—46no—
649C2×D4—3166no—
650C2×D4—31612no—
651C2×D4—7924no—
652C2×D4—794no—
653C2×D4—7912no—
654C2×D4—794no—
655C2×D4—7912no—
656C2×D4—7912no—
657C2×D4—7912no—
658C2×D4—7912no—
659C2×D4—794no—
660C2×D4—7912no—
661C2×D4—7912no—
662C2×D4—1584no—
663C2×D4—15812no—
664C2×D4—1584no—
665C2×D4—15812no—
666C2×D4—15812no—
667C2×D4—15812no—
668C2×D4—1584no—
669C2×D4—15812no—
670C2×D4—15812no—
671C2×D4C23×D79112yes—
672C2×D4C23×D79112yes—
673C22×C4—212no—
674C22×C4—212no—
675C22×C4—3166no—
676C22×C4—7912no—
677C22×C4—791no—
678C22×C4—793no—
679C22×C4—7912no—
680C22×C4—7924no—
681C22×C4—7924no—
682C22×C4—793no—
683C22×C4—793no—
684C22×C4—791no—
685C22×C4—794no—
686C22×C4—7924no—
687C22×C4—7912no—
688C22×C4—7912no—
689C22×C4—1584no—
690C22×C4—15824no—
691C22×C4—15824no—
692C22×C4—15812no—
693C22×C4—15812no—
694C22×C4C23×D79112yes—
695C22×C4C23×D79112yes—
696C22×C4C23×D7911yescharacteristic
697C22×C4C23×D7913yes—
698C22×C4C23×D7911yescharacteristic
699C22×C4C23×D7913yes—
700C22×C4C23×D7913yes—
701C4⋊C4—7924no—
702C4⋊C4—794no—
703C4⋊C4—7912no—
704C4⋊C4—7924no—
705C4⋊C4—7912no—
706C4⋊C4—7912no—
707C4⋊C4C23×D79112yes—
708C4⋊C4C23×D79112yes—
709C22⋊C4—7912no—
710C22⋊C4—7912no—
711C22⋊C4—7912no—
712C22⋊C4—794no—
713C22⋊C4—7912no—
714C22⋊C4—7912no—
715C22⋊C4—7924no—
716C22⋊C4C23×D79112yes—
717C22⋊C4C23×D79124yes—
718C22⋊C4C23×D7914yes—
719C42—7912no—
720C42—7912no—
721C42—7912no—
722C42C23×D79112yes—
723C23—22no—
724C23—26no—
725C23—22no—
726C23—26no—
727C23—22no—
728C23—26no—
729C23—792no—
730C23—794no—
731C23—796no—
732C23—792no—
733C23—1586no—
734C23—1582no—
735C23—1586no—
736C23—1582no—
737C23—1582no—
738C23—1586no—
739C23—1582no—
740C23—1582no—
741C23C24×D7912yes—
742C23C24×D7916yes—
743C23C24×D7911yescharacteristic
744Q8—224no—
745Q8—7948no—
746Q8—15824no—
747Q8—15824no—
748Q8—15824no—
749Q8C2×D4×D79116yes—
750D4—224no—
751D4—412no—
752D4—31612no—
753D4—31624no—
754D4—1588no—
755D4—15824no—
756D4—1588no—
757D4—15824no—
758D4—15824no—
759D4—15824no—
760D4—1588no—
761D4—15824no—
762D4—15824no—
763C2×C4—22no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—224no—
768C2×C4—224no—
769C2×C4—31612no—
770C2×C4—794no—
771C2×C4—792no—
772C2×C4—796no—
773C2×C4—7912no—
774C2×C4—7948no—
775C2×C4—796no—
776C2×C4—792no—
777C2×C4—796no—
778C2×C4—15848no—
779C2×C4—1588no—
780C2×C4—15848no—
781C2×C4—1586no—
782C2×C4—1586no—
783C2×C4—1582no—
784C2×C4—15824no—
785C2×C4—15824no—
786C2×C4C2×D4×D79112yes—
787C2×C4C24×D7912yes—
788C2×C4C24×D7916yes—
789C2×C4C24×D7912yes—
790C2×C4C24×D7916yes—
791C2×C4C24×D7916yes—
792C22—22no—
793C22—26no—
794C22—22no—
795C22—26no—
796C22—22no—
797C22—26no—
798C22—44no—
799C22—412no—
800C22—31612no—
801C22—3164no—
802C22—794no—
803C22—1586no—
804C22—1582no—
805C22—1586no—
806C22—1582no—
807C22—1582no—
808C22—1586no—
809C22—1588no—
810C22—1582no—
811C22—1582no—
812C22C22×D4×D7912yes—
813C222−1+4×D7912yes—
814C22#1909939912yes—
815C22C25×D7911yescharacteristic
816C4—22no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—7912no—
821C4—794no—
822C4—1586no—
823C4—1582no—
824C4—1586no—
825C4C22×D4×D79112yes—
826C2—42no—
827C2—46no—
828C2—3166no—
829C2—3162no—
830C2—1584no—
831C2#2377716814yesdirect product factor
832C2C23×D4×D7911yescharacteristic
833C2C2×2−1+4×D7911yescharacteristic
834C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#548×C79C2
socleC23×C79C25
hypercenterC2×#548D79
hypocenterC79C2×#3497
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14579209C2semidirect
2. C22×#14579208C2semidirect
3. #23777168C2direct (N × H)
4. C2×#19099232C2semidirect
5. C2×#19099231C2semidirect
6. C2×Q8×C22⋊D79C2semidirect
7. C2×#19099226C2semidirect
8. C2×#19099225C2semidirect
9. C2×#19099222C2semidirect
10. C2×#19099221C2semidirect
11. C2×#19099143C2semidirect
12. C2×#19099142C2semidirect
13. C2×#19099112C2semidirect
14. C2×#19099110C2semidirect
15. C2×C4×Q8×D79C2semidirect
16. C2×#548×C79C2semidirect
18. C2×#14579209C22semidirect
20. C2×#14579208C22semidirect
32. #19099232C22semidirect
33. #19099231C22semidirect
34. Q8×C22⋊D79C22semidirect
35. #19099226C22semidirect
36. #19099225C22semidirect
37. #19099222C22semidirect
38. #19099221C22semidirect
39. #19099143C22semidirect
40. #19099142C22semidirect
41. #19099112C22semidirect
42. #19099110C22semidirect
68. C4×Q8×D79C22semidirect
78. #548×C79C22semidirect
108. C2×Q8×D79D4semidirect
220. Q8×D79C2×D4semidirect
354. C2×Dic792−1+4semidirect
407. Dic79C2×2−1+4semidirect
411. C2×C79#3497semidirect
428. C2×#548D79semidirect
434. C79C2×#3497semidirect
459. #548C2×D79semidirect
831. C2#23777168direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145792092
C22×#145792082
#237771682
C2×#190992322
C2×#190992312
C2×Q8×C22⋊D792
C2×#190992262
C2×#190992252
C2×#190992222
C2×#190992212
C2×#190991432
C2×#190991422
C2×#190991122
C2×#190991102
C2×C4×Q8×D792
C2×#548×C792
C2×#349779