Finite Group Databasebeta

← #30617025

Subgroups — #30617025

Order 15616.

1044 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840801C211yesmaximal, characteristic, complemented
2C2×SD16×#6923C211yesmaximal, characteristic, complemented
3#21462311C211yesmaximal, characteristic
4#21462259C211yesmaximal, characteristic, complemented
5#21461986C211yesmaximal, characteristic
6#21461932C211yesmaximal, characteristic, complemented
7#21461897C211yesmaximal, characteristic, complemented
8#21461896C211yesmaximal, characteristic, complemented
9#21461815C211yesmaximal, characteristic, complemented
10#21461815C211yesmaximal, characteristic, complemented
11#21461690C211yesmaximal, characteristic, complemented
12#21461608C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic, complemented
14#102×#6923C211yesmaximal, characteristic, complemented
15#460×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20#16840801—24no—
21SD16×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24D61⋊(C4⋊C8)C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33#16840714C2211yescharacteristic
34#16840714C2211yescharacteristic
35#16840710—21no—
36#16840710—21no—
37#16840710—21no—
38#16840710—21no—
39#16840706C2211yescharacteristic
40C4⋊C4×#6923—21no—
41C4⋊C4×#6923—21no—
42C4⋊C4×#6923C2211yescharacteristic
43C4⋊C4×#6923C2211yescharacteristic
44C4×C4⋊#6923—21no—
45C4×C4⋊#6923C2211yescharacteristic
46#16840698—21no—
47#16840698C2211yescharacteristic
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×SD16×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56#127×D61C2211yescharacteristic
57C4×Q8×D61C2211yescharacteristic
58#16839963C411yescharacteristic, complemented
59#16839962C411yescharacteristic, complemented
60#16839961C411yescharacteristic, complemented
61#16839961C411yescharacteristic, complemented
62#16839960C411yescharacteristic, complemented
63#16839960C411yescharacteristic, complemented
64#16839959C411yescharacteristic, complemented
65C4⋊C8×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67#102×D61C2211yescharacteristic
68C61×#460C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C2×D61⋊C8C2311yescharacteristic
72C2×D61⋊C8C2311yescharacteristic
73Q8×#6923—22no—
74Q8×#6923—22no—
75Q8×#6923—22no—
76Q8×#6923D414yescomplemented
77D4×#6923—22no—
78D4×#6923—22no—
79D4×#6923—22no—
80D4×#6923—22no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923—21no—
98C2×C4×#6923C2311yescharacteristic
99C2×C4×#6923C2311yescharacteristic
100#14519846—22no—
101#14519845—22no—
102#14519844—21no—
103C4⋊#92420—21no—
104#14519840—22no—
105#14519840—22no—
106#14519839—22no—
107#14519839—22no—
108#14519839—22no—
109#14519839—22no—
110#14519831—22no—
111C8×#6923—22no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4D411yescharacteristic
118(C2×#6923)⋊C4D411yescharacteristic
119(C2×#6923)⋊C4D411yescharacteristic
120(C2×#6923)⋊C4D411yescharacteristic
121C2×Q8×D61C2311yescharacteristic
122C2×D4×D61—21no—
123C2×D4×D61—21no—
124C2×D4×D61C2311yescharacteristic
125C2×D4×D61C2311yescharacteristic
126C2×#11758190C2×C411yescharacteristic, complemented
127C2×#11758190C2×C411yescharacteristic, complemented
128C2×#11758200C2×C411yescharacteristic, complemented
129C2×#11758200C2×C411yescharacteristic, complemented
130C2×#11758201C2×C411yescharacteristic, complemented
131C2×#11758201C2×C411yescharacteristic, complemented
132SD16×D61—22no—
133SD16×D61—22no—
134SD16×D61—22no—
135SD16×D61—22no—
136C2×C8×D61C2311yescharacteristic
137C2×C8×D61C2311yescharacteristic
138#14519774C2×C411yescharacteristic
139#14519773—21no—
140#14519773—21no—
141#14519773C2×C411yescharacteristic
142#14519773C2×C411yescharacteristic
143Q8×Dic61C2×C411yescharacteristic, complemented
144C4×Dic122—21no—
145C4×Dic122C2×C411yescharacteristic, complemented
146#14519742—21no—
147#14519742C2×C411yescharacteristic, complemented
148C4⋊C4×D61—21no—
149C4⋊C4×D61C2311yescharacteristic
150C42×D61—21no—
151C42×D61C2311yescharacteristic
152C4⋊#92418C2×C411yescharacteristic, complemented
153#14519706C2×C411yescharacteristic, complemented
154#14519706C2×C411yescharacteristic, complemented
155#14519699C2×C411yescharacteristic, complemented
156#14519699C2×C411yescharacteristic, complemented
157#14519698C2×C411yescharacteristic, complemented
158#14519698C2×C411yescharacteristic, complemented
159#14519697C2×C411yescharacteristic, complemented
160#14519697C2×C411yescharacteristic, complemented
161C2×SD16×C61C2×C411yescharacteristic, complemented
162C2×SD16×C61C2×C411yescharacteristic, complemented
163#127×C61C2×C411yescharacteristic
164C4×Q8×C61C2×C411yescharacteristic, complemented
165C4⋊C8×C61C2×C411yescharacteristic, complemented
166#102×C61C2×C411yescharacteristic, complemented
167#102×C61C2×C411yescharacteristic, complemented
168C23×D61—21no—
169C23×D61—21no—
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—42no—
175C22×#6923—42no—
176C22×#6923—81no—
177C22×#6923—81no—
178C22×#6923—81no—
179C22×#6923—81no—
180C22×#6923C2×D411yescharacteristic
181C22×#6923C2×D411yescharacteristic
182C22×#6923C2×D411yescharacteristic
183C22×#6923C2×D411yescharacteristic
184C2×Q8×C61C22×C411yescharacteristic
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61C22×C411yescharacteristic
188C2×D4×C61C22×C411yescharacteristic
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C2×C22⋊D61—21no—
195Q8×D61—21no—
196Q8×D61—21no—
197Q8×D61C2×D412yes—
198Q8×D61#4112yes—
199D4×D61—21no—
200D4×D61—21no—
201D4×D61—21no—
202D4×D61—21no—
203D4×D61—21no—
204D4×D61—21no—
205D4×D61—21no—
206D4×D61—21no—
207D4×D61—81no—
208D4×D61—81no—
209D4×D61—81no—
210D4×D61—81no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244C22×C411yescharacteristic
214C2×D244C22×C411yescharacteristic
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61C2×D411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2411yescharacteristic
220C2×Dic122—21no—
221C2×Dic122C22×C411yescharacteristic
222C22⋊#6923—42no—
223C22⋊#6923—42no—
224C22⋊#6923—81no—
225C22⋊#6923—81no—
226C22⋊#6923—81no—
227C22⋊#6923—81no—
228C2×#92420—21no—
229C2×#92420—21no—
230C4⋊#6923—24no—
231C4⋊#6923—24no—
232C4⋊#6923—21no—
233C4⋊#6923—21no—
234C4⋊#6923—21no—
235C4⋊#6923—21no—
236C4⋊#6923—21no—
237C4⋊#6923—21no—
238C4⋊#6923C2×D412yes—
239C4⋊#6923#4112yes—
240C4×#6923—24no—
241C4×#6923—24no—
242C4×#6923—21no—
243C4×#6923—21no—
244C4×#6923—81no—
245C4×#6923—81no—
246C4×#6923—81no—
247C4×#6923C2×D412yes—
248C4×#6923#4112yes—
249D61⋊C8—21no—
250D61⋊C8—21no—
251D61⋊C8—21no—
252D61⋊C8—21no—
253SD16×C61—22no—
254SD16×C61—22no—
255C2×C8×C61C22×C411yescharacteristic
256C2×C8×C61C22×C411yescharacteristic
257C4⋊C4×C61—21no—
258C4⋊C4×C61C22×C411yescharacteristic
259C42×C61—21no—
260C42×C61C22×C411yescharacteristic
261#11758201—22no—
262#11758201—22no—
263#11758200—22no—
264#11758200—22no—
265C4⋊Dic61—21no—
266C4⋊Dic61C22×C411yescharacteristic
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61—21no—
273C4×Dic61C22×C411yescharacteristic
274C4×Dic61#4111yescharacteristic
275C4×Dic61#4111yescharacteristic
276C2×#92418C22×C411yescharacteristic
277C2×#92418C22×C411yescharacteristic
278#11758190—22no—
279#11758190—22no—
280C8×D61—21no—
281C8×D61—21no—
282C8×D61—21no—
283C8×D61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61C22×D411yescharacteristic
301C2×#6923—21no—
302C2×#6923—21no—
303C2×#6923—21no—
304C2×#6923—21no—
305C2×#6923—22no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—22no—
309C2×#6923—21no—
310C2×#6923—21no—
311C2×#6923—21no—
312C2×#6923—21no—
313C2×#6923—41no—
314C2×#6923—41no—
315C2×#6923—41no—
316C2×#6923—41no—
317C2×#6923—41no—
318C2×#6923—41no—
319C2×#6923—41no—
320C2×#6923—41no—
321C2×#6923—41no—
322C2×#6923—41no—
323C2×#6923—84no—
324C2×#6923—84no—
325C2×#6923#12112yes—
326C2×#6923#12112yes—
327Q8×C61—21no—
328Q8×C61C4×D412yes—
329D4×C61—21no—
330D4×C61—21no—
331D4×C61—21no—
332D4×C61—21no—
333D4×C61—81no—
334D4×C61—81no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61C4×D411yescharacteristic
338C2×C4×C61C4×D411yescharacteristic
339C2×C4×C61C23×C411yescharacteristic
340C22⋊D61—41no—
341C22⋊D61—41no—
342C22⋊D61—41no—
343C22⋊D61—41no—
344C22⋊D61—81no—
345C22⋊D61—81no—
346C22⋊D61—81no—
347C22⋊D61—81no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61C4×D411yescharacteristic
351C2×Dic61C4×D411yescharacteristic
352C2×Dic61C2×#4111yescharacteristic
353D244—21no—
354D244—21no—
355D244—21no—
356D244—21no—
357D244—81no—
358D244—81no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—41no—
366C4×D61—41no—
367C4×D61C22×D411yescharacteristic
368C4×D61C2×#4111yescharacteristic
369C4×D61C2×#4111yescharacteristic
370C4×D61C2×#4111yescharacteristic
371Dic122—21no—
372Dic122—22no—
373Dic122—22no—
374Dic122C4×D412yes—
375#92420—41no—
376#92420—41no—
377C8×C61—21no—
378C8×C61—21no—
379#92418—21no—
380#92418—21no—
381#21515—611nomaximal, Sylow
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61C2×C4×D411yescharacteristic
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—81no—
396C2×D61—81no—
397C2×D61—81no—
398C2×D61—81no—
399C2×D61—81no—
400C2×D61—81no—
401C2×D61—81no—
402C2×D61—81no—
403C2×D61C2×#12111yescharacteristic
404C2×D61#52511yescharacteristic
405C2×D61#57611yescharacteristic
406C2×D61#57711yescharacteristic
407C2×D61#57711yescharacteristic
408C2×D61#57711yescharacteristic
409#6923—22no—
410#6923—22no—
411#6923—41no—
412#6923—42no—
413#6923—41no—
414#6923—42no—
415#6923—81no—
416#6923—81no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—22no—
420C4×C61—41no—
421C4×C61C2×C4×D411yescharacteristic
422C4×C61C4×#4111yescharacteristic
423Dic61—21no—
424Dic61—21no—
425Dic61—22no—
426Dic61—41no—
427Dic61#52911yescharacteristic
428Dic61#53211yescharacteristic
429C2×#460—611no—
430C2×#440—611no—
431C2×C4×SD16—611no—
432#2328—611no—
433#2276—611no—
434#1982—611no—
435#1949—611no—
436#1926—611no—
437#1925—611no—
438#1880—611no—
439#1880—611no—
440#1805—611no—
441#1768—611no—
442#1762—611no—
443C4×#102—611no—
444C2×C61—81no—
445C2×C61—81no—
446C2×C61C4×#12111yescharacteristic
447C2×C61#294611yescharacteristic
448C2×C61#294911yescharacteristic
449D61—81no—
450D61—81no—
451D61#304311yescharacteristic
452D61#304511yescharacteristic
453D61#311911yescharacteristic
454D61#312611yescharacteristic
455C22×SD16—611no—
456C22×SD16—611no—
457C2×#127—611no—
458C2×C4×Q8—611no—
459C2×C4×Q8—611no—
460C2×C4×Q8—611no—
461C2×C4×D4—611no—
462C2×C4×D4—611no—
463#460—611no—
464#460—611no—
465#460—611no—
466#460—611no—
467#460—611no—
468#460—611no—
469#460—611no—
470#460#692311yescharacteristic, complemented
471#440—1224no—
472C4×SD16—1224no—
473C2×#107—611no—
474C2×#106—611no—
475C2×C4⋊C8—611no—
476C2×C4⋊C8—611no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#97—611no—
486C2×C4×C8—611no—
487#390—611no—
488#390—611no—
489#386—1221no—
490#386—1221no—
491#386—1221no—
492#386—1221no—
493#382—611no—
494C4×C4⋊C4—611no—
495C4×C4⋊C4—611no—
496C4×C4⋊C4—611no—
497C4×C4⋊C4—1221no—
498C4×C4⋊C4—1221no—
499C4×C4⋊C4—1221no—
500#376—611no—
501#376—1221no—
502#340—611no—
503#340—611no—
504#340—611no—
505#340—611no—
506#336—611no—
507#336—611no—
508C61#2151511yescharacteristic, complemented, Sylow
509C22×Q8—611no—
510C22×D4—611no—
511C22×D4—611no—
512C22×D4—1221no—
513C22×D4—1221no—
514C23×C4—1221no—
515C23×C4—1221no—
516C2×SD16—611no—
517C2×SD16—611no—
518C2×SD16—611no—
519C2×SD16—611no—
520C2×SD16—611no—
521C2×SD16—611no—
522C2×SD16—1222no—
523C2×SD16—1222no—
524C2×SD16—1222no—
525C2×SD16—1222no—
526C2×SD16C2×#692311yescharacteristic, complemented
527C2×SD16C2×#692311yescharacteristic, complemented
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—611no—
531C22×C8—611no—
532#127—611no—
533#127—611no—
534#127—611no—
535#127—1221no—
536#127—1221no—
537#127C2×#692311yescharacteristic
538C4×Q8—614no—
539C4×Q8—611no—
540C4×Q8—611no—
541C4×Q8—611no—
542C4×Q8—1221no—
543C4×Q8—1221no—
544C4×Q8—1222no—
545C4×Q8—1222no—
546C4×Q8—1222no—
547C4×Q8C2×#692311yescharacteristic, complemented
548C4×D4—1222no—
549C4×D4—1222no—
550C4×D4—1222no—
551C4×D4—1222no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—1221no—
570C2×C42—1221no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42—1221no—
574C2×C42—1221no—
575#107—1222no—
576#106—1222no—
577C4⋊C8—611no—
578C4⋊C8—611no—
579C4⋊C8—611no—
580C4⋊C8—1221no—
581C4⋊C8—1221no—
582C4⋊C8C2×#692311yescharacteristic, complemented
583#103—1222no—
584#103—1222no—
585#102—611no—
586#102—611no—
587#102—611no—
588#102—611no—
589#102—611no—
590#102—611no—
591#102—1222no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102C2×#692311yescharacteristic, complemented
596#102C2×#692311yescharacteristic, complemented
597#97—1222no—
598C4×C8—1222no—
599#95—611no—
600#95—611no—
601#95—611no—
602#95—611no—
603#95—1221no—
604#95—1221no—
605#95—1221no—
606#95—1221no—
607#95—1221no—
608C24—1221no—
609C24—1221no—
610C2×Q8—612no—
611C2×Q8—612no—
612C2×Q8—611no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8C22×#692311yescharacteristic
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—611no—
620C2×D4—611no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—4881no—
638C2×D4—4881no—
639C2×D4—4881no—
640C2×D4—4881no—
641C2×D4C22×#692311yescharacteristic
642C2×D4C22×#692311yescharacteristic
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—4881no—
657C22×C4—4881no—
658C22×C4—4881no—
659C22×C4—4881no—
660C22×C4—2442no—
661C22×C4—2442no—
662SD16—22no—
663SD16—22no—
664SD16—1222no—
665SD16—1222no—
666SD16—1222no—
667SD16—1222no—
668SD16—1222no—
669SD16—1222no—
670C2×C8—611no—
671C2×C8—611no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8C22×#692311yescharacteristic
683C2×C8C22×#692311yescharacteristic
684C4⋊C4—21no—
685C4⋊C4—612no—
686C4⋊C4—612no—
687C4⋊C4—611no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1224no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1224no—
699C4⋊C4—1221no—
700C4⋊C4C22×#692311yescharacteristic
701C22⋊C4—4881no—
702C22⋊C4—4881no—
703C22⋊C4—4881no—
704C22⋊C4—4881no—
705C22⋊C4—2442no—
706C22⋊C4—2442no—
707C42—21no—
708C42—612no—
709C42—612no—
710C42—611no—
711C42—611no—
712C42—611no—
713C42—1221no—
714C42—1221no—
715C42—1221no—
716C42—1221no—
717C42—1224no—
718C42—1224no—
719C42—1221no—
720C42—4881no—
721C42—4881no—
722C42—4881no—
723C42C22×#692311yescharacteristic
724C23—21no—
725C23—21no—
726C23—611no—
727C23—1221no—
728C23—1221no—
729C23—2441no—
730C23—2441no—
731C23—2441no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738C23—2441no—
739C23—2441no—
740C23—2441no—
741Q8—21no—
742Q8—612no—
743Q8—1222no—
744Q8—1222no—
745Q8—1221no—
746Q8D4×#692312yes—
747D4—21no—
748D4—21no—
749D4—21no—
750D4—21no—
751D4—81no—
752D4—81no—
753D4—1221no—
754D4—1221no—
755D4—1221no—
756D4—1221no—
757D4—4881no—
758D4—4881no—
759D4—4881no—
760D4—4881no—
761D4—4881no—
762D4—4881no—
763D4—2441no—
764D4—2441no—
765D4—2441no—
766D4—2441no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—611no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—612no—
775C2×C4—612no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—4884no—
799C2×C4—4884no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4D4×#692311yescharacteristic
813C2×C4D4×#692311yescharacteristic
814C2×C4C23×#692311yescharacteristic
815C8—21no—
816C8—21no—
817C8—1221no—
818C8—1221no—
819C8—2441no—
820C8—2441no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—611no—
828C22—611no—
829C22—611no—
830C22—611no—
831C22—611no—
832C22—611no—
833C22—4881no—
834C22—4881no—
835C22—4881no—
836C22—4881no—
837C22—4881no—
838C22—4881no—
839C22—4881no—
840C22—4881no—
841C22—2441no—
842C22—2441no—
843C22—2441no—
844C22—2441no—
845C22—2441no—
846C22—2441no—
847C22C2×D4×#692311yescharacteristic
848C4—22no—
849C4—21no—
850C4—21no—
851C4—41no—
852C4—611no—
853C4—611no—
854C4—1222no—
855C4—1222no—
856C4—1222no—
857C4—1221no—
858C4—1221no—
859C4—4881no—
860C4—4881no—
861C4—2441no—
862C4—2441no—
863C4—2442no—
864C4—2442no—
865C4—2441no—
866C4C2×D4×#692311yescharacteristic
867C4#41×#692311yescharacteristic
868C2—81no—
869C2—81no—
870C2—611no—
871C2—611no—
872C2—611no—
873C2—611no—
874C2—4881no—
875C2—4881no—
876C2#121×#692311yescharacteristic
877C2#2146257611yescharacteristic
878C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#460C4
socleC22×C61C2×C4×D4
prime radical#127×D61C22
cosocleC2×C4×D61C24
hypercenter#460#6923
hypocenterC61#21515
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#16840801C2semidirect
2. C2×SD16×#6923C2semidirect
4. #21462259C2semidirect
6. #21461932C2semidirect
7. #21461897C2semidirect
8. #21461896C2semidirect
9. #21461815C2semidirect
10. #21461815C2semidirect
11. #21461690C2semidirect
12. #21461608C2semidirect
13. #21461590C2semidirect
14. #102×#6923C2semidirect
58. #16839963C4semidirect
59. #16839962C4semidirect
60. #16839961C4semidirect
61. #16839961C4semidirect
62. #16839960C4semidirect
63. #16839960C4semidirect
64. #16839959C4semidirect
68. C61×#460C4semidirect
76. Q8×#6923D4semidirect
126. C2×#11758190C2×C4semidirect
127. C2×#11758190C2×C4semidirect
128. C2×#11758200C2×C4semidirect
129. C2×#11758200C2×C4semidirect
130. C2×#11758201C2×C4semidirect
131. C2×#11758201C2×C4semidirect
143. Q8×Dic61C2×C4semidirect
145. C4×Dic122C2×C4semidirect
147. #14519742C2×C4semidirect
152. C4⋊#92418C2×C4semidirect
153. #14519706C2×C4semidirect
154. #14519706C2×C4semidirect
155. #14519699C2×C4semidirect
156. #14519699C2×C4semidirect
157. #14519698C2×C4semidirect
158. #14519698C2×C4semidirect
159. #14519697C2×C4semidirect
160. #14519697C2×C4semidirect
161. C2×SD16×C61C2×C4semidirect
162. C2×SD16×C61C2×C4semidirect
164. C4×Q8×C61C2×C4semidirect
165. C4⋊C8×C61C2×C4semidirect
166. #102×C61C2×C4semidirect
167. #102×C61C2×C4semidirect
470. #460#6923semidirect
508. C61#21515semidirect
526. C2×SD16C2×#6923semidirect
527. C2×SD16C2×#6923semidirect
547. C4×Q8C2×#6923semidirect
582. C4⋊C8C2×#6923semidirect
595. #102C2×#6923semidirect
596. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408012
C2×SD16×#69232
#214623112
#214622592
#214619862
#214619322
#214618972
#214618962
#214618152
#214616902
#214616082
#214615902
#102×#69232
#460×D612
#2151561