Finite Group Databasebeta

← #30622202

Subgroups — #30622202

Order 15616.

982 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
1C2×#16840801C211yesmaximal, characteristic
2C2×SD16×#6923C211yesmaximal, characteristic
3#21462348C211yesmaximal, characteristic, complemented
4#21462332C211yesmaximal, characteristic
5#21461950C211yesmaximal, characteristic, complemented
6#21461932C211yesmaximal, characteristic, complemented
7#21461910C211yesmaximal, characteristic, complemented
8#21461908C211yesmaximal, characteristic, complemented
9#21461812C211yesmaximal, characteristic
10#21461812C211yesmaximal, characteristic
11#21461785C211yesmaximal, characteristic, complemented
12#21461783C211yesmaximal, characteristic, complemented
13#21461620C211yesmaximal, characteristic, complemented
14#21461589C211yesmaximal, characteristic
15#461×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20#16840801—24no—
21SD16×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24C2×#14519840C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30#16840721C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34(C2×#6923)⋊Q8C2211yescharacteristic
35#16840713—21no—
36#16840713C2211yescharacteristic
37#16840713C2211yescharacteristic
38#16840711—21no—
39#16840711—21no—
40#16840709—21no—
41#16840709—21no—
42#16840706C2211yescharacteristic
43#16840704—21no—
44C4⋊C4×#6923—21no—
45C4×C4⋊#6923C2211yescharacteristic
46C4×C4⋊#6923C2211yescharacteristic
47C2×(C2×#6923)⋊C4—21no—
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×SD16×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56C4⋊Q8×D61C2211yescharacteristic
57C4×D4×D61C2211yescharacteristic
58#16839968C411yescharacteristic, complemented
59#16839967C411yescharacteristic, complemented
60#16839966C411yescharacteristic, complemented
61#16839966C411yescharacteristic, complemented
62#16839965C411yescharacteristic, complemented
63#16839965C411yescharacteristic, complemented
64#16839964C411yescharacteristic, complemented
65C4⋊C8×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67#103×D61C2211yescharacteristic
68C61×#461C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C2×D61⋊C8C2311yescharacteristic
72C2×D61⋊C8C2311yescharacteristic
73Q8×#6923—22no—
74Q8×#6923—22no—
75Q8×#6923—41no—
76Q8×#6923—41no—
77D4×#6923—22no—
78D4×#6923—22no—
79D4×#6923—41no—
80D4×#6923—41no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923D411yescharacteristic
86C2×C4⋊#6923D411yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923C2311yescharacteristic
97C2×C4×#6923C2311yescharacteristic
98#14519846—22no—
99#14519845—22no—
100#14519840—22no—
101#14519840—22no—
102#14519840—41no—
103#14519840—41no—
104#14519839—22no—
105#14519839D414yes—
106#14519832—21no—
107#14519832—21no—
108#14519831—22no—
109C8×#6923—22no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
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)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4D411yescharacteristic
120(C2×#6923)⋊C4D411yescharacteristic
121C2×Q8×D61C2311yescharacteristic
122C2×Q8×D61C2311yescharacteristic
123C2×D4×D61C2311yescharacteristic
124C22×C4×D61—21no—
125C2×#11758190C2×C411yescharacteristic
126C2×#11758190C2×C411yescharacteristic
127C2×#11758200C2×C411yescharacteristic
128C2×#11758200C2×C411yescharacteristic
129C2×#11758201C2×C411yescharacteristic
130C2×#11758201C2×C411yescharacteristic
131SD16×D61—22no—
132SD16×D61—22no—
133SD16×D61—22no—
134SD16×D61—22no—
135C2×C8×D61C2311yescharacteristic
136C2×C8×D61C2311yescharacteristic
137#14519777C2×C411yescharacteristic, complemented
138#14519776—21no—
139#14519776—21no—
140#14519775C2×C411yescharacteristic, complemented
141#14519775C2×C411yescharacteristic, complemented
142C4×D244C2×C411yescharacteristic
143D4×Dic61C2×C411yescharacteristic
144#14519739C2×C411yescharacteristic
145C4×C22⋊D61—21no—
146#14519737—21no—
147C4⋊C4×D61—21no—
148C4⋊C4×D61—21no—
149C4⋊C4×D61C2311yescharacteristic
150C22⋊C4×D61—21no—
151C42×D61C2311yescharacteristic
152C4⋊#92418C2×C411yescharacteristic, complemented
153#14519706C2×C411yescharacteristic, complemented
154#14519706C2×C411yescharacteristic, complemented
155#14519702C2×C411yescharacteristic, complemented
156#14519702C2×C411yescharacteristic, complemented
157#14519701C2×C411yescharacteristic, complemented
158#14519701C2×C411yescharacteristic, complemented
159#14519700C2×C411yescharacteristic, complemented
160#14519700C2×C411yescharacteristic, complemented
161C2×SD16×C61C2×C411yescharacteristic
162C2×SD16×C61C2×C411yescharacteristic
163C4⋊Q8×C61C2×C411yescharacteristic, complemented
164C4×D4×C61C2×C411yescharacteristic
165C4⋊C8×C61C2×C411yescharacteristic, complemented
166#103×C61C2×C411yescharacteristic, complemented
167#103×C61C2×C411yescharacteristic, complemented
168C23×D61—21no—
169C22×#6923—21no—
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—42no—
174C22×#6923—42no—
175C22×#6923—42no—
176C22×#6923—42no—
177C22×#6923—81no—
178C22×#6923—81no—
179C22×#6923C2×D411yescharacteristic
180C22×#6923C2×D411yescharacteristic
181C22×#6923C2×D411yescharacteristic
182C22×#6923C2×D411yescharacteristic
183C2×Q8×C61C22×C411yescharacteristic
184C2×Q8×C61C22×C411yescharacteristic
185C2×D4×C61C22×C411yescharacteristic
186C22×C4×C61—21no—
187C2×C22⋊D61—21no—
188C22×Dic61—21no—
189Q8×D61—21no—
190Q8×D61—21no—
191Q8×D61—21no—
192Q8×D61—21no—
193Q8×D61—21no—
194Q8×D61—21no—
195Q8×D61—21no—
196Q8×D61—21no—
197D4×D61—21no—
198D4×D61—21no—
199D4×D61C2×D412yes—
200D4×D61#4112yes—
201C2×D244C22×C411yescharacteristic
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—81no—
208C2×C4×D61—81no—
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2411yescharacteristic
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122C22×C411yescharacteristic
215C2×Dic122C22×C411yescharacteristic
216C22⋊#6923—42no—
217C22⋊#6923—42no—
218C2×#92420—21no—
219C2×#92420—21no—
220C4⋊#6923—22no—
221C4⋊#6923—21no—
222C4⋊#6923—21no—
223C4⋊#6923—21no—
224C4⋊#6923—21no—
225C4⋊#6923—21no—
226C4⋊#6923—21no—
227C4⋊#6923—21no—
228C4⋊#6923—41no—
229C4⋊#6923—42no—
230C4⋊#6923—42no—
231C4⋊#6923—81no—
232C4⋊#6923—81no—
233C4⋊#6923C2×D412yes—
234C4×#6923—21no—
235C4×#6923—21no—
236C4×#6923—21no—
237C4×#6923—21no—
238C4×#6923—42no—
239C4×#6923—42no—
240C4×#6923—42no—
241D61⋊C8—21no—
242D61⋊C8—21no—
243D61⋊C8—21no—
244D61⋊C8C2×D412yes—
245SD16×C61—22no—
246SD16×C61—22no—
247C2×C8×C61C22×C411yescharacteristic
248C2×C8×C61C22×C411yescharacteristic
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61C22×C411yescharacteristic
252C22⋊C4×C61—21no—
253C42×C61C22×C411yescharacteristic
254C22⋊Dic61—21no—
255#11758201—22no—
256#11758201—22no—
257#11758200—22no—
258#11758200—22no—
259#11758198—21no—
260#11758198—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61C22×C411yescharacteristic
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269C4×Dic61C22×C411yescharacteristic
270C4×Dic61#4111yescharacteristic
271C4×Dic61#4111yescharacteristic
272C2×#92418C22×C411yescharacteristic
273C2×#92418C22×C411yescharacteristic
274#11758190—22no—
275#11758190—22no—
276C8×D61—21no—
277C8×D61—21no—
278C8×D61—21no—
279C8×D61—21no—
280C23×C61—21no—
281C22×D61—21no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61C22×D411yescharacteristic
289C2×#6923—21no—
290C2×#6923—21no—
291C2×#6923—21no—
292C2×#6923—21no—
293C2×#6923—21no—
294C2×#6923—22no—
295C2×#6923—21no—
296C2×#6923—21no—
297C2×#6923—21no—
298C2×#6923—21no—
299C2×#6923—21no—
300C2×#6923—21no—
301C2×#6923—41no—
302C2×#6923—41no—
303C2×#6923—41no—
304C2×#6923—41no—
305C2×#6923—41no—
306C2×#6923—41no—
307C2×#6923—41no—
308C2×#6923—41no—
309C2×#6923—41no—
310C2×#6923—41no—
311C2×#6923—41no—
312C2×#6923—84no—
313C2×#6923—84no—
314C2×#6923#13712yes—
315Q8×C61—21no—
316Q8×C61—21no—
317Q8×C61—21no—
318Q8×C61—21no—
319D4×C61—21no—
320D4×C61C4×D412yes—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—81no—
325C2×C4×C61C4×D411yescharacteristic
326C2×C4×C61C4×D411yescharacteristic
327C2×C4×C61C23×C411yescharacteristic
328C22⋊D61—22no—
329C22⋊D61—22no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—81no—
334C2×Dic61C4×D411yescharacteristic
335C2×Dic61C4×D411yescharacteristic
336C2×Dic61C2×#4111yescharacteristic
337D244—21no—
338D244C4×D412yes—
339C4×D61—21no—
340C4×D61—21no—
341C4×D61—21no—
342C4×D61—21no—
343C4×D61—41no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—81no—
350C4×D61—81no—
351C4×D61C22×D411yescharacteristic
352C4×D61C2×#4111yescharacteristic
353C4×D61H(5,𝔽2)11yescharacteristic
354C4×D612−1+411yescharacteristic
355Dic122—21no—
356Dic122—21no—
357Dic122—21no—
358Dic122—21no—
359Dic122—41no—
360Dic122—41no—
361Dic122—41no—
362Dic122—41no—
363#92420—22no—
364#92420—41no—
365C8×C61—21no—
366C8×C61—21no—
367#92418—21no—
368#92418—21no—
369#23012—611nomaximal, Sylow
370C22×C61—22no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61C2×C4×D411yescharacteristic
374C2×D61—22no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61D4211yescharacteristic
382C2×D61#54811yescharacteristic
383C2×D61C2×#13711yescharacteristic
384C2×D61#57511yescharacteristic
385C2×D61#57711yescharacteristic
386C2×D61#57711yescharacteristic
387#6923—22no—
388#6923—41no—
389#6923—41no—
390#6923—41no—
391#6923—42no—
392#6923—81no—
393#6923—81no—
394#6923—81no—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—41no—
398C4×C61—41no—
399C4×C61—41no—
400C4×C61C2×C4×D411yescharacteristic
401C4×C61#52011yescharacteristic
402Dic61—21no—
403Dic61—21no—
404Dic61—41no—
405Dic61—41no—
406Dic61—41no—
407Dic61#54711yescharacteristic
408Dic61#55311yescharacteristic
409C2×#461—611no—
410C2×#440—611no—
411C2×C4×SD16—611no—
412#2365—611no—
413#2349—611no—
414#1960—611no—
415#1949—611no—
416#1935—611no—
417#1933—611no—
418#1877—611no—
419#1877—611no—
420#1865—611no—
421#1863—611no—
422#1771—611no—
423#1762—611no—
424C2×C61—42no—
425C2×C61#236111yescharacteristic
426C2×C61C4×#13711yescharacteristic
427C2×C61#294911yescharacteristic
428D61—42no—
429D61#326611yescharacteristic
430D61#326711yescharacteristic
431D61#337211yescharacteristic
432D61#337611yescharacteristic
433C22×SD16—611no—
434C22×SD16—611no—
435C2×C4⋊Q8—611no—
436C2×C4×Q8—611no—
437C2×C4×Q8—611no—
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440C2×C4×D4—611no—
441#461—611no—
442#461—611no—
443#461—611no—
444#461—611no—
445#461—611no—
446#461—611no—
447#461—611no—
448#461#692311yescharacteristic, complemented
449#440—1224no—
450C4×SD16—1224no—
451C2×#107—611no—
452C2×#106—611no—
453C2×C4⋊C8—611no—
454C2×#103—611no—
455C2×#103—611no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#102—611no—
461C2×#102—611no—
462C2×#97—611no—
463C2×#97—611no—
464C2×C4×C8—611no—
465#391—611no—
466#391—611no—
467#389—611no—
468#389—611no—
469#389—1221no—
470#387—1221no—
471#387—1221no—
472#385—1221no—
473#385—1221no—
474#382—611no—
475#380—1221no—
476C4×C4⋊C4—611no—
477C4×C4⋊C4—611no—
478C4×C4⋊C4—1221no—
479C2×#95—1221no—
480#340—611no—
481#340—611no—
482#340—611no—
483#340—611no—
484#336—611no—
485#336—611no—
486C61#2301211yescharacteristic, complemented, Sylow
487C22×Q8—611no—
488C22×Q8—611no—
489C22×D4—611no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4—1221no—
493C2×SD16—611no—
494C2×SD16—611no—
495C2×SD16—611no—
496C2×SD16—611no—
497C2×SD16—611no—
498C2×SD16—611no—
499C2×SD16—1222no—
500C2×SD16—1222no—
501C2×SD16—1222no—
502C2×SD16—1222no—
503C2×SD16C2×#692311yescharacteristic
504C2×SD16C2×#692311yescharacteristic
505C22×C8—611no—
506C22×C8—611no—
507C22×C8—611no—
508C22×C8—611no—
509C4⋊Q8—611no—
510C4⋊Q8—611no—
511C4⋊Q8—611no—
512C4⋊Q8—1221no—
513C4⋊Q8—1221no—
514C4⋊Q8C2×#692311yescharacteristic, complemented
515C4×Q8—1222no—
516C4×Q8—1222no—
517C4×Q8—2441no—
518C4×Q8—2441no—
519C4×D4—611no—
520C4×D4—611no—
521C4×D4—611no—
522C4×D4—1221no—
523C4×D4—1221no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—2441no—
527C4×D4—2441no—
528C4×D4C2×#692311yescharacteristic
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C42—611no—
546C2×C42—611no—
547C2×C42—611no—
548C2×C42—1221no—
549C2×C42—1221no—
550C2×C42—1221no—
551#107—1222no—
552#106—1222no—
553C4⋊C8—611no—
554C4⋊C8—611no—
555C4⋊C8—611no—
556C4⋊C8C2×#692311yescharacteristic, complemented
557#103—611no—
558#103—611no—
559#103—611no—
560#103—611no—
561#103—611no—
562#103—611no—
563#103—1222no—
564#103—1222no—
565#103—2441no—
566#103—2441no—
567#103C2×#692311yescharacteristic, complemented
568#103C2×#692311yescharacteristic, complemented
569#102—614no—
570#102—1222no—
571#97—1221no—
572#97—1221no—
573#97—1222no—
574C4×C8—1222no—
575#95—611no—
576#95—611no—
577#95—1221no—
578#95—1221no—
579#95—1221no—
580#95—1221no—
581#95—1221no—
582#95—1221no—
583#95—1221no—
584#95—1221no—
585#95—1221no—
586C24—1221no—
587C2×Q8—611no—
588C2×Q8—611no—
589C2×Q8—1221no—
590C2×Q8—1221no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8C22×#692311yescharacteristic
600C2×Q8C22×#692311yescharacteristic
601C2×D4—612no—
602C2×D4—612no—
603C2×D4—611no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4C22×#692311yescharacteristic
608C22×C4—21no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—4881no—
627C22×C4—4881no—
628C22×C4—4881no—
629C22×C4—4881no—
630C22×C4—2442no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4—2442no—
634SD16—22no—
635SD16—22no—
636SD16—1222no—
637SD16—1222no—
638SD16—1222no—
639SD16—1222no—
640SD16—1222no—
641SD16—1222no—
642C2×C8—612no—
643C2×C8—611no—
644C2×C8—611no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8C22×#692311yescharacteristic
655C2×C8C22×#692311yescharacteristic
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—612no—
659C4⋊C4—611no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1222no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—4881no—
676C4⋊C4—4881no—
677C4⋊C4—2441no—
678C4⋊C4—2442no—
679C4⋊C4—2442no—
680C4⋊C4C22×#692311yescharacteristic
681C22⋊C4—21no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—2442no—
686C22⋊C4—2442no—
687C42—611no—
688C42—611no—
689C42—611no—
690C42—1221no—
691C42—1221no—
692C42—1221no—
693C42—1221no—
694C42—2442no—
695C42—2442no—
696C42—2442no—
697C42C22×#692311yescharacteristic
698C23—21no—
699C23—611no—
700C23—1222no—
701C23—1222no—
702C23—1221no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707Q8—21no—
708Q8—21no—
709Q8—21no—
710Q8—21no—
711Q8—1221no—
712Q8—1221no—
713Q8—1221no—
714Q8—1221no—
715Q8—2441no—
716Q8—2441no—
717Q8—2441no—
718Q8—2441no—
719D4—21no—
720D4—612no—
721D4—1222no—
722D4—1222no—
723D4—1221no—
724D4D4×#692312yes—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—81no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—611no—
732C2×C4—611no—
733C2×C4—611no—
734C2×C4—612no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1222no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—4881no—
757C2×C4—4881no—
758C2×C4—4884no—
759C2×C4—4881no—
760C2×C4—4884no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4—2441no—
778C2×C4D4×#692311yescharacteristic
779C2×C4D4×#692311yescharacteristic
780C2×C4C23×#692311yescharacteristic
781C8—21no—
782C8—21no—
783C8—1222no—
784C8—1221no—
785C8—1221no—
786C8—2441no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—611no—
791C22—611no—
792C22—611no—
793C22—611no—
794C22—611no—
795C22—611no—
796C22—1222no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22—2441no—
802C22—2441no—
803C22C2×D4×#692311yescharacteristic
804C4—21no—
805C4—21no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—611no—
810C4—611no—
811C4—1222no—
812C4—1221no—
813C4—1221no—
814C4—4881no—
815C4—4881no—
816C4—4881no—
817C4—2441no—
818C4—2441no—
819C4—2441no—
820C4—2442no—
821C4—2441no—
822C4—2441no—
823C4—2441no—
824C4C2×D4×#692311yescharacteristic
825C4#1684083111yescharacteristic
826C2—42no—
827C2—611no—
828C2—611no—
829C2—611no—
830C2—611no—
831C2—2442no—
832C2#2146234411yescharacteristic
833C2#137×#692311yescharacteristic
834C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#461C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#461#6923
hypocenterC61#23012
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
3. #21462348C2semidirect
5. #21461950C2semidirect
6. #21461932C2semidirect
7. #21461910C2semidirect
8. #21461908C2semidirect
11. #21461785C2semidirect
12. #21461783C2semidirect
13. #21461620C2semidirect
58. #16839968C4semidirect
59. #16839967C4semidirect
60. #16839966C4semidirect
61. #16839966C4semidirect
62. #16839965C4semidirect
63. #16839965C4semidirect
64. #16839964C4semidirect
68. C61×#461C4semidirect
137. #14519777C2×C4semidirect
140. #14519775C2×C4semidirect
141. #14519775C2×C4semidirect
152. C4⋊#92418C2×C4semidirect
153. #14519706C2×C4semidirect
154. #14519706C2×C4semidirect
155. #14519702C2×C4semidirect
156. #14519702C2×C4semidirect
157. #14519701C2×C4semidirect
158. #14519701C2×C4semidirect
159. #14519700C2×C4semidirect
160. #14519700C2×C4semidirect
163. C4⋊Q8×C61C2×C4semidirect
165. C4⋊C8×C61C2×C4semidirect
166. #103×C61C2×C4semidirect
167. #103×C61C2×C4semidirect
448. #461#6923semidirect
486. C61#23012semidirect
514. C4⋊Q8C2×#6923semidirect
556. C4⋊C8C2×#6923semidirect
567. #103C2×#6923semidirect
568. #103C2×#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
#214623482
#214623322
#214619502
#214619322
#214619102
#214619082
#214618122
#214617852
#214617832
#214616202
#214615892
#461×D612
#2301261