Finite Group Databasebeta

← #30621751

Subgroups — #30621751

Order 15616.

1130 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C211yesmaximal, characteristic, complemented
2C2×#16840752C211yesmaximal, characteristic
3#21462345C211yesmaximal, characteristic, complemented
4#21462322C211yesmaximal, characteristic
5#21461965C211yesmaximal, characteristic, complemented
6#21461908C211yesmaximal, characteristic, complemented
7#21461898C211yesmaximal, characteristic, complemented
8#21461832C211yesmaximal, characteristic, complemented
9#21461813C211yesmaximal, characteristic, complemented
10#21461812C211yesmaximal, characteristic, complemented
11#21461782C211yesmaximal, characteristic, complemented
12#21461770C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic, complemented
14#21461554C211yesmaximal, characteristic, complemented
15#452×D61C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20C2×#14519856C2211yescharacteristic
21SD16×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24#16840752—24no—
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×C8×#6923C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34(C2×#6923)⋊Q8C2211yescharacteristic
35(C2×#6923)⋊Q8C2211yescharacteristic
36#16840713C2211yescharacteristic
37#16840712—21no—
38#16840712—21no—
39#16840711—21no—
40#16840710—21no—
41#16840710—21no—
42#16840705—21no—
43#16840704C2211yescharacteristic
44C4⋊C4×#6923—21no—
45C4⋊C4×#6923C2211yescharacteristic
46C4×C22⋊#6923C2211yescharacteristic
47C2×(C2×#6923)⋊C4—21no—
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×#41×D61C2211yescharacteristic
55C2×Q16×D61C2211yescharacteristic
56C2×SD16×D61C2211yescharacteristic
57C22⋊Q8×D61C2211yescharacteristic
58#16839927C411yescharacteristic, complemented
59#16839926C411yescharacteristic, complemented
60#16839925C411yescharacteristic, complemented
61#16839924C411yescharacteristic, complemented
62#16839923C411yescharacteristic, complemented
63#16839922C411yescharacteristic, complemented
64#16839921C411yescharacteristic, complemented
65#103×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#452C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C2×D61⋊C8—22no—
72C2×D61⋊C8—21no—
73C2×D61⋊C8—41no—
74C2×D61⋊C8C2311yescharacteristic
75C2×D61⋊C8C2311yescharacteristic
76C22×#92420—21no—
77Q8×#6923—22no—
78Q8×#6923—41no—
79D4×#6923—22no—
80D4×#6923—22no—
81D4×#6923—41no—
82D4×#6923—41no—
83#14519856—22no—
84#14519856—41no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923—21no—
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923D411yescharacteristic
96C2×C22⋊#6923D411yescharacteristic
97C2×C4×#6923—21no—
98C2×C4×#6923—21no—
99C2×C4×#6923—21no—
100C2×C4×#6923C2311yescharacteristic
101C2×C4×#6923C2311yescharacteristic
102#14519846—41no—
103#14519845—22no—
104#14519840—22no—
105#14519840—22no—
106#14519840—22no—
107#14519840—41no—
108#14519839—22no—
109#14519839D414yes—
110C8×#6923—22no—
111C8×#6923—41no—
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)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4D411yescharacteristic
122(C2×#6923)⋊C4D411yescharacteristic
123C2×#11758226C2×C411yescharacteristic
124C2×#11758222—21no—
125C2×#11758222C2×C411yescharacteristic
126C2×#11758224—21no—
127C2×#11758224C2×C411yescharacteristic
128#41×D61—22no—
129#41×D61—22no—
130#41×D61—41no—
131#41×D61—41no—
132C2×Q8×D61C2311yescharacteristic
133C2×Q8×D61C2311yescharacteristic
134C2×D4×D61—21no—
135C2×D4×D61C2311yescharacteristic
136C22×C4×D61—21no—
137C22×C4×D61C2311yescharacteristic
138C2×Dic244C2×C411yescharacteristic, complemented
139C2×#11758202C2×C411yescharacteristic, complemented
140C2×#11758202C2×C411yescharacteristic, complemented
141Q16×D61—41no—
142Q16×D61—41no—
143C2×#11758190C2×C411yescharacteristic
144C2×#11758200C2×C411yescharacteristic
145C2×#11758201C2×C411yescharacteristic
146SD16×D61—22no—
147SD16×D61—22no—
148C2×C8×D61C2311yescharacteristic
149C2×C8×D61C2311yescharacteristic
150#14519757C2×C411yescharacteristic, complemented
151#14519756C2×C411yescharacteristic, complemented
152#14519755—21no—
153#14519754—21no—
154#14519753C2×C411yescharacteristic, complemented
155C4⋊C4×D61—21no—
156C4⋊C4×D61C2311yescharacteristic
157C22⋊C4×D61—21no—
158#14519702C2×C411yescharacteristic, complemented
159#14519701C2×C411yescharacteristic, complemented
160#14519700C2×C411yescharacteristic, complemented
161#14519699C2×C411yescharacteristic
162#14519698C2×C411yescharacteristic
163#14519697C2×C411yescharacteristic
164C22⋊#92418C2×C411yescharacteristic, complemented
165#14519689C2×C411yescharacteristic, complemented
166#14519689C2×C411yescharacteristic, complemented
167C2×#41×C61C2×C411yescharacteristic
168C2×Q16×C61C2×C411yescharacteristic, complemented
169C2×SD16×C61C2×C411yescharacteristic
170C22⋊Q8×C61C2×C411yescharacteristic, complemented
171#103×C61C2×C411yescharacteristic, complemented
172#102×C61C2×C411yescharacteristic
173C22⋊C8×C61C2×C411yescharacteristic, complemented
174C23×D61—21no—
175C23×D61C2×D411yescharacteristic
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—42no—
181C22×#6923—42no—
182C22×#6923—42no—
183C22×#6923—42no—
184C22×#6923—81no—
185C22×#6923—81no—
186C22×#6923C2×D411yescharacteristic
187C22×#6923C2×D411yescharacteristic
188C22×#6923C2×D411yescharacteristic
189C22×#6923C2×D411yescharacteristic
190#41×C61—22no—
191#41×C61—41no—
192C2×Q8×C61C22×C411yescharacteristic
193C2×Q8×C61C22×C411yescharacteristic
194C2×D4×C61—21no—
195C2×D4×C61C22×C411yescharacteristic
196C22×C4×C61—21no—
197C22×C4×C61C22×C411yescharacteristic
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C22×Dic61—21no—
202C22×Dic61#4111yescharacteristic
203#11758226—22no—
204#11758226—41no—
205Q8×D61—21no—
206Q8×D61—21no—
207Q8×D61—21no—
208Q8×D61—21no—
209Q8×D61—21no—
210Q8×D61—21no—
211Q8×D61—21no—
212Q8×D61—21no—
213#11758224—22no—
214#11758224—41no—
215#11758224—42no—
216#11758224—42no—
217D4×D61—21no—
218D4×D61—21no—
219D4×D61—42no—
220D4×D61—42no—
221D4×D61C2×D412yes—
222D4×D61#4112yes—
223#11758222—22no—
224#11758222—41no—
225#11758222—42no—
226#11758222—42no—
227C2×D244—21no—
228C2×D244C22×C411yescharacteristic
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—42no—
239C2×C4×D61—42no—
240C2×C4×D61C22×C411yescharacteristic
241C2×C4×D61C2×D411yescharacteristic
242C2×C4×D61#4111yescharacteristic
243C2×C4×D61C2411yescharacteristic
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122C22×C411yescharacteristic
247C2×Dic122C22×C411yescharacteristic
248C22⋊#6923—22no—
249C22⋊#6923—22no—
250C22⋊#6923—42no—
251C22⋊#6923—42no—
252C22⋊#6923—42no—
253C22⋊#6923—81no—
254C2×#92420—21no—
255C2×#92420—21no—
256C2×#92420—42no—
257C4⋊#6923—21no—
258C4⋊#6923—21no—
259C4⋊#6923—21no—
260C4⋊#6923—21no—
261C4⋊#6923—21no—
262C4⋊#6923—21no—
263C4⋊#6923—21no—
264C4⋊#6923—42no—
265C4⋊#6923—42no—
266C4⋊#6923C2×D412yes—
267C4×#6923—21no—
268C4×#6923—21no—
269C4×#6923—21no—
270C4×#6923—21no—
271C4×#6923—42no—
272C4×#6923—42no—
273C4×#6923—42no—
274D61⋊C8—21no—
275D61⋊C8—21no—
276D61⋊C8—21no—
277D61⋊C8—42no—
278D61⋊C8C2×D412yes—
279Q16×C61—41no—
280SD16×C61—22no—
281C2×C8×C61C22×C411yescharacteristic
282C2×C8×C61C22×C411yescharacteristic
283C4⋊C4×C61—21no—
284C4⋊C4×C61C22×C411yescharacteristic
285C22⋊C4×C61—21no—
286C22⋊Dic61—21no—
287#11758202—41no—
288#11758202—41no—
289#11758201—22no—
290#11758200—22no—
291#11758198—21no—
292#11758198—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61C22×C411yescharacteristic
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298C2×#92418C22×C411yescharacteristic
299C2×#92418C22×C411yescharacteristic
300Dic244—41no—
301#11758190—22no—
302C8×D61—21no—
303C8×D61—21no—
304C8×D61—21no—
305C8×D61—21no—
306C23×C61—21no—
307C23×C61C4×D411yescharacteristic
308C22×D61—21no—
309C22×D61—21no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61C4×D411yescharacteristic
322C22×D61C22×D411yescharacteristic
323C2×#6923—21no—
324C2×#6923—21no—
325C2×#6923—21no—
326C2×#6923—21no—
327C2×#6923—21no—
328C2×#6923—22no—
329C2×#6923—21no—
330C2×#6923—21no—
331C2×#6923—21no—
332C2×#6923—21no—
333C2×#6923—21no—
334C2×#6923—41no—
335C2×#6923—41no—
336C2×#6923—41no—
337C2×#6923—41no—
338C2×#6923—41no—
339C2×#6923—41no—
340C2×#6923—41no—
341C2×#6923—41no—
342C2×#6923—41no—
343C2×#6923—41no—
344C2×#6923—41no—
345C2×#6923—84no—
346C2×#6923—84no—
347C2×#6923#13512yes—
348C2×#6923#13512yes—
349Q8×C61—21no—
350Q8×C61—21no—
351Q8×C61—21no—
352Q8×C61—21no—
353D4×C61—21no—
354D4×C61—42no—
355D4×C61C4×D412yes—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—42no—
362C2×C4×C61C4×D411yescharacteristic
363C2×C4×C61C23×C411yescharacteristic
364C22⋊D61—22no—
365C22⋊D61—22no—
366C22⋊D61—42no—
367C22⋊D61—42no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61—42no—
374C2×Dic61C4×D411yescharacteristic
375C2×Dic61C2×#4111yescharacteristic
376D244—21no—
377D244—42no—
378D244C4×D412yes—
379C4×D61—21no—
380C4×D61—21no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—42no—
386C4×D61—42no—
387C4×D61—41no—
388C4×D61—41no—
389C4×D61—41no—
390C4×D61—41no—
391C4×D61—41no—
392C4×D61—41no—
393C4×D61C22×D411yescharacteristic
394C4×D61C2×#4111yescharacteristic
395C4×D61H(5,𝔽2)11yescharacteristic
396C4×D61H(5,𝔽2)11yescharacteristic
397Dic122—21no—
398Dic122—21no—
399Dic122—21no—
400Dic122—21no—
401Dic122—41no—
402Dic122—41no—
403Dic122—41no—
404Dic122—41no—
405#92420—22no—
406#92420—41no—
407C8×C61—21no—
408C8×C61—21no—
409#92418—21no—
410#92418—21no—
411#22876—611nomaximal, Sylow
412C22×C61—21no—
413C22×C61—22no—
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61C2×C4×D411yescharacteristic
419C2×D61—21no—
420C2×D61—22no—
421C2×D61—21no—
422C2×D61—21no—
423C2×D61—41no—
424C2×D61—41no—
425C2×D61—42no—
426C2×D61—41no—
427C2×D61—41no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61—41no—
431C2×D61—41no—
432C2×D61—42no—
433C2×D61D4211yescharacteristic
434C2×D61#54611yescharacteristic
435C2×D61C2×#13511yescharacteristic
436C2×D61C2×#13511yescharacteristic
437C2×D61#57711yescharacteristic
438C2×D61#57811yescharacteristic
439#6923—22no—
440#6923—22no—
441#6923—41no—
442#6923—42no—
443#6923—41no—
444#6923—81no—
445#6923—81no—
446#6923—81no—
447C4×C61—21no—
448C4×C61—41no—
449C4×C61—41no—
450C4×C61—41no—
451C4×C61C2×C4×D411yescharacteristic
452C4×C61#51811yescharacteristic
453Dic61—21no—
454Dic61—41no—
455Dic61—41no—
456Dic61—41no—
457Dic61#54611yescharacteristic
458Dic61#55111yescharacteristic
459C2×#452—611no—
460C2×C4×SD16—611no—
461C2×#416—611no—
462#2362—611no—
463#2339—611no—
464#1969—611no—
465#1933—611no—
466#1927—611no—
467#1892—611no—
468#1878—611no—
469#1877—611no—
470#1862—611no—
471#1854—611no—
472C4×#102—611no—
473C8×C22⋊C4—611no—
474C2×C61—41no—
475C2×C61—42no—
476C2×C61#235811yescharacteristic
477C2×C61C4×#13511yescharacteristic
478C2×C61#294711yescharacteristic
479D61—41no—
480D61—42no—
481D61#328211yescharacteristic
482D61#328311yescharacteristic
483D61#329611yescharacteristic
484D61#330211yescharacteristic
485C22×#41—611no—
486C22×Q16—611no—
487C22×SD16—611no—
488C23×C8—611no—
489C2×C22⋊Q8—611no—
490C2×C4×Q8—611no—
491C2×C4×D4—611no—
492C2×C4×D4—611no—
493C2×#117—611no—
494#452—611no—
495#452—611no—
496#452—611no—
497#452—611no—
498#452—611no—
499#452—611no—
500#452—611no—
501#452#692311yescharacteristic, complemented
502C4×SD16—1224no—
503C2×#107—611no—
504C2×#106—611no—
505#416—1224no—
506C2×#103—611no—
507C2×#103—611no—
508C2×#103—611no—
509C2×#103—611no—
510C2×#103—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×C22⋊C8—611no—
515C2×C4×C8—611no—
516C2×C4×C8—611no—
517#391—611no—
518#391—611no—
519#391—611no—
520#389—611no—
521#388—1221no—
522#388—1221no—
523#387—1221no—
524#386—1221no—
525#386—1221no—
526#381—1221no—
527#380—611no—
528C4×C4⋊C4—611no—
529C4×C4⋊C4—1221no—
530C4×C22⋊C4—611no—
531C2×#95—1221no—
532#340—611no—
533#340—611no—
534#340—611no—
535#340—611no—
536#336—611no—
537#336—611no—
538C61#2287611yescharacteristic, complemented, Sylow
539C2×#41—611no—
540C2×#41—611no—
541C2×#41—611no—
542C2×#41—1221no—
543C2×#41—1221no—
544C2×#41—1222no—
545C2×#41—1222no—
546C2×#41—2441no—
547C2×#41—2441no—
548C2×#41C2×#692311yescharacteristic
549C22×Q8—611no—
550C22×Q8—611no—
551C22×D4—611no—
552C22×D4—1221no—
553C23×C4—611no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4—1221no—
557C2×Q16—611no—
558C2×Q16—611no—
559C2×Q16—611no—
560C2×Q16—2441no—
561C2×Q16—2441no—
562C2×Q16C2×#692311yescharacteristic, complemented
563C2×SD16—611no—
564C2×SD16—611no—
565C2×SD16—611no—
566C2×SD16—1222no—
567C2×SD16—1222no—
568C2×SD16C2×#692311yescharacteristic
569C22×C8—611no—
570C22×C8—611no—
571C22×C8—611no—
572C22×C8—611no—
573C22×C8—1222no—
574C22×C8—1221no—
575C22×C8—1221no—
576C22×C8—2441no—
577C22⋊Q8—611no—
578C22⋊Q8—611no—
579C22⋊Q8—611no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582C22⋊Q8C2×#692311yescharacteristic, complemented
583C4×Q8—1222no—
584C4×Q8—2441no—
585C4×D4—1222no—
586C4×D4—1222no—
587C4×D4—2441no—
588C4×D4—2441no—
589#117—1222no—
590#117—2441no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—1221no—
597C2×C4⋊C4—1221no—
598C2×C4⋊C4—1221no—
599C2×C22⋊C4—611no—
600C2×C22⋊C4—611no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C42—611no—
607C2×C42—611no—
608C2×C42—1221no—
609C2×C42—1221no—
610C2×C42—1221no—
611#107—2441no—
612#106—1222no—
613#103—611no—
614#103—611no—
615#103—611no—
616#103—1222no—
617#103—1222no—
618#103—1222no—
619#103—2441no—
620#103C2×#692311yescharacteristic, complemented
621#102—614no—
622#102—611no—
623#102—611no—
624#102—611no—
625#102—1222no—
626#102C2×#692311yescharacteristic
627C22⋊C8—611no—
628C22⋊C8—611no—
629C22⋊C8—611no—
630C22⋊C8C2×#692311yescharacteristic, complemented
631C4×C8—1222no—
632C4×C8—2441no—
633#95—611no—
634#95—611no—
635#95—1221no—
636#95—1221no—
637#95—1221no—
638#95—1221no—
639#95—1221no—
640#95—1221no—
641#95—1221no—
642#95—1221no—
643#95—1221no—
644C24—611no—
645C24—1221no—
646#41—22no—
647#41—41no—
648#41—1222no—
649#41—1222no—
650#41—1222no—
651#41—2441no—
652#41—2442no—
653#41—2442no—
654#41—2441no—
655#41—2442no—
656#41—2442no—
657#41—2441no—
658C2×Q8—611no—
659C2×Q8—611no—
660C2×Q8—1221no—
661C2×Q8—1221no—
662C2×Q8—1221no—
663C2×Q8—1221no—
664C2×Q8—1221no—
665C2×Q8—1221no—
666C2×Q8—1221no—
667C2×Q8—1221no—
668C2×Q8—1221no—
669C2×Q8—1221no—
670C2×Q8C22×#692311yescharacteristic
671C2×Q8C22×#692311yescharacteristic
672C2×D4—21no—
673C2×D4—612no—
674C2×D4—612no—
675C2×D4—611no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—2442no—
683C2×D4—2442no—
684C2×D4C22×#692311yescharacteristic
685C22×C4—21no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—4881no—
710C22×C4—4881no—
711C22×C4—2442no—
712C22×C4—2442no—
713C22×C4—2442no—
714C22×C4—2442no—
715C22×C4—2442no—
716C22×C4—2442no—
717C22×C4C22×#692311yescharacteristic
718Q16—41no—
719Q16—2441no—
720Q16—2441no—
721Q16—2441no—
722SD16—22no—
723SD16—1222no—
724SD16—1222no—
725SD16—1222no—
726C2×C8—612no—
727C2×C8—611no—
728C2×C8—611no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C2×C8—1221no—
733C2×C8—1221no—
734C2×C8—1221no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—2442no—
739C2×C8—2442no—
740C2×C8C22×#692311yescharacteristic
741C2×C8C22×#692311yescharacteristic
742C4⋊C4—21no—
743C4⋊C4—612no—
744C4⋊C4—611no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—2442no—
757C4⋊C4—2442no—
758C4⋊C4C22×#692311yescharacteristic
759C22⋊C4—21no—
760C22⋊C4—1221no—
761C22⋊C4—1221no—
762C22⋊C4—1222no—
763C22⋊C4—1222no—
764C22⋊C4—1221no—
765C22⋊C4—4881no—
766C22⋊C4—2442no—
767C22⋊C4—2442no—
768C22⋊C4—2442no—
769C42—1221no—
770C42—1221no—
771C42—1221no—
772C42—1221no—
773C42—2442no—
774C42—2442no—
775C42—2442no—
776C23—21no—
777C23—611no—
778C23—611no—
779C23—1221no—
780C23—1221no—
781C23—1221no—
782C23—1221no—
783C23—1222no—
784C23—1222no—
785C23—1221no—
786C23—1221no—
787C23—1221no—
788C23—2441no—
789C23—2441no—
790C23—2441no—
791C23—2441no—
792C23D4×#692311yescharacteristic
793Q8—21no—
794Q8—21no—
795Q8—21no—
796Q8—21no—
797Q8—1221no—
798Q8—1221no—
799Q8—1221no—
800Q8—1221no—
801Q8—2441no—
802Q8—2441no—
803Q8—2441no—
804Q8—2441no—
805D4—21no—
806D4—42no—
807D4—612no—
808D4—1222no—
809D4—1222no—
810D4—1221no—
811D4—2442no—
812D4—2442no—
813D4—2442no—
814D4D4×#692312yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—42no—
821C2×C4—611no—
822C2×C4—611no—
823C2×C4—611no—
824C2×C4—611no—
825C2×C4—611no—
826C2×C4—612no—
827C2×C4—612no—
828C2×C4—611no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1222no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—1221no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—4884no—
852C2×C4—4884no—
853C2×C4—2442no—
854C2×C4—2442no—
855C2×C4—2441no—
856C2×C4—2441no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2442no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4D4×#692311yescharacteristic
874C2×C4C23×#692311yescharacteristic
875C8—21no—
876C8—21no—
877C8—1222no—
878C8—1221no—
879C8—1221no—
880C8—2441no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—22no—
885C22—41no—
886C22—41no—
887C22—611no—
888C22—611no—
889C22—611no—
890C22—611no—
891C22—611no—
892C22—611no—
893C22—1221no—
894C22—1221no—
895C22—1221no—
896C22—1222no—
897C22—2442no—
898C22—2442no—
899C22—2441no—
900C22—2441no—
901C22—2441no—
902C22—2441no—
903C22—2442no—
904C22—2442no—
905C22—2441no—
906C22—2441no—
907C22C2×D4×#692311yescharacteristic
908C4—21no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—611no—
913C4—611no—
914C4—1222no—
915C4—1222no—
916C4—1221no—
917C4—4881no—
918C4—4881no—
919C4—4881no—
920C4—2441no—
921C4—2441no—
922C4—2442no—
923C4—2441no—
924C4—2441no—
925C4—2441no—
926C4C2×D4×#692311yescharacteristic
927C4#1684082911yescharacteristic
928C2—41no—
929C2—42no—
930C2—611no—
931C2—611no—
932C2—611no—
933C2—611no—
934C2—2441no—
935C2—2442no—
936C2#2146234111yescharacteristic
937C2#135×#692311yescharacteristic
938C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#452C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#452#6923
hypocenterC61#22876
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×SD16×#6923C2semidirect
3. #21462345C2semidirect
5. #21461965C2semidirect
6. #21461908C2semidirect
7. #21461898C2semidirect
8. #21461832C2semidirect
9. #21461813C2semidirect
10. #21461812C2semidirect
11. #21461782C2semidirect
12. #21461770C2semidirect
13. #102×#6923C2semidirect
14. #21461554C2semidirect
58. #16839927C4semidirect
59. #16839926C4semidirect
60. #16839925C4semidirect
61. #16839924C4semidirect
62. #16839923C4semidirect
63. #16839922C4semidirect
64. #16839921C4semidirect
68. C61×#452C4semidirect
138. C2×Dic244C2×C4semidirect
139. C2×#11758202C2×C4semidirect
140. C2×#11758202C2×C4semidirect
150. #14519757C2×C4semidirect
151. #14519756C2×C4semidirect
154. #14519753C2×C4semidirect
158. #14519702C2×C4semidirect
159. #14519701C2×C4semidirect
160. #14519700C2×C4semidirect
164. C22⋊#92418C2×C4semidirect
165. #14519689C2×C4semidirect
166. #14519689C2×C4semidirect
168. C2×Q16×C61C2×C4semidirect
170. C22⋊Q8×C61C2×C4semidirect
171. #103×C61C2×C4semidirect
173. C22⋊C8×C61C2×C4semidirect
501. #452#6923semidirect
538. C61#22876semidirect
562. C2×Q16C2×#6923semidirect
582. C22⋊Q8C2×#6923semidirect
620. #103C2×#6923semidirect
630. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×#69232
C2×#168407522
#214623452
#214623222
#214619652
#214619082
#214618982
#214618322
#214618132
#214618122
#214617822
#214617702
#102×#69232
#214615542
#452×D612
#2287661