Finite Group Databasebeta

← #30621777

Subgroups — #30621777

Order 15616.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840804C211yesmaximal, characteristic, complemented
2#21462549C211yesmaximal, characteristic, complemented
3C22×#14519841C211yesmaximal, characteristic, complemented
4#21462407C211yesmaximal, characteristic, complemented
5#21461972C211yesmaximal, characteristic, complemented
6#21461913C211yesmaximal, characteristic, complemented
7#21461900C211yesmaximal, characteristic, complemented
8#21461837C211yesmaximal, characteristic, complemented
9#21461810C211yesmaximal, characteristic, complemented
10#21461810C211yesmaximal, characteristic, complemented
11#21461786C211yesmaximal, characteristic, complemented
12#21461771C211yesmaximal, characteristic, complemented
13#21461594C211yesmaximal, characteristic, complemented
14C22⋊C8×#6923C211yesmaximal, characteristic, complemented
15#21455032C211yesmaximal, characteristic
16C2×#14519864C2211yescharacteristic
17C2×#14519864C2211yescharacteristic
18C2×#14519864C2211yescharacteristic, complemented
19C22×#11758213C2211yescharacteristic
20C22×C4×#6923C2211yescharacteristic
21#16840804—24no—
22#16840795—21no—
23#16840793—21no—
24#16840791—21no—
25D4×#92420—21no—
26C2×#14519848C2211yescharacteristic, complemented
27C2×#14519848C2211yescharacteristic, complemented
28#16840769C2211yescharacteristic, complemented
29C2×#14519841—24no—
30C2×#14519841C2211yescharacteristic
31C2×#14519841C2211yescharacteristic
32C2×#14519841C2211yescharacteristic
33C2×#14519841C2211yescharacteristic
34C2×#14519841C2211yescharacteristic, complemented
35C2×#14519841C2211yescharacteristic, complemented
36#16840736C2211yescharacteristic
37#16840736C2211yescharacteristic
38#16840736C2211yescharacteristic, complemented
39#16840735—21no—
40#16840735—21no—
41#16840733C2211yescharacteristic
42#16840732—21no—
43D61⋊(C22⋊C8)C2211yescharacteristic
44C2×C22⋊#92420—21no—
45#16840727C2211yescharacteristic, complemented
46C2×C8×#6923C2211yescharacteristic, complemented
47C2×C8×#6923C2211yescharacteristic, complemented
48#16840638C2211yescharacteristic, complemented
49#16840638C2211yescharacteristic, complemented
50#16840632C2211yescharacteristic, complemented
51#16840632C2211yescharacteristic, complemented
52(C2×#6923)⋊C8C2211yescharacteristic, complemented
53(C2×#6923)⋊C8C2211yescharacteristic, complemented
54C22×#11758224C2211yescharacteristic
55C2×#14519796C2211yescharacteristic
56C2×#14519796C2211yescharacteristic
57#16840272C2211yescharacteristic
58#16839925C411yescharacteristic, complemented
59#16839925C411yescharacteristic, complemented
60#16839920C411yescharacteristic, complemented
61#16839913C411yescharacteristic, complemented
62#16839904C411yescharacteristic, complemented
63#16839904C411yescharacteristic, complemented
64#16839900C411yescharacteristic, complemented
65#16839755C2211yescharacteristic
66#16839755C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#447C411yescharacteristic, complemented
69C23×#6923—21no—
70#14519864—22no—
71#14519864—22no—
72#14519864—22no—
73#14519864—41no—
74#14519864—41no—
75#14519864—41no—
76C2×#11758213—22no—
77C2×#11758213—21no—
78C2×#11758213—41no—
79C2×#11758213C2311yescharacteristic
80C2×#11758213C2311yescharacteristic
81C2×#11758213C2311yescharacteristic
82C2×#11758213C2311yescharacteristic
83C2×#11758217—21no—
84C2×#11758217—21no—
85C2×#11758217—21no—
86C2×D61⋊C8C2311yescharacteristic
87C2×D61⋊C8C2311yescharacteristic
88C22×#92420—21no—
89C22×#92420—21no—
90C22×#92420—21no—
91C22×#92420—21no—
92C2×C4×#6923—22no—
93C2×C4×#6923—21no—
94C2×C4×#6923—41no—
95C2×C4×#6923C2311yescharacteristic
96C2×C4×#6923C2311yescharacteristic
97#14519848—22no—
98#14519848—41no—
99#14519844—21no—
100C4⋊#92420—21no—
101#14519841—22no—
102#14519841—22no—
103#14519841—22no—
104#14519841—22no—
105#14519841—41no—
106#14519841D414yescomplemented
107#14519834—21no—
108#14519834D411yescharacteristic
109#14519834D411yescharacteristic
110C22⋊#92420—21no—
111C22⋊#92420—21no—
112C22⋊#92420—21no—
113C22⋊#92420—21no—
114C22⋊#92420—21no—
115C22⋊#92420—21no—
116C22⋊#92420—21no—
117C22⋊#92420D411yescharacteristic
118C22⋊#92420D411yescharacteristic
119#14519832—21no—
120C4×#92420—21no—
121C8×#6923—22no—
122C8×#6923—41no—
123C2×#11758224—22no—
124C2×#11758224—22no—
125C2×#11758224—21no—
126C2×#11758224—21no—
127C2×#11758224—41no—
128C2×#11758224—41no—
129C2×#11758224C2×C411yescharacteristic
130C2×#11758224C2×C411yescharacteristic
131C2×#11758224C2311yescharacteristic
132C2×#11758224C2311yescharacteristic
133C2×#11758224C2311yescharacteristic
134C22×Dic122C2×C411yescharacteristic
135C22×C22⋊D61—21no—
136C23×Dic61—21no—
137C22×C4×D61C2311yescharacteristic
138#14519796—22no—
139#14519796—22no—
140#14519796—41no—
141#14519796—41no—
142C2×Dic244C2×C411yescharacteristic, complemented
143C2×Dic244C2×C411yescharacteristic, complemented
144C2×#11758200C2×C411yescharacteristic, complemented
145C2×#11758200C2×C411yescharacteristic, complemented
146C2×#11758200C2×C411yescharacteristic, complemented
147C2×#11758200C2×C411yescharacteristic, complemented
148C2×C8×D61C2311yescharacteristic
149C2×C8×D61C2311yescharacteristic
150#14519759—21no—
151#14519757C2×C411yescharacteristic
152#14519756C2×C411yescharacteristic
153#14519748C2×C411yescharacteristic
154#14519745—21no—
155D4×Dic61—21no—
156#14519737—21no—
157#14519735C2311yescharacteristic
158#14519702C2×C411yescharacteristic, complemented
159#14519702C2×C411yescharacteristic, complemented
160#14519700C2×C411yescharacteristic, complemented
161#14519700C2×C411yescharacteristic, complemented
162#14519698C2×C411yescharacteristic, complemented
163#14519698C2×C411yescharacteristic, complemented
164C22⋊#92418C2×C411yescharacteristic
165#14519689C2×C411yescharacteristic
166#14519689C2×C411yescharacteristic
167C22×D4×C61C2×C411yescharacteristic
168C2×D8×C61C2×C411yescharacteristic, complemented
169C2×D8×C61C2×C411yescharacteristic, complemented
170#121×C61C2×C411yescharacteristic
171#102×C61C2×C411yescharacteristic, complemented
172#102×C61C2×C411yescharacteristic, complemented
173C22⋊C8×C61C2×C411yescharacteristic
174C24×C61—21no—
175C23×D61#4111yescharacteristic
176C22×#6923—21no—
177C22×#6923—24no—
178C22×#6923—21no—
179C22×#6923—42no—
180C22×#6923—42no—
181C2×D4×C61—22no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—41no—
185C2×D4×C61C22×C411yescharacteristic
186C2×D4×C61C22×C411yescharacteristic
187C2×D4×C61C22×C411yescharacteristic
188C22×C4×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—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—42no—
204C22×Dic61—42no—
205C22×Dic61C2×D411yescharacteristic
206#11758224—22no—
207#11758224—21no—
208#11758224—21no—
209#11758224—21no—
210#11758224—21no—
211#11758224—21no—
212#11758224—21no—
213#11758224—21no—
214#11758224—21no—
215#11758224—21no—
216#11758224—21no—
217#11758224—22no—
218#11758224—41no—
219#11758224—41no—
220#11758224—42no—
221#11758224—42no—
222#11758224—42no—
223#11758224—42no—
224#11758224C2×D412yes—
225#11758224#4112yes—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61#4111yescharacteristic
233C2×C4×D61C2411yescharacteristic
234C2×Dic122—22no—
235C2×Dic122—21no—
236C2×Dic122—41no—
237C2×Dic122C22×C411yescharacteristic
238C2×Dic122C22×C411yescharacteristic
239C2×Dic122C22×C411yescharacteristic
240#11758217—42no—
241#11758217—42no—
242#11758217—42no—
243C2×#92420—21no—
244C2×#92420—21no—
245C2×#92420—21no—
246C2×#92420—21no—
247C2×#92420—42no—
248C2×#92420—42no—
249C2×#92420—42no—
250C2×#92420—42no—
251C2×#92420C2×D411yescharacteristic
252C2×#92420C2×D411yescharacteristic
253C2×#92420C2×D411yescharacteristic
254C2×#92420C2×D411yescharacteristic
255C4×#6923—21no—
256C4×#6923—21no—
257C4×#6923—21no—
258C4×#6923—42no—
259C4×#6923C2×D412yes—
260#11758213—21no—
261#11758213—21no—
262#11758213—21no—
263#11758213—21no—
264#11758213—21no—
265#11758213—21no—
266#11758213—21no—
267#11758213—42no—
268#11758213C2×D412yes—
269D61⋊C8—21no—
270D61⋊C8—21no—
271D61⋊C8—21no—
272D61⋊C8—21no—
273D8×C61—22no—
274D8×C61—41no—
275C2×C8×C61C22×C411yescharacteristic
276C2×C8×C61C22×C411yescharacteristic
277C4⋊C4×C61C22×C411yescharacteristic
278C22⋊C4×C61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281#11758200—22no—
282#11758200—22no—
283#11758200—41no—
284#11758200—41no—
285#11758198—21no—
286#11758198—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61C22×C411yescharacteristic
289#11758196—21no—
290C4×Dic61—21no—
291C2×#92418C22×C411yescharacteristic
292C2×#92418C22×C411yescharacteristic
293Dic244—22no—
294Dic244—41no—
295C8×D61—21no—
296C8×D61—21no—
297C8×D61—21no—
298C8×D61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61—81no—
305C23×C61C4×D411yescharacteristic
306C22×D61—22no—
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—41no—
310C22×D61C4×D411yescharacteristic
311C22×D61C2×#4111yescharacteristic
312C2×#6923—22no—
313C2×#6923—22no—
314C2×#6923—22no—
315C2×#6923—22no—
316C2×#6923—48no—
317C2×#6923—41no—
318C2×#6923—41no—
319D4×C61—21no—
320D4×C61—21no—
321D4×C61—21no—
322D4×C61—21no—
323D4×C61—21no—
324D4×C61—42no—
325D4×C61—42no—
326D4×C61C4×D412yes—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61C4×D411yescharacteristic
331C2×C4×C61C23×C411yescharacteristic
332C22⋊D61—22no—
333C22⋊D61—22no—
334C22⋊D61—42no—
335C22⋊D61—42no—
336C22⋊D61—41no—
337C22⋊D61—41no—
338C22⋊D61—41no—
339C22⋊D61—41no—
340C22⋊D61—81no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—42no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61C4×D411yescharacteristic
357C2×Dic61C22×D411yescharacteristic
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61C22×D411yescharacteristic
365C4×D61C2×#4111yescharacteristic
366C4×D61H(5,𝔽2)11yescharacteristic
367C4×D61H(5,𝔽2)11yescharacteristic
368Dic122—21no—
369Dic122—21no—
370Dic122—21no—
371Dic122—21no—
372Dic122—21no—
373Dic122—42no—
374Dic122C4×D412yes—
375#92420—21no—
376#92420—21no—
377#92420—22no—
378#92420—21no—
379#92420—21no—
380#92420—41no—
381#92420—41no—
382#92420—41no—
383C8×C61—21no—
384C8×C61—21no—
385#92418—21no—
386#92418—21no—
387#22888—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—22no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—84no—
400C22×C61#44312yescomplemented
401C22×C61C2×C4×D411yescharacteristic
402C2×D61—21no—
403C2×D61—21no—
404C2×D61—21no—
405C2×D61—21no—
406C2×D61—21no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61#54611yescharacteristic
410C2×D61#55111yescharacteristic
411#6923—24no—
412#6923—42no—
413C4×C61—21no—
414C4×C61—41no—
415C4×C61C2×C4×D411yescharacteristic
416C4×C61#51811yescharacteristic
417Dic61—22no—
418Dic61—21no—
419Dic61—41no—
420Dic61—41no—
421Dic61—41no—
422Dic61D4211yescharacteristic
423Dic61#54611yescharacteristic
424#3002—611no—
425C2×#443—611no—
426#2933—611no—
427C22×#104—611no—
428#2880—611no—
429#1974—611no—
430#1937—611no—
431#1929—611no—
432#1896—611no—
433#1876—611no—
434#1876—611no—
435#1866—611no—
436#1855—611no—
437#1764—611no—
438C4×C22⋊C8—611no—
439C2×C61—22no—
440C2×C61—42no—
441C2×C61—81no—
442C2×C61—81no—
443C2×C61#235811yescharacteristic
444C2×C61C2×#44311yescharacteristic
445C2×C61#295611yescharacteristic
446D61—21no—
447D61—21no—
448D61—41no—
449C22×#41—611no—
450C2×#135—611no—
451C2×#135—611no—
452C2×#131—611no—
453C2×#131—611no—
454C2×#131—611no—
455C22×M16—611no—
456#525—611no—
457C22×C42—611no—
458#452—611no—
459#452—611no—
460#451—611no—
461#450—611no—
462#449—611no—
463#449—611no—
464#448—611no—
465#447#692311yescharacteristic, complemented
466#443—1224no—
467#436—1221no—
468#435—1221no—
469#435—1221no—
470C8×D4—1221no—
471C2×#108—611no—
472C2×#108—611no—
473#424—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104—611no—
478C2×#104—611no—
479C2×#104—611no—
480C2×#104—1224no—
481#416—611no—
482#416—611no—
483#408—611no—
484#408—611no—
485#408—611no—
486#408—1221no—
487#408—1221no—
488#407—611no—
489#407—1221no—
490C2×C22⋊C8—611no—
491C2×C22⋊C8—611no—
492C2×C22⋊C8—1221no—
493#405—611no—
494C2×C4×C8—611no—
495C2×C4×C8—611no—
496#341—611no—
497#341—611no—
498#339—611no—
499#339—611no—
500#336—611no—
501#336—611no—
502C61#2288811yescharacteristic, complemented, Sylow
503C2×#41—611no—
504C2×#41—611no—
505C2×#41—611no—
506C2×#41—611no—
507C2×#41—611no—
508C2×#41—1221no—
509C2×#41—1221no—
510C2×#41—1222no—
511C2×#41—1222no—
512C2×#41—2441no—
513C2×#41—2441no—
514C22×Q8—611no—
515C22×D4—1221no—
516C22×D4C2×#692311yescharacteristic
517C23×C4—611no—
518C23×C4—1221no—
519C23×C4—1221no—
520#135—1222no—
521#135—1222no—
522#135—2441no—
523#135—2441no—
524C2×Q16—611no—
525C2×Q16—611no—
526C2×SD16—611no—
527C2×SD16—611no—
528C2×SD16—611no—
529C2×SD16—611no—
530C2×D8C2×#692311yescharacteristic, complemented
531C2×D8C2×#692311yescharacteristic, complemented
532#131—1222no—
533#131—1222no—
534#131—1222no—
535#131—2441no—
536#131—2441no—
537#131—2441no—
538C2×M16—611no—
539C2×M16—611no—
540C2×M16—611no—
541C2×M16—611no—
542C2×M16—1221no—
543C2×M16—1221no—
544C2×M16—1221no—
545C2×M16—1221no—
546C2×M16—1222no—
547C2×M16—2441no—
548C22×C8—611no—
549C22×C8—611no—
550C22×C8—611no—
551C22×C8—611no—
552C22×C8—1221no—
553C22×C8—1221no—
554C22×C8—1221no—
555C22×C8—1221no—
556#123—1221no—
557C22⋊Q8—611no—
558C22⋊Q8—611no—
559#121—611no—
560#121C2×#692311yescharacteristic
561#120—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564#117—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—1222no—
568C2×C42—1221no—
569C2×C42—2441no—
570#108—1222no—
571#108—2441no—
572C4⋊C8—1221no—
573C4⋊C8—1221no—
574#104—614no—
575#104—1222no—
576#104—1222no—
577#104—1222no—
578#104—1222no—
579#104—2441no—
580#103—611no—
581#103—611no—
582#103—611no—
583#103—611no—
584#102—611no—
585#102—611no—
586#102C2×#692311yescharacteristic, complemented
587#102C2×#692311yescharacteristic, complemented
588C22⋊C8—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601C22⋊C8—1221no—
602C22⋊C8—1221no—
603C22⋊C8C2×#692311yescharacteristic
604#97—1221no—
605C4×C8—1222no—
606C4×C8—1221no—
607C4×C8—2441no—
608C24—21no—
609C24—611no—
610#41—612no—
611#41—612no—
612#41—1221no—
613#41—1221no—
614#41—1221no—
615#41—1221no—
616#41—1221no—
617#41—1221no—
618#41—1221no—
619#41—1221no—
620#41—1221no—
621#41—1221no—
622#41—1222no—
623#41—1222no—
624#41—2442no—
625#41—2442no—
626#41—2441no—
627#41—2441no—
628#41—2442no—
629#41—2442no—
630C2×Q8—611no—
631C2×Q8—611no—
632C2×Q8—611no—
633C2×Q8—1222no—
634C2×Q8—1221no—
635C2×Q8—2441no—
636C2×D4—22no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—41no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4C22×#692311yescharacteristic
649C2×D4C22×#692311yescharacteristic
650C2×D4C22×#692311yescharacteristic
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1224no—
668C22×C4—1221no—
669C22×C4—2442no—
670C22×C4—2442no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4C22×#692311yescharacteristic
674Q16—1222no—
675Q16—2441no—
676SD16—1222no—
677SD16—1222no—
678SD16—2441no—
679SD16—2441no—
680D8—22no—
681D8—41no—
682M16—612no—
683M16—1221no—
684M16—1221no—
685M16—1221no—
686M16—1221no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—2442no—
691M16—2442no—
692M16—2442no—
693M16—2442no—
694C2×C8—611no—
695C2×C8—611no—
696C2×C8—611no—
697C2×C8—611no—
698C2×C8—611no—
699C2×C8—611no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—2442no—
713C2×C8—2442no—
714C2×C8—2442no—
715C2×C8—2442no—
716C2×C8C22×#692311yescharacteristic
717C2×C8C22×#692311yescharacteristic
718C4⋊C4—611no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4C22×#692311yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—1221no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C42—612no—
728C42—1221no—
729C42—1221no—
730C42—1221no—
731C42—1221no—
732C42—2442no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—42no—
737C23—42no—
738C23—81no—
739C23—611no—
740C23—611no—
741C23—1221no—
742C23—1221no—
743C23—1222no—
744C23—2441no—
745C23D4×#692311yescharacteristic
746Q8—612no—
747Q8—1221no—
748Q8—1221no—
749Q8—1221no—
750Q8—1221no—
751Q8—1221no—
752Q8—2442no—
753D4—21no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—42no—
760D4—1222no—
761D4—1222no—
762D4—4881no—
763D4—2442no—
764D4—2442no—
765D4—2441no—
766D4—2441no—
767D4—2441no—
768D4—2441no—
769D4D4×#692312yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—611no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1221no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1222no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2442no—
802C2×C4—2442no—
803C2×C4—2442no—
804C2×C4—2448no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4D4×#692311yescharacteristic
808C2×C4C23×#692311yescharacteristic
809C8—21no—
810C8—21no—
811C8—1221no—
812C8—1221no—
813C8—1221no—
814C8—1221no—
815C8—1222no—
816C8—1221no—
817C8—1221no—
818C8—2441no—
819C8—2441no—
820C8—2441no—
821C22—21no—
822C22—21no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—84no—
833C22—611no—
834C22—611no—
835C22—1221no—
836C22—1221no—
837C22—1221no—
838C22—1221no—
839C22—1221no—
840C22—2442no—
841C22—2442no—
842C22#1684080412yescomplemented
843C22C2×D4×#692311yescharacteristic
844C4—21no—
845C4—41no—
846C4—611no—
847C4—611no—
848C4—1224no—
849C4—1221no—
850C4—1222no—
851C4—2442no—
852C4—2441no—
853C4—2441no—
854C4—2441no—
855C4C2×D4×#692311yescharacteristic
856C4#1684082911yescharacteristic
857C2—22no—
858C2—42no—
859C2—81no—
860C2—81no—
861C2—1221no—
862C2—1221no—
863C2—2441no—
864C2#2146234111yescharacteristic
865C2C2×#1684080411yescharacteristic
866C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#447C4
socleC22×C61C2×C4×D4
prime radical#21455032C2
cosocleC2×C4×D61C24
hypercenter#447#6923
hypocenterC61#22888
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#16840804C2semidirect
2. #21462549C2semidirect
3. C22×#14519841C2semidirect
4. #21462407C2semidirect
5. #21461972C2semidirect
6. #21461913C2semidirect
7. #21461900C2semidirect
8. #21461837C2semidirect
9. #21461810C2semidirect
10. #21461810C2semidirect
11. #21461786C2semidirect
12. #21461771C2semidirect
13. #21461594C2semidirect
14. C22⋊C8×#6923C2semidirect
18. C2×#14519864C22semidirect
26. C2×#14519848C22semidirect
27. C2×#14519848C22semidirect
28. #16840769C22semidirect
34. C2×#14519841C22semidirect
35. C2×#14519841C22semidirect
38. #16840736C22semidirect
45. #16840727C22semidirect
46. C2×C8×#6923C22semidirect
47. C2×C8×#6923C22semidirect
48. #16840638C22semidirect
49. #16840638C22semidirect
50. #16840632C22semidirect
51. #16840632C22semidirect
52. (C2×#6923)⋊C8C22semidirect
53. (C2×#6923)⋊C8C22semidirect
58. #16839925C4semidirect
59. #16839925C4semidirect
60. #16839920C4semidirect
61. #16839913C4semidirect
62. #16839904C4semidirect
63. #16839904C4semidirect
64. #16839900C4semidirect
68. C61×#447C4semidirect
106. #14519841D4semidirect
142. C2×Dic244C2×C4semidirect
143. C2×Dic244C2×C4semidirect
144. C2×#11758200C2×C4semidirect
145. C2×#11758200C2×C4semidirect
146. C2×#11758200C2×C4semidirect
147. C2×#11758200C2×C4semidirect
158. #14519702C2×C4semidirect
159. #14519702C2×C4semidirect
160. #14519700C2×C4semidirect
161. #14519700C2×C4semidirect
162. #14519698C2×C4semidirect
163. #14519698C2×C4semidirect
168. C2×D8×C61C2×C4semidirect
169. C2×D8×C61C2×C4semidirect
171. #102×C61C2×C4semidirect
172. #102×C61C2×C4semidirect
400. C22×C61#443semidirect
465. #447#6923semidirect
502. C61#22888semidirect
530. C2×D8C2×#6923semidirect
531. C2×D8C2×#6923semidirect
586. #102C2×#6923semidirect
587. #102C2×#6923semidirect
842. C22#16840804semidirect

Maximal subgroups

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

subgroupindex
C2×#168408042
#214625492
C22×#145198412
#214624072
#214619722
#214619132
#214619002
#214618372
#214618102
#214617862
#214617712
#214615942
C22⋊C8×#69232
#214550322
#2288861