Finite Group Databasebeta

← #30620221

Subgroups — #30620221

Order 15616.

1362 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840809C211yesmaximal, characteristic, complemented
2C2×#16840804C211yesmaximal, characteristic, complemented
3#21462409C211yesmaximal, characteristic, complemented
4#21462407C211yesmaximal, characteristic, complemented
5#21461975C211yesmaximal, characteristic, complemented
6#21461971C211yesmaximal, characteristic, complemented
7#21461810C211yesmaximal, characteristic, complemented
8#21461810C211yesmaximal, characteristic, complemented
9#21461808C211yesmaximal, characteristic, complemented
10#21461808C211yesmaximal, characteristic, complemented
11#21461700C211yesmaximal, characteristic, complemented
12#21461661C211yesmaximal, characteristic, complemented
13#21461660C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15C2×#16840558C211yesmaximal, characteristic
16C2×#14519864C2211yescharacteristic, complemented
17C2×#14519864C2211yescharacteristic, complemented
18C2×#14519864C2211yescharacteristic, complemented
19C2×#14519864C2211yescharacteristic, complemented
20#16840809—24no—
21#16840804—24no—
22C2×#14519848C2211yescharacteristic, complemented
23C2×#14519847C2211yescharacteristic, complemented
24C2×#14519842C2211yescharacteristic, complemented
25C2×#14519842C2211yescharacteristic, complemented
26C2×#14519841C2211yescharacteristic, complemented
27C2×#14519841C2211yescharacteristic, complemented
28C2×#14519841C2211yescharacteristic, complemented
29C2×#14519841C2211yescharacteristic, complemented
30C2×#14519841C2211yescharacteristic, complemented
31C2×#14519841C2211yescharacteristic, complemented
32#16840737C2211yescharacteristic, complemented
33#16840737C2211yescharacteristic, complemented
34#16840736C2211yescharacteristic, complemented
35#16840736C2211yescharacteristic, complemented
36#16840735—21no—
37#16840735—21no—
38#16840735—21no—
39#16840735—21no—
40#16840734—21no—
41#16840733C2211yescharacteristic
42#16840733C2211yescharacteristic
43#16840732—21no—
44C2×#14519834—21no—
45D61⋊(C22⋊C8)C2211yescharacteristic
46C2×C22⋊#92420—21no—
47C2×#14519831C2211yescharacteristic, complemented
48C2×C8×#6923C2211yescharacteristic, complemented
49C4×C22⋊#6923C2211yescharacteristic
50#16840638C2211yescharacteristic, complemented
51#16840638C2211yescharacteristic, complemented
52(C2×#6923)⋊C8C2211yescharacteristic, complemented
53(C2×#6923)⋊C8C2211yescharacteristic, complemented
54C22×#11758224C2211yescharacteristic
55C2×#41×D61C2211yescharacteristic
56#16840558—24no—
57#16840558—24no—
58C2×#14519810C411yescharacteristic, complemented
59C2×#14519807C411yescharacteristic, complemented
60C2×#14519806C411yescharacteristic, complemented
61C2×#14519806C411yescharacteristic, complemented
62C2×#14519803C411yescharacteristic, complemented
63C2×#14519801C411yescharacteristic, complemented
64C2×#14519801C411yescharacteristic, complemented
65C2×#14519798C2211yescharacteristic
66C2×#14519798C2211yescharacteristic
67C2×#14519796C2211yescharacteristic
68C2×#14519796C2211yescharacteristic
69C2×M16×D61C2211yescharacteristic
70C2×AGL(1,ℤ/8)×C61C411yescharacteristic, complemented
71#14519864—22no—
72#14519864—22no—
73#14519864—22no—
74#14519864—22no—
75#14519864—41no—
76#14519864—41no—
77#14519864—41no—
78#14519864—41no—
79C2×#11758213C2311yescharacteristic
80C2×#11758213C2311yescharacteristic
81C2×#11758213C2311yescharacteristic
82C2×#11758213C2311yescharacteristic
83C2×#11758217—21no—
84C2×#11758217—21no—
85C2×#11758217—21no—
86C2×#11758217—21no—
87C2×D61⋊C8C2311yescharacteristic
88C2×D61⋊C8C2311yescharacteristic
89C22×#92420—21no—
90C22×#92420—21no—
91C22×#92420—21no—
92C22×#92420—21no—
93C2×C22⋊#6923—21no—
94C2×C4×#6923C2311yescharacteristic
95C2×C4×#6923C2311yescharacteristic
96#14519848—22no—
97#14519847—22no—
98#14519842—41no—
99#14519842—41no—
100#14519841—22no—
101#14519841—22no—
102#14519841—22no—
103#14519841—22no—
104#14519841—41no—
105#14519841—41no—
106#14519834—21no—
107#14519834—21no—
108#14519834—21no—
109#14519834—21no—
110#14519834—21no—
111#14519834—21no—
112#14519834D411yescharacteristic
113#14519834D411yescharacteristic
114C22⋊#92420—21no—
115C22⋊#92420—21no—
116C22⋊#92420—21no—
117C22⋊#92420—21no—
118C22⋊#92420—21no—
119C22⋊#92420—21no—
120C22⋊#92420D411yescharacteristic
121C22⋊#92420D411yescharacteristic
122#14519831—22no—
123C8×#6923—22no—
124(C2×#6923)⋊C4—21no—
125C2×#11758226C2311yescharacteristic
126C2×#11758222—21no—
127C2×#11758222C2×C411yescharacteristic
128C2×#11758224—22no—
129C2×#11758224—22no—
130C2×#11758224—21no—
131C2×#11758224—21no—
132C2×#11758224—21no—
133C2×#11758224—41no—
134C2×#11758224—41no—
135C2×#11758224C2×C411yescharacteristic
136C2×#11758224C2×C411yescharacteristic
137C2×#11758224C2311yescharacteristic
138C2×#11758224C2311yescharacteristic
139C2×#11758224C2311yescharacteristic
140#41×D61—22no—
141#41×D61—22no—
142#41×D61—41no—
143#41×D61—41no—
144C22×Dic122C2×C411yescharacteristic
145C2×Q8×D61C2×C411yescharacteristic
146C22×C22⋊D61—21no—
147C2×D4×D61—21no—
148C2×D4×D61C2×C411yescharacteristic
149C23×Dic61—21no—
150C22×C4×D61—21no—
151C22×C4×D61C2311yescharacteristic
152#14519810—24no—
153#14519807—24no—
154#14519806—24no—
155#14519806—24no—
156#14519803—24no—
157#14519801—24no—
158#14519801—24no—
159#14519798—22no—
160#14519798—22no—
161#14519798—22no—
162#14519798—22no—
163#14519796—22no—
164#14519796—22no—
165#14519796D414yes—
166#14519796D414yes—
167C2×Dic244C2×C411yescharacteristic
168C2×Dic244C2×C411yescharacteristic
169C2×#11758202C2×C411yescharacteristic
170C2×#11758202C2×C411yescharacteristic
171C2×#11758190C2×C411yescharacteristic
172C2×#11758190C2×C411yescharacteristic
173C2×#11758200C2×C411yescharacteristic
174C2×#11758200C2×C411yescharacteristic
175C2×#11758200C2×C411yescharacteristic
176C2×#11758200C2×C411yescharacteristic
177C2×#11758199C2×C411yescharacteristic
178C2×#11758199C2×C411yescharacteristic
179C2×#11758194C2×C411yescharacteristic
180C2×#11758189C2×C411yescharacteristic
181C2×#11758189C2×C411yescharacteristic
182M16×D61—22no—
183M16×D61—22no—
184C2×C8×D61C2311yescharacteristic
185C2×C8×D61C2311yescharacteristic
186C2×#41×C61C2×C411yescharacteristic
187C22×D4×C61C2×C411yescharacteristic
188AGL(1,ℤ/8)×C61—24no—
189C2×SD16×C61C2×C411yescharacteristic
190C2×SD16×C61C2×C411yescharacteristic
191C2×D8×C61C2×C411yescharacteristic
192C2×D8×C61C2×C411yescharacteristic
193C2×M16×C61C2×C411yescharacteristic
194C24×C61—21no—
195C23×D61—21no—
196C23×D61#4111yescharacteristic
197C22×#6923—21no—
198C22×#6923—21no—
199#41×C61—22no—
200#41×C61—41no—
201C2×Q8×C61C22×C411yescharacteristic
202C2×D4×C61—22no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—41no—
206C2×D4×C61C22×C411yescharacteristic
207C2×D4×C61C22×C411yescharacteristic
208C2×D4×C61C22×C411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61C22×C411yescharacteristic
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—42no—
219C2×C22⋊D61—42no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—42no—
227C22×Dic61—42no—
228C22×Dic61C2×D411yescharacteristic
229#11758226—21no—
230#11758226—21no—
231#11758226—21no—
232#11758226—21no—
233Q8×D61—22no—
234Q8×D61—41no—
235#11758224—22no—
236#11758224—21no—
237#11758224—21no—
238#11758224—21no—
239#11758224—21no—
240#11758224—21no—
241#11758224—21no—
242#11758224—21no—
243#11758224—21no—
244#11758224—22no—
245#11758224—41no—
246#11758224—41no—
247#11758224—42no—
248#11758224—42no—
249#11758224—42no—
250#11758224—42no—
251#11758224—42no—
252#11758224—42no—
253#11758224C2×D412yes—
254#11758224C2×D412yes—
255#11758224C2×D412yes—
256#11758224C2×D412yes—
257D4×D61—22no—
258D4×D61—41no—
259D4×D61—42no—
260D4×D61—42no—
261#11758222—22no—
262#11758222—41no—
263#11758222—42no—
264#11758222—42no—
265C2×D244—21no—
266C2×D244C22×C411yescharacteristic
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—42no—
275C2×C4×D61—42no—
276C2×C4×D61C22×C411yescharacteristic
277C2×C4×D61C2×D411yescharacteristic
278C2×C4×D61#4111yescharacteristic
279C2×C4×D61C2411yescharacteristic
280C2×Dic122—22no—
281C2×Dic122—21no—
282C2×Dic122—21no—
283C2×Dic122—41no—
284C2×Dic122C22×C411yescharacteristic
285C2×Dic122C22×C411yescharacteristic
286C2×Dic122C22×C411yescharacteristic
287C22⋊#6923—42no—
288#11758217—42no—
289#11758217—42no—
290#11758217—42no—
291#11758217—42no—
292C2×#92420—21no—
293C2×#92420—21no—
294C2×#92420—21no—
295C2×#92420—21no—
296C2×#92420—42no—
297C2×#92420—42no—
298C2×#92420—42no—
299C2×#92420—42no—
300C2×#92420C2×D411yescharacteristic
301C2×#92420C2×D411yescharacteristic
302C2×#92420C2×D411yescharacteristic
303C2×#92420C2×D411yescharacteristic
304C4×#6923—21no—
305C4×#6923—21no—
306C4×#6923—21no—
307C4×#6923—21no—
308#11758213—21no—
309#11758213—21no—
310#11758213—21no—
311#11758213—21no—
312#11758213—21no—
313#11758213—21no—
314#11758213—21no—
315#11758213—21no—
316D61⋊C8—21no—
317D61⋊C8—21no—
318D61⋊C8—21no—
319D61⋊C8—21no—
320SD16×C61—22no—
321SD16×C61—22no—
322D8×C61—22no—
323D8×C61C22⋊C414yescomplemented
324M16×C61—22no—
325C2×C8×C61C22×C411yescharacteristic
326C2×C8×C61C22×C411yescharacteristic
327#11758202—22no—
328#11758202—22no—
329#11758200—22no—
330#11758200—22no—
331#11758200C22⋊C414yescomplemented
332#11758200C22⋊C414yescomplemented
333#11758199—22no—
334#11758199—22no—
335#11758194—22no—
336C2×#92418C22×C411yescharacteristic
337C2×#92418C22×C411yescharacteristic
338Dic244—22no—
339Dic244C22⋊C414yescomplemented
340#11758190—22no—
341#11758190—22no—
342#11758189—22no—
343#11758189—22no—
344C8×D61—21no—
345C8×D61—21no—
346C8×D61C2×D412yes—
347C8×D61C2×D412yes—
348C23×C61—21no—
349C23×C61—21no—
350C23×C61—21no—
351C23×C61—42no—
352C23×C61—42no—
353C23×C61—81no—
354C23×C61C4×D411yescharacteristic
355C22×D61—21no—
356C22×D61—21no—
357C22×D61—21no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—42no—
361C22×D61—42no—
362C22×D61—81no—
363C22×D61C4×D411yescharacteristic
364C22×D61C2×#4111yescharacteristic
365C2×#6923—22no—
366C2×#6923—41no—
367C2×#6923—41no—
368C2×#6923—41no—
369C2×#6923—41no—
370C2×#6923—41no—
371Q8×C61—21no—
372Q8×C61—21no—
373D4×C61—21no—
374D4×C61—21no—
375D4×C61—21no—
376D4×C61—21no—
377D4×C61—42no—
378D4×C61—42no—
379D4×C61C2×C22⋊C412yes—
380D4×C61C2×C22⋊C412yes—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—42no—
385C2×C4×C61C4×D411yescharacteristic
386C2×C4×C61C23×C411yescharacteristic
387C22⋊D61—22no—
388C22⋊D61—22no—
389C22⋊D61—22no—
390C22⋊D61—22no—
391C22⋊D61—42no—
392C22⋊D61—42no—
393C22⋊D61—42no—
394C22⋊D61—42no—
395C22⋊D61—41no—
396C22⋊D61—41no—
397C2×Dic61—21no—
398C2×Dic61—21no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—21no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—42no—
407C2×Dic61—42no—
408C2×Dic61—42no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61C4×D411yescharacteristic
412C2×Dic61C22×D411yescharacteristic
413D244—21no—
414D244—21no—
415D244—41no—
416D244—41no—
417C4×D61—21no—
418C4×D61—21no—
419C4×D61—21no—
420C4×D61—21no—
421C4×D61—21no—
422C4×D61—21no—
423C4×D61—42no—
424C4×D61—42no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61C22×D411yescharacteristic
428C4×D61C22×D411yescharacteristic
429C4×D61H(5,𝔽2)11yescharacteristic
430C4×D61H(5,𝔽2)11yescharacteristic
431Dic122—21no—
432Dic122—21no—
433Dic122—21no—
434Dic122—21no—
435Dic122—42no—
436Dic122—42no—
437Dic122C2×C22⋊C412yes—
438Dic122C2×C22⋊C412yes—
439#92420—21no—
440#92420—21no—
441#92420—21no—
442#92420—21no—
443#92420—41no—
444#92420—41no—
445#92420—41no—
446#92420—41no—
447C8×C61—21no—
448C8×C61C2×C22⋊C412yes—
449#92418—21no—
450#92418C2×C22⋊C412yes—
451#22453—611nomaximal, Sylow
452C22×C61—21no—
453C22×C61—22no—
454C22×C61—22no—
455C22×C61—21no—
456C22×C61—21no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61—41no—
461C22×C61—41no—
462C22×C61—41no—
463C22×C61—41no—
464C22×C61—84no—
465C22×C61C2×C4×D411yescharacteristic
466C2×D61—21no—
467C2×D61—21no—
468C2×D61—21no—
469C2×D61—21no—
470C2×D61—21no—
471C2×D61—41no—
472C2×D61—41no—
473C2×D61—41no—
474C2×D61—81no—
475C2×D61—81no—
476C2×D61—84no—
477C2×D61#54611yescharacteristic
478C2×D61#54611yescharacteristic
479#6923—42no—
480#6923—81no—
481C4×C61—21no—
482C4×C61—41no—
483C4×C61C22×C22⋊C411yescharacteristic
484C4×C61#51811yescharacteristic
485Dic61—22no—
486Dic61—22no—
487Dic61—21no—
488Dic61—41no—
489Dic61D4211yescharacteristic
490Dic61D4211yescharacteristic
491C2×#575—611no—
492C2×#444—611no—
493C2×#443—611no—
494#2880—611no—
495#2880—611no—
496#1975—611no—
497#1974—611no—
498#1876—611no—
499#1876—611no—
500#1876—611no—
501#1876—611no—
502#1811—611no—
503#1789—611no—
504#1789—611no—
505#1753—611no—
506C2×C61—41no—
507C2×C61—42no—
508C2×C61—42no—
509C2×C61—81no—
510C2×C61D4×C22⋊C411yescharacteristic
511C2×C61#295511yescharacteristic
512C2×C61#295611yescharacteristic
513D61—21no—
514D61—21no—
515D61—41no—
516D61—81no—
517C22×#41—611no—
518C22×#41—611no—
519#575—1224no—
520#575—1224no—
521C2×#137—611no—
522C2×#137—611no—
523C2×#137—611no—
524C2×#137—611no—
525C2×AGL(1,ℤ/8)—611no—
526C2×AGL(1,ℤ/8)—611no—
527C2×AGL(1,ℤ/8)—611no—
528C2×AGL(1,ℤ/8)#692311yescharacteristic, complemented
529C2×#135—611no—
530C2×#135—611no—
531C2×#135—611no—
532C2×#135—611no—
533C2×#131—611no—
534C2×#131—611no—
535C2×#131—611no—
536C2×#131—611no—
537C22×M16—611no—
538#444—1224no—
539#443—1224no—
540C2×#108—611no—
541C2×#108—611no—
542C2×#104—611no—
543C2×#104—611no—
544C2×#104—611no—
545C2×#104—611no—
546C2×#104—611no—
547C2×#104—611no—
548C2×#104—611no—
549C2×#104—611no—
550#408—611no—
551#408—611no—
552#408—611no—
553#408—611no—
554#408—1221no—
555#408—1221no—
556#408—1221no—
557#408—1221no—
558#407—611no—
559#407—611no—
560#407—1221no—
561#407—1221no—
562C2×C22⋊C8—611no—
563C2×C22⋊C8—1221no—
564C2×C22⋊C8—1221no—
565C2×#97—611no—
566C2×C4×C8—611no—
567C4×C22⋊C4—611no—
568#341—611no—
569#341—611no—
570#336—611no—
571#336—611no—
572C61#2245311yescharacteristic, complemented, Sylow
573C2×#41—611no—
574C2×#41—611no—
575C2×#41—611no—
576C2×#41—611no—
577C2×#41—611no—
578C2×#41—611no—
579C2×#41—611no—
580C2×#41—1221no—
581C2×#41—1221no—
582C2×#41—1221no—
583C2×#41—1221no—
584C2×#41—1222no—
585C2×#41—1222no—
586C2×#41—1222no—
587C2×#41—1222no—
588C2×#41—2441no—
589C2×#41—2441no—
590C2×#41—2441no—
591C2×#41—2441no—
592C2×#41C2×#692311yescharacteristic
593C22×Q8—611no—
594C22×Q8—611no—
595C22×D4—611no—
596C22×D4—1221no—
597C22×D4—1221no—
598C22×D4C2×#692311yescharacteristic
599C23×C4—611no—
600C23×C4—1221no—
601C23×C4—1221no—
602#137—1224no—
603#137—1224no—
604#137—1224no—
605#137—1224no—
606AGL(1,ℤ/8)—24no—
607AGL(1,ℤ/8)—1224no—
608AGL(1,ℤ/8)—1224no—
609AGL(1,ℤ/8)—1224no—
610#135—614no—
611#135—614no—
612#135—1222no—
613#135—1222no—
614#135—1222no—
615#135—1222no—
616#135—1222no—
617#135—1222no—
618C2×Q16—611no—
619C2×Q16—611no—
620C2×Q16—611no—
621C2×Q16—611no—
622C2×SD16—611no—
623C2×SD16—611no—
624C2×SD16—611no—
625C2×SD16—611no—
626C2×SD16—611no—
627C2×SD16—611no—
628C2×SD16C2×#692311yescharacteristic
629C2×SD16C2×#692311yescharacteristic
630C2×D8—611no—
631C2×D8—611no—
632C2×D8C2×#692311yescharacteristic
633C2×D8C2×#692311yescharacteristic
634#131—1222no—
635#131—1222no—
636#131—1222no—
637#131—1222no—
638#131—2441no—
639#131—2441no—
640#131—2441no—
641#131—2441no—
642C2×M16—611no—
643C2×M16—611no—
644C2×M16—611no—
645C2×M16—611no—
646C2×M16—611no—
647C2×M16—611no—
648C2×M16—611no—
649C2×M16—1222no—
650C2×M16—1222no—
651C2×M16—1221no—
652C2×M16—1221no—
653C2×M16—1221no—
654C2×M16—1221no—
655C2×M16C2×#692311yescharacteristic
656C22×C8—611no—
657C22×C8—611no—
658C22×C8—611no—
659C22×C8—611no—
660C22×C8—1221no—
661C22×C8—1221no—
662C22×C8—1221no—
663C22×C8—1221no—
664C2×C22⋊C4—1221no—
665C2×C42—611no—
666C2×C42—611no—
667#108—1222no—
668#108—1222no—
669#104—1222no—
670#104—1222no—
671#104—1222no—
672#104—1222no—
673#104—2441no—
674#104—2441no—
675#104—2441no—
676#104—2441no—
677C22⋊C8—611no—
678C22⋊C8—611no—
679C22⋊C8—611no—
680C22⋊C8—611no—
681C22⋊C8—1221no—
682C22⋊C8—1221no—
683C22⋊C8—1221no—
684C22⋊C8—1221no—
685C22⋊C8—1221no—
686C22⋊C8—1221no—
687C22⋊C8—1221no—
688C22⋊C8—1221no—
689C22⋊C8—1221no—
690C22⋊C8—1221no—
691C22⋊C8—1221no—
692C22⋊C8—1221no—
693#97—1222no—
694C4×C8—1222no—
695#95—1221no—
696C24—21no—
697C24—611no—
698C24—1221no—
699#41—22no—
700#41—41no—
701#41—612no—
702#41—612no—
703#41—612no—
704#41—612no—
705#41—1222no—
706#41—1221no—
707#41—1221no—
708#41—1221no—
709#41—1221no—
710#41—1221no—
711#41—1221no—
712#41—1221no—
713#41—1221no—
714#41—1221no—
715#41—1221no—
716#41—1221no—
717#41—1221no—
718#41—1222no—
719#41—1222no—
720#41—2441no—
721#41—2442no—
722#41—2442no—
723#41—2442no—
724#41—2442no—
725#41—2442no—
726#41—2442no—
727#41—2441no—
728#41—2441no—
729#41—2442no—
730#41—2442no—
731C2×Q8—611no—
732C2×Q8—611no—
733C2×Q8—611no—
734C2×Q8—1221no—
735C2×Q8—1222no—
736C2×Q8—1221no—
737C2×Q8—1222no—
738C2×Q8—2441no—
739C2×Q8—2441no—
740C2×Q8C22×#692311yescharacteristic
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—41no—
745C2×D4—611no—
746C2×D4—1221no—
747C2×D4—1221no—
748C2×D4—1221no—
749C2×D4—1221no—
750C2×D4—1222no—
751C2×D4—1221no—
752C2×D4—1221no—
753C2×D4—1221no—
754C2×D4—1221no—
755C2×D4—2441no—
756C2×D4—2442no—
757C2×D4—2442no—
758C2×D4—2442no—
759C2×D4—2442no—
760C2×D4C22×#692311yescharacteristic
761C2×D4C22×#692311yescharacteristic
762C2×D4C22×#692311yescharacteristic
763C22×C4—21no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—2442no—
785C22×C4—2442no—
786C22×C4—2442no—
787C22×C4—2442no—
788C22×C4C22×#692311yescharacteristic
789Q16—614no—
790Q16—1222no—
791Q16—1222no—
792Q16—1222no—
793SD16—22no—
794SD16—22no—
795SD16—614no—
796SD16—614no—
797SD16—1222no—
798SD16—1222no—
799SD16—1222no—
800SD16—1222no—
801D8—22no—
802D8—1222no—
803D8—1222no—
804D8C22⋊#692314yescomplemented
805M16—22no—
806M16—1222no—
807M16—1222no—
808M16—1222no—
809M16—1221no—
810M16—1221no—
811M16—1221no—
812M16—1221no—
813M16—1221no—
814M16—1221no—
815M16—1221no—
816M16—1221no—
817M16—2442no—
818M16—2442no—
819M16—2442no—
820M16—2442no—
821C2×C8—611no—
822C2×C8—612no—
823C2×C8—612no—
824C2×C8—611no—
825C2×C8—611no—
826C2×C8—611no—
827C2×C8—611no—
828C2×C8—611no—
829C2×C8—1221no—
830C2×C8—1221no—
831C2×C8—1221no—
832C2×C8—1221no—
833C2×C8—1221no—
834C2×C8—1221no—
835C2×C8—1221no—
836C2×C8—1221no—
837C2×C8—1221no—
838C2×C8—1221no—
839C2×C8—2442no—
840C2×C8—2442no—
841C2×C8—2442no—
842C2×C8—2442no—
843C2×C8C22×#692311yescharacteristic
844C2×C8C22×#692311yescharacteristic
845C22⋊C4—2442no—
846C42—1221no—
847C42—1221no—
848C42—1221no—
849C42—1221no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—42no—
854C23—42no—
855C23—81no—
856C23—611no—
857C23—611no—
858C23—1221no—
859C23—1221no—
860C23—1221no—
861C23—4881no—
862C23—2441no—
863C23—2441no—
864C23—2442no—
865C23—2442no—
866C23D4×#692311yescharacteristic
867Q8—21no—
868Q8—21no—
869Q8—612no—
870Q8—612no—
871Q8—1221no—
872Q8—1221no—
873Q8—1221no—
874Q8—1221no—
875Q8—2442no—
876Q8—2442no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—21no—
881D4—42no—
882D4—42no—
883D4—1222no—
884D4—1222no—
885D4—1222no—
886D4—1222no—
887D4—1221no—
888D4—1221no—
889D4—2441no—
890D4—2441no—
891D4—2442no—
892D4—2442no—
893D4—2442no—
894D4—2442no—
895D4—2441no—
896D4—2441no—
897D4C2×C22⋊#692312yes—
898D4C2×C22⋊#692312yes—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—42no—
903C2×C4—611no—
904C2×C4—611no—
905C2×C4—611no—
906C2×C4—611no—
907C2×C4—611no—
908C2×C4—611no—
909C2×C4—1221no—
910C2×C4—1221no—
911C2×C4—1221no—
912C2×C4—1221no—
913C2×C4—1222no—
914C2×C4—1222no—
915C2×C4—1222no—
916C2×C4—1222no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—1221no—
922C2×C4—1221no—
923C2×C4—1222no—
924C2×C4—1221no—
925C2×C4—2442no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2442no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2442no—
932C2×C4—2442no—
933C2×C4—2442no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4D4×#692311yescharacteristic
940C2×C4C23×#692311yescharacteristic
941C8—21no—
942C8—612no—
943C8—1221no—
944C8—1221no—
945C8—1221no—
946C8—1221no—
947C8—1221no—
948C8—2441no—
949C8—2441no—
950C8—2441no—
951C8—2441no—
952C8C2×C22⋊#692312yes—
953C22—21no—
954C22—22no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—84no—
966C22—611no—
967C22—611no—
968C22—1221no—
969C22—1221no—
970C22—1221no—
971C22—1221no—
972C22—1221no—
973C22—4881no—
974C22—4881no—
975C22—4884no—
976C22—2441no—
977C22—2441no—
978C22—2441no—
979C22C2×D4×#692311yescharacteristic
980C4—21no—
981C4—41no—
982C4—611no—
983C4—611no—
984C4—1221no—
985C4—1222no—
986C4—1222no—
987C4—4881no—
988C4—2442no—
989C4—2441no—
990C4C22×C22⋊#692311yescharacteristic
991C4#1684082911yescharacteristic
992C2—41no—
993C2—42no—
994C2—42no—
995C2—81no—
996C2—1221no—
997C2—1221no—
998C2—4881no—
999C2—2441no—
1000C2D4×C22⋊#692311yescharacteristic
1001C2#2146259111yescharacteristic
1002C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×AGL(1,ℤ/8)×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×#16840558C2
cosocleC2×C4×D61C24
hypercenterC2×AGL(1,ℤ/8)#6923
hypocenterC61#22453
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#16840809C2semidirect
2. C2×#16840804C2semidirect
3. #21462409C2semidirect
4. #21462407C2semidirect
5. #21461975C2semidirect
6. #21461971C2semidirect
7. #21461810C2semidirect
8. #21461810C2semidirect
9. #21461808C2semidirect
10. #21461808C2semidirect
11. #21461700C2semidirect
12. #21461661C2semidirect
13. #21461660C2semidirect
14. #21461559C2semidirect
16. C2×#14519864C22semidirect
17. C2×#14519864C22semidirect
18. C2×#14519864C22semidirect
19. C2×#14519864C22semidirect
22. C2×#14519848C22semidirect
23. C2×#14519847C22semidirect
24. C2×#14519842C22semidirect
25. C2×#14519842C22semidirect
26. C2×#14519841C22semidirect
27. C2×#14519841C22semidirect
28. C2×#14519841C22semidirect
29. C2×#14519841C22semidirect
30. C2×#14519841C22semidirect
31. C2×#14519841C22semidirect
32. #16840737C22semidirect
33. #16840737C22semidirect
34. #16840736C22semidirect
35. #16840736C22semidirect
47. C2×#14519831C22semidirect
48. C2×C8×#6923C22semidirect
50. #16840638C22semidirect
51. #16840638C22semidirect
52. (C2×#6923)⋊C8C22semidirect
53. (C2×#6923)⋊C8C22semidirect
58. C2×#14519810C4semidirect
59. C2×#14519807C4semidirect
60. C2×#14519806C4semidirect
61. C2×#14519806C4semidirect
62. C2×#14519803C4semidirect
63. C2×#14519801C4semidirect
64. C2×#14519801C4semidirect
70. C2×AGL(1,ℤ/8)×C61C4semidirect
323. D8×C61C22⋊C4semidirect
331. #11758200C22⋊C4semidirect
332. #11758200C22⋊C4semidirect
339. Dic244C22⋊C4semidirect
528. C2×AGL(1,ℤ/8)#6923semidirect
572. C61#22453semidirect
804. D8C22⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408092
C2×#168408042
#214624092
#214624072
#214619752
#214619712
#214618102
#214618082
#214617002
#214616612
#214616602
#214615592
C2×#168405582
#2245361