Finite Group Databasebeta

← #30620223

Subgroups — #30620223

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×#16840808C211yesmaximal, characteristic, complemented
2C2×#16840806C211yesmaximal, characteristic, complemented
3#21462410C211yesmaximal, characteristic, complemented
4#21462408C211yesmaximal, characteristic, complemented
5#21461975C211yesmaximal, characteristic, complemented
6#21461971C211yesmaximal, characteristic, complemented
7#21461811C211yesmaximal, characteristic, complemented
8#21461811C211yesmaximal, characteristic, complemented
9#21461809C211yesmaximal, characteristic, complemented
10#21461809C211yesmaximal, characteristic, complemented
11#21461700C211yesmaximal, characteristic, complemented
12#21461662C211yesmaximal, characteristic, complemented
13#21461661C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15C2×#16840561C211yesmaximal, characteristic
16C2×#14519865C2211yescharacteristic, complemented
17C2×#14519865C2211yescharacteristic, complemented
18C2×#14519865C2211yescharacteristic, complemented
19C2×#14519865C2211yescharacteristic, complemented
20#16840808—24no—
21#16840806—24no—
22C2×#14519848C2211yescharacteristic, complemented
23C2×#14519847C2211yescharacteristic, complemented
24C2×#14519842C2211yescharacteristic, complemented
25C2×#14519842C2211yescharacteristic, complemented
26C2×#14519842C2211yescharacteristic, complemented
27C2×#14519842C2211yescharacteristic, complemented
28C2×#14519842C2211yescharacteristic, complemented
29C2×#14519842C2211yescharacteristic, complemented
30C2×#14519841C2211yescharacteristic, complemented
31C2×#14519841C2211yescharacteristic, complemented
32#16840737—21no—
33#16840737—21no—
34#16840737C2211yescharacteristic, complemented
35#16840737C2211yescharacteristic, complemented
36#16840736—21no—
37#16840736—21no—
38#16840736C2211yescharacteristic, complemented
39#16840736C2211yescharacteristic, complemented
40#16840733—21no—
41#16840733—21no—
42#16840733C2211yescharacteristic
43#16840733C2211yescharacteristic
44D61⋊(C22⋊C8)—21no—
45D61⋊(C22⋊C8)—21no—
46D61⋊(C22⋊C8)C2211yescharacteristic
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×#11758226C2211yescharacteristic
55C2×#41×D61C2211yescharacteristic
56#16840561—24no—
57#16840561—24no—
58C2×#14519809C411yescharacteristic, complemented
59C2×#14519809C411yescharacteristic, complemented
60C2×#14519808C411yescharacteristic, complemented
61C2×#14519805C411yescharacteristic, complemented
62C2×#14519804C411yescharacteristic, complemented
63C2×#14519804C411yescharacteristic, complemented
64C2×#14519802C411yescharacteristic, complemented
65C2×#14519800C2211yescharacteristic
66C2×#14519800C2211yescharacteristic
67C2×#14519798C2211yescharacteristic
68C2×#14519798C2211yescharacteristic
69C2×M16×D61C2211yescharacteristic
70C2×#137×C61C411yescharacteristic, complemented
71#14519865—22no—
72#14519865—22no—
73#14519865—22no—
74#14519865—22no—
75#14519865—41no—
76#14519865—41no—
77#14519865—41no—
78#14519865—41no—
79C2×#11758213—21no—
80C2×#11758213—21no—
81C2×#11758213—21no—
82C2×#11758213—21no—
83C2×#11758213C2311yescharacteristic
84C2×#11758213C2311yescharacteristic
85C2×#11758213C2311yescharacteristic
86C2×#11758213C2311yescharacteristic
87C2×D61⋊C8—21no—
88C2×D61⋊C8—21no—
89C2×D61⋊C8—21no—
90C2×D61⋊C8—21no—
91C2×D61⋊C8C2311yescharacteristic
92C2×D61⋊C8C2311yescharacteristic
93C2×C22⋊#6923—21no—
94C2×C4×#6923C2311yescharacteristic
95C2×C4×#6923C2311yescharacteristic
96#14519848—22no—
97#14519847—22no—
98#14519842—22no—
99#14519842—22no—
100#14519842—22no—
101#14519842—22no—
102#14519842—41no—
103#14519842—41no—
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×#11758226—21no—
126C2×#11758226—21no—
127C2×#11758226—22no—
128C2×#11758226—22no—
129C2×#11758226—41no—
130C2×#11758226—41no—
131C2×#11758226C2×C411yescharacteristic
132C2×#11758226C2×C411yescharacteristic
133C2×#11758226C2311yescharacteristic
134C2×#11758226C2311yescharacteristic
135C2×#11758226C2311yescharacteristic
136C2×#11758222—21no—
137C2×#11758222C2×C411yescharacteristic
138C2×#11758224—21no—
139C2×#11758224C2311yescharacteristic
140#41×D61—22no—
141#41×D61—22no—
142#41×D61—41no—
143#41×D61—41no—
144C2×Q8×D61C2×C411yescharacteristic
145C22×D244—21no—
146C22×D244C2×C411yescharacteristic
147C2×D4×D61—21no—
148C2×D4×D61C2×C411yescharacteristic
149C22×C4×D61—21no—
150C22×C4×D61—21no—
151C22×C4×D61C2311yescharacteristic
152#14519809—24no—
153#14519809—24no—
154#14519808—24no—
155#14519805—24no—
156#14519804—24no—
157#14519804—24no—
158#14519802—24no—
159#14519800—22no—
160#14519800—22no—
161#14519800D414yes—
162#14519800D414yes—
163#14519798—22no—
164#14519798—22no—
165#14519798—22no—
166#14519798—22no—
167C2×#11758202C2×C411yescharacteristic
168C2×#11758202C2×C411yescharacteristic
169C2×#11758190C2×C411yescharacteristic
170C2×#11758190C2×C411yescharacteristic
171C2×#11758201C2×C411yescharacteristic
172C2×#11758201C2×C411yescharacteristic
173C2×#11758201C2×C411yescharacteristic
174C2×#11758201C2×C411yescharacteristic
175C2×D488C2×C411yescharacteristic
176C2×D488C2×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×Q8×C61C2×C411yescharacteristic
188#137×C61—24no—
189C2×Q16×C61C2×C411yescharacteristic
190C2×Q16×C61C2×C411yescharacteristic
191C2×SD16×C61C2×C411yescharacteristic
192C2×SD16×C61C2×C411yescharacteristic
193C2×M16×C61C2×C411yescharacteristic
194C23×D61—21no—
195C23×D61—21no—
196C23×D61#4111yescharacteristic
197C22×#6923—21no—
198C22×#6923—21no—
199#41×C61—22no—
200#41×C61—41no—
201C2×Q8×C61—21no—
202C2×Q8×C61—22no—
203C2×Q8×C61—41no—
204C2×Q8×C61C22×C411yescharacteristic
205C2×Q8×C61C22×C411yescharacteristic
206C2×Q8×C61C22×C411yescharacteristic
207C2×D4×C61—21no—
208C2×D4×C61C22×C411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61C22×C411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C22×Dic61—21no—
216C22×Dic61C2×D411yescharacteristic
217#11758226—21no—
218#11758226—21no—
219#11758226—21no—
220#11758226—21no—
221#11758226—22no—
222#11758226—22no—
223#11758226—21no—
224#11758226—21no—
225#11758226—21no—
226#11758226—21no—
227#11758226—42no—
228#11758226—42no—
229#11758226—41no—
230#11758226—41no—
231#11758226—42no—
232#11758226—42no—
233#11758226C2×D412yes—
234#11758226C2×D412yes—
235#11758226C2×D412yes—
236#11758226C2×D412yes—
237Q8×D61—22no—
238Q8×D61—41no—
239#11758224—21no—
240#11758224—21no—
241#11758224—21no—
242#11758224—21no—
243#11758224—42no—
244#11758224—42no—
245D4×D61—22no—
246D4×D61—41no—
247D4×D61—42no—
248D4×D61—42no—
249#11758222—22no—
250#11758222—41no—
251#11758222—42no—
252#11758222—42no—
253C2×D244—21no—
254C2×D244—21no—
255C2×D244—22no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—41no—
261C2×D244—42no—
262C2×D244—42no—
263C2×D244C22×C411yescharacteristic
264C2×D244C22×C411yescharacteristic
265C2×D244C22×C411yescharacteristic
266C2×C4×D61—21no—
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—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—42no—
278C2×C4×D61—42no—
279C2×C4×D61—42no—
280C2×C4×D61—42no—
281C2×C4×D61C22×C411yescharacteristic
282C2×C4×D61C2×D411yescharacteristic
283C2×C4×D61#4111yescharacteristic
284C2×C4×D61C2411yescharacteristic
285C2×Dic122—21no—
286C2×Dic122C22×C411yescharacteristic
287C22⋊#6923—42no—
288C2×#92420—21no—
289C2×#92420—21no—
290C2×#92420—21no—
291C2×#92420—21no—
292C2×#92420C2×D411yescharacteristic
293C2×#92420C2×D411yescharacteristic
294C2×#92420C2×D411yescharacteristic
295C2×#92420C2×D411yescharacteristic
296C4×#6923—21no—
297C4×#6923—21no—
298C4×#6923—21no—
299C4×#6923—21no—
300#11758213—21no—
301#11758213—21no—
302#11758213—21no—
303#11758213—21no—
304#11758213—21no—
305#11758213—21no—
306#11758213—21no—
307#11758213—21no—
308#11758213—42no—
309#11758213—42no—
310#11758213—42no—
311#11758213—42no—
312D61⋊C8—21no—
313D61⋊C8—21no—
314D61⋊C8—21no—
315D61⋊C8—21no—
316D61⋊C8—42no—
317D61⋊C8—42no—
318D61⋊C8—42no—
319D61⋊C8—42no—
320Q16×C61—22no—
321Q16×C61C22⋊C414yescomplemented
322SD16×C61—22no—
323SD16×C61—22no—
324M16×C61—22no—
325C2×C8×C61C22×C411yescharacteristic
326C2×C8×C61C22×C411yescharacteristic
327#11758202—22no—
328#11758202—22no—
329#11758201—22no—
330#11758201—22no—
331#11758201C22⋊C414yescomplemented
332#11758201C22⋊C414yescomplemented
333#11758199—22no—
334#11758199—22no—
335#11758194—22no—
336C2×#92418C22×C411yescharacteristic
337C2×#92418C22×C411yescharacteristic
338D488—22no—
339D488C22⋊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×C61C4×D411yescharacteristic
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—21no—
353C22×D61—21no—
354C22×D61—21no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—42no—
358C22×D61—42no—
359C22×D61—42no—
360C22×D61—42no—
361C22×D61—81no—
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—
373Q8×C61—21no—
374Q8×C61—21no—
375Q8×C61—42no—
376Q8×C61C2×C22⋊C412yes—
377Q8×C61C2×C22⋊C412yes—
378D4×C61—21no—
379D4×C61—21no—
380D4×C61—42no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—42no—
387C2×C4×C61—42no—
388C2×C4×C61C4×D411yescharacteristic
389C2×C4×C61C23×C411yescharacteristic
390C22⋊D61—42no—
391C22⋊D61—42no—
392C22⋊D61—41no—
393C22⋊D61—41no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61C4×D411yescharacteristic
400C2×Dic61C22×D411yescharacteristic
401D244—22no—
402D244—22no—
403D244—22no—
404D244—22no—
405D244—21no—
406D244—21no—
407D244—21no—
408D244—21no—
409D244—42no—
410D244—42no—
411D244—42no—
412D244—41no—
413D244—41no—
414D244C2×C22⋊C412yes—
415D244C2×C22⋊C412yes—
416C4×D61—21no—
417C4×D61—21no—
418C4×D61—21no—
419C4×D61—21no—
420C4×D61—22no—
421C4×D61—22no—
422C4×D61—22no—
423C4×D61—22no—
424C4×D61—21no—
425C4×D61—21no—
426C4×D61—42no—
427C4×D61—42no—
428C4×D61—42no—
429C4×D61—42no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61C22×D411yescharacteristic
433C4×D61C22×D411yescharacteristic
434C4×D61H(5,𝔽2)11yescharacteristic
435C4×D61H(5,𝔽2)11yescharacteristic
436Dic122—21no—
437Dic122—21no—
438Dic122—42no—
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—21no—
454C22×C61—21no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61C2×C4×D411yescharacteristic
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—22no—
463C2×D61—22no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—41no—
472C2×D61—41no—
473C2×D61—81no—
474C2×D61—81no—
475C2×D61—84no—
476C2×D61—84no—
477C2×D61#54611yescharacteristic
478C2×D61#54611yescharacteristic
479#6923—42no—
480#6923—81no—
481C4×C61—22no—
482C4×C61—21no—
483C4×C61—22no—
484C4×C61—41no—
485C4×C61C22×C22⋊C411yescharacteristic
486C4×C61#51811yescharacteristic
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—81no—
508C2×C61D4×C22⋊C411yescharacteristic
509C2×C61#295511yescharacteristic
510C2×C61#295611yescharacteristic
511D61—21no—
512D61—21no—
513D61—41no—
514D61—42no—
515D61—42no—
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#692311yescharacteristic, complemented
525C2×AGL(1,ℤ/8)—611no—
526C2×AGL(1,ℤ/8)—611no—
527C2×AGL(1,ℤ/8)—611no—
528C2×AGL(1,ℤ/8)—611no—
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×Q8C2×#692311yescharacteristic
595C22×D4—611no—
596C22×D4—611no—
597C22×D4—1221no—
598C22×D4—1221no—
599C23×C4—611no—
600C23×C4—1221no—
601C23×C4—1221no—
602#137—24no—
603#137—1224no—
604#137—1224no—
605#137—1224no—
606AGL(1,ℤ/8)—1224no—
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×Q16C2×#692311yescharacteristic
621C2×Q16C2×#692311yescharacteristic
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×D8—611no—
633C2×D8—611no—
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—611no—
697C24—1221no—
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—21no—
732C2×Q8—22no—
733C2×Q8—41no—
734C2×Q8—611no—
735C2×Q8—1221no—
736C2×Q8—1222no—
737C2×Q8—2441no—
738C2×Q8C22×#692311yescharacteristic
739C2×Q8C22×#692311yescharacteristic
740C2×Q8C22×#692311yescharacteristic
741C2×D4—21no—
742C2×D4—611no—
743C2×D4—611no—
744C2×D4—611no—
745C2×D4—1222no—
746C2×D4—1221no—
747C2×D4—1221no—
748C2×D4—1221no—
749C2×D4—1221no—
750C2×D4—1221no—
751C2×D4—1221no—
752C2×D4—1222no—
753C2×D4—1221no—
754C2×D4—1221no—
755C2×D4—1221no—
756C2×D4—2441no—
757C2×D4—2442no—
758C2×D4—2442no—
759C2×D4—2441no—
760C2×D4—2442no—
761C2×D4—2442no—
762C2×D4C22×#692311yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—611no—
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—22no—
790Q16—1222no—
791Q16—1222no—
792Q16C22⋊#692314yescomplemented
793SD16—22no—
794SD16—22no—
795SD16—614no—
796SD16—614no—
797SD16—1222no—
798SD16—1222no—
799SD16—1222no—
800SD16—1222no—
801D8—614no—
802D8—1222no—
803D8—1222no—
804D8—1222no—
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—611no—
852C23—611no—
853C23—1221no—
854C23—1221no—
855C23—1221no—
856C23—1221no—
857C23—1221no—
858C23—4881no—
859C23—4881no—
860C23—2441no—
861C23—2441no—
862C23—2442no—
863C23—2442no—
864C23—2442no—
865C23—2442no—
866C23D4×#692311yescharacteristic
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8—1221no—
873Q8—1221no—
874Q8—2442no—
875Q8C2×C22⋊#692312yes—
876Q8C2×C22⋊#692312yes—
877D4—21no—
878D4—21no—
879D4—42no—
880D4—612no—
881D4—612no—
882D4—1222no—
883D4—1222no—
884D4—1222no—
885D4—1222no—
886D4—1221no—
887D4—1221no—
888D4—1221no—
889D4—1221no—
890D4—2442no—
891D4—2442no—
892D4—2441no—
893D4—2441no—
894D4—2442no—
895D4—2442no—
896D4—2442no—
897D4—2441no—
898D4—2441no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—611no—
907C2×C4—611no—
908C2×C4—611no—
909C2×C4—611no—
910C2×C4—611no—
911C2×C4—611no—
912C2×C4—1222no—
913C2×C4—1222no—
914C2×C4—1222no—
915C2×C4—1222no—
916C2×C4—1221no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—1221no—
922C2×C4—1221no—
923C2×C4—1221no—
924C2×C4—1222no—
925C2×C4—1221no—
926C2×C4—2442no—
927C2×C4—2442no—
928C2×C4—2442no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2442no—
932C2×C4—2441no—
933C2×C4—2441no—
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—21no—
955C22—21no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—611no—
960C22—611no—
961C22—1221no—
962C22—1221no—
963C22—1221no—
964C22—1222no—
965C22—1222no—
966C22—1221no—
967C22—1221no—
968C22—4881no—
969C22—4881no—
970C22—4884no—
971C22—4884no—
972C22—2441no—
973C22—2441no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22—2441no—
978C22—2441no—
979C22C2×D4×#692311yescharacteristic
980C4—21no—
981C4—22no—
982C4—22no—
983C4—41no—
984C4—611no—
985C4—611no—
986C4—1221no—
987C4—4881no—
988C4—2442no—
989C4—2441no—
990C4C22×C22⋊#692311yescharacteristic
991C4#1684082911yescharacteristic
992C2—41no—
993C2—81no—
994C2—1221no—
995C2—1221no—
996C2—4881no—
997C2—2441no—
998C2—2442no—
999C2—2442no—
1000C2D4×C22⋊#692311yescharacteristic
1001C2#2146259211yescharacteristic
1002C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#137×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×#16840561C2
cosocleC2×C4×D61C24
hypercenterC2×#137#6923
hypocenterC61#22453
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#16840808C2semidirect
2. C2×#16840806C2semidirect
3. #21462410C2semidirect
4. #21462408C2semidirect
5. #21461975C2semidirect
6. #21461971C2semidirect
7. #21461811C2semidirect
8. #21461811C2semidirect
9. #21461809C2semidirect
10. #21461809C2semidirect
11. #21461700C2semidirect
12. #21461662C2semidirect
13. #21461661C2semidirect
14. #21461559C2semidirect
16. C2×#14519865C22semidirect
17. C2×#14519865C22semidirect
18. C2×#14519865C22semidirect
19. C2×#14519865C22semidirect
22. C2×#14519848C22semidirect
23. C2×#14519847C22semidirect
24. C2×#14519842C22semidirect
25. C2×#14519842C22semidirect
26. C2×#14519842C22semidirect
27. C2×#14519842C22semidirect
28. C2×#14519842C22semidirect
29. C2×#14519842C22semidirect
30. C2×#14519841C22semidirect
31. C2×#14519841C22semidirect
34. #16840737C22semidirect
35. #16840737C22semidirect
38. #16840736C22semidirect
39. #16840736C22semidirect
47. C2×#14519831C22semidirect
48. C2×C8×#6923C22semidirect
50. #16840638C22semidirect
51. #16840638C22semidirect
52. (C2×#6923)⋊C8C22semidirect
53. (C2×#6923)⋊C8C22semidirect
58. C2×#14519809C4semidirect
59. C2×#14519809C4semidirect
60. C2×#14519808C4semidirect
61. C2×#14519805C4semidirect
62. C2×#14519804C4semidirect
63. C2×#14519804C4semidirect
64. C2×#14519802C4semidirect
70. C2×#137×C61C4semidirect
321. Q16×C61C22⋊C4semidirect
331. #11758201C22⋊C4semidirect
332. #11758201C22⋊C4semidirect
339. D488C22⋊C4semidirect
524. C2×#137#6923semidirect
572. C61#22453semidirect
792. Q16C22⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408082
C2×#168408062
#214624102
#214624082
#214619752
#214619712
#214618112
#214618092
#214617002
#214616622
#214616612
#214615592
C2×#168405612
#2245361