Finite Group Databasebeta

← #30616873

Subgroups — #30616873

Order 15616.

1552 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×#6923C211yesmaximal, characteristic, complemented
2C2×#16840803C211yesmaximal, characteristic, complemented
3C2×#16840801C211yesmaximal, characteristic, complemented
4#121×#6923C211yesmaximal, characteristic, complemented
5#21461815C211yesmaximal, characteristic, complemented
6#21461814C211yesmaximal, characteristic, complemented
7#21461807C211yesmaximal, characteristic, complemented
8#21461785C211yesmaximal, characteristic, complemented
9#21461782C211yesmaximal, characteristic, complemented
10#21461770C211yesmaximal, characteristic, complemented
11#21461659C211yesmaximal, characteristic, complemented
12#21461592C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic, complemented
14#21461547C211yesmaximal, characteristic, complemented
15#449×D61C211yesmaximal, characteristic
16#41×#6923—24no—
17#41×#6923—24no—
18C2×Q8×#6923C2211yescharacteristic
19C2×Q8×#6923C2211yescharacteristic
20C2×D4×#6923—21no—
21C2×D4×#6923—21no—
22C2×D4×#6923—21no—
23C2×D4×#6923C2211yescharacteristic
24C2×D4×#6923C2211yescharacteristic
25C2×D4×#6923C2211yescharacteristic
26C2×#14519856—21no—
27C2×#14519856C2211yescharacteristic
28C22×C4×#6923—21no—
29C22×C4×#6923C2211yescharacteristic
30#16840803—24no—
31#16840801—24no—
32C2×#14519846C2211yescharacteristic
33C2×#14519845C2211yescharacteristic
34C2×#14519840C2211yescharacteristic
35C2×#14519840C2211yescharacteristic
36C2×#14519839C2211yescharacteristic
37C2×#14519839C2211yescharacteristic
38C2×#14519839C2211yescharacteristic
39C2×#14519839C2211yescharacteristic
40D61⋊(C22⋊C8)C2211yescharacteristic
41C2×#14519831C2211yescharacteristic
42C2×#14519831C2211yescharacteristic
43#16840714C2211yescharacteristic
44#16840713C2211yescharacteristic
45#16840712—21no—
46#16840710—21no—
47#16840704C2211yescharacteristic
48C4⋊C4×#6923C2211yescharacteristic
49C22⋊C4×#6923—21no—
50#16840636C2211yescharacteristic
51#16840636C2211yescharacteristic
52#16840635C2211yescharacteristic
53#16840635C2211yescharacteristic
54(C2×#6923)⋊C8C2211yescharacteristic
55(C2×#6923)⋊C8C2211yescharacteristic
56C2×#41×D61C2211yescharacteristic
57C2×SD16×D61C2211yescharacteristic
58C2×D8×D61C2211yescharacteristic
59#121×D61C2211yescharacteristic
60#16839910C411yescharacteristic, complemented
61#16839909C411yescharacteristic, complemented
62#16839908C411yescharacteristic, complemented
63#16839907C411yescharacteristic, complemented
64#16839906C411yescharacteristic, complemented
65#16839905C411yescharacteristic, complemented
66#16839904C411yescharacteristic, complemented
67#103×D61C2211yescharacteristic
68#102×D61C2211yescharacteristic
69C22⋊C8×D61C2211yescharacteristic
70C61×#449C411yescharacteristic, complemented
71C23×#6923—21no—
72C23×#6923—21no—
73C23×#6923—21no—
74C23×#6923D411yescharacteristic
75C23×#6923D411yescharacteristic
76C2×D61⋊C8C2311yescharacteristic
77C2×D61⋊C8C2311yescharacteristic
78Q8×#6923—22no—
79Q8×#6923—22no—
80Q8×#6923—22no—
81Q8×#6923D414yescomplemented
82D4×#6923—28no—
83D4×#6923—28no—
84D4×#6923—22no—
85D4×#6923—22no—
86D4×#6923—22no—
87D4×#6923—22no—
88D4×#6923—22no—
89D4×#6923—44no—
90D4×#6923D414yescomplemented
91#14519856—28no—
92#14519856—22no—
93#14519856—22no—
94C2×C4⋊#6923—21no—
95C2×C4⋊#6923—21no—
96C2×C4⋊#6923—21no—
97C2×C4⋊#6923C2311yescharacteristic
98C2×C4⋊#6923C2311yescharacteristic
99C2×C4⋊#6923C2311yescharacteristic
100C2×C4⋊#6923C2311yescharacteristic
101C2×C22⋊#6923—21no—
102C2×C22⋊#6923—21no—
103C2×C22⋊#6923—21no—
104C2×C22⋊#6923—21no—
105C2×C22⋊#6923—21no—
106C2×C22⋊#6923—21no—
107C2×C22⋊#6923—21no—
108C2×C4×#6923—28no—
109C2×C4×#6923—21no—
110C2×C4×#6923—21no—
111C2×C4×#6923—21no—
112C2×C4×#6923—22no—
113C2×C4×#6923—22no—
114C2×C4×#6923—21no—
115C2×C4×#6923D411yescharacteristic
116C2×C4×#6923D411yescharacteristic
117C2×C4×#6923C2311yescharacteristic
118C2×C4×#6923C2311yescharacteristic
119#14519846—22no—
120#14519845—22no—
121#14519840—22no—
122#14519840—22no—
123#14519839—22no—
124#14519839—22no—
125#14519839—22no—
126#14519839—22no—
127#14519834—21no—
128C22⋊#92420—21no—
129#14519831—22no—
130#14519831—22no—
131(C2×#6923)⋊C4—21no—
132(C2×#6923)⋊C4—21no—
133(C2×#6923)⋊C4—21no—
134C2×#11758226C2×C411yescharacteristic, complemented
135C2×#11758222—21no—
136C2×#11758222C2×C411yescharacteristic, complemented
137C2×#11758224—21no—
138C2×#11758224C2×C411yescharacteristic, complemented
139#41×D61—22no—
140#41×D61—22no—
141#41×D61—22no—
142#41×D61—22no—
143C2×Q8×D61C2311yescharacteristic
144C2×D4×D61—21no—
145C2×D4×D61—21no—
146C2×D4×D61C2311yescharacteristic
147C2×D4×D61C2311yescharacteristic
148C22×C4×D61—21no—
149C22×C4×D61C2311yescharacteristic
150C2×#11758190C2×C411yescharacteristic, complemented
151C2×#11758200C2×C411yescharacteristic, complemented
152C2×#11758201C2×C411yescharacteristic, complemented
153SD16×D61—22no—
154SD16×D61—22no—
155C2×D488C2×C411yescharacteristic, complemented
156C2×#11758199C2×C411yescharacteristic, complemented
157C2×#11758199C2×C411yescharacteristic, complemented
158D8×D61—22no—
159D8×D61—22no—
160C2×C8×D61C2311yescharacteristic
161C2×C8×D61C2311yescharacteristic
162#14519752C2×C411yescharacteristic, complemented
163#14519751C2×C411yescharacteristic, complemented
164#14519750—21no—
165#14519749—21no—
166#14519748C2×C411yescharacteristic, complemented
167C4⋊C4×D61C2311yescharacteristic
168C22⋊C4×D61—21no—
169#14519702C2×C411yescharacteristic, complemented
170#14519701C2×C411yescharacteristic, complemented
171#14519700C2×C411yescharacteristic, complemented
172#14519699C2×C411yescharacteristic, complemented
173#14519698C2×C411yescharacteristic, complemented
174#14519697C2×C411yescharacteristic, complemented
175C22⋊#92418C2×C411yescharacteristic, complemented
176#14519689C2×C411yescharacteristic, complemented
177#14519689C2×C411yescharacteristic, complemented
178C2×#41×C61C2×C411yescharacteristic, complemented
179C2×SD16×C61C2×C411yescharacteristic, complemented
180C2×D8×C61C2×C411yescharacteristic, complemented
181#121×C61C2×C411yescharacteristic, complemented
182#103×C61C2×C411yescharacteristic, complemented
183#102×C61C2×C411yescharacteristic, complemented
184C22⋊C8×C61C2×C411yescharacteristic, complemented
185C23×D61—21no—
186C23×D61—21no—
187C23×D61C2×D411yescharacteristic
188C22×#6923—24no—
189C22×#6923—21no—
190C22×#6923—21no—
191C22×#6923—22no—
192C22×#6923—22no—
193C22×#6923—24no—
194C22×#6923—22no—
195C22×#6923—21no—
196C22×#6923—21no—
197C22×#6923—41no—
198C22×#6923—41no—
199C22×#6923—41no—
200C22×#6923—42no—
201C22×#6923—42no—
202C22×#6923—42no—
203C22×#6923—42no—
204C22×#6923—42no—
205C22×#6923—42no—
206C22×#6923—42no—
207C22×#6923C2×D411yescharacteristic
208C22×#6923C2×D411yescharacteristic
209C22×#6923C2×D411yescharacteristic
210C22×#6923C2×D411yescharacteristic
211#41×C61—22no—
212#41×C61—22no—
213C2×Q8×C61C22×C411yescharacteristic
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61C22×C411yescharacteristic
217C2×D4×C61C22×C411yescharacteristic
218C22×C4×C61—21no—
219C22×C4×C61C22×C411yescharacteristic
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C22×Dic61—21no—
227C22×Dic61#4111yescharacteristic
228#11758226—22no—
229#11758226—22no—
230Q8×D61—21no—
231Q8×D61—21no—
232Q8×D61C2×D412yes—
233Q8×D61#4112yes—
234#11758224—24no—
235#11758224—24no—
236#11758224—22no—
237#11758224—22no—
238D4×D61—24no—
239D4×D61—24no—
240D4×D61—21no—
241D4×D61—21no—
242D4×D61—21no—
243D4×D61—21no—
244D4×D61—21no—
245D4×D61—21no—
246D4×D61—42no—
247D4×D61—42no—
248D4×D61C2×D412yes—
249D4×D61#4112yes—
250#11758222—24no—
251#11758222—24no—
252#11758222—22no—
253#11758222—22no—
254C2×D244—21no—
255C2×D244—21no—
256C2×D244C22×C411yescharacteristic
257C2×D244C22×C411yescharacteristic
258C2×C4×D61—24no—
259C2×C4×D61—24no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61C22×C411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61#4111yescharacteristic
271C2×C4×D61C2411yescharacteristic
272C2×Dic122—21no—
273C2×Dic122C22×C411yescharacteristic
274C22⋊#6923—24no—
275C22⋊#6923—24no—
276C22⋊#6923—24no—
277C22⋊#6923—42no—
278C22⋊#6923—42no—
279C22⋊#6923—42no—
280C22⋊#6923—42no—
281C2×#92420—21no—
282C2×#92420—21no—
283C4⋊#6923—24no—
284C4⋊#6923—24no—
285C4⋊#6923—21no—
286C4⋊#6923—21no—
287C4⋊#6923—21no—
288C4⋊#6923—21no—
289C4⋊#6923—21no—
290C4⋊#6923—21no—
291C4⋊#6923—42no—
292C4⋊#6923C2×D412yes—
293C4⋊#6923C2×D412yes—
294C4×#6923—24no—
295C4×#6923—24no—
296C4×#6923—22no—
297C4×#6923—24no—
298C4×#6923—22no—
299C4×#6923—21no—
300C4×#6923—21no—
301C4×#6923—42no—
302C4×#6923C2×D412yes—
303C4×#6923C2×D412yes—
304D61⋊C8—21no—
305D61⋊C8—21no—
306D61⋊C8—21no—
307D61⋊C8—21no—
308SD16×C61—22no—
309D8×C61—22no—
310C2×C8×C61C22×C411yescharacteristic
311C2×C8×C61C22×C411yescharacteristic
312C4⋊C4×C61C22×C411yescharacteristic
313C22⋊C4×C61—21no—
314C22⋊Dic61—21no—
315#11758201—22no—
316#11758200—22no—
317#11758199—22no—
318#11758199—22no—
319#11758198—21no—
320#11758198—21no—
321C4⋊Dic61C22×C411yescharacteristic
322#11758196—21no—
323C2×#92418C22×C411yescharacteristic
324C2×#92418C22×C411yescharacteristic
325D488—22no—
326#11758190—22no—
327C8×D61—21no—
328C8×D61—21no—
329C8×D61—21no—
330C8×D61—21no—
331C23×C61—21no—
332C23×C61—21no—
333C23×C61C4×D411yescharacteristic
334C22×D61—21no—
335C22×D61—21no—
336C22×D61—22no—
337C22×D61—21no—
338C22×D61—22no—
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61C4×D411yescharacteristic
355C22×D61C22×D411yescharacteristic
356C2×#6923—21no—
357C2×#6923—21no—
358C2×#6923—21no—
359C2×#6923—21no—
360C2×#6923—21no—
361C2×#6923—21no—
362C2×#6923—21no—
363C2×#6923—22no—
364C2×#6923—22no—
365C2×#6923—21no—
366C2×#6923—21no—
367C2×#6923—44no—
368C2×#6923—44no—
369C2×#6923—48no—
370C2×#6923—48no—
371C2×#6923—41no—
372C2×#6923—41no—
373C2×#6923—41no—
374C2×#6923—41no—
375C2×#6923—41no—
376C2×#6923—41no—
377C2×#6923—41no—
378C2×#6923—41no—
379C2×#6923—41no—
380C2×#6923—41no—
381C2×#6923—84no—
382C2×#6923#12012yes—
383C2×#6923#12012yes—
384C2×#6923AGL(1,ℤ/8)12yes—
385Q8×C61—21no—
386Q8×C61C4×D412yescomplemented
387D4×C61—24no—
388D4×C61—21no—
389D4×C61—21no—
390D4×C61—21no—
391D4×C61—42no—
392D4×C61C4×D412yescomplemented
393C2×C4×C61—24no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61C4×D411yescharacteristic
399C2×C4×C61C23×C411yescharacteristic
400C22⋊D61—24no—
401C22⋊D61—24no—
402C22⋊D61—22no—
403C22⋊D61—22no—
404C22⋊D61—42no—
405C22⋊D61—42no—
406C22⋊D61—41no—
407C22⋊D61—41no—
408C2×Dic61—24no—
409C2×Dic61—21no—
410C2×Dic61—21no—
411C2×Dic61—21no—
412C2×Dic61—21no—
413C2×Dic61C4×D411yescharacteristic
414C2×Dic61C2×#4111yescharacteristic
415D244—24no—
416D244—21no—
417D244—21no—
418D244—21no—
419D244—42no—
420D244C4×D412yescomplemented
421C4×D61—24no—
422C4×D61—24no—
423C4×D61—21no—
424C4×D61—22no—
425C4×D61—21no—
426C4×D61—22no—
427C4×D61—21no—
428C4×D61—21no—
429C4×D61—21no—
430C4×D61—21no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61C22×D411yescharacteristic
434C4×D61C22×D411yescharacteristic
435C4×D61C2×#4111yescharacteristic
436C4×D61C2×#4111yescharacteristic
437Dic122—21no—
438Dic122—22no—
439Dic122—22no—
440Dic122C4×D412yescomplemented
441#92420—41no—
442#92420—41no—
443C8×C61—21no—
444C8×C61—21no—
445#92418—21no—
446#92418—21no—
447#21456—611nomaximal, Sylow
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—22no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61C2×C4×D411yescharacteristic
458C2×D61—21no—
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—22no—
462C2×D61—41no—
463C2×D61—41no—
464C2×D61—41no—
465C2×D61—42no—
466C2×D61—41no—
467C2×D61—42no—
468C2×D61—41no—
469C2×D61—42no—
470C2×D61—41no—
471C2×D61—42no—
472C2×D61—41no—
473C2×D61—41no—
474C2×D61—41no—
475C2×D61—81no—
476C2×D61—81no—
477C2×D61—81no—
478C2×D61—81no—
479C2×D61C2×#12011yescharacteristic
480C2×D61#52511yescharacteristic
481C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
482C2×D61#57511yescharacteristic
483C2×D61#57511yescharacteristic
484C2×D61#57511yescharacteristic
485#6923—22no—
486#6923—22no—
487#6923—22no—
488#6923—41no—
489#6923—42no—
490#6923—42no—
491#6923—81no—
492#6923—81no—
493C4×C61—22no—
494C4×C61—21no—
495C4×C61—41no—
496C4×C61C2×C4×D411yescharacteristic
497C4×C61C2×C4×D411yescharacteristic
498Dic61—22no—
499Dic61—21no—
500Dic61—41no—
501Dic61#52511yescharacteristic
502Dic61#52511yescharacteristic
503C2×C4×#41—611no—
504C2×#449—611no—
505C2×#442—611no—
506C2×#440—611no—
507C4×#121—611no—
508#1880—611no—
509#1879—611no—
510#1875—611no—
511#1865—611no—
512#1862—611no—
513#1854—611no—
514#1788—611no—
515#1763—611no—
516#1762—611no—
517#1749—611no—
518C2×C61—41no—
519C2×C61—42no—
520C2×C61—81no—
521C2×C61C4×#12011yescharacteristic
522C2×C61#294311yescharacteristic
523C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
524D61—41no—
525D61—42no—
526D61—81no—
527D61#300511yescharacteristic
528D61#300611yescharacteristic
529D61#311111yescharacteristic
530D61#311511yescharacteristic
531C22×#41—611no—
532C22×SD16—611no—
533C22×D8—611no—
534C2×#121—611no—
535C4×#41—1224no—
536C4×#41—1224no—
537C2×C4×Q8—611no—
538C2×C4×Q8—611no—
539C2×C4×D4—611no—
540C2×C4×D4—611no—
541C2×C4×D4—611no—
542C2×C4×D4—1221no—
543C2×C4×D4—1221no—
544C2×C4×D4—1221no—
545C2×#117—611no—
546C2×#117—1221no—
547C22×C42—611no—
548C22×C42—1221no—
549#449—611no—
550#449—611no—
551#449—611no—
552#449—611no—
553#449—611no—
554#449—611no—
555#449—611no—
556#449#692311yescharacteristic, complemented
557#442—1224no—
558#440—1224no—
559C2×#107—611no—
560C2×#106—611no—
561C2×#103—611no—
562C2×#103—611no—
563C2×#103—611no—
564C2×#102—611no—
565C2×#102—611no—
566C2×#102—611no—
567C2×#102—611no—
568C2×#102—611no—
569C2×C22⋊C8—611no—
570C2×C22⋊C8—611no—
571C2×#97—611no—
572C2×#97—611no—
573#390—611no—
574#389—611no—
575#388—1221no—
576#386—1221no—
577#380—611no—
578C4×C4⋊C4—611no—
579C4×C22⋊C4—1221no—
580#340—611no—
581#340—611no—
582#340—611no—
583#340—611no—
584#336—611no—
585#336—611no—
586C61#2145611yescharacteristic, complemented, Sylow
587C2×#41—611no—
588C2×#41—611no—
589C2×#41—611no—
590C2×#41—1221no—
591C2×#41—1221no—
592C2×#41—1222no—
593C2×#41—1222no—
594C2×#41—1222no—
595C2×#41—1222no—
596C2×#41C2×#692311yescharacteristic, complemented
597C22×Q8—611no—
598C22×D4—611no—
599C22×D4—611no—
600C22×D4—1221no—
601C22×D4—1221no—
602C23×C4—611no—
603C23×C4—611no—
604C23×C4—611no—
605C23×C4—1221no—
606C23×C4—1221no—
607C23×C4—1221no—
608C23×C4—1221no—
609C2×SD16—611no—
610C2×SD16—611no—
611C2×SD16—611no—
612C2×SD16—1222no—
613C2×SD16—1222no—
614C2×SD16C2×#692311yescharacteristic, complemented
615C2×D8—611no—
616C2×D8—611no—
617C2×D8—611no—
618C2×D8—1222no—
619C2×D8—1222no—
620C2×D8C2×#692311yescharacteristic, complemented
621C22×C8—611no—
622C22×C8—611no—
623C22×C8—611no—
624C22×C8—611no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—1221no—
629#121—1221no—
630#121C2×#692311yescharacteristic, complemented
631C4×Q8—614no—
632C4×Q8—1222no—
633C4×Q8—1222no—
634C4×Q8—1222no—
635C4×D4—614no—
636C4×D4—1222no—
637C4×D4—1222no—
638C4×D4—1222no—
639C4×D4—1222no—
640C4×D4—1222no—
641C4×D4—1228no—
642C4×D4—1228no—
643C4×D4—2444no—
644#117—1222no—
645#117—1222no—
646#117—1228no—
647C2×C4⋊C4—611no—
648C2×C4⋊C4—611no—
649C2×C4⋊C4—611no—
650C2×C4⋊C4—611no—
651C2×C4⋊C4—611no—
652C2×C4⋊C4—1221no—
653C2×C4⋊C4—1221no—
654C2×C4⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1221no—
659C2×C22⋊C4—1221no—
660C2×C22⋊C4—1221no—
661C2×C22⋊C4—1221no—
662C2×C22⋊C4—1221no—
663C2×C42—611no—
664C2×C42—611no—
665C2×C42—611no—
666C2×C42—611no—
667C2×C42—1222no—
668C2×C42—1222no—
669C2×C42—1221no—
670C2×C42—1221no—
671C2×C42—1221no—
672C2×C42—1228no—
673C2×C42—1221no—
674#107—1222no—
675#106—1222no—
676#103—611no—
677#103—611no—
678#103—611no—
679#103—1222no—
680#103—1222no—
681#103C2×#692311yescharacteristic, complemented
682#102—611no—
683#102—611no—
684#102—611no—
685#102—1222no—
686#102—1222no—
687#102—1222no—
688#102—1222no—
689#102C2×#692311yescharacteristic, complemented
690C22⋊C8—611no—
691C22⋊C8—611no—
692C22⋊C8—611no—
693C22⋊C8—1221no—
694C22⋊C8—1221no—
695C22⋊C8C2×#692311yescharacteristic, complemented
696#97—1222no—
697#97—1222no—
698#95—1221no—
699#95—1221no—
700#95—1221no—
701C24—611no—
702C24—1221no—
703C24—1221no—
704#41—22no—
705#41—22no—
706#41—1222no—
707#41—1222no—
708#41—1224no—
709#41—1224no—
710#41—1222no—
711#41—1224no—
712#41—1224no—
713#41—1222no—
714#41—1222no—
715#41—1222no—
716C2×Q8—612no—
717C2×Q8—612no—
718C2×Q8—611no—
719C2×Q8—1221no—
720C2×Q8—1221no—
721C2×Q8—1221no—
722C2×Q8C22×#692311yescharacteristic
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—612no—
726C2×D4—612no—
727C2×D4—611no—
728C2×D4—611no—
729C2×D4—1221no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1224no—
740C2×D4—1224no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—1221no—
745C2×D4—2442no—
746C2×D4—2442no—
747C2×D4C22×#692311yescharacteristic
748C2×D4C22×#692311yescharacteristic
749C22×C4—21no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1224no—
766C22×C4—1224no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1224no—
770C22×C4—1222no—
771C22×C4—1222no—
772C22×C4—1222no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1224no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—2442no—
780C22×C4—2442no—
781C22×C4—2441no—
782C22×C4—2441no—
783C22×C4—2441no—
784C22×C4—2442no—
785C22×C4—2442no—
786C22×C4—2442no—
787C22×C4—2442no—
788C22×C4—2442no—
789C22×C4C22×#692311yescharacteristic
790SD16—22no—
791SD16—1222no—
792SD16—1222no—
793SD16—1222no—
794D8—22no—
795D8—1222no—
796D8—1222no—
797D8—1222no—
798C2×C8—611no—
799C2×C8—611no—
800C2×C8—1221no—
801C2×C8—1221no—
802C2×C8—1221no—
803C2×C8—1221no—
804C2×C8—1221no—
805C2×C8—1221no—
806C2×C8—1221no—
807C2×C8—1221no—
808C2×C8—1221no—
809C2×C8—1221no—
810C2×C8C22×#692311yescharacteristic
811C2×C8C22×#692311yescharacteristic
812C4⋊C4—612no—
813C4⋊C4—612no—
814C4⋊C4—611no—
815C4⋊C4—1221no—
816C4⋊C4—1221no—
817C4⋊C4—1221no—
818C4⋊C4—1224no—
819C4⋊C4—1221no—
820C4⋊C4—1221no—
821C4⋊C4—1221no—
822C4⋊C4—1221no—
823C4⋊C4—1224no—
824C4⋊C4—2442no—
825C4⋊C4C22×#692311yescharacteristic
826C22⋊C4—21no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1224no—
830C22⋊C4—1224no—
831C22⋊C4—1224no—
832C22⋊C4—1221no—
833C22⋊C4—2442no—
834C22⋊C4—2442no—
835C22⋊C4—2442no—
836C22⋊C4—2442no—
837C42—612no—
838C42—612no—
839C42—1222no—
840C42—1222no—
841C42—1221no—
842C42—1221no—
843C42—1224no—
844C42—1224no—
845C42—1224no—
846C42—2442no—
847C23—21no—
848C23—21no—
849C23—611no—
850C23—611no—
851C23—1222no—
852C23—1221no—
853C23—1221no—
854C23—1222no—
855C23—1221no—
856C23—1221no—
857C23—1221no—
858C23—1221no—
859C23—1221no—
860C23—1221no—
861C23—2441no—
862C23—2441no—
863C23—2441no—
864C23—2441no—
865C23—2441no—
866C23—2441no—
867C23—2441no—
868C23—2441no—
869C23—2441no—
870C23—2441no—
871C23D4×#692311yescharacteristic
872Q8—21no—
873Q8—612no—
874Q8—1222no—
875Q8—1222no—
876Q8—1221no—
877Q8D4×#692312yescomplemented
878D4—24no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—42no—
883D4—612no—
884D4—1224no—
885D4—1222no—
886D4—1222no—
887D4—1224no—
888D4—1224no—
889D4—1221no—
890D4—1221no—
891D4—1221no—
892D4—2442no—
893D4—2441no—
894D4—2441no—
895D4—2442no—
896D4—2442no—
897D4D4×#692312yescomplemented
898C2×C4—24no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—611no—
904C2×C4—611no—
905C2×C4—611no—
906C2×C4—611no—
907C2×C4—611no—
908C2×C4—612no—
909C2×C4—612no—
910C2×C4—612no—
911C2×C4—611no—
912C2×C4—1221no—
913C2×C4—1221no—
914C2×C4—1221no—
915C2×C4—1222no—
916C2×C4—1221no—
917C2×C4—1222no—
918C2×C4—1224no—
919C2×C4—1224no—
920C2×C4—1221no—
921C2×C4—1221no—
922C2×C4—1224no—
923C2×C4—1221no—
924C2×C4—1221no—
925C2×C4—1221no—
926C2×C4—1221no—
927C2×C4—1221no—
928C2×C4—1221no—
929C2×C4—1221no—
930C2×C4—1221no—
931C2×C4—1221no—
932C2×C4—1222no—
933C2×C4—1222no—
934C2×C4—1221no—
935C2×C4—1221no—
936C2×C4—1221no—
937C2×C4—1221no—
938C2×C4—4884no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2444no—
942C2×C4—2444no—
943C2×C4—2448no—
944C2×C4—2448no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4—2441no—
952C2×C4—2441no—
953C2×C4—2441no—
954C2×C4—2441no—
955C2×C4D4×#692311yescharacteristic
956C2×C4C23×#692311yescharacteristic
957C8—21no—
958C8—21no—
959C8—1221no—
960C8—1221no—
961C8—2441no—
962C8—2441no—
963C22—21no—
964C22—22no—
965C22—21no—
966C22—21no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—611no—
973C22—611no—
974C22—611no—
975C22—611no—
976C22—611no—
977C22—611no—
978C22—1222no—
979C22—1221no—
980C22—1221no—
981C22—1221no—
982C22—4881no—
983C22—4881no—
984C22—4881no—
985C22—4881no—
986C22—2441no—
987C22—2441no—
988C22—2442no—
989C22—2442no—
990C22—2441no—
991C22—2441no—
992C22—2442no—
993C22—2442no—
994C22—2441no—
995C22—2441no—
996C22—2441no—
997C22—2441no—
998C22—2441no—
999C22C2×D4×#692311yescharacteristic
1000C4—21no—
1001C4—22no—
1002C4—41no—
1003C4—611no—
1004C4—611no—
1005C4—1222no—
1006C4—1222no—
1007C4—1222no—
1008C4—1221no—
1009C4—1222no—
1010C4—4881no—
1011C4—4881no—
1012C4—2441no—
1013C4—2442no—
1014C4—2442no—
1015C4—2441no—
1016C4C2×D4×#692311yescharacteristic
1017C4C2×D4×#692311yescharacteristic
1018C2—41no—
1019C2—42no—
1020C2—81no—
1021C2—611no—
1022C2—611no—
1023C2—611no—
1024C2—611no—
1025C2—4881no—
1026C2—2441no—
1027C2—2442no—
1028C2#120×#692311yescharacteristic
1029C2#2146257311yescharacteristic
1030C2AGL(1,ℤ/8)×#692311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#449C4
socleC22×C61C2×C4×D4
prime radical#449×D61C2
cosocleC2×C4×D61C24
hypercenter#449#6923
hypocenterC61#21456
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#41×#6923C2semidirect
2. C2×#16840803C2semidirect
3. C2×#16840801C2semidirect
4. #121×#6923C2semidirect
5. #21461815C2semidirect
6. #21461814C2semidirect
7. #21461807C2semidirect
8. #21461785C2semidirect
9. #21461782C2semidirect
10. #21461770C2semidirect
11. #21461659C2semidirect
12. #21461592C2semidirect
13. #21461590C2semidirect
14. #21461547C2semidirect
60. #16839910C4semidirect
61. #16839909C4semidirect
62. #16839908C4semidirect
63. #16839907C4semidirect
64. #16839906C4semidirect
65. #16839905C4semidirect
66. #16839904C4semidirect
70. C61×#449C4semidirect
81. Q8×#6923D4semidirect
90. D4×#6923D4semidirect
134. C2×#11758226C2×C4semidirect
136. C2×#11758222C2×C4semidirect
138. C2×#11758224C2×C4semidirect
150. C2×#11758190C2×C4semidirect
151. C2×#11758200C2×C4semidirect
152. C2×#11758201C2×C4semidirect
155. C2×D488C2×C4semidirect
156. C2×#11758199C2×C4semidirect
157. C2×#11758199C2×C4semidirect
162. #14519752C2×C4semidirect
163. #14519751C2×C4semidirect
166. #14519748C2×C4semidirect
169. #14519702C2×C4semidirect
170. #14519701C2×C4semidirect
171. #14519700C2×C4semidirect
172. #14519699C2×C4semidirect
173. #14519698C2×C4semidirect
174. #14519697C2×C4semidirect
175. C22⋊#92418C2×C4semidirect
176. #14519689C2×C4semidirect
177. #14519689C2×C4semidirect
178. C2×#41×C61C2×C4semidirect
179. C2×SD16×C61C2×C4semidirect
180. C2×D8×C61C2×C4semidirect
181. #121×C61C2×C4semidirect
182. #103×C61C2×C4semidirect
183. #102×C61C2×C4semidirect
184. C22⋊C8×C61C2×C4semidirect
386. Q8×C61C4×D4semidirect
392. D4×C61C4×D4semidirect
420. D244C4×D4semidirect
440. Dic122C4×D4semidirect
556. #449#6923semidirect
586. C61#21456semidirect
596. C2×#41C2×#6923semidirect
614. C2×SD16C2×#6923semidirect
620. C2×D8C2×#6923semidirect
630. #121C2×#6923semidirect
681. #103C2×#6923semidirect
689. #102C2×#6923semidirect
695. C22⋊C8C2×#6923semidirect
877. Q8D4×#6923semidirect
897. D4D4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#41×#69232
C2×#168408032
C2×#168408012
#121×#69232
#214618152
#214618142
#214618072
#214617852
#214617822
#214617702
#214616592
#214615922
#214615902
#214615472
#449×D612
#2145661