Finite Group Databasebeta

← #30622260

Subgroups — #30622260

Order 15616.

1082 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×#6923C211yesmaximal, characteristic, complemented
2C2×#16840773C211yesmaximal, characteristic, complemented
3#21462346C211yesmaximal, characteristic, complemented
4#21462344C211yesmaximal, characteristic, complemented
5#21461968C211yesmaximal, characteristic, complemented
6#21461922C211yesmaximal, characteristic, complemented
7#21461897C211yesmaximal, characteristic, complemented
8#21461896C211yesmaximal, characteristic, complemented
9#21461807C211yesmaximal, characteristic, complemented
10#21461806C211yesmaximal, characteristic, complemented
11#21461784C211yesmaximal, characteristic, complemented
12#21461782C211yesmaximal, characteristic, complemented
13#21461635C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15#469×D61C211yesmaximal, characteristic
16C2×D4×#6923—21no—
17C2×D4×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×#14519856C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21D8×#6923—24no—
22#16840773—24no—
23C2×#14519846C2211yescharacteristic
24C2×#14519846C2211yescharacteristic
25C2×#14519845C2211yescharacteristic
26C2×#14519845C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31D61⋊(C22⋊C8)C2211yescharacteristic
32C2×#14519831C2211yescharacteristic
33C2×C8×#6923C2211yescharacteristic
34#16840714—21no—
35#16840714C2211yescharacteristic
36#16840714C2211yescharacteristic
37#16840713C2211yescharacteristic
38#16840713C2211yescharacteristic
39#16840712—21no—
40#16840712—21no—
41#16840710—21no—
42#16840710—21no—
43#16840709—21no—
44C4⋊C4×#6923C2211yescharacteristic
45C4⋊C4×#6923C2211yescharacteristic
46C22⋊C4×#6923—21no—
47C4×C22⋊#6923C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×D8×D61C2211yescharacteristic
55C2×M16×D61C2211yescharacteristic
56#121×D61C2211yescharacteristic
57#121×D61C2211yescharacteristic
58#16840016C411yescharacteristic, complemented
59#16840015C411yescharacteristic, complemented
60#16840014C411yescharacteristic, complemented
61#16840014C411yescharacteristic, complemented
62#16840013C411yescharacteristic, complemented
63#16840013C411yescharacteristic, complemented
64#16840012C411yescharacteristic, complemented
65#106×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67#102×D61C2211yescharacteristic
68C61×#469C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C23×#6923—21no—
72C2×D61⋊C8C2311yescharacteristic
73C2×D61⋊C8C2311yescharacteristic
74D4×#6923—22no—
75D4×#6923—22no—
76D4×#6923—41no—
77D4×#6923—41no—
78D4×#6923—44no—
79#14519856—22no—
80#14519856—41no—
81C2×C4⋊#6923—22no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923—41no—
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923—21no—
97C2×C22⋊#6923D411yescharacteristic
98C2×C22⋊#6923D411yescharacteristic
99C2×C4×#6923—21no—
100C2×C4×#6923—21no—
101C2×C4×#6923—21no—
102C2×C4×#6923C2311yescharacteristic
103C2×C4×#6923C2311yescharacteristic
104#14519846—22no—
105#14519846D414yescomplemented
106#14519845—22no—
107#14519845—22no—
108#14519839—22no—
109#14519839—22no—
110#14519839—41no—
111#14519839—41no—
112#14519834—21no—
113C22⋊#92420—21no—
114#14519831—22no—
115C8×#6923—22no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4D411yescharacteristic
121(C2×#6923)⋊C4D411yescharacteristic
122C2×D4×D61—21no—
123C2×D4×D61—21no—
124C2×D4×D61C2311yescharacteristic
125C2×D4×D61C2311yescharacteristic
126C22×C4×D61C2311yescharacteristic
127C2×D488C2×C411yescharacteristic, complemented
128C2×#11758199C2×C411yescharacteristic, complemented
129C2×#11758199C2×C411yescharacteristic, complemented
130D8×D61—22no—
131D8×D61—22no—
132C2×#11758194C2×C411yescharacteristic, complemented
133C2×#11758189C2×C411yescharacteristic, complemented
134C2×#11758189C2×C411yescharacteristic, complemented
135M16×D61—22no—
136M16×D61—22no—
137C2×C8×D61C2311yescharacteristic
138C2×C8×D61C2311yescharacteristic
139#14519752C2×C411yescharacteristic, complemented
140#14519752C2×C411yescharacteristic, complemented
141#14519751C2×C411yescharacteristic, complemented
142#14519751C2×C411yescharacteristic, complemented
143#14519750—21no—
144#14519750—21no—
145#14519749—21no—
146#14519749—21no—
147#14519748C2×C411yescharacteristic, complemented
148#14519748C2×C411yescharacteristic, complemented
149C4⋊C4×D61C2311yescharacteristic
150C4⋊C4×D61C2311yescharacteristic
151C22⋊C4×D61—21no—
152C22⋊C4×D61—21no—
153#14519709C2×C411yescharacteristic, complemented
154#14519708C2×C411yescharacteristic, complemented
155#14519708C2×C411yescharacteristic, complemented
156#14519699C2×C411yescharacteristic, complemented
157#14519699C2×C411yescharacteristic, complemented
158#14519698C2×C411yescharacteristic, complemented
159#14519698C2×C411yescharacteristic, complemented
160#14519697C2×C411yescharacteristic, complemented
161#14519697C2×C411yescharacteristic, complemented
162C2×D8×C61C2×C411yescharacteristic, complemented
163C2×M16×C61C2×C411yescharacteristic, complemented
164#121×C61C2×C411yescharacteristic, complemented
165#121×C61C2×C411yescharacteristic, complemented
166#106×C61C2×C411yescharacteristic, complemented
167#102×C61C2×C411yescharacteristic, complemented
168#102×C61C2×C411yescharacteristic, complemented
169C23×D61—21no—
170C23×D61—21no—
171C23×D61C2×D411yescharacteristic
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—21no—
175C22×#6923—21no—
176C22×#6923—42no—
177C22×#6923—42no—
178C22×#6923—42no—
179C22×#6923—42no—
180C22×#6923—42no—
181C22×#6923—42no—
182C22×#6923—81no—
183C22×#6923—81no—
184C22×#6923—81no—
185C22×#6923C2×D411yescharacteristic
186C22×#6923C2×D411yescharacteristic
187C22×#6923C2×D411yescharacteristic
188C22×#6923C2×D411yescharacteristic
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61C22×C411yescharacteristic
192C2×D4×C61C22×C411yescharacteristic
193C22×C4×C61C22×C411yescharacteristic
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C22×Dic61#4111yescharacteristic
201D4×D61—21no—
202D4×D61—21no—
203D4×D61—21no—
204D4×D61—21no—
205D4×D61—21no—
206D4×D61—21no—
207D4×D61—21no—
208D4×D61—21no—
209D4×D61—42no—
210D4×D61—42no—
211D4×D61—81no—
212D4×D61—81no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244C22×C411yescharacteristic
216C2×D244C22×C411yescharacteristic
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61C22×C411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61#4111yescharacteristic
226C2×C4×D61C2411yescharacteristic
227C22⋊#6923—22no—
228C22⋊#6923—41no—
229C22⋊#6923—42no—
230C22⋊#6923—42no—
231C22⋊#6923—42no—
232C22⋊#6923—42no—
233C22⋊#6923—42no—
234C22⋊#6923—81no—
235C22⋊#6923—81no—
236C2×#92420—21no—
237C2×#92420—21no—
238C4⋊#6923—21no—
239C4⋊#6923—21no—
240C4⋊#6923—21no—
241C4⋊#6923—21no—
242C4⋊#6923—21no—
243C4⋊#6923—21no—
244C4⋊#6923—42no—
245C4⋊#6923—42no—
246C4⋊#6923—81no—
247C4⋊#6923C2×D412yes—
248C4⋊#6923C2×D412yes—
249C4×#6923—21no—
250C4×#6923—21no—
251C4×#6923—21no—
252C4×#6923—21no—
253C4×#6923—42no—
254C4×#6923—42no—
255C4×#6923—81no—
256D61⋊C8—21no—
257D61⋊C8—21no—
258D61⋊C8—21no—
259D61⋊C8—21no—
260D8×C61—22no—
261M16×C61—22no—
262C2×C8×C61C22×C411yescharacteristic
263C2×C8×C61C22×C411yescharacteristic
264C4⋊C4×C61C22×C411yescharacteristic
265C4⋊C4×C61C22×C411yescharacteristic
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C22⋊Dic61—21no—
269C22⋊Dic61—21no—
270#11758199—22no—
271#11758199—22no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276C4⋊Dic61C22×C411yescharacteristic
277C4⋊Dic61C22×C411yescharacteristic
278#11758196—21no—
279#11758196—21no—
280#11758194—22no—
281C2×#92418C22×C411yescharacteristic
282C2×#92418C22×C411yescharacteristic
283D488—22no—
284#11758189—22no—
285#11758189—22no—
286C8×D61—21no—
287C8×D61—21no—
288C8×D61C2×D412yes—
289C8×D61#4112yes—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61C4×D411yescharacteristic
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61C4×D411yescharacteristic
314C22×D61C22×D411yescharacteristic
315C2×#6923—21no—
316C2×#6923—21no—
317C2×#6923—21no—
318C2×#6923—22no—
319C2×#6923—22no—
320C2×#6923—21no—
321C2×#6923—21no—
322C2×#6923—21no—
323C2×#6923—21no—
324C2×#6923—21no—
325C2×#6923—21no—
326C2×#6923—21no—
327C2×#6923—21no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333C2×#6923—41no—
334C2×#6923—41no—
335C2×#6923—41no—
336C2×#6923—41no—
337C2×#6923—41no—
338C2×#6923—84no—
339C2×#6923—84no—
340C2×#6923—84no—
341C2×#6923AGL(1,ℤ/8)12yes—
342D4×C61—21no—
343D4×C61—21no—
344D4×C61—21no—
345D4×C61—21no—
346D4×C61—42no—
347D4×C61—81no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61C4×D411yescharacteristic
353C2×C4×C61C23×C411yescharacteristic
354C22⋊D61—42no—
355C22⋊D61—42no—
356C22⋊D61—41no—
357C22⋊D61—41no—
358C22⋊D61—41no—
359C22⋊D61—41no—
360C22⋊D61—81no—
361C22⋊D61—81no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61C4×D411yescharacteristic
367C2×Dic61C2×#4111yescharacteristic
368D244—21no—
369D244—21no—
370D244—21no—
371D244—21no—
372D244—42no—
373D244—81no—
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—21no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—41no—
381C4×D61—41no—
382C4×D61—41no—
383C4×D61—41no—
384C4×D61C22×D411yescharacteristic
385C4×D61C2×#4111yescharacteristic
386C4×D61H(5,𝔽2)11yescharacteristic
387C4×D612−1+411yescharacteristic
388#92420—41no—
389#92420—41no—
390C8×C61—21no—
391C8×C61C4×D412yescomplemented
392#92418—21no—
393#92418C4×D412yescomplemented
394#23037—611nomaximal, Sylow
395C22×C61—21no—
396C22×C61—21no—
397C22×C61—21no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61C2×C4×D411yescharacteristic
405C2×D61—21no—
406C2×D61—21no—
407C2×D61—21no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61—41no—
414C2×D61—41no—
415C2×D61—41no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—81no—
419C2×D61—81no—
420C2×D61—81no—
421C2×D61—81no—
422C2×D61—81no—
423C2×D61—81no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61D4211yescharacteristic
427C2×D61#54711yescharacteristic
428C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
429C2×D61#57511yescharacteristic
430C2×D61#57611yescharacteristic
431C2×D61#57711yescharacteristic
432#6923—22no—
433#6923—41no—
434#6923—41no—
435#6923—42no—
436#6923—42no—
437#6923—41no—
438#6923—81no—
439#6923—81no—
440C4×C61—21no—
441C4×C61—41no—
442C4×C61—41no—
443C4×C61C2×C4×D411yescharacteristic
444C4×C61#52011yescharacteristic
445Dic61—21no—
446Dic61—41no—
447Dic61—41no—
448Dic61#54811yescharacteristic
449Dic61#55311yescharacteristic
450C2×#469—611no—
451C2×C4×D8—611no—
452C2×#428—611no—
453#2363—611no—
454#2361—611no—
455#1972—611no—
456#1941—611no—
457#1926—611no—
458#1925—611no—
459#1875—611no—
460#1874—611no—
461#1864—611no—
462#1862—611no—
463#1776—611no—
464#1753—611no—
465C2×C61—41no—
466C2×C61—81no—
467C2×C61—81no—
468C2×C61#236111yescharacteristic
469C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
470C2×C61#294611yescharacteristic
471D61—41no—
472D61—81no—
473D61—81no—
474D61#326411yescharacteristic
475D61#327111yescharacteristic
476D61#335411yescharacteristic
477D61#335511yescharacteristic
478C22×D8—611no—
479C22×M16—611no—
480C2×#121—611no—
481C2×#121—611no—
482C2×C4×D4—611no—
483C2×C4×D4—611no—
484C2×C4×D4—1221no—
485C2×#117—611no—
486C22×C4⋊C4—611no—
487#469—611no—
488#469—611no—
489#469—611no—
490#469—611no—
491#469—611no—
492#469—611no—
493#469—611no—
494#469#692311yescharacteristic, complemented
495C4×D8—1224no—
496#428—1224no—
497C2×#107—611no—
498C2×#107—611no—
499C2×#106—611no—
500C2×#106—611no—
501C2×#106—611no—
502C2×#102—611no—
503C2×#102—611no—
504C2×#102—611no—
505C2×#102—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×C22⋊C8—611no—
509C2×#97—611no—
510C2×C4×C8—611no—
511#390—611no—
512#390—611no—
513#390—1221no—
514#389—611no—
515#389—611no—
516#388—1221no—
517#388—1221no—
518#386—1221no—
519#386—1221no—
520#385—1221no—
521C4×C4⋊C4—611no—
522C4×C4⋊C4—611no—
523C4×C22⋊C4—611no—
524C4×C22⋊C4—1221no—
525#340—611no—
526#340—611no—
527#340—611no—
528#340—611no—
529#336—611no—
530#336—611no—
531C61#2303711yescharacteristic, complemented, Sylow
532C22×D4—611no—
533C22×D4—611no—
534C22×D4—1221no—
535C22×D4—1221no—
536C23×C4—611no—
537C23×C4—1221no—
538C23×C4—1221no—
539C23×C4—1221no—
540C2×D8—611no—
541C2×D8—611no—
542C2×D8—611no—
543C2×D8—1222no—
544C2×D8—1222no—
545C2×D8C2×#692311yescharacteristic, complemented
546C2×M16—611no—
547C2×M16—611no—
548C2×M16—611no—
549C2×M16—1222no—
550C2×M16—1222no—
551C2×M16C2×#692311yescharacteristic, complemented
552C22×C8—611no—
553C22×C8—611no—
554C22×C8—611no—
555C22×C8—611no—
556#121—611no—
557#121—611no—
558#121—611no—
559#121—611no—
560#121—611no—
561#121—611no—
562#121—1221no—
563#121—1221no—
564#121—1221no—
565#121—1221no—
566#121C2×#692311yescharacteristic, complemented
567#121C2×#692311yescharacteristic, complemented
568C4×D4—1222no—
569C4×D4—1222no—
570C4×D4—2441no—
571C4×D4—2441no—
572C4×D4—2444no—
573#117—1222no—
574#117—2441no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—611no—
577C2×C4⋊C4—611no—
578C2×C4⋊C4—611no—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—611no—
581C2×C4⋊C4—1222no—
582C2×C4⋊C4—1221no—
583C2×C4⋊C4—1221no—
584C2×C4⋊C4—1221no—
585C2×C4⋊C4—2441no—
586C2×C22⋊C4—611no—
587C2×C22⋊C4—611no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C22⋊C4—1221no—
594C2×C22⋊C4—1221no—
595C2×C22⋊C4—1221no—
596C2×C22⋊C4—1221no—
597C2×C42—611no—
598C2×C42—611no—
599C2×C42—1221no—
600C2×C42—1221no—
601C2×C42—1221no—
602#107—614no—
603#107—1222no—
604#106—611no—
605#106—611no—
606#106—611no—
607#106—1222no—
608#106—1222no—
609#106C2×#692311yescharacteristic, complemented
610#102—611no—
611#102—611no—
612#102—611no—
613#102—611no—
614#102—611no—
615#102—611no—
616#102—1222no—
617#102—1222no—
618#102—2441no—
619#102—2441no—
620#102C2×#692311yescharacteristic, complemented
621#102C2×#692311yescharacteristic, complemented
622C22⋊C8—1221no—
623C22⋊C8—1221no—
624#97—1222no—
625C4×C8—1222no—
626#95—611no—
627#95—611no—
628#95—1221no—
629#95—1221no—
630#95—1221no—
631#95—1221no—
632C24—611no—
633C24—1221no—
634C24—1221no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—611no—
638C2×D4—611no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—4881no—
656C2×D4—4881no—
657C2×D4—2442no—
658C2×D4—2442no—
659C2×D4C22×#692311yescharacteristic
660C2×D4C22×#692311yescharacteristic
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—4881no—
681C22×C4—4881no—
682C22×C4—4881no—
683C22×C4—2442no—
684C22×C4—2442no—
685C22×C4—2442no—
686C22×C4—2442no—
687C22×C4—2442no—
688C22×C4—2442no—
689C22×C4C22×#692311yescharacteristic
690D8—22no—
691D8—1222no—
692D8—1222no—
693D8—1222no—
694M16—22no—
695M16—1222no—
696M16—1222no—
697M16—1222no—
698C2×C8—611no—
699C2×C8—612no—
700C2×C8—612no—
701C2×C8—611no—
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×C8C22×#692311yescharacteristic
711C2×C8C22×#692311yescharacteristic
712C4⋊C4—612no—
713C4⋊C4—612no—
714C4⋊C4—611no—
715C4⋊C4—611no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—4881no—
725C4⋊C4—2442no—
726C4⋊C4—2442no—
727C4⋊C4C22×#692311yescharacteristic
728C4⋊C4C22×#692311yescharacteristic
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4—1222no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—4881no—
739C22⋊C4—4881no—
740C22⋊C4—2441no—
741C22⋊C4—2442no—
742C22⋊C4—2442no—
743C22⋊C4—2442no—
744C22⋊C4—2442no—
745C22⋊C4—2442no—
746C42—1221no—
747C42—1221no—
748C42—1221no—
749C42—1221no—
750C42—4881no—
751C42—2442no—
752C42—2442no—
753C23—21no—
754C23—21no—
755C23—611no—
756C23—611no—
757C23—1221no—
758C23—1221no—
759C23—1221no—
760C23—1221no—
761C23—1221no—
762C23—1221no—
763C23—1221no—
764C23—1221no—
765C23—2441no—
766C23—2441no—
767C23—2441no—
768C23—2441no—
769C23—2441no—
770C23—2441no—
771C23—2441no—
772C23—2441no—
773C23—2441no—
774C23—2441no—
775C23—2441no—
776C23—2441no—
777C23D4×#692311yescharacteristic
778D4—21no—
779D4—21no—
780D4—21no—
781D4—21no—
782D4—42no—
783D4—81no—
784D4—1221no—
785D4—1221no—
786D4—1221no—
787D4—1221no—
788D4—4881no—
789D4—4881no—
790D4—4881no—
791D4—2442no—
792D4—2441no—
793D4—2441no—
794D4—2441no—
795D4—2441no—
796D4—2442no—
797D4—2442no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—611no—
803C2×C4—611no—
804C2×C4—611no—
805C2×C4—611no—
806C2×C4—611no—
807C2×C4—612no—
808C2×C4—611no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1222no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1222no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—4884no—
833C2×C4—4884no—
834C2×C4—4884no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4D4×#692311yescharacteristic
850C2×C4C23×#692311yescharacteristic
851C8—21no—
852C8—612no—
853C8—1221no—
854C8—2441no—
855C8—2441no—
856C8D4×#692312yescomplemented
857C22—21no—
858C22—21no—
859C22—21no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—611no—
867C22—611no—
868C22—611no—
869C22—611no—
870C22—611no—
871C22—611no—
872C22—1221no—
873C22—1221no—
874C22—1221no—
875C22—4881no—
876C22—4881no—
877C22—4881no—
878C22—4881no—
879C22—4881no—
880C22—4881no—
881C22—4881no—
882C22—4881no—
883C22—2441no—
884C22—2441no—
885C22—2441no—
886C22—2441no—
887C22—2441no—
888C22—2441no—
889C22—2441no—
890C22—2441no—
891C22—2441no—
892C22—2441no—
893C22C2×D4×#692311yescharacteristic
894C4—21no—
895C4—41no—
896C4—41no—
897C4—611no—
898C4—611no—
899C4—1222no—
900C4—1221no—
901C4—4881no—
902C4—4881no—
903C4—2441no—
904C4—2441no—
905C4—2441no—
906C4—2442no—
907C4—2442no—
908C4—2441no—
909C4—2441no—
910C4C2×D4×#692311yescharacteristic
911C4#1684083111yescharacteristic
912C2—41no—
913C2—81no—
914C2—81no—
915C2—611no—
916C2—611no—
917C2—611no—
918C2—611no—
919C2—4881no—
920C2—4881no—
921C2—2441no—
922C2#2146234411yescharacteristic
923C2AGL(1,ℤ/8)×#692311yescharacteristic
924C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#469C4
socleC22×C61C2×C4×D4
prime radical#469×D61C2
cosocleC2×C4×D61C24
hypercenter#469#6923
hypocenterC61#23037
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×#6923C2semidirect
2. C2×#16840773C2semidirect
3. #21462346C2semidirect
4. #21462344C2semidirect
5. #21461968C2semidirect
6. #21461922C2semidirect
7. #21461897C2semidirect
8. #21461896C2semidirect
9. #21461807C2semidirect
10. #21461806C2semidirect
11. #21461784C2semidirect
12. #21461782C2semidirect
13. #21461635C2semidirect
14. #21461559C2semidirect
58. #16840016C4semidirect
59. #16840015C4semidirect
60. #16840014C4semidirect
61. #16840014C4semidirect
62. #16840013C4semidirect
63. #16840013C4semidirect
64. #16840012C4semidirect
68. C61×#469C4semidirect
105. #14519846D4semidirect
127. C2×D488C2×C4semidirect
128. C2×#11758199C2×C4semidirect
129. C2×#11758199C2×C4semidirect
132. C2×#11758194C2×C4semidirect
133. C2×#11758189C2×C4semidirect
134. C2×#11758189C2×C4semidirect
139. #14519752C2×C4semidirect
140. #14519752C2×C4semidirect
141. #14519751C2×C4semidirect
142. #14519751C2×C4semidirect
147. #14519748C2×C4semidirect
148. #14519748C2×C4semidirect
153. #14519709C2×C4semidirect
154. #14519708C2×C4semidirect
155. #14519708C2×C4semidirect
156. #14519699C2×C4semidirect
157. #14519699C2×C4semidirect
158. #14519698C2×C4semidirect
159. #14519698C2×C4semidirect
160. #14519697C2×C4semidirect
161. #14519697C2×C4semidirect
162. C2×D8×C61C2×C4semidirect
163. C2×M16×C61C2×C4semidirect
164. #121×C61C2×C4semidirect
165. #121×C61C2×C4semidirect
166. #106×C61C2×C4semidirect
167. #102×C61C2×C4semidirect
168. #102×C61C2×C4semidirect
391. C8×C61C4×D4semidirect
393. #92418C4×D4semidirect
494. #469#6923semidirect
531. C61#23037semidirect
545. C2×D8C2×#6923semidirect
551. C2×M16C2×#6923semidirect
566. #121C2×#6923semidirect
567. #121C2×#6923semidirect
609. #106C2×#6923semidirect
620. #102C2×#6923semidirect
621. #102C2×#6923semidirect
856. C8D4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×D8×#69232
C2×#168407732
#214623462
#214623442
#214619682
#214619222
#214618972
#214618962
#214618072
#214618062
#214617842
#214617822
#214616352
#214615592
#469×D612
#2303761