Finite Group Databasebeta

← #30622590

Subgroups — #30622590

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462346C211yesmaximal, characteristic, complemented
2#21462344C211yesmaximal, characteristic, complemented
3#21461911C211yesmaximal, characteristic, complemented
4#21461909C211yesmaximal, characteristic, complemented
5#21461882C211yesmaximal, characteristic, complemented
6#21461882C211yesmaximal, characteristic, complemented
7#21461814C211yesmaximal, characteristic, complemented
8#21461814C211yesmaximal, characteristic, complemented
9#21461807C211yesmaximal, characteristic, complemented
10#21461806C211yesmaximal, characteristic, complemented
11#21461590C211yesmaximal, characteristic, complemented
12#102×#6923C211yesmaximal, characteristic, complemented
13#21461559C211yesmaximal, characteristic, complemented
14#21461507C211yesmaximal, characteristic, complemented
15#469×D61C211yesmaximal, characteristic
16C2×D4×#6923—21no—
17C2×D4×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×#14519856C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21C2×#14519839C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25D61⋊(C22⋊C8)C2211yescharacteristic
26C2×#14519831C2211yescharacteristic
27C2×C8×#6923C2211yescharacteristic
28#16840714—21no—
29#16840714C2211yescharacteristic
30#16840714C2211yescharacteristic
31#16840713C2211yescharacteristic
32#16840713C2211yescharacteristic
33#16840712—21no—
34#16840712—21no—
35#16840710—21no—
36#16840710—21no—
37#16840709—21no—
38C4⋊C4×#6923C2211yescharacteristic
39C4⋊C4×#6923C2211yescharacteristic
40C22⋊C4×#6923—21no—
41C4×C22⋊#6923C2211yescharacteristic
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840636C2211yescharacteristic
45#16840636C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×D8×D61C2211yescharacteristic
53C2×M16×D61C2211yescharacteristic
54#121×D61C2211yescharacteristic
55#121×D61C2211yescharacteristic
56#16840016C411yescharacteristic, complemented
57#16840015C411yescharacteristic, complemented
58#16840014C411yescharacteristic, complemented
59#16840014C411yescharacteristic, complemented
60#16840013C411yescharacteristic, complemented
61#16840013C411yescharacteristic, complemented
62#16840012C411yescharacteristic, complemented
63#106×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#469C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C23×#6923—21no—
70C2×D61⋊C8C2311yescharacteristic
71C2×D61⋊C8C2311yescharacteristic
72D4×#6923—22no—
73D4×#6923—22no—
74D4×#6923—41no—
75D4×#6923—41no—
76D4×#6923—44no—
77#14519856—22no—
78#14519856—41no—
79C2×C4⋊#6923—22no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—41no—
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923D411yescharacteristic
96C2×C22⋊#6923D411yescharacteristic
97C2×C4×#6923—21no—
98C2×C4×#6923—21no—
99C2×C4×#6923—21no—
100C2×C4×#6923C2311yescharacteristic
101C2×C4×#6923C2311yescharacteristic
102#14519839—22no—
103#14519839—22no—
104#14519839—41no—
105#14519839—41no—
106#14519834—21no—
107C22⋊#92420—21no—
108#14519831—41no—
109C8×#6923—41no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4D411yescharacteristic
115(C2×#6923)⋊C4D411yescharacteristic
116C2×D4×D61—21no—
117C2×D4×D61—21no—
118C2×D4×D61C2311yescharacteristic
119C2×D4×D61C2311yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C2×D488C2×C411yescharacteristic, complemented
122C2×#11758199C2×C411yescharacteristic, complemented
123C2×#11758199C2×C411yescharacteristic, complemented
124D8×D61—41no—
125D8×D61—41no—
126C2×#11758194C2×C411yescharacteristic, complemented
127C2×#11758189C2×C411yescharacteristic, complemented
128C2×#11758189C2×C411yescharacteristic, complemented
129M16×D61—41no—
130M16×D61—41no—
131C2×C8×D61C2311yescharacteristic
132C2×C8×D61C2311yescharacteristic
133#14519752C2×C411yescharacteristic, complemented
134#14519752C2×C411yescharacteristic, complemented
135#14519751C2×C411yescharacteristic, complemented
136#14519751C2×C411yescharacteristic, complemented
137#14519750—21no—
138#14519750—21no—
139#14519749—21no—
140#14519749—21no—
141#14519748C2×C411yescharacteristic, complemented
142#14519748C2×C411yescharacteristic, complemented
143C4⋊C4×D61C2311yescharacteristic
144C4⋊C4×D61C2311yescharacteristic
145C22⋊C4×D61—21no—
146C22⋊C4×D61—21no—
147#14519709C2×C411yescharacteristic, complemented
148#14519708C2×C411yescharacteristic, complemented
149#14519708C2×C411yescharacteristic, complemented
150#14519699C2×C411yescharacteristic, complemented
151#14519699C2×C411yescharacteristic, complemented
152#14519698C2×C411yescharacteristic, complemented
153#14519698C2×C411yescharacteristic, complemented
154#14519697C2×C411yescharacteristic, complemented
155#14519697C2×C411yescharacteristic, complemented
156C2×D8×C61C2×C411yescharacteristic, complemented
157C2×M16×C61C2×C411yescharacteristic, complemented
158#121×C61C2×C411yescharacteristic, complemented
159#121×C61C2×C411yescharacteristic, complemented
160#106×C61C2×C411yescharacteristic, complemented
161#102×C61C2×C411yescharacteristic, complemented
162#102×C61C2×C411yescharacteristic, complemented
163C23×D61—21no—
164C23×D61—21no—
165C23×D61C2×D411yescharacteristic
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—21no—
169C22×#6923—21no—
170C22×#6923—42no—
171C22×#6923—42no—
172C22×#6923—42no—
173C22×#6923—42no—
174C22×#6923—42no—
175C22×#6923—42no—
176C22×#6923—81no—
177C22×#6923—81no—
178C22×#6923—81no—
179C22×#6923C2×D411yescharacteristic
180C22×#6923C2×D411yescharacteristic
181C22×#6923C2×D411yescharacteristic
182C22×#6923C2×D411yescharacteristic
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61C22×C411yescharacteristic
186C2×D4×C61C22×C411yescharacteristic
187C22×C4×C61C22×C411yescharacteristic
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C22×Dic61#4111yescharacteristic
195D4×D61—21no—
196D4×D61—21no—
197D4×D61—21no—
198D4×D61—21no—
199D4×D61—21no—
200D4×D61—21no—
201D4×D61—21no—
202D4×D61—21no—
203D4×D61—42no—
204D4×D61—42no—
205D4×D61—81no—
206D4×D61—81no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244C22×C411yescharacteristic
210C2×D244C22×C411yescharacteristic
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61C22×C411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61#4111yescharacteristic
220C2×C4×D61C2411yescharacteristic
221C22⋊#6923—22no—
222C22⋊#6923—41no—
223C22⋊#6923—42no—
224C22⋊#6923—42no—
225C22⋊#6923—42no—
226C22⋊#6923—42no—
227C22⋊#6923—42no—
228C22⋊#6923—81no—
229C22⋊#6923—81no—
230C2×#92420—21no—
231C2×#92420—21no—
232C4⋊#6923—21no—
233C4⋊#6923—21no—
234C4⋊#6923—21no—
235C4⋊#6923—21no—
236C4⋊#6923—21no—
237C4⋊#6923—21no—
238C4⋊#6923—42no—
239C4⋊#6923—42no—
240C4⋊#6923—81no—
241C4⋊#6923#4112yes—
242C4⋊#6923#4112yes—
243C4×#6923—21no—
244C4×#6923—21no—
245C4×#6923—21no—
246C4×#6923—21no—
247C4×#6923—42no—
248C4×#6923—42no—
249C4×#6923—81no—
250D61⋊C8—21no—
251D61⋊C8—21no—
252D61⋊C8—21no—
253D61⋊C8—21no—
254D8×C61—41no—
255M16×C61—41no—
256C2×C8×C61C22×C411yescharacteristic
257C2×C8×C61C22×C411yescharacteristic
258C4⋊C4×C61C22×C411yescharacteristic
259C4⋊C4×C61C22×C411yescharacteristic
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264#11758199—41no—
265#11758199—41no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270C4⋊Dic61C22×C411yescharacteristic
271C4⋊Dic61C22×C411yescharacteristic
272#11758196—21no—
273#11758196—21no—
274#11758194—41no—
275C2×#92418C22×C411yescharacteristic
276C2×#92418C22×C411yescharacteristic
277D488—41no—
278#11758189—41no—
279#11758189—41no—
280C8×D61—21no—
281C8×D61—21no—
282C8×D61—21no—
283C8×D61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61C4×D411yescharacteristic
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61C4×D411yescharacteristic
308C22×D61C22×D411yescharacteristic
309C2×#6923—21no—
310C2×#6923—21no—
311C2×#6923—21no—
312C2×#6923—21no—
313C2×#6923—21no—
314C2×#6923—22no—
315C2×#6923—22no—
316C2×#6923—21no—
317C2×#6923—21no—
318C2×#6923—21no—
319C2×#6923—21no—
320C2×#6923—21no—
321C2×#6923—21no—
322C2×#6923—41no—
323C2×#6923—41no—
324C2×#6923—41no—
325C2×#6923—41no—
326C2×#6923—41no—
327C2×#6923—41no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—84no—
333C2×#6923—84no—
334C2×#6923—84no—
335C2×#6923AGL(1,ℤ/8)12yes—
336D4×C61—21no—
337D4×C61—21no—
338D4×C61—21no—
339D4×C61—21no—
340D4×C61—42no—
341D4×C61—81no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61C4×D411yescharacteristic
347C2×C4×C61C23×C411yescharacteristic
348C22⋊D61—42no—
349C22⋊D61—42no—
350C22⋊D61—41no—
351C22⋊D61—41no—
352C22⋊D61—41no—
353C22⋊D61—41no—
354C22⋊D61—81no—
355C22⋊D61—81no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61C4×D411yescharacteristic
361C2×Dic61C2×#4111yescharacteristic
362D244—21no—
363D244—21no—
364D244—21no—
365D244—21no—
366D244—42no—
367D244—81no—
368C4×D61—21no—
369C4×D61—21no—
370C4×D61—21no—
371C4×D61—21no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—41no—
375C4×D61—41no—
376C4×D61—41no—
377C4×D61—41no—
378C4×D61C2×#4111yescharacteristic
379C4×D61C2×#4111yescharacteristic
380C4×D61H(5,𝔽2)11yescharacteristic
381C4×D61H(5,𝔽2)11yescharacteristic
382#92420—41no—
383#92420—41no—
384C8×C61—21no—
385C8×C61—21no—
386#92418—21no—
387#92418—21no—
388#23143—611nomaximal, Sylow
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61C2×C4×D411yescharacteristic
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—81no—
413C2×D61—81no—
414C2×D61—81no—
415C2×D61—81no—
416C2×D61—81no—
417C2×D61—81no—
418C2×D61—81no—
419C2×D61—81no—
420C2×D61#54611yescharacteristic
421C2×D61#54611yescharacteristic
422C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
423C2×D61#57511yescharacteristic
424C2×D61#57611yescharacteristic
425C2×D61#57711yescharacteristic
426#6923—22no—
427#6923—42no—
428#6923—41no—
429#6923—41no—
430#6923—42no—
431#6923—41no—
432#6923—81no—
433#6923—81no—
434C4×C61—21no—
435C4×C61—41no—
436C4×C61—41no—
437C4×C61C4×#4111yescharacteristic
438C4×C61#51811yescharacteristic
439Dic61—21no—
440Dic61—41no—
441Dic61—41no—
442Dic61#55311yescharacteristic
443Dic61#55311yescharacteristic
444C2×#469—611no—
445#2363—611no—
446#2361—611no—
447#1936—611no—
448#1934—611no—
449#1920—611no—
450#1920—611no—
451#1879—611no—
452#1879—611no—
453#1875—611no—
454#1874—611no—
455#1762—611no—
456C4×#102—611no—
457#1753—611no—
458#1736—611no—
459C2×C61—41no—
460C2×C61—81no—
461C2×C61—81no—
462C2×C61#236411yescharacteristic
463C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
464C2×C61#294611yescharacteristic
465D61—41no—
466D61—81no—
467D61—81no—
468D61#330611yescharacteristic
469D61#330911yescharacteristic
470D61#332511yescharacteristic
471D61#332611yescharacteristic
472C22×D8—611no—
473C22×M16—611no—
474C2×#121—611no—
475C2×#121—611no—
476C2×C4×D4—611no—
477C2×C4×D4—611no—
478C2×C4×D4—1221no—
479C2×#117—611no—
480C22×C4⋊C4—611no—
481#469—611no—
482#469—611no—
483#469—611no—
484#469—611no—
485#469—611no—
486#469—611no—
487#469—611no—
488#469#692311yescharacteristic, complemented
489C2×#106—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×C22⋊C8—611no—
497C2×#97—611no—
498C2×C4×C8—611no—
499#390—611no—
500#390—611no—
501#390—1221no—
502#389—611no—
503#389—611no—
504#388—1221no—
505#388—1221no—
506#386—1221no—
507#386—1221no—
508#385—1221no—
509C4×C4⋊C4—611no—
510C4×C4⋊C4—611no—
511C4×C22⋊C4—611no—
512C4×C22⋊C4—1221no—
513#340—611no—
514#340—611no—
515#340—611no—
516#340—611no—
517#340—611no—
518#340—611no—
519#340—611no—
520#340—611no—
521#336—611no—
522#336—611no—
523C61#2314311yescharacteristic, complemented, Sylow
524C22×D4—611no—
525C22×D4—611no—
526C22×D4—1221no—
527C22×D4—1221no—
528C23×C4—611no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4—1221no—
532C2×D8—611no—
533C2×D8—611no—
534C2×D8—611no—
535C2×D8—2441no—
536C2×D8—2441no—
537C2×D8C2×#692311yescharacteristic, complemented
538C2×M16—611no—
539C2×M16—611no—
540C2×M16—611no—
541C2×M16—2441no—
542C2×M16—2441no—
543C2×M16C2×#692311yescharacteristic, complemented
544C22×C8—611no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—611no—
548#121—611no—
549#121—611no—
550#121—611no—
551#121—611no—
552#121—611no—
553#121—611no—
554#121—1221no—
555#121—1221no—
556#121—1221no—
557#121—1221no—
558#121C2×#692311yescharacteristic, complemented
559#121C2×#692311yescharacteristic, complemented
560C4×D4—1222no—
561C4×D4—1222no—
562C4×D4—2441no—
563C4×D4—2441no—
564C4×D4—2444no—
565#117—1222no—
566#117—2441no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—1222no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—2441no—
578C2×C22⋊C4—611no—
579C2×C22⋊C4—611no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C42—611no—
590C2×C42—611no—
591C2×C42—1221no—
592C2×C42—1221no—
593C2×C42—1221no—
594#106—611no—
595#106—611no—
596#106—611no—
597#106C2×#692311yescharacteristic, complemented
598#102—611no—
599#102—611no—
600#102—611no—
601#102—611no—
602#102—611no—
603#102—611no—
604#102—1222no—
605#102—1222no—
606#102—2441no—
607#102—2441no—
608#102C2×#692311yescharacteristic, complemented
609#102C2×#692311yescharacteristic, complemented
610C22⋊C8—1221no—
611C22⋊C8—1221no—
612#97—2441no—
613C4×C8—2441no—
614#95—611no—
615#95—611no—
616#95—1221no—
617#95—1221no—
618#95—1221no—
619#95—1221no—
620C24—611no—
621C24—1221no—
622C24—1221no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—611no—
626C2×D4—611no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—4881no—
644C2×D4—4881no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4C22×#692311yescharacteristic
648C2×D4C22×#692311yescharacteristic
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—4881no—
669C22×C4—4881no—
670C22×C4—4881no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4C22×#692311yescharacteristic
678D8—41no—
679D8—2441no—
680D8—2441no—
681D8—2441no—
682M16—41no—
683M16—2441no—
684M16—2441no—
685M16—2441no—
686C2×C8—611no—
687C2×C8—611no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8C22×#692311yescharacteristic
699C2×C8C22×#692311yescharacteristic
700C4⋊C4—612no—
701C4⋊C4—612no—
702C4⋊C4—611no—
703C4⋊C4—611no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—4881no—
713C4⋊C4—2442no—
714C4⋊C4—2442no—
715C4⋊C4C22×#692311yescharacteristic
716C4⋊C4C22×#692311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—1221no—
723C22⋊C4—1222no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—4881no—
727C22⋊C4—4881no—
728C22⋊C4—2442no—
729C22⋊C4—2441no—
730C22⋊C4—2442no—
731C22⋊C4—2442no—
732C22⋊C4—2442no—
733C22⋊C4—2442no—
734C42—1221no—
735C42—1221no—
736C42—1221no—
737C42—1221no—
738C42—4881no—
739C42—2442no—
740C42—2442no—
741C23—21no—
742C23—21no—
743C23—611no—
744C23—611no—
745C23—1221no—
746C23—1221no—
747C23—1221no—
748C23—1221no—
749C23—1221no—
750C23—1221no—
751C23—1221no—
752C23—1221no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23—2441no—
761C23—2441no—
762C23—2441no—
763C23—2441no—
764C23—2441no—
765C23D4×#692311yescharacteristic
766D4—21no—
767D4—21no—
768D4—21no—
769D4—21no—
770D4—42no—
771D4—81no—
772D4—1221no—
773D4—1221no—
774D4—1221no—
775D4—1221no—
776D4—4881no—
777D4—4881no—
778D4—4881no—
779D4—2442no—
780D4—2441no—
781D4—2441no—
782D4—2441no—
783D4—2441no—
784D4—2442no—
785D4—2442no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—611no—
791C2×C4—611no—
792C2×C4—611no—
793C2×C4—611no—
794C2×C4—611no—
795C2×C4—612no—
796C2×C4—611no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1222no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1222no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—4884no—
821C2×C4—4884no—
822C2×C4—4884no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4D4×#692311yescharacteristic
838C2×C4C23×#692311yescharacteristic
839C8—21no—
840C8—21no—
841C8—1221no—
842C8—1221no—
843C8—2441no—
844C8—2441no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—611no—
855C22—611no—
856C22—611no—
857C22—611no—
858C22—611no—
859C22—611no—
860C22—1221no—
861C22—1221no—
862C22—1221no—
863C22—4881no—
864C22—4881no—
865C22—4881no—
866C22—4881no—
867C22—4881no—
868C22—4881no—
869C22—4881no—
870C22—4881no—
871C22—2441no—
872C22—2441no—
873C22—2441no—
874C22—2441no—
875C22—2441no—
876C22—2441no—
877C22—2441no—
878C22—2441no—
879C22—2441no—
880C22—2441no—
881C22C2×D4×#692311yescharacteristic
882C4—21no—
883C4—41no—
884C4—41no—
885C4—611no—
886C4—611no—
887C4—1222no—
888C4—1221no—
889C4—4881no—
890C4—4881no—
891C4—2441no—
892C4—2441no—
893C4—2441no—
894C4—2442no—
895C4—2442no—
896C4—2441no—
897C4—2441no—
898C4#41×#692311yescharacteristic
899C4#1684082911yescharacteristic
900C2—41no—
901C2—81no—
902C2—81no—
903C2—611no—
904C2—611no—
905C2—611no—
906C2—611no—
907C2—4881no—
908C2—4881no—
909C2—2441no—
910C2#2146234711yescharacteristic
911C2AGL(1,ℤ/8)×#692311yescharacteristic
912C2#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#23143
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. #21462346C2semidirect
2. #21462344C2semidirect
3. #21461911C2semidirect
4. #21461909C2semidirect
5. #21461882C2semidirect
6. #21461882C2semidirect
7. #21461814C2semidirect
8. #21461814C2semidirect
9. #21461807C2semidirect
10. #21461806C2semidirect
11. #21461590C2semidirect
12. #102×#6923C2semidirect
13. #21461559C2semidirect
14. #21461507C2semidirect
56. #16840016C4semidirect
57. #16840015C4semidirect
58. #16840014C4semidirect
59. #16840014C4semidirect
60. #16840013C4semidirect
61. #16840013C4semidirect
62. #16840012C4semidirect
66. C61×#469C4semidirect
121. C2×D488C2×C4semidirect
122. C2×#11758199C2×C4semidirect
123. C2×#11758199C2×C4semidirect
126. C2×#11758194C2×C4semidirect
127. C2×#11758189C2×C4semidirect
128. C2×#11758189C2×C4semidirect
133. #14519752C2×C4semidirect
134. #14519752C2×C4semidirect
135. #14519751C2×C4semidirect
136. #14519751C2×C4semidirect
141. #14519748C2×C4semidirect
142. #14519748C2×C4semidirect
147. #14519709C2×C4semidirect
148. #14519708C2×C4semidirect
149. #14519708C2×C4semidirect
150. #14519699C2×C4semidirect
151. #14519699C2×C4semidirect
152. #14519698C2×C4semidirect
153. #14519698C2×C4semidirect
154. #14519697C2×C4semidirect
155. #14519697C2×C4semidirect
156. C2×D8×C61C2×C4semidirect
157. C2×M16×C61C2×C4semidirect
158. #121×C61C2×C4semidirect
159. #121×C61C2×C4semidirect
160. #106×C61C2×C4semidirect
161. #102×C61C2×C4semidirect
162. #102×C61C2×C4semidirect
488. #469#6923semidirect
523. C61#23143semidirect
537. C2×D8C2×#6923semidirect
543. C2×M16C2×#6923semidirect
558. #121C2×#6923semidirect
559. #121C2×#6923semidirect
597. #106C2×#6923semidirect
608. #102C2×#6923semidirect
609. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623462
#214623442
#214619112
#214619092
#214618822
#214618142
#214618072
#214618062
#214615902
#102×#69232
#214615592
#214615072
#469×D612
#2314361