Finite Group Databasebeta

← #30622476

Subgroups — #30622476

Order 15616.

994 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#21462349C211yesmaximal, characteristic, complemented
2#21462340C211yesmaximal, characteristic, complemented
3#21461968C211yesmaximal, characteristic, complemented
4#21461966C211yesmaximal, characteristic, complemented
5#21461951C211yesmaximal, characteristic, complemented
6#21461932C211yesmaximal, characteristic, complemented
7#21461897C211yesmaximal, characteristic, complemented
8#21461896C211yesmaximal, characteristic, complemented
9#21461814C211yesmaximal, characteristic, complemented
10#21461814C211yesmaximal, characteristic, complemented
11#21461620C211yesmaximal, characteristic, complemented
12#21461590C211yesmaximal, characteristic, complemented
13#21461589C211yesmaximal, characteristic, complemented
14#102×#6923C211yesmaximal, characteristic, complemented
15#459×D61C211yesmaximal, characteristic
16C2×D4×#6923—21no—
17C2×D4×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
21C2×#14519839C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27#16840721C2211yescharacteristic
28C2×#14519831C2211yescharacteristic
29C2×C8×#6923C2211yescharacteristic
30#16840714—21no—
31#16840714C2211yescharacteristic
32#16840714C2211yescharacteristic
33#16840714C2211yescharacteristic
34#16840714C2211yescharacteristic
35#16840712—21no—
36#16840712—21no—
37#16840710—21no—
38#16840710—21no—
39#16840706C2211yescharacteristic
40#16840705—21no—
41C4⋊C4×#6923C2211yescharacteristic
42C4⋊C4×#6923C2211yescharacteristic
43C4×C4⋊#6923C2211yescharacteristic
44C4×C4⋊#6923C2211yescharacteristic
45C4×C22⋊#6923—21no—
46#16840636C2211yescharacteristic
47#16840636C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×D8×D61C2211yescharacteristic
53C2×D8×D61C2211yescharacteristic
54#127×D61C2211yescharacteristic
55C4×D4×D61C2211yescharacteristic
56#16839958C411yescharacteristic, complemented
57#16839957C411yescharacteristic, complemented
58#16839956C411yescharacteristic, complemented
59#16839956C411yescharacteristic, complemented
60#16839955C411yescharacteristic, complemented
61#16839955C411yescharacteristic, complemented
62#16839954C411yescharacteristic, complemented
63C4⋊C8×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#459C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—41no—
74D4×#6923—41no—
75D4×#6923—44no—
76C2×C4⋊#6923D411yescharacteristic
77C2×C4⋊#6923D411yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923C2311yescharacteristic
96C2×C4×#6923C2311yescharacteristic
97#14519846—41no—
98#14519845—41no—
99#14519839—22no—
100#14519839—22no—
101#14519839—22no—
102#14519839—22no—
103#14519839—41no—
104#14519839—41no—
105#14519832—21no—
106#14519832—21no—
107#14519831—41no—
108C8×#6923—41no—
109(C2×#6923)⋊C4—21no—
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
120C2×D4×D61C2311yescharacteristic
121C22×C4×D61—21no—
122C2×D488C2×C411yescharacteristic, complemented
123C2×D488C2×C411yescharacteristic, complemented
124C2×#11758199C2×C411yescharacteristic, complemented
125C2×#11758199C2×C411yescharacteristic, complemented
126C2×#11758199C2×C411yescharacteristic, complemented
127C2×#11758199C2×C411yescharacteristic, complemented
128D8×D61—41no—
129D8×D61—41no—
130D8×D61—41no—
131D8×D61—41no—
132C2×C8×D61C2311yescharacteristic
133C2×C8×D61C2311yescharacteristic
134#14519774C2×C411yescharacteristic
135#14519773—21no—
136#14519773—21no—
137#14519773C2×C411yescharacteristic
138#14519773C2×C411yescharacteristic
139C4×D244C2×C411yescharacteristic, complemented
140D4×Dic61C2×C411yescharacteristic, complemented
141#14519739C2×C411yescharacteristic, complemented
142C4×C22⋊D61—21no—
143#14519737—21no—
144C4⋊C4×D61C2311yescharacteristic
145C22⋊C4×D61—21no—
146C42×D61C2311yescharacteristic
147C4⋊#92418C2×C411yescharacteristic, complemented
148#14519706C2×C411yescharacteristic, complemented
149#14519706C2×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×D8×C61C2×C411yescharacteristic, complemented
158#127×C61C2×C411yescharacteristic
159C4×D4×C61C2×C411yescharacteristic, complemented
160C4⋊C8×C61C2×C411yescharacteristic, complemented
161#102×C61C2×C411yescharacteristic, complemented
162#102×C61C2×C411yescharacteristic, complemented
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
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—81no—
175C22×#6923—81no—
176C22×#6923C2×D411yescharacteristic
177C22×#6923C2×D411yescharacteristic
178C22×#6923C2×D411yescharacteristic
179C22×#6923C2×D411yescharacteristic
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61C22×C411yescharacteristic
183C2×D4×C61C22×C411yescharacteristic
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61—21no—
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C22×Dic61—21no—
194D4×D61—21no—
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—21no—
204D4×D61—21no—
205D4×D61—21no—
206D4×D61—42no—
207D4×D61—42no—
208D4×D61—81no—
209D4×D61—81no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244C22×C411yescharacteristic
213C2×D244C22×C411yescharacteristic
214C2×D244C22×C411yescharacteristic
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—81no—
219C2×C4×D61—81no—
220C2×C4×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2411yescharacteristic
223C22⋊#6923—42no—
224C22⋊#6923—42no—
225C22⋊#6923—42no—
226C22⋊#6923—42no—
227C22⋊#6923—42no—
228C22⋊#6923—42no—
229C22⋊#6923—81no—
230C22⋊#6923—81no—
231C22⋊#6923—81no—
232C22⋊#6923—81no—
233C2×#92420—21no—
234C2×#92420—21no—
235C4⋊#6923—22no—
236C4⋊#6923—21no—
237C4⋊#6923—21no—
238C4⋊#6923—21no—
239C4⋊#6923—21no—
240C4⋊#6923—21no—
241C4⋊#6923—21no—
242C4⋊#6923—21no—
243C4⋊#6923—41no—
244C4⋊#6923#4112yes—
245C4×#6923—21no—
246C4×#6923—21no—
247C4×#6923—21no—
248C4×#6923—21no—
249C4×#6923—42no—
250C4×#6923—81no—
251C4×#6923—81no—
252D61⋊C8—21no—
253D61⋊C8—21no—
254D61⋊C8—21no—
255D61⋊C8#4112yes—
256D8×C61—41no—
257D8×C61—41no—
258C2×C8×C61C22×C411yescharacteristic
259C2×C8×C61C22×C411yescharacteristic
260C4⋊C4×C61C22×C411yescharacteristic
261C22⋊C4×C61—21no—
262C42×C61C22×C411yescharacteristic
263C22⋊Dic61—21no—
264#11758199—41no—
265#11758199—41no—
266#11758199—41no—
267#11758199—41no—
268#11758198—21no—
269#11758198—21no—
270C4⋊Dic61C22×C411yescharacteristic
271#11758196—21no—
272C4×Dic61C22×C411yescharacteristic
273C4×Dic61#4111yescharacteristic
274C4×Dic61#4111yescharacteristic
275C2×#92418C22×C411yescharacteristic
276C2×#92418C22×C411yescharacteristic
277D488—41no—
278D488—41no—
279C8×D61—21no—
280C8×D61—21no—
281C8×D61—21no—
282C8×D61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
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×D61C22×D411yescharacteristic
308C2×#6923—21no—
309C2×#6923—21no—
310C2×#6923—21no—
311C2×#6923—21no—
312C2×#6923—21no—
313C2×#6923—22no—
314C2×#6923—21no—
315C2×#6923—21no—
316C2×#6923—21no—
317C2×#6923—21no—
318C2×#6923—21no—
319C2×#6923—21no—
320C2×#6923—41no—
321C2×#6923—41no—
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—84no—
332C2×#6923—84no—
333C2×#6923AGL(1,ℤ/8)12yes—
334D4×C61—21no—
335D4×C61—21no—
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—81no—
344C2×C4×C61C4×D411yescharacteristic
345C2×C4×C61C4×D411yescharacteristic
346C2×C4×C61C23×C411yescharacteristic
347C22⋊D61—42no—
348C22⋊D61—42no—
349C22⋊D61—41no—
350C22⋊D61—41no—
351C22⋊D61—41no—
352C22⋊D61—41no—
353C22⋊D61—41no—
354C22⋊D61—41no—
355C22⋊D61—81no—
356C22⋊D61—81no—
357C2×Dic61—21no—
358C2×Dic61—81no—
359C2×Dic61C4×D411yescharacteristic
360C2×Dic61C4×D411yescharacteristic
361C2×Dic61C2×#4111yescharacteristic
362D244—21no—
363D244—21no—
364D244—21no—
365D244—21no—
366D244—21no—
367D244—21no—
368D244—42no—
369D244—81no—
370C4×D61—21no—
371C4×D61—21no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—41no—
375C4×D61—41no—
376C4×D61—81no—
377C4×D61—81no—
378C4×D61C2×#4111yescharacteristic
379C4×D61C2×#4111yescharacteristic
380C4×D61H(5,𝔽2)11yescharacteristic
381C4×D61H(5,𝔽2)11yescharacteristic
382#92420—22no—
383#92420—41no—
384C8×C61—21no—
385C8×C61—21no—
386#92418—21no—
387#92418—21no—
388#23108—611nomaximal, Sylow
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61C2×C4×D411yescharacteristic
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—81no—
409C2×D61—81no—
410C2×D61—81no—
411C2×D61—81no—
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#55011yescharacteristic
422C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
423C2×D61#57511yescharacteristic
424C2×D61#57611yescharacteristic
425C2×D61#57611yescharacteristic
426#6923—22no—
427#6923—41no—
428#6923—41no—
429#6923—41no—
430#6923—42no—
431#6923—81no—
432#6923—81no—
433#6923—81no—
434C4×C61—21no—
435C4×C61—21no—
436C4×C61—41no—
437C4×C61C4×#4111yescharacteristic
438C4×C61#51811yescharacteristic
439Dic61—21no—
440Dic61—21no—
441Dic61—41no—
442Dic61#55311yescharacteristic
443Dic61#55511yescharacteristic
444C2×#459—611no—
445#2366—611no—
446#2357—611no—
447#1972—611no—
448#1970—611no—
449#1961—611no—
450#1949—611no—
451#1926—611no—
452#1925—611no—
453#1879—611no—
454#1879—611no—
455#1771—611no—
456#1762—611no—
457#1762—611no—
458C4×#102—611no—
459C2×C61—81no—
460C2×C61—81no—
461C2×C61—81no—
462C2×C61#236311yescharacteristic
463C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
464C2×C61#294811yescharacteristic
465D61—81no—
466D61—81no—
467D61—81no—
468D61#330911yescharacteristic
469D61#331811yescharacteristic
470D61#339911yescharacteristic
471D61#340311yescharacteristic
472C22×D8—611no—
473C22×D8—611no—
474C2×#127—611no—
475C2×C4×D4—611no—
476C2×C4×D4—611no—
477C2×C4×D4—611no—
478C2×C4×D4—1221no—
479#459—611no—
480#459—611no—
481#459—611no—
482#459—611no—
483#459—611no—
484#459—611no—
485#459—611no—
486#459#692311yescharacteristic, complemented
487C2×#107—611no—
488C2×#106—611no—
489C2×C4⋊C8—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102—611no—
498C2×#97—611no—
499C2×#97—611no—
500C2×C4×C8—611no—
501#390—611no—
502#390—611no—
503#390—611no—
504#390—611no—
505#390—1221no—
506#388—1221no—
507#388—1221no—
508#386—1221no—
509#386—1221no—
510#382—611no—
511#381—1221no—
512C4×C4⋊C4—611no—
513C4×C4⋊C4—611no—
514C4×C4⋊C4—611no—
515C4×C4⋊C4—611no—
516C4×C22⋊C4—1221no—
517#340—611no—
518#340—611no—
519#340—611no—
520#340—611no—
521#336—611no—
522#336—611no—
523C61#2310811yescharacteristic, complemented, Sylow
524C22×D4—611no—
525C22×D4—611no—
526C22×D4—611no—
527C22×D4—1221no—
528C22×D4—1221no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4—1221no—
532C2×D8—611no—
533C2×D8—611no—
534C2×D8—611no—
535C2×D8—611no—
536C2×D8—611no—
537C2×D8—611no—
538C2×D8—2441no—
539C2×D8—2441no—
540C2×D8—2441no—
541C2×D8—2441no—
542C2×D8C2×#692311yescharacteristic, complemented
543C2×D8C2×#692311yescharacteristic, complemented
544C22×C8—611no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—611no—
548#127—611no—
549#127—611no—
550#127—611no—
551#127—1221no—
552#127—1221no—
553#127C2×#692311yescharacteristic
554C4×D4—611no—
555C4×D4—611no—
556C4×D4—611no—
557C4×D4—1221no—
558C4×D4—1221no—
559C4×D4—1222no—
560C4×D4—1222no—
561C4×D4—2441no—
562C4×D4—2441no—
563C4×D4—2444no—
564C4×D4C2×#692311yescharacteristic, complemented
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—611no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C42—611no—
584C2×C42—611no—
585C2×C42—611no—
586C2×C42—1221no—
587C2×C42—1221no—
588C2×C42—1221no—
589#107—2441no—
590#106—2441no—
591C4⋊C8—611no—
592C4⋊C8—611no—
593C4⋊C8—611no—
594C4⋊C8C2×#692311yescharacteristic, complemented
595#102—611no—
596#102—611no—
597#102—611no—
598#102—611no—
599#102—611no—
600#102—611no—
601#102—1222no—
602#102—1222no—
603#102—1222no—
604#102—1222no—
605#102—2441no—
606#102—2441no—
607#102C2×#692311yescharacteristic, complemented
608#102C2×#692311yescharacteristic, complemented
609#97—1221no—
610#97—1221no—
611#97—2441no—
612C4×C8—2441no—
613#95—611no—
614#95—611no—
615#95—1221no—
616#95—1221no—
617#95—1221no—
618#95—1221no—
619#95—1221no—
620C24—1221no—
621C24—1221no—
622C24—1221no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—611no—
626C2×D4—611no—
627C2×D4—611no—
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—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—4881no—
650C2×D4—4881no—
651C2×D4—2442no—
652C2×D4—2442no—
653C2×D4C22×#692311yescharacteristic
654C2×D4C22×#692311yescharacteristic
655C2×D4C22×#692311yescharacteristic
656C22×C4—21no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—4881no—
673C22×C4—4881no—
674C22×C4—4881no—
675C22×C4—4881no—
676C22×C4—2442no—
677C22×C4—2442no—
678C22×C4—2442no—
679C22×C4—2442no—
680D8—41no—
681D8—41no—
682D8—2441no—
683D8—2441no—
684D8—2441no—
685D8—2441no—
686D8—2441no—
687D8—2441no—
688C2×C8—612no—
689C2×C8—611no—
690C2×C8—611no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8C22×#692311yescharacteristic
701C2×C8C22×#692311yescharacteristic
702C4⋊C4—612no—
703C4⋊C4—611no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1222no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—2441no—
714C4⋊C4C22×#692311yescharacteristic
715C22⋊C4—21no—
716C22⋊C4—1221no—
717C22⋊C4—1221no—
718C22⋊C4—1221no—
719C22⋊C4—4881no—
720C22⋊C4—4881no—
721C22⋊C4—4881no—
722C22⋊C4—4881no—
723C22⋊C4—2442no—
724C22⋊C4—2442no—
725C22⋊C4—2442no—
726C22⋊C4—2442no—
727C22⋊C4—2442no—
728C22⋊C4—2442no—
729C42—611no—
730C42—611no—
731C42—611no—
732C42—1221no—
733C42—1221no—
734C42—1221no—
735C42—1221no—
736C42—4881no—
737C42—4881no—
738C42—2442no—
739C42C22×#692311yescharacteristic
740C23—21no—
741C23—21no—
742C23—21no—
743C23—611no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—2441no—
748C23—2441no—
749C23—2441no—
750C23—2441no—
751C23—2441no—
752C23—2441no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23—2441no—
761C23—2441no—
762C23—2441no—
763C23—2441no—
764C23—2441no—
765D4—21no—
766D4—21no—
767D4—21no—
768D4—21no—
769D4—21no—
770D4—21no—
771D4—42no—
772D4—81no—
773D4—1221no—
774D4—1221no—
775D4—1221no—
776D4—1221no—
777D4—1221no—
778D4—1221no—
779D4—4881no—
780D4—4881no—
781D4—4881no—
782D4—2442no—
783D4—2441no—
784D4—2441no—
785D4—2441no—
786D4—2441no—
787D4—2441no—
788D4—2441no—
789D4—2442no—
790D4—2442no—
791C2×C4—21no—
792C2×C4—81no—
793C2×C4—611no—
794C2×C4—611no—
795C2×C4—611no—
796C2×C4—611no—
797C2×C4—611no—
798C2×C4—612no—
799C2×C4—611no—
800C2×C4—611no—
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—1221no—
812C2×C4—1221no—
813C2×C4—1222no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—4881no—
819C2×C4—4881no—
820C2×C4—4881no—
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×C4D4×#692311yescharacteristic
837C2×C4D4×#692311yescharacteristic
838C2×C4C23×#692311yescharacteristic
839C8—21no—
840C8—21no—
841C8—1222no—
842C8—1221no—
843C8—1221no—
844C8—2441no—
845C22—41no—
846C22—41no—
847C22—41no—
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—4881no—
861C22—4881no—
862C22—4881no—
863C22—4881no—
864C22—4881no—
865C22—4881no—
866C22—4881no—
867C22—4881no—
868C22—4881no—
869C22—4881no—
870C22—4881no—
871C22—4881no—
872C22—2441no—
873C22—2441no—
874C22—2441no—
875C22—2441no—
876C22—2441no—
877C22—2441no—
878C22—2441no—
879C22—2441no—
880C22—2441no—
881C22C2×D4×#692311yescharacteristic
882C4—21no—
883C4—21no—
884C4—41no—
885C4—611no—
886C4—611no—
887C4—1222no—
888C4—1221no—
889C4—1221no—
890C4—4881no—
891C4—4881no—
892C4—4881no—
893C4—2441no—
894C4—2441no—
895C4—2441no—
896C4—2442no—
897C4—2441no—
898C4#41×#692311yescharacteristic
899C4#1684082911yescharacteristic
900C2—81no—
901C2—81no—
902C2—81no—
903C2—611no—
904C2—611no—
905C2—611no—
906C2—611no—
907C2—4881no—
908C2—4881no—
909C2—4881no—
910C2#2146234611yescharacteristic
911C2AGL(1,ℤ/8)×#692311yescharacteristic
912C2#2146257811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#459C4
socleC22×C61C2×C4×D4
prime radical#459×D61C2
cosocleC2×C4×D61C24
hypercenter#459#6923
hypocenterC61#23108
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #21462349C2semidirect
2. #21462340C2semidirect
3. #21461968C2semidirect
4. #21461966C2semidirect
5. #21461951C2semidirect
6. #21461932C2semidirect
7. #21461897C2semidirect
8. #21461896C2semidirect
9. #21461814C2semidirect
10. #21461814C2semidirect
11. #21461620C2semidirect
12. #21461590C2semidirect
13. #21461589C2semidirect
14. #102×#6923C2semidirect
56. #16839958C4semidirect
57. #16839957C4semidirect
58. #16839956C4semidirect
59. #16839956C4semidirect
60. #16839955C4semidirect
61. #16839955C4semidirect
62. #16839954C4semidirect
66. C61×#459C4semidirect
122. C2×D488C2×C4semidirect
123. C2×D488C2×C4semidirect
124. C2×#11758199C2×C4semidirect
125. C2×#11758199C2×C4semidirect
126. C2×#11758199C2×C4semidirect
127. C2×#11758199C2×C4semidirect
139. C4×D244C2×C4semidirect
140. D4×Dic61C2×C4semidirect
141. #14519739C2×C4semidirect
147. C4⋊#92418C2×C4semidirect
148. #14519706C2×C4semidirect
149. #14519706C2×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×D8×C61C2×C4semidirect
159. C4×D4×C61C2×C4semidirect
160. C4⋊C8×C61C2×C4semidirect
161. #102×C61C2×C4semidirect
162. #102×C61C2×C4semidirect
486. #459#6923semidirect
523. C61#23108semidirect
542. C2×D8C2×#6923semidirect
543. C2×D8C2×#6923semidirect
564. C4×D4C2×#6923semidirect
594. C4⋊C8C2×#6923semidirect
607. #102C2×#6923semidirect
608. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623492
#214623402
#214619682
#214619662
#214619512
#214619322
#214618972
#214618962
#214618142
#214616202
#214615902
#214615892
#102×#69232
#459×D612
#2310861