Finite Group Databasebeta

← #30622189

Subgroups — #30622189

Order 15616.

1034 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C211yesmaximal, characteristic, complemented
2C2×D8×#6923C211yesmaximal, characteristic
3#21462350C211yesmaximal, characteristic, complemented
4#21462332C211yesmaximal, characteristic, complemented
5#21461948C211yesmaximal, characteristic, complemented
6#21461932C211yesmaximal, characteristic, complemented
7#21461909C211yesmaximal, characteristic, complemented
8#21461908C211yesmaximal, characteristic, complemented
9#21461814C211yesmaximal, characteristic
10#21461812C211yesmaximal, characteristic, complemented
11#21461784C211yesmaximal, characteristic, complemented
12#21461783C211yesmaximal, characteristic, complemented
13#21461612C211yesmaximal, characteristic, complemented
14C4×#14519839C211yesmaximal, characteristic, complemented
15#463×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20SD16×#6923—24no—
21D8×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24C2×#14519840C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C4×D61⋊C8C2211yescharacteristic
31C2×C8×#6923C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34#16840714C2211yescharacteristic
35#16840713C2211yescharacteristic
36#16840713C2211yescharacteristic
37#16840712—21no—
38#16840712—21no—
39#16840709—21no—
40#16840709—21no—
41#16840709—21no—
42#16840706C2211yescharacteristic
43#16840704—21no—
44C4×C4⋊#6923C2211yescharacteristic
45C4×C4⋊#6923C2211yescharacteristic
46C22⋊C4×#6923—21no—
47C2×(C2×#6923)⋊C4—21no—
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×SD16×D61C2211yescharacteristic
55C2×D8×D61C2211yescharacteristic
56#124×D61C2211yescharacteristic
57C4×D4×D61C2211yescharacteristic
58#16839980C411yescharacteristic, complemented
59#16839979C411yescharacteristic, complemented
60#16839978C411yescharacteristic, complemented
61#16839977C411yescharacteristic, complemented
62#16839976C411yescharacteristic, complemented
63#16839975C411yescharacteristic, complemented
64#16839974C411yescharacteristic, complemented
65C4⋊C8×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67#102×D61C2211yescharacteristic
68C61×#463C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C23×#6923—21no—
72C2×D61⋊C8C2311yescharacteristic
73C2×D61⋊C8C2311yescharacteristic
74Q8×#6923—22no—
75Q8×#6923—41no—
76D4×#6923—22no—
77D4×#6923—22no—
78D4×#6923—22no—
79D4×#6923—41no—
80D4×#6923—41no—
81D4×#6923—41no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923D411yescharacteristic
86C2×C4⋊#6923D411yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923—21no—
98C2×C4×#6923C2311yescharacteristic
99C2×C4×#6923C2311yescharacteristic
100#14519846—22no—
101#14519845—22no—
102#14519840—22no—
103#14519840—41no—
104#14519839—22no—
105#14519839—22no—
106#14519839—41no—
107#14519839D414yes—
108C4×#92420—21no—
109C4×#92420—21no—
110C8×#6923—22no—
111C8×#6923—22no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4D411yescharacteristic
120(C2×#6923)⋊C4D411yescharacteristic
121C2×Q8×D61C2311yescharacteristic
122C2×D4×D61C2311yescharacteristic
123C2×D4×D61C2311yescharacteristic
124C22×C4×D61—21no—
125C2×#11758190C2×C411yescharacteristic, complemented
126C2×#11758200C2×C411yescharacteristic, complemented
127C2×#11758201C2×C411yescharacteristic, complemented
128SD16×D61—22no—
129SD16×D61—22no—
130C2×D488C2×C411yescharacteristic
131C2×#11758199C2×C411yescharacteristic
132C2×#11758199C2×C411yescharacteristic
133D8×D61—22no—
134D8×D61—22no—
135C2×C8×D61C2311yescharacteristic
136C2×C8×D61C2311yescharacteristic
137#14519766C2×C411yescharacteristic, complemented
138#14519765C2×C411yescharacteristic, complemented
139#14519764C2×C411yescharacteristic, complemented
140#14519763—21no—
141#14519763—21no—
142C4×D244C2×C411yescharacteristic, complemented
143D4×Dic61C2×C411yescharacteristic, complemented
144#14519739C2×C411yescharacteristic, complemented
145C4×C22⋊D61—21no—
146#14519737—21no—
147C4⋊C4×D61C2311yescharacteristic
148C22⋊C4×D61—21no—
149C22⋊C4×D61—21no—
150C22⋊C4×D61—21no—
151C42×D61C2311yescharacteristic
152C4⋊#92418C2×C411yescharacteristic, complemented
153#14519706C2×C411yescharacteristic, complemented
154#14519706C2×C411yescharacteristic, complemented
155#14519702C2×C411yescharacteristic, complemented
156#14519701C2×C411yescharacteristic, complemented
157#14519700C2×C411yescharacteristic, complemented
158#14519699C2×C411yescharacteristic, complemented
159#14519698C2×C411yescharacteristic, complemented
160#14519697C2×C411yescharacteristic, complemented
161C2×SD16×C61C2×C411yescharacteristic, complemented
162C2×D8×C61C2×C411yescharacteristic
163#124×C61C2×C411yescharacteristic, complemented
164C4×D4×C61C2×C411yescharacteristic, complemented
165C4⋊C8×C61C2×C411yescharacteristic, complemented
166#103×C61C2×C411yescharacteristic, complemented
167#102×C61C2×C411yescharacteristic, complemented
168C23×D61—21no—
169C23×D61—21no—
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—42no—
175C22×#6923—42no—
176C22×#6923—42no—
177C22×#6923—42no—
178C22×#6923—42no—
179C22×#6923—42no—
180C22×#6923—81no—
181C22×#6923—81no—
182C22×#6923—81no—
183C22×#6923C2×D411yescharacteristic
184C22×#6923C2×D411yescharacteristic
185C22×#6923C2×D411yescharacteristic
186C22×#6923C2×D411yescharacteristic
187C2×Q8×C61C22×C411yescharacteristic
188C2×D4×C61C22×C411yescharacteristic
189C2×D4×C61C22×C411yescharacteristic
190C22×C4×C61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C22×Dic61—21no—
194Q8×D61—21no—
195Q8×D61—21no—
196Q8×D61—21no—
197Q8×D61—21no—
198D4×D61—21no—
199D4×D61—21no—
200D4×D61—21no—
201D4×D61—21no—
202D4×D61—21no—
203D4×D61—21no—
204D4×D61C2×D412yes—
205D4×D61#4112yes—
206C2×D244C22×C411yescharacteristic
207C2×D244C22×C411yescharacteristic
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—81no—
213C2×C4×D61—81no—
214C2×C4×D61C2×D411yescharacteristic
215C2×C4×D61C2×D411yescharacteristic
216C2×C4×D61C2411yescharacteristic
217C2×Dic122—21no—
218C2×Dic122C22×C411yescharacteristic
219C22⋊#6923—42no—
220C22⋊#6923—42no—
221C22⋊#6923—42no—
222C22⋊#6923—42no—
223C22⋊#6923—81no—
224C2×#92420—21no—
225C2×#92420—21no—
226C4⋊#6923—22no—
227C4⋊#6923—22no—
228C4⋊#6923—21no—
229C4⋊#6923—21no—
230C4⋊#6923—21no—
231C4⋊#6923—21no—
232C4⋊#6923—21no—
233C4⋊#6923—21no—
234C4⋊#6923—21no—
235C4⋊#6923—42no—
236C4⋊#6923—81no—
237C4⋊#6923—81no—
238C4⋊#6923C2×D412yes—
239C4×#6923—21no—
240C4×#6923—21no—
241C4×#6923—21no—
242C4×#6923—21no—
243C4×#6923—42no—
244C4×#6923—81no—
245D61⋊C8—21no—
246D61⋊C8—21no—
247D61⋊C8—21no—
248D61⋊C8C2×D412yes—
249SD16×C61—22no—
250D8×C61—22no—
251C2×C8×C61C22×C411yescharacteristic
252C2×C8×C61C22×C411yescharacteristic
253C4⋊C4×C61C22×C411yescharacteristic
254C22⋊C4×C61—21no—
255C22⋊C4×C61—21no—
256C22⋊C4×C61—21no—
257C42×C61C22×C411yescharacteristic
258C22⋊Dic61—21no—
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261#11758201—22no—
262#11758200—22no—
263#11758199—22no—
264#11758199—22no—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271C4⋊Dic61C22×C411yescharacteristic
272#11758196—21no—
273C4×Dic61C22×C411yescharacteristic
274C4×Dic61#4111yescharacteristic
275C4×Dic61#4111yescharacteristic
276C2×#92418C22×C411yescharacteristic
277C2×#92418C22×C411yescharacteristic
278D488—22no—
279#11758190—22no—
280C8×D61—21no—
281C8×D61—21no—
282C8×D61—21no—
283C8×D61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C22×D61—21no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—21no—
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×D61C22×D411yescharacteristic
301C2×#6923—21no—
302C2×#6923—21no—
303C2×#6923—21no—
304C2×#6923—21no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—22no—
308C2×#6923—21no—
309C2×#6923—21no—
310C2×#6923—21no—
311C2×#6923—21no—
312C2×#6923—41no—
313C2×#6923—41no—
314C2×#6923—41no—
315C2×#6923—41no—
316C2×#6923—41no—
317C2×#6923—41no—
318C2×#6923—41no—
319C2×#6923—41no—
320C2×#6923—41no—
321C2×#6923—41no—
322C2×#6923—41no—
323C2×#6923—84no—
324C2×#6923—84no—
325C2×#6923—84no—
326C2×#6923#13512yes—
327C2×#6923#13512yes—
328Q8×C61—21no—
329Q8×C61—21no—
330D4×C61—21no—
331D4×C61—21no—
332D4×C61—21no—
333D4×C61C4×D412yes—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—81no—
337C2×C4×C61C4×D411yescharacteristic
338C2×C4×C61C4×D411yescharacteristic
339C2×C4×C61C23×C411yescharacteristic
340C22⋊D61—22no—
341C22⋊D61—22no—
342C22⋊D61—41no—
343C22⋊D61—41no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—81no—
347C2×Dic61C4×D411yescharacteristic
348C2×Dic61C4×D411yescharacteristic
349C2×Dic61C2×#4111yescharacteristic
350D244—21no—
351D244—21no—
352D244—21no—
353D244C4×D412yes—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—41no—
362C4×D61—81no—
363C4×D61—81no—
364C4×D61C22×D411yescharacteristic
365C4×D61C2×#4111yescharacteristic
366C4×D61H(5,𝔽2)11yescharacteristic
367C4×D612−1+411yescharacteristic
368Dic122—21no—
369Dic122—21no—
370Dic122—41no—
371Dic122—41no—
372#92420—22no—
373#92420—41no—
374C8×C61—21no—
375C8×C61—21no—
376#92418—21no—
377#92418—21no—
378#22999—611nomaximal, Sylow
379C22×C61—22no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61C2×C4×D411yescharacteristic
386C2×D61—22no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61—81no—
397C2×D61—81no—
398C2×D61—81no—
399C2×D61—81no—
400C2×D61D4211yescharacteristic
401C2×D61#54811yescharacteristic
402C2×D61C2×#13511yescharacteristic
403C2×D61C2×#13511yescharacteristic
404C2×D61#57611yescharacteristic
405C2×D61#57711yescharacteristic
406#6923—22no—
407#6923—22no—
408#6923—41no—
409#6923—42no—
410#6923—41no—
411#6923—81no—
412#6923—81no—
413#6923—81no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61C2×C4×D411yescharacteristic
419C4×C61#52011yescharacteristic
420Dic61—21no—
421Dic61—21no—
422Dic61—41no—
423Dic61—41no—
424Dic61#54711yescharacteristic
425Dic61#55311yescharacteristic
426C2×#463—611no—
427C2×C4×SD16—611no—
428C2×C4×D8—611no—
429#2367—611no—
430#2349—611no—
431#1958—611no—
432#1949—611no—
433#1934—611no—
434#1933—611no—
435#1879—611no—
436#1877—611no—
437#1864—611no—
438#1863—611no—
439C8×C4⋊C4—611no—
440C4×#102—611no—
441C2×C61—42no—
442C2×C61—81no—
443C2×C61#236111yescharacteristic
444C2×C61C4×#13511yescharacteristic
445C2×C61#294611yescharacteristic
446D61—42no—
447D61—81no—
448D61#328011yescharacteristic
449D61#328211yescharacteristic
450D61#336011yescharacteristic
451D61#336111yescharacteristic
452C22×SD16—611no—
453C22×D8—611no—
454C2×#124—611no—
455C2×C4×Q8—611no—
456C2×C4×D4—611no—
457C2×C4×D4—611no—
458C2×C4×D4—611no—
459C2×C4×D4—611no—
460#463—611no—
461#463—611no—
462#463—611no—
463#463—611no—
464#463—611no—
465#463—611no—
466#463—611no—
467#463#692311yescharacteristic, complemented
468C4×SD16—1224no—
469C4×D8—1224no—
470C2×#107—611no—
471C2×#106—611no—
472C2×C4⋊C8—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#103—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×C4×C8—611no—
482C2×C4×C8—611no—
483C2×C4×C8—611no—
484#391—611no—
485#390—611no—
486#389—611no—
487#389—611no—
488#388—1221no—
489#388—1221no—
490#385—1221no—
491#385—1221no—
492#385—1221no—
493#382—611no—
494#380—1221no—
495C4×C4⋊C4—611no—
496C4×C4⋊C4—611no—
497C4×C22⋊C4—1221no—
498C2×#95—1221no—
499#340—611no—
500#340—611no—
501#340—611no—
502#340—611no—
503#336—611no—
504#336—611no—
505C61#2299911yescharacteristic, complemented, Sylow
506C22×Q8—611no—
507C22×D4—611no—
508C22×D4—611no—
509C23×C4—1221no—
510C23×C4—1221no—
511C23×C4—1221no—
512C23×C4—1221no—
513C2×SD16—611no—
514C2×SD16—611no—
515C2×SD16—611no—
516C2×SD16—1222no—
517C2×SD16—1222no—
518C2×SD16C2×#692311yescharacteristic, complemented
519C2×D8—611no—
520C2×D8—611no—
521C2×D8—611no—
522C2×D8—1222no—
523C2×D8—1222no—
524C2×D8C2×#692311yescharacteristic
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8—611no—
529#124—611no—
530#124—611no—
531#124—611no—
532#124—1221no—
533#124—1221no—
534#124C2×#692311yescharacteristic, complemented
535C4×Q8—1222no—
536C4×Q8—2441no—
537C4×D4—611no—
538C4×D4—611no—
539C4×D4—611no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4—1222no—
543C4×D4—1222no—
544C4×D4—1222no—
545C4×D4—2441no—
546C4×D4—2441no—
547C4×D4—2441no—
548C4×D4C2×#692311yescharacteristic, complemented
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—1221no—
571C2×C42—1221no—
572#107—1222no—
573#106—1222no—
574C4⋊C8—611no—
575C4⋊C8—611no—
576C4⋊C8—611no—
577C4⋊C8C2×#692311yescharacteristic, complemented
578#103—611no—
579#103—611no—
580#103—611no—
581#103—1222no—
582#103—2441no—
583#103C2×#692311yescharacteristic, complemented
584#102—614no—
585#102—611no—
586#102—611no—
587#102—611no—
588#102—1222no—
589#102—1222no—
590#102—2441no—
591#102C2×#692311yescharacteristic, complemented
592C4×C8—1221no—
593C4×C8—1221no—
594C4×C8—1222no—
595C4×C8—1222no—
596#95—611no—
597#95—611no—
598#95—1221no—
599#95—1221no—
600#95—1221no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605C24—1221no—
606C24—1221no—
607C2×Q8—611no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×Q8C22×#692311yescharacteristic
614C2×D4—612no—
615C2×D4—612no—
616C2×D4—611no—
617C2×D4—611no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—1221no—
626C2×D4C22×#692311yescharacteristic
627C2×D4C22×#692311yescharacteristic
628C22×C4—21no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—4881no—
646C22×C4—4881no—
647C22×C4—4881no—
648C22×C4—4881no—
649C22×C4—4881no—
650C22×C4—2442no—
651C22×C4—2442no—
652C22×C4—2442no—
653C22×C4—2442no—
654C22×C4—2442no—
655C22×C4—2442no—
656SD16—22no—
657SD16—1222no—
658SD16—1222no—
659SD16—1222no—
660D8—22no—
661D8—1222no—
662D8—1222no—
663D8—1222no—
664C2×C8—612no—
665C2×C8—611no—
666C2×C8—611no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8C22×#692311yescharacteristic
677C2×C8C22×#692311yescharacteristic
678C4⋊C4—612no—
679C4⋊C4—611no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1222no—
683C4⋊C4—1222no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—4881no—
691C4⋊C4—4881no—
692C4⋊C4—2442no—
693C4⋊C4C22×#692311yescharacteristic
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—1221no—
698C22⋊C4—1221no—
699C22⋊C4—1221no—
700C22⋊C4—1221no—
701C22⋊C4—1221no—
702C22⋊C4—1221no—
703C22⋊C4—1221no—
704C22⋊C4—1221no—
705C22⋊C4—1221no—
706C22⋊C4—4881no—
707C22⋊C4—2442no—
708C22⋊C4—2442no—
709C22⋊C4—2442no—
710C22⋊C4—2442no—
711C42—611no—
712C42—611no—
713C42—611no—
714C42—1221no—
715C42—1221no—
716C42—1221no—
717C42—1221no—
718C42—4881no—
719C42—2442no—
720C42C22×#692311yescharacteristic
721C23—21no—
722C23—21no—
723C23—611no—
724C23—1222no—
725C23—1222no—
726C23—1221no—
727C23—1221no—
728C23—2441no—
729C23—2441no—
730C23—2441no—
731C23—2441no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738Q8—21no—
739Q8—21no—
740Q8—1221no—
741Q8—1221no—
742Q8—2441no—
743Q8—2441no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—612no—
748D4—1222no—
749D4—1222no—
750D4—1221no—
751D4—1221no—
752D4—1221no—
753D4—2441no—
754D4—2441no—
755D4D4×#692312yes—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—81no—
759C2×C4—611no—
760C2×C4—611no—
761C2×C4—611no—
762C2×C4—611no—
763C2×C4—611no—
764C2×C4—612no—
765C2×C4—612no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1222no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—4881no—
786C2×C4—4881no—
787C2×C4—4884no—
788C2×C4—4884no—
789C2×C4—4881no—
790C2×C4—4884no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4D4×#692311yescharacteristic
807C2×C4D4×#692311yescharacteristic
808C2×C4C23×#692311yescharacteristic
809C8—21no—
810C8—21no—
811C8—1222no—
812C8—1221no—
813C8—1221no—
814C8—2441no—
815C22—22no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—611no—
822C22—611no—
823C22—611no—
824C22—611no—
825C22—611no—
826C22—611no—
827C22—1222no—
828C22—4881no—
829C22—4881no—
830C22—4881no—
831C22—4881no—
832C22—2442no—
833C22—2442no—
834C22—2442no—
835C22—2442no—
836C22—2441no—
837C22—2441no—
838C22—2441no—
839C22—2441no—
840C22—2441no—
841C22C2×D4×#692311yescharacteristic
842C4—21no—
843C4—21no—
844C4—41no—
845C4—41no—
846C4—611no—
847C4—611no—
848C4—1222no—
849C4—1222no—
850C4—1221no—
851C4—1221no—
852C4—4881no—
853C4—4881no—
854C4—4881no—
855C4—2441no—
856C4—2441no—
857C4—2442no—
858C4—2441no—
859C4—2441no—
860C4C2×D4×#692311yescharacteristic
861C4#1684083111yescharacteristic
862C2—42no—
863C2—81no—
864C2—611no—
865C2—611no—
866C2—611no—
867C2—611no—
868C2—4881no—
869C2—2442no—
870C2#2146234411yescharacteristic
871C2#135×#692311yescharacteristic
872C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#463C4
socleC22×C61C2×C4×D4
prime radicalC2×D8×D61C22
cosocleC2×C4×D61C24
hypercenter#463#6923
hypocenterC61#22999
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×#6923C2semidirect
3. #21462350C2semidirect
4. #21462332C2semidirect
5. #21461948C2semidirect
6. #21461932C2semidirect
7. #21461909C2semidirect
8. #21461908C2semidirect
10. #21461812C2semidirect
11. #21461784C2semidirect
12. #21461783C2semidirect
13. #21461612C2semidirect
14. C4×#14519839C2semidirect
58. #16839980C4semidirect
59. #16839979C4semidirect
60. #16839978C4semidirect
61. #16839977C4semidirect
62. #16839976C4semidirect
63. #16839975C4semidirect
64. #16839974C4semidirect
68. C61×#463C4semidirect
125. C2×#11758190C2×C4semidirect
126. C2×#11758200C2×C4semidirect
127. C2×#11758201C2×C4semidirect
137. #14519766C2×C4semidirect
138. #14519765C2×C4semidirect
139. #14519764C2×C4semidirect
142. C4×D244C2×C4semidirect
143. D4×Dic61C2×C4semidirect
144. #14519739C2×C4semidirect
152. C4⋊#92418C2×C4semidirect
153. #14519706C2×C4semidirect
154. #14519706C2×C4semidirect
155. #14519702C2×C4semidirect
156. #14519701C2×C4semidirect
157. #14519700C2×C4semidirect
158. #14519699C2×C4semidirect
159. #14519698C2×C4semidirect
160. #14519697C2×C4semidirect
161. C2×SD16×C61C2×C4semidirect
163. #124×C61C2×C4semidirect
164. C4×D4×C61C2×C4semidirect
165. C4⋊C8×C61C2×C4semidirect
166. #103×C61C2×C4semidirect
167. #102×C61C2×C4semidirect
467. #463#6923semidirect
505. C61#22999semidirect
518. C2×SD16C2×#6923semidirect
534. #124C2×#6923semidirect
548. C4×D4C2×#6923semidirect
577. C4⋊C8C2×#6923semidirect
583. #103C2×#6923semidirect
591. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×#69232
C2×D8×#69232
#214623502
#214623322
#214619482
#214619322
#214619092
#214619082
#214618142
#214618122
#214617842
#214617832
#214616122
C4×#145198392
#463×D612
#2299961