Finite Group Databasebeta

← #30616071

Subgroups — #30616071

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462302C211yesmaximal, characteristic, complemented
2#21462258C211yesmaximal, characteristic, complemented
3#21461897C211yesmaximal, characteristic, complemented
4#21461896C211yesmaximal, characteristic, complemented
5#21461882C211yesmaximal, characteristic, complemented
6#21461881C211yesmaximal, characteristic, complemented
7#21461814C211yesmaximal, characteristic
8#21461814C211yesmaximal, characteristic
9#21461784C211yesmaximal, characteristic, complemented
10#21461782C211yesmaximal, characteristic, complemented
11#21461633C211yesmaximal, characteristic, complemented
12C4×#14519839C211yesmaximal, characteristic, complemented
13C4×#14519839C211yesmaximal, characteristic, complemented
14#21461539C211yesmaximal, characteristic, complemented
15#442×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20C2×#14519839C2211yescharacteristic
21C2×#14519839C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C4×D61⋊C8C2211yescharacteristic
25#16840714C2211yescharacteristic
26#16840714C2211yescharacteristic
27#16840713C2211yescharacteristic
28#16840713C2211yescharacteristic
29#16840712—21no—
30#16840712—21no—
31#16840705—21no—
32#16840704—21no—
33C4⋊C4×#6923C2211yescharacteristic
34C4⋊C4×#6923C2211yescharacteristic
35C4×C4⋊#6923C2211yescharacteristic
36C4×C4⋊#6923C2211yescharacteristic
37C22⋊C4×#6923—21no—
38C22⋊C4×#6923—21no—
39C4×C22⋊#6923—21no—
40#16840698C2211yescharacteristic
41C2×(C2×#6923)⋊C4—21no—
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48(C2×#6923)⋊C8C2211yescharacteristic
49(C2×#6923)⋊C8C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×D8×D61C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54C4×D4×D61C2211yescharacteristic
55#16839875C411yescharacteristic, complemented
56#16839874C411yescharacteristic, complemented
57#16839873C411yescharacteristic, complemented
58#16839872C411yescharacteristic, complemented
59#16839872C411yescharacteristic, complemented
60#16839871C411yescharacteristic, complemented
61#16839871C411yescharacteristic, complemented
62#106×D61C2211yescharacteristic
63#102×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#97×D61C2211yescharacteristic
66C61×#442C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—22no—
74D4×#6923—22no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923C2311yescharacteristic
92C2×C4×#6923C2311yescharacteristic
93#14519846—22no—
94#14519845—22no—
95#14519839—22no—
96#14519839—22no—
97#14519839—22no—
98#14519839—22no—
99C4×#92420—21no—
100C4×#92420—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4D411yescharacteristic
108(C2×#6923)⋊C4D411yescharacteristic
109(C2×#6923)⋊C4D411yescharacteristic
110(C2×#6923)⋊C4D411yescharacteristic
111C2×D4×D61C2311yescharacteristic
112C2×D4×D61C2311yescharacteristic
113C22×C4×D61—21no—
114C22×C4×D61—21no—
115C2×D488C2×C411yescharacteristic
116C2×#11758199C2×C411yescharacteristic
117C2×#11758199C2×C411yescharacteristic
118D8×D61—22no—
119D8×D61—22no—
120C2×C8×D61C2311yescharacteristic
121C2×C8×D61C2311yescharacteristic
122C4×D244C2×C411yescharacteristic
123C4×D244C2×C411yescharacteristic, complemented
124D4×Dic61C2×C411yescharacteristic
125D4×Dic61C2×C411yescharacteristic, complemented
126#14519739C2×C411yescharacteristic
127#14519739C2×C411yescharacteristic, complemented
128C4×C22⋊D61—21no—
129C4×C22⋊D61—21no—
130#14519737—21no—
131#14519737—21no—
132C4⋊C4×D61C2311yescharacteristic
133C4⋊C4×D61C2311yescharacteristic
134C22⋊C4×D61—21no—
135C22⋊C4×D61—21no—
136C42×D61C2311yescharacteristic
137#14519709C2×C411yescharacteristic, complemented
138#14519708C2×C411yescharacteristic, complemented
139#14519708C2×C411yescharacteristic, complemented
140#14519699C2×C411yescharacteristic
141#14519699C2×C411yescharacteristic, complemented
142#14519698C2×C411yescharacteristic
143#14519698C2×C411yescharacteristic, complemented
144#14519697C2×C411yescharacteristic
145#14519697C2×C411yescharacteristic, complemented
146#14519688C2×C411yescharacteristic, complemented
147#14519687C2×C411yescharacteristic, complemented
148#14519687C2×C411yescharacteristic, complemented
149C2×D8×C61C2×C411yescharacteristic
150C4×D4×C61C2×C411yescharacteristic
151C4×D4×C61C2×C411yescharacteristic, complemented
152#106×C61C2×C411yescharacteristic, complemented
153#102×C61C2×C411yescharacteristic
154#102×C61C2×C411yescharacteristic, complemented
155#97×C61C2×C411yescharacteristic, complemented
156C23×D61—21no—
157C23×D61—21no—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—24no—
161C22×#6923—24no—
162C22×#6923—21no—
163C22×#6923—21no—
164C22×#6923—81no—
165C22×#6923—81no—
166C22×#6923—81no—
167C22×#6923—81no—
168C22×#6923C2×D411yescharacteristic
169C22×#6923C2×D411yescharacteristic
170C22×#6923C2×D411yescharacteristic
171C22×#6923C2×D411yescharacteristic
172C2×D4×C61C22×C411yescharacteristic
173C2×D4×C61C22×C411yescharacteristic
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C2×C22⋊D61—21no—
177C2×C22⋊D61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180D4×D61—21no—
181D4×D61—21no—
182D4×D61—21no—
183D4×D61—21no—
184D4×D61—21no—
185D4×D61—21no—
186D4×D61#4112yes—
187D4×D61#4112yes—
188C2×D244C22×C411yescharacteristic
189C2×D244C22×C411yescharacteristic
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—81no—
197C2×C4×D61—81no—
198C2×C4×D61—81no—
199C2×C4×D61—81no—
200C2×C4×D61C2×D411yescharacteristic
201C2×C4×D61C2×D411yescharacteristic
202C2×C4×D61C2411yescharacteristic
203C22⋊#6923—24no—
204C22⋊#6923—24no—
205C22⋊#6923—81no—
206C22⋊#6923—81no—
207C22⋊#6923—81no—
208C22⋊#6923—81no—
209C2×#92420—21no—
210C2×#92420—21no—
211C4⋊#6923—21no—
212C4⋊#6923—21no—
213C4⋊#6923—21no—
214C4⋊#6923—21no—
215C4⋊#6923—21no—
216C4⋊#6923—21no—
217C4⋊#6923—81no—
218C4⋊#6923—81no—
219C4⋊#6923#4112yes—
220C4⋊#6923#4112yes—
221C4×#6923—21no—
222C4×#6923—21no—
223C4×#6923—21no—
224C4×#6923—21no—
225C4×#6923—81no—
226C4×#6923—81no—
227C4×#6923—81no—
228C4×#6923—81no—
229D61⋊C8—21no—
230D61⋊C8—21no—
231D61⋊C8—21no—
232D61⋊C8—21no—
233D8×C61—22no—
234C2×C8×C61C22×C411yescharacteristic
235C2×C8×C61C22×C411yescharacteristic
236C4⋊C4×C61C22×C411yescharacteristic
237C4⋊C4×C61C22×C411yescharacteristic
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C42×C61C22×C411yescharacteristic
241C22⋊Dic61—21no—
242C22⋊Dic61—21no—
243#11758199—22no—
244#11758199—22no—
245#11758198—21no—
246#11758198—21no—
247#11758198—21no—
248#11758198—21no—
249C4⋊Dic61C22×C411yescharacteristic
250C4⋊Dic61C22×C411yescharacteristic
251#11758196—21no—
252#11758196—21no—
253C4×Dic61C22×C411yescharacteristic
254C4×Dic61#4111yescharacteristic
255C4×Dic61#4111yescharacteristic
256C2×#92418C22×C411yescharacteristic
257C2×#92418C22×C411yescharacteristic
258D488—22no—
259C8×D61—21no—
260C8×D61—21no—
261C8×D61—21no—
262C8×D61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C22×D61—21no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—21no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61C22×D411yescharacteristic
280C2×#6923—21no—
281C2×#6923—21no—
282C2×#6923—21no—
283C2×#6923—21no—
284C2×#6923—22no—
285C2×#6923—22no—
286C2×#6923—21no—
287C2×#6923—21no—
288C2×#6923—21no—
289C2×#6923—21no—
290C2×#6923—21no—
291C2×#6923—21no—
292C2×#6923—21no—
293C2×#6923—21no—
294C2×#6923—41no—
295C2×#6923—41no—
296C2×#6923—41no—
297C2×#6923—41no—
298C2×#6923—41no—
299C2×#6923—41no—
300C2×#6923—41no—
301C2×#6923—41no—
302C2×#6923—41no—
303C2×#6923—41no—
304C2×#6923—84no—
305C2×#6923—84no—
306D4×C61—21no—
307D4×C61—21no—
308D4×C61—21no—
309D4×C61#11712yes—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—81no—
313C2×C4×C61—81no—
314C2×C4×C61C4×D411yescharacteristic
315C2×C4×C61C4×D411yescharacteristic
316C2×C4×C61C23×C411yescharacteristic
317C22⋊D61—22no—
318C22⋊D61—22no—
319C22⋊D61—41no—
320C22⋊D61—41no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—81no—
324C2×Dic61—81no—
325C2×Dic61C4×D411yescharacteristic
326C2×Dic61C4×D411yescharacteristic
327C2×Dic61C2×#4111yescharacteristic
328D244—21no—
329D244—21no—
330D244—21no—
331D244#11712yes—
332C4×D61—21no—
333C4×D61—21no—
334C4×D61—21no—
335C4×D61—21no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—81no—
341C4×D61—81no—
342C4×D61—81no—
343C4×D61—81no—
344C4×D61C2×#4111yescharacteristic
345C4×D61C2×#4111yescharacteristic
346C4×D61C2×#4111yescharacteristic
347C4×D61C2×#4111yescharacteristic
348#92420—41no—
349#92420—41no—
350C8×C61—21no—
351C8×C61—21no—
352#92418—21no—
353#92418—21no—
354#21126—611nomaximal, Sylow
355C22×C61—22no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61C2×C4×D411yescharacteristic
362C2×D61—22no—
363C2×D61—41no—
364C2×D61—41no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C2×D61#52511yescharacteristic
377C2×D61#52511yescharacteristic
378C2×D61#57611yescharacteristic
379C2×D61#57611yescharacteristic
380C2×D61#57711yescharacteristic
381C2×D61#57711yescharacteristic
382#6923—41no—
383#6923—42no—
384#6923—41no—
385#6923—41no—
386#6923—42no—
387#6923—41no—
388#6923—81no—
389#6923—81no—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61C2×#11711yescharacteristic
395C4×C61C4×#4111yescharacteristic
396Dic61—21no—
397Dic61—21no—
398Dic61—41no—
399Dic61—41no—
400Dic61#52911yescharacteristic
401Dic61#52911yescharacteristic
402C2×#442—611no—
403#2319—611no—
404#2275—611no—
405#1926—611no—
406#1925—611no—
407#1920—611no—
408#1919—611no—
409#1879—611no—
410#1879—611no—
411#1864—611no—
412#1862—611no—
413#1776—611no—
414C4×#102—611no—
415C4×#102—611no—
416#1746—611no—
417C2×C61—42no—
418C2×C61—81no—
419C2×C61#229011yescharacteristic
420C2×C61#294611yescharacteristic
421C2×C61#294611yescharacteristic
422D61—42no—
423D61—81no—
424D61#311811yescharacteristic
425D61#311911yescharacteristic
426D61#312211yescharacteristic
427D61#312511yescharacteristic
428C22×D8—611no—
429C2×C4×D4—611no—
430C2×C4×D4—611no—
431C2×C4×D4—611no—
432C2×C4×D4—611no—
433#442—611no—
434#442—611no—
435#442—611no—
436#442—611no—
437#442—611no—
438#442—611no—
439#442—611no—
440#442#692311yescharacteristic, complemented
441C2×#107—611no—
442C2×#106—611no—
443C2×#106—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#97—611no—
451C2×C4×C8—611no—
452#390—611no—
453#390—611no—
454#389—611no—
455#389—611no—
456#388—1221no—
457#388—1221no—
458#381—1221no—
459#380—1221no—
460C4×C4⋊C4—611no—
461C4×C4⋊C4—611no—
462C4×C4⋊C4—611no—
463C4×C4⋊C4—611no—
464C4×C22⋊C4—1221no—
465C4×C22⋊C4—1221no—
466C4×C22⋊C4—1221no—
467#376—611no—
468C2×#95—1221no—
469#340—611no—
470#340—611no—
471#340—611no—
472#340—611no—
473#340—611no—
474#340—611no—
475#336—611no—
476#336—611no—
477#336—611no—
478#336—611no—
479C61#2112611yescharacteristic, complemented, Sylow
480C22×D4—611no—
481C22×D4—611no—
482C23×C4—1221no—
483C23×C4—1221no—
484C23×C4—1221no—
485C23×C4—1221no—
486C2×D8—611no—
487C2×D8—611no—
488C2×D8—611no—
489C2×D8—1222no—
490C2×D8—1222no—
491C2×D8C2×#692311yescharacteristic
492C22×C8—611no—
493C22×C8—611no—
494C22×C8—611no—
495C22×C8—611no—
496C4×D4—611no—
497C4×D4—611no—
498C4×D4—611no—
499C4×D4—611no—
500C4×D4—611no—
501C4×D4—611no—
502C4×D4—1221no—
503C4×D4—1221no—
504C4×D4—1221no—
505C4×D4—1221no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4C2×#692311yescharacteristic
511C4×D4C2×#692311yescharacteristic, complemented
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C42—611no—
529C2×C42—611no—
530C2×C42—611no—
531C2×C42—1221no—
532C2×C42—1221no—
533C2×C42—1221no—
534C2×C42—1221no—
535#107—1222no—
536#106—611no—
537#106—611no—
538#106—611no—
539#106—1222no—
540#106C2×#692311yescharacteristic, complemented
541#102—611no—
542#102—611no—
543#102—611no—
544#102—611no—
545#102—611no—
546#102—611no—
547#102—1222no—
548#102—1222no—
549#102—1222no—
550#102—1222no—
551#102C2×#692311yescharacteristic
552#102C2×#692311yescharacteristic, complemented
553#97—611no—
554#97—611no—
555#97—611no—
556#97C2×#692311yescharacteristic, complemented
557C4×C8—1221no—
558C4×C8—1221no—
559#95—611no—
560#95—611no—
561#95—611no—
562#95—611no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566#95—1221no—
567#95—1221no—
568#95—1221no—
569C24—1221no—
570C24—1221no—
571C2×D4—612no—
572C2×D4—612no—
573C2×D4—611no—
574C2×D4—611no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4C22×#692311yescharacteristic
584C2×D4C22×#692311yescharacteristic
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1224no—
601C22×C4—1224no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—4881no—
609C22×C4—4881no—
610C22×C4—4881no—
611C22×C4—4881no—
612C22×C4—4881no—
613C22×C4—4881no—
614C22×C4—4881no—
615C22×C4—4881no—
616D8—22no—
617D8—1222no—
618D8—1222no—
619D8—1222no—
620C2×C8—611no—
621C2×C8—611no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8C22×#692311yescharacteristic
633C2×C8C22×#692311yescharacteristic
634C4⋊C4—612no—
635C4⋊C4—612no—
636C4⋊C4—611no—
637C4⋊C4—611no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—4881no—
647C4⋊C4—4881no—
648C4⋊C4C22×#692311yescharacteristic
649C4⋊C4C22×#692311yescharacteristic
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—1221no—
653C22⋊C4—1221no—
654C22⋊C4—1221no—
655C22⋊C4—1221no—
656C22⋊C4—1224no—
657C22⋊C4—1224no—
658C22⋊C4—1221no—
659C22⋊C4—1221no—
660C22⋊C4—4881no—
661C22⋊C4—4881no—
662C22⋊C4—4881no—
663C22⋊C4—4881no—
664C42—611no—
665C42—611no—
666C42—611no—
667C42—1221no—
668C42—1221no—
669C42—1221no—
670C42—1221no—
671C42—4881no—
672C42—4881no—
673C42—4881no—
674C42—4881no—
675C42C22×#692311yescharacteristic
676C23—21no—
677C23—21no—
678C23—611no—
679C23—1222no—
680C23—1222no—
681C23—1221no—
682C23—1221no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691C23—2441no—
692C23—2441no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—612no—
697D4—1222no—
698D4—1222no—
699D4—1221no—
700D4—1221no—
701D4—1221no—
702D4—2441no—
703D4—2441no—
704D4#1451985612yes—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—611no—
710C2×C4—611no—
711C2×C4—611no—
712C2×C4—611no—
713C2×C4—611no—
714C2×C4—611no—
715C2×C4—611no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—4881no—
737C2×C4—4881no—
738C2×C4—4881no—
739C2×C4—4881no—
740C2×C4—4881no—
741C2×C4—4881no—
742C2×C4—4884no—
743C2×C4—4884no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4D4×#692311yescharacteristic
759C2×C4D4×#692311yescharacteristic
760C2×C4C23×#692311yescharacteristic
761C8—21no—
762C8—21no—
763C8—1221no—
764C8—1221no—
765C8—2441no—
766C8—2441no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—611no—
774C22—611no—
775C22—611no—
776C22—611no—
777C22—611no—
778C22—611no—
779C22—1222no—
780C22—4881no—
781C22—4881no—
782C22—4881no—
783C22—4881no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2441no—
789C22—2441no—
790C22—2441no—
791C22—2441no—
792C22—2441no—
793C22C2×D4×#692311yescharacteristic
794C4—21no—
795C4—21no—
796C4—41no—
797C4—41no—
798C4—611no—
799C4—611no—
800C4—1221no—
801C4—1221no—
802C4—4881no—
803C4—4881no—
804C4—2441no—
805C4—2441no—
806C4—2441no—
807C4—2441no—
808C4—2442no—
809C4—2442no—
810C4—2441no—
811C4—2441no—
812C4C2×#1451985611yescharacteristic
813C4#41×#692311yescharacteristic
814C2—42no—
815C2—81no—
816C2—611no—
817C2—611no—
818C2—611no—
819C2—611no—
820C2—4881no—
821C2—2442no—
822C2#2146227311yescharacteristic
823C2#2146257611yescharacteristic
824C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#442C4
socleC22×C61C2×C4×D4
prime radicalC2×D8×D61C22
cosocleC2×C4×D61C24
hypercenter#442#6923
hypocenterC61#21126
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #21462302C2semidirect
2. #21462258C2semidirect
3. #21461897C2semidirect
4. #21461896C2semidirect
5. #21461882C2semidirect
6. #21461881C2semidirect
9. #21461784C2semidirect
10. #21461782C2semidirect
11. #21461633C2semidirect
12. C4×#14519839C2semidirect
13. C4×#14519839C2semidirect
14. #21461539C2semidirect
55. #16839875C4semidirect
56. #16839874C4semidirect
57. #16839873C4semidirect
58. #16839872C4semidirect
59. #16839872C4semidirect
60. #16839871C4semidirect
61. #16839871C4semidirect
66. C61×#442C4semidirect
123. C4×D244C2×C4semidirect
125. D4×Dic61C2×C4semidirect
127. #14519739C2×C4semidirect
137. #14519709C2×C4semidirect
138. #14519708C2×C4semidirect
139. #14519708C2×C4semidirect
141. #14519699C2×C4semidirect
143. #14519698C2×C4semidirect
145. #14519697C2×C4semidirect
146. #14519688C2×C4semidirect
147. #14519687C2×C4semidirect
148. #14519687C2×C4semidirect
151. C4×D4×C61C2×C4semidirect
152. #106×C61C2×C4semidirect
154. #102×C61C2×C4semidirect
155. #97×C61C2×C4semidirect
440. #442#6923semidirect
479. C61#21126semidirect
511. C4×D4C2×#6923semidirect
540. #106C2×#6923semidirect
552. #102C2×#6923semidirect
556. #97C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623022
#214622582
#214618972
#214618962
#214618822
#214618812
#214618142
#214617842
#214617822
#214616332
C4×#145198392
#214615392
#442×D612
#2112661