Finite Group Databasebeta

← #29700242

Subgroups — #29700242

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839836C211yesmaximal, characteristic, complemented
2C2×#16839835C211yesmaximal, characteristic, complemented
3C2×#16839728C211yesmaximal, characteristic, complemented
4C2×#16839727C211yesmaximal, characteristic, complemented
5#21449035C211yesmaximal, characteristic
6#21446617C211yesmaximal, characteristic, complemented
7#21446433C211yesmaximal, characteristic, complemented
8#21446432C211yesmaximal, characteristic, complemented
9#21446111C211yesmaximal, characteristic, complemented
10#21446110C211yesmaximal, characteristic, complemented
11#21446110C211yesmaximal, characteristic, complemented
12#21446004C211yesmaximal, characteristic, complemented
13#21446003C211yesmaximal, characteristic, complemented
14#21445596C211yesmaximal, characteristic, complemented
15C61×#1752C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×C4×C22⋊D61C2211yescharacteristic
24#16839836—24no—
25#16839835—24no—
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29#16839728—24no—
30#16839727—24no—
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519689C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519687C2211yescharacteristic
42#16839683C411yescharacteristic
43#16839680C411yescharacteristic
44#16839678C411yescharacteristic
45#16839678C411yescharacteristic
46#16839675C411yescharacteristic
47#16839672C411yescharacteristic
48#16839671C411yescharacteristic
49#16839671C411yescharacteristic
50C4×#11758198C2211yescharacteristic
51C4×#11758198C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C2×#97×C61C2211yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C22×Dic122C2×C411yescharacteristic
70C22×D244C2×C411yescharacteristic
71C22×D244C2×C411yescharacteristic
72C22×D244C2×C411yescharacteristic
73C22×C22⋊D61C2×C411yescharacteristic
74C22×C22⋊D61C2×C411yescharacteristic
75C22×C22⋊D61C2×C411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C22×C4×D61C2311yescharacteristic
79C2×#11758194—22no—
80C2×#11758194—22no—
81C2×#11758194—41no—
82C2×#11758189—22no—
83C2×#11758189—22no—
84C2×#11758189—41no—
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C2×C8×D61—22no—
90C2×C8×D61—22no—
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—41no—
94C2×C8×D61—41no—
95C4×D244—22no—
96C4×D244—22no—
97C4×D244—41no—
98C4×D244—41no—
99C4×C22⋊D61—22no—
100C4×C22⋊D61—22no—
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×C4⋊Dic61C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×C22⋊Dic61C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C4⋊#92418—22no—
116C4⋊#92418—41no—
117#14519706—22no—
118C22⋊#92418—22no—
119#14519689—22no—
120#14519689—22no—
121#14519689—22no—
122#14519689—22no—
123#14519689—22no—
124#14519689—22no—
125#14519689—22no—
126#14519689—41no—
127#14519689D414yescomplemented
128#14519687—22no—
129#14519684C2×C411yescharacteristic
130#14519684C2×C411yescharacteristic
131#14519684C2×C411yescharacteristic
132#14519684C2×C411yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C22×C8×C61—22no—
135C22×C8×C61—22no—
136C22×C8×C61—41no—
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C22⋊C4×C61C2×C411yescharacteristic
143C2×C42×C61C2311yescharacteristic
144C2×C42×C61C2311yescharacteristic
145C22⋊C8×C61D414yescomplemented
146#97×C61—22no—
147#97×C61—41no—
148#95×C61C2×C411yescharacteristic
149#95×C61C2×C411yescharacteristic
150C24×C61C22×C411yescharacteristic
151C23×D61C22×C411yescharacteristic
152C23×D61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C2×D412yes—
164C22×C4×C61#4112yes—
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—41no—
173C2×C22⋊D61—41no—
174C2×C22⋊D61—41no—
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180#11758222—44no—
181#11758222—44no—
182#11758222—44no—
183#11758222—44no—
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—41no—
190C2×D244—41no—
191C2×D244—41no—
192C2×D244—41no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61C2×D412yes—
210C2×C4×D61#4112yes—
211C2×Dic122—22no—
212C2×Dic122—22no—
213C2×Dic122—41no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—44no—
224C2×C8×C61C2×D412yes—
225C2×C8×C61C2×D412yes—
226C2×C8×C61C2×D412yes—
227C22⋊C4×C61—41no—
228C22⋊C4×C61—41no—
229C42×C61—21no—
230C42×C61—21no—
231C42×C61—21no—
232C42×C61—21no—
233C22⋊Dic61—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—41no—
238#11758198—41no—
239#11758198—41no—
240#11758198—41no—
241#11758198—41no—
242#11758198—41no—
243C4⋊Dic61—22no—
244C4⋊Dic61—41no—
245#11758196—22no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248#11758194—44no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418C2×D412yes—
261#11758189—44no—
262C8×D61—44no—
263C8×D61—44no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61C4×D412yes—
271C23×C61C23×C411yescharacteristic
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61C4×D412yes—
292C22×D61#13112yes—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61C4×D412yes—
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61H(5,𝔽2)11yescharacteristic
317C2×C4×C61H(5,𝔽2)11yescharacteristic
318C22⋊D61—44no—
319C22⋊D61—44no—
320C22⋊D61—44no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61C4×D412yes—
336D244—44no—
337D244—44no—
338D244—44no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—41no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351Dic122—44no—
352C8×C61—22no—
353C8×C61—22no—
354C8×C61—22no—
355C8×C61—41no—
356#92418—22no—
357#92418—41no—
358#92418—41no—
359#92418—41no—
360#22851—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61C2×C4×D411yescharacteristic
369C22×C61C2×C4×D411yescharacteristic
370C22×C61#51811yescharacteristic
371C22×C61C2×#13111yescharacteristic
372C22×C61#56811yescharacteristic
373C22×C61#56811yescharacteristic
374C22×C61#56811yescharacteristic
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C4×C61—22no—
397C4×C61—41no—
398C4×C61—41no—
399C4×C61—41no—
400C4×C61—41no—
401C4×C61D4211yescharacteristic
402C4×C61#54611yescharacteristic
403C4×C61#54611yescharacteristic
404C4×C61#55111yescharacteristic
405Dic61—22no—
406Dic61—41no—
407Dic61—41no—
408Dic61—41no—
409Dic61—41no—
410C2×#435—611no—
411C2×#435—611no—
412C2×#408—611no—
413C2×#408—611no—
414#2388—611no—
415#1955—611no—
416#1924—611no—
417#1924—611no—
418#1869—611no—
419#1869—611no—
420#1869—611no—
421#1851—611no—
422#1851—611no—
423#1752—611no—
424#1752D6111yescharacteristic, complemented
425C2×C61—42no—
426C2×C61#235811yescharacteristic
427C2×C61#293211yescharacteristic
428C2×C61#293211yescharacteristic
429C2×C61#293311yescharacteristic
430C2×C61#293311yescharacteristic
431C2×C61#297611yescharacteristic
432C2×C61#298011yescharacteristic
433D61—42no—
434D61—42no—
435D61—81no—
436C22×#41—611no—
437C22×M16—611no—
438C22×M16—611no—
439C23×C8—611no—
440C23×C8—611no—
441C23×C8C2×D6111yescharacteristic
442C2×C4×D4—611no—
443C2×C4×D4—611no—
444C2×C4×D4—611no—
445#435—1224no—
446#435—1224no—
447C2×C4⋊C8—611no—
448C2×C4⋊C8—611no—
449C2×C4⋊C8—611no—
450#408—1224no—
451#408—1224no—
452C2×C22⋊C8—611no—
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×C22⋊C8—611no—
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461C2×C22⋊C8—611no—
462C2×C22⋊C8C2×D6111yescharacteristic
463C2×#97—611no—
464C2×#97C2×D6111yescharacteristic
465C2×#97C2×D6111yescharacteristic
466#395—611no—
467#394—611no—
468#394—611no—
469#394—611no—
470#393—611no—
471#392—611no—
472#392—611no—
473#392—611no—
474C4×C22⋊C4—611no—
475C4×C22⋊C4—611no—
476C4×C22⋊C4C2×D6111yescharacteristic
477#336—611no—
478#336—611no—
479#336—611no—
480#336—611no—
481#336C2×D6111yescharacteristic
482#336C2×D6111yescharacteristic
483C61#2285111yescharacteristic, complemented, Sylow
484C2×#41—1222no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—1222no—
488C2×#41—2441no—
489C2×#41—2441no—
490C22×Q8—611no—
491C22×D4—611no—
492C22×D4—611no—
493C22×D4—611no—
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4C22×D6111yescharacteristic
501C2×M16—1222no—
502C2×M16—1222no—
503C2×M16—1222no—
504C2×M16—1222no—
505C2×M16—2441no—
506C2×M16—2441no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8—611no—
511C22×C8—611no—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8—1222no—
515C22×C8—1222no—
516C22×C8—1222no—
517C22×C8—1222no—
518C22×C8—2441no—
519C22×C8—2441no—
520C22×C8C22×D6111yescharacteristic
521C22×C8C22×D6111yescharacteristic
522C22×C8C22×D6111yescharacteristic
523C22×C8C22×D6111yescharacteristic
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—2441no—
529C4×D4—2441no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—611no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4—611no—
541C2×C22⋊C4—611no—
542C2×C22⋊C4—611no—
543C2×C22⋊C4C4×D6111yescharacteristic
544C2×C22⋊C4C4×D6111yescharacteristic
545C2×C42—611no—
546C2×C42C22×D6111yescharacteristic
547C2×C42C22×D6111yescharacteristic
548C4⋊C8—1222no—
549C4⋊C8—1222no—
550C4⋊C8—2441no—
551C22⋊C8—614no—
552C22⋊C8—1222no—
553C22⋊C8—1222no—
554C22⋊C8—1222no—
555C22⋊C8—1222no—
556C22⋊C8—1222no—
557C22⋊C8—1222no—
558C22⋊C8—1222no—
559C22⋊C8—1222no—
560C22⋊C8—2441no—
561C22⋊C8D24414yescomplemented
562#97—22no—
563#97—41no—
564#97—1222no—
565#95—611no—
566#95—611no—
567#95—611no—
568#95—611no—
569#95C4×D6111yescharacteristic
570#95C4×D6111yescharacteristic
571C24—611no—
572C24—611no—
573C24—611no—
574C24C2×C4×D6111yescharacteristic
575#41—2444no—
576#41—2444no—
577#41—2444no—
578#41—2444no—
579C2×Q8—1222no—
580C2×Q8—1222no—
581C2×Q8—2441no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—2441no—
594C2×D4—2441no—
595C2×D4—2441no—
596C2×D4—2441no—
597C2×D4—2441no—
598C2×D4—2441no—
599C2×D4—2441no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—611no—
605C22×C4—612no—
606C22×C4—612no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4C2×C4×D6111yescharacteristic
628C22×C4C2×C4×D6111yescharacteristic
629C22×C4C2×C4×D6111yescharacteristic
630C22×C4C2×C4×D6111yescharacteristic
631C22×C4C2×C4×D6111yescharacteristic
632C22×C4C2×D24412yes—
633C22×C4#1175822212yes—
634C22×C4C23×D6111yescharacteristic
635M16—2444no—
636M16—2444no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—44no—
647C2×C8—612no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—2444no—
660C2×C8—2444no—
661C2×C8C2×D24412yes—
662C2×C8C2×D24412yes—
663C2×C8D4×D6112yes—
664C4⋊C4—1222no—
665C4⋊C4—1222no—
666C4⋊C4—2441no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—1222no—
672C22⋊C4—1222no—
673C22⋊C4—2441no—
674C22⋊C4—2441no—
675C22⋊C4—2441no—
676C22⋊C4—2441no—
677C22⋊C4—2441no—
678C22⋊C4—2441no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—1221no—
684C42—1221no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—612no—
692C23—612no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1221no—
698C23—1221no—
699C23—1221no—
700C23—1221no—
701C23—1221no—
702C23—1221no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23C4×D24412yes—
713C23C22×C4×D6111yescharacteristic
714Q8—2444no—
715D4—2444no—
716D4—2444no—
717D4—2444no—
718D4—2444no—
719D4—2444no—
720D4—2444no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—612no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4C4×D24412yes—
767C2×C4C2×D4×D6111yescharacteristic
768C2×C4C22×D24411yescharacteristic
769C2×C4#41×D6111yescharacteristic
770C2×C4C2×#1175822211yescharacteristic
771C2×C4#1451982211yescharacteristic
772C2×C4#1451982311yescharacteristic
773C8—22no—
774C8—22no—
775C8—22no—
776C8—41no—
777C8—1222no—
778C8—2441no—
779C8—2441no—
780C8—2441no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—1222no—
789C22—1222no—
790C22—1222no—
791C22—1222no—
792C22—1222no—
793C22—1222no—
794C22—2441no—
795C22—2441no—
796C22—2441no—
797C22—2441no—
798C22—2441no—
799C22—2441no—
800C22—2441no—
801C22—2441no—
802C22—2441no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22—2441no—
809C22C4×D4×D6111yescharacteristic
810C22C2×C4×D24411yescharacteristic
811C22#1684023411yescharacteristic
812C22#131×D6111yescharacteristic
813C22#1684052711yescharacteristic
814C22#1684052811yescharacteristic
815C22#1684052811yescharacteristic
816C4—22no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—1222no—
822C4—2441no—
823C4—2441no—
824C4—2441no—
825C4—2441no—
826C4D4×D24411yescharacteristic
827C4#1684040211yescharacteristic
828C4#1684040711yescharacteristic
829C4#1684043611yescharacteristic
830C2—42no—
831C2—4881no—
832C2—2442no—
833C2—2442no—
834C2#2144880111yescharacteristic
835C2#2145453311yescharacteristic
836C2#2145453811yescharacteristic
837C2#2145454211yescharacteristic
838C2#2145454711yescharacteristic
839C2#2145486611yescharacteristic
840C2#2145488711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1752C2
prime radical#21449035C2
cosocleC22×C4×C61C24
hypercenter#1752D61
hypocenterC61#22851
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
1. C2×#16839836C2semidirect
2. C2×#16839835C2semidirect
3. C2×#16839728C2semidirect
4. C2×#16839727C2semidirect
6. #21446617C2semidirect
7. #21446433C2semidirect
8. #21446432C2semidirect
9. #21446111C2semidirect
10. #21446110C2semidirect
11. #21446110C2semidirect
12. #21446004C2semidirect
13. #21446003C2semidirect
14. #21445596C2semidirect
15. C61×#1752C2semidirect
127. #14519689D4semidirect
145. C22⋊C8×C61D4semidirect
424. #1752D61semidirect
483. C61#22851semidirect
561. C22⋊C8D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168398362
C2×#168398352
C2×#168397282
C2×#168397272
#214490352
#214466172
#214464332
#214464322
#214461112
#214461102
#214460042
#214460032
#214455962
C61×#17522
#2285161