Finite Group Databasebeta

← #29696756

Subgroups — #29696756

Order 15616.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840290C211yesmaximal, characteristic
2C2×#16839892C211yesmaximal, characteristic, complemented
3C2×#16839890C211yesmaximal, characteristic, complemented
4#21446617C211yesmaximal, characteristic, complemented
5#21446615C211yesmaximal, characteristic, complemented
6#21446615C211yesmaximal, characteristic, complemented
7#21446615C211yesmaximal, characteristic, complemented
8#21446613C211yesmaximal, characteristic, complemented
9#21446611C211yesmaximal, characteristic, complemented
10#21445803C211yesmaximal, characteristic, complemented
11#21445802C211yesmaximal, characteristic, complemented
12#21445798C211yesmaximal, characteristic, complemented
13#21445584C211yesmaximal, characteristic, complemented
14#21445580C211yesmaximal, characteristic, complemented
15C61×#1750C211yesmaximal, characteristic, complemented
16#16840290—24no—
17#16840290—24no—
18C2×#14519772C411yescharacteristic
19C2×#14519770C411yescharacteristic
20C2×#14519767C411yescharacteristic
21C2×#14519763C411yescharacteristic
22C2×#14519762C411yescharacteristic
23C2×#14519759C411yescharacteristic
24C2×#14519755C411yescharacteristic
25C2×#14519750C411yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×D244C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519734C2211yescharacteristic
31C2×C42×D61C2211yescharacteristic
32#16839892—24no—
33#16839890—24no—
34C2×C4⋊#92418C2211yescharacteristic
35C2×C4⋊#92418C2211yescharacteristic
36C2×#14519706C2211yescharacteristic
37C2×#14519706C2211yescharacteristic
38C2×#14519706C2211yescharacteristic
39C2×#14519706C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519689C2211yescharacteristic
48C2×#14519689C2211yescharacteristic
49C2×#14519689C2211yescharacteristic
50C2×#14519687C2211yescharacteristic
51C2×#14519687C2211yescharacteristic
52C2×#14519687C2211yescharacteristic
53C2×C8×Dic61C2211yescharacteristic
54#16839517C2211yescharacteristic
55#16839517C2211yescharacteristic
56C2×#117×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×#97×C61C2211yescharacteristic
60C2×C4×C8×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122C2×C411yescharacteristic
64C22×D244C2×C411yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic
66C22×C22⋊D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2×C411yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519772—24no—
76#14519770—24no—
77#14519767—24no—
78#14519763—24no—
79#14519762—24no—
80#14519759—24no—
81#14519755—24no—
82#14519750—24no—
83C4×Dic122D414yes—
84C4×Dic122D414yes—
85C4×D244—22no—
86C4×D244—22no—
87C4×C22⋊D61—22no—
88C4×C22⋊D61—22no—
89C4×C22⋊D61—22no—
90C4×C22⋊D61—22no—
91#14519734—22no—
92#14519734—22no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×C22⋊Dic61C2×C411yescharacteristic
102C2×C22⋊Dic61C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C42×D61—22no—
114C42×D61—22no—
115C4⋊#92418—22no—
116C4⋊#92418—22no—
117#14519706—22no—
118#14519706—22no—
119#14519706—22no—
120#14519706—22no—
121C22⋊#92418—41no—
122C22⋊#92418—41no—
123#14519689—22no—
124#14519689—22no—
125#14519689—22no—
126#14519689—22no—
127#14519689—41no—
128#14519689—41no—
129#14519689—41no—
130#14519689—41no—
131#14519687—22no—
132#14519687—22no—
133#14519687—22no—
134C8×Dic61—22no—
135C23×C4×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140#117×C61—22no—
141#117×C61—22no—
142C2×C4⋊C4×C61C2×C411yescharacteristic
143C2×C4⋊C4×C61C2×C411yescharacteristic
144C2×C22⋊C4×C61C2×C411yescharacteristic
145C2×C22⋊C4×C61C2×C411yescharacteristic
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C22⋊C8×C61—22no—
149C22⋊C8×C61—22no—
150#97×C61—22no—
151C4×C8×C61—22no—
152C24×C61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—41no—
171C2×C22⋊D61—41no—
172C2×C22⋊D61—41no—
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C2×D244—22no—
180C2×D244—22no—
181C2×D244—41no—
182C2×C4×D61—22no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—41no—
198C2×C4×D61—41no—
199C2×C4×D61—41no—
200C2×Dic122—41no—
201C2×Dic122—41no—
202C2×Dic122C22⋊C414yes—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61#4112yes—
214C2×C8×C61#4112yes—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—22no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61C2×D412yes—
222C42×C61C2×D412yes—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225#11758198—22no—
226#11758198—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231C4⋊Dic61—22no—
232C4⋊Dic61C22⋊C414yes—
233#11758196—22no—
234#11758196—22no—
235#11758196—22no—
236#11758196—22no—
237#11758196C22⋊C414yes—
238#11758196C22⋊C414yes—
239C4×Dic61—22no—
240C4×Dic61—22no—
241C4×Dic61C2×D412yes—
242C4×Dic61C2×D412yes—
243C4×Dic61C2×D412yes—
244C4×Dic61C2×D412yes—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61C23×C411yescharacteristic
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61#13112yes—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61C2×C22⋊C412yes—
297C2×C4×C61C2×C22⋊C412yes—
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C612−1+411yescharacteristic
304C22⋊D61—44no—
305C22⋊D61—44no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61C2×C22⋊C412yes—
321C2×Dic61C2×C22⋊C412yes—
322C2×Dic61C2×C22⋊C412yes—
323C2×Dic61C2×C22⋊C412yes—
324D244—44no—
325C4×D61—44no—
326C4×D61—44no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335Dic122—44no—
336C8×C61—22no—
337C8×C61—22no—
338C8×C61—41no—
339C8×C61—41no—
340#92418—41no—
341#92418—41no—
342#92418—41no—
343#92418—41no—
344#22533—611nomaximal, Sylow
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61C22×C22⋊C411yescharacteristic
353C22×C61C4×#4111yescharacteristic
354C22×C61#52011yescharacteristic
355C22×C61C2×#13111yescharacteristic
356C22×C61#56811yescharacteristic
357C22×C61#56811yescharacteristic
358C22×C61#56811yescharacteristic
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—41no—
363C2×D61—41no—
364C2×D61—41no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C4×C61—22no—
374C4×C61—22no—
375C4×C61—41no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61#54811yescharacteristic
379C4×C61#54811yescharacteristic
380C4×C61#55011yescharacteristic
381C4×C61#55011yescharacteristic
382Dic61—22no—
383Dic61—22no—
384Dic61—22no—
385Dic61—22no—
386Dic61—41no—
387Dic61—41no—
388C2×#529—611no—
389C2×#446—611no—
390C2×#446—611no—
391#1955—611no—
392#1955—611no—
393#1955—611no—
394#1955—611no—
395#1954—611no—
396#1954—611no—
397#1798—611no—
398#1798—611no—
399#1797—611no—
400#1750—611no—
401#1750D6111yescharacteristic, complemented
402#1749—611no—
403C2×C61—81no—
404C2×C61#234111yescharacteristic
405C2×C61#287911yescharacteristic
406C2×C61#288011yescharacteristic
407C2×C61#296711yescharacteristic
408C2×C61#296811yescharacteristic
409C2×C61#299211yescharacteristic
410C2×C61#299511yescharacteristic
411D61—42no—
412D61—81no—
413#529—1224no—
414#529—1224no—
415C2×#126—611no—
416C2×#126—611no—
417C2×#125—611no—
418C2×#124—611no—
419C2×#123—611no—
420C2×#123—611no—
421C2×C22⋊Q8—611no—
422C2×#121—611no—
423C2×C4×Q8—611no—
424C2×C4×D4—611no—
425C2×C4×D4—611no—
426C2×C4×D4—611no—
427C2×#117—611no—
428C2×#117C2×D6111yescharacteristic
429C22×C42—611no—
430#446—1224no—
431#446—1224no—
432C2×C4⋊C8—611no—
433C2×C4⋊C8—611no—
434C2×C4⋊C8—611no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8—611no—
437C2×C4⋊C8—611no—
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—611no—
448C2×C22⋊C8C2×D6111yescharacteristic
449C2×C22⋊C8C2×D6111yescharacteristic
450C2×#97—611no—
451C2×#97—611no—
452C2×#97—611no—
453C2×#97C2×D6111yescharacteristic
454C2×C4×C8—611no—
455C2×C4×C8C2×D6111yescharacteristic
456#336—611no—
457#336—611no—
458#336C2×D6111yescharacteristic
459#336C2×D6111yescharacteristic
460C61#2253311yescharacteristic, complemented, Sylow
461C22×Q8—611no—
462C22×D4—611no—
463C22×D4—611no—
464C22×D4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4C22×D6111yescharacteristic
470C22×C8—611no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8C22×D6111yescharacteristic
475C22×C8C22×D6111yescharacteristic
476C22×C8C22×D6111yescharacteristic
477C22×C8C22×D6111yescharacteristic
478#126—1224no—
479#126—1224no—
480#125—1224no—
481#124—1224no—
482#123—1224no—
483#123—1224no—
484C22⋊Q8—1224no—
485#121—1224no—
486C4×Q8—614no—
487C4×Q8—614no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—1222no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494#117—22no—
495#117—22no—
496#117—1222no—
497#117—1222no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4C4×D6111yescharacteristic
507C2×C4⋊C4C4×D6111yescharacteristic
508C2×C22⋊C4—611no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—611no—
511C2×C22⋊C4—611no—
512C2×C22⋊C4—611no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4C4×D6111yescharacteristic
517C2×C22⋊C4C4×D6111yescharacteristic
518C2×C42—611no—
519C2×C42—611no—
520C2×C42—611no—
521C2×C42—611no—
522C2×C42—1222no—
523C2×C42—1222no—
524C2×C42C22×D6111yescharacteristic
525C2×C42C22×D6111yescharacteristic
526C4⋊C8—1222no—
527C4⋊C8—1222no—
528C4⋊C8—1222no—
529C4⋊C8—1222no—
530C4⋊C8—1222no—
531C4⋊C8—1222no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—1222no—
535C22⋊C8—1222no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C22⋊C8—2441no—
539C22⋊C8—2441no—
540C22⋊C8—2441no—
541C22⋊C8—2441no—
542C22⋊C8—2441no—
543C22⋊C8—2441no—
544#97—22no—
545#97—1222no—
546#97—1222no—
547#97—1222no—
548C4×C8—22no—
549C4×C8—1222no—
550C24—611no—
551C24—611no—
552C24C2×C4×D6111yescharacteristic
553C2×Q8—614no—
554C2×Q8—2441no—
555C2×Q8—2441no—
556C2×D4—1222no—
557C2×D4—1222no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—2441no—
562C2×D4—2441no—
563C2×D4—2441no—
564C2×D4—2441no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—2441no—
593C22×C4—2441no—
594C22×C4—2441no—
595C22×C4C2×C4×D6111yescharacteristic
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C23×D6111yescharacteristic
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8#1175822212yes—
624C2×C8#1175822212yes—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—614no—
628C4⋊C4—614no—
629C4⋊C4—614no—
630C4⋊C4—1222no—
631C4⋊C4—1222no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4—1222no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C42—21no—
646C42—21no—
647C42—612no—
648C42—612no—
649C42—612no—
650C42—612no—
651C42—1222no—
652C42—1222no—
653C42D4×D6112yes—
654C42D4×D6112yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—612no—
663C23—1221no—
664C23—1221no—
665C23—1221no—
666C23—1221no—
667C23—1221no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23C22×C4×D6111yescharacteristic
677Q8—2444no—
678D4—2444no—
679D4—2444no—
680D4—2444no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—612no—
699C2×C4—612no—
700C2×C4—612no—
701C2×C4—612no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—2444no—
717C2×C4—2444no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4C22⋊C4×D6112yes—
727C2×C4C22⋊C4×D6112yes—
728C2×C4C2×D4×D6111yescharacteristic
729C2×C4C2×D4×D6111yescharacteristic
730C2×C4C2×#1175822211yescharacteristic
731C2×C4C2×#1175822211yescharacteristic
732C2×C4#1451982311yescharacteristic
733C2×C4#1451982411yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C8—2441no—
739C8—2441no—
740C8—2441no—
741C8—2441no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—1222no—
750C22—1222no—
751C22—1222no—
752C22—2441no—
753C22—2441no—
754C22—2441no—
755C22—2441no—
756C22—2441no—
757C22—2441no—
758C22—2441no—
759C22—2441no—
760C22—2441no—
761C22—2441no—
762C22—2441no—
763C22C2×C22⋊C4×D6111yescharacteristic
764C22C4×#1175822211yescharacteristic
765C22#1684024211yescharacteristic
766C22#131×D6111yescharacteristic
767C22#1684052711yescharacteristic
768C22#1684052711yescharacteristic
769C22#1684052711yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—1222no—
776C4—1222no—
777C4—1222no—
778C4—1222no—
779C4—2441no—
780C4—2441no—
781C4#1684042111yescharacteristic
782C4#1684042111yescharacteristic
783C4#1684043311yescharacteristic
784C4#1684043311yescharacteristic
785C2—81no—
786C2—4881no—
787C2—2442no—
788C2#2144865911yescharacteristic
789C2#2145426111yescharacteristic
790C2#2145426711yescharacteristic
791C2#2145480011yescharacteristic
792C2#2145480911yescharacteristic
793C2#2145495311yescharacteristic
794C2#2145498411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1750C2
prime radicalC2×#14519750C4
cosocleC22×C4×C61C24
hypercenter#1750D61
hypocenterC61#22533
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#16839892C2semidirect
3. C2×#16839890C2semidirect
4. #21446617C2semidirect
5. #21446615C2semidirect
6. #21446615C2semidirect
7. #21446615C2semidirect
8. #21446613C2semidirect
9. #21446611C2semidirect
10. #21445803C2semidirect
11. #21445802C2semidirect
12. #21445798C2semidirect
13. #21445584C2semidirect
14. #21445580C2semidirect
15. C61×#1750C2semidirect
401. #1750D61semidirect
460. C61#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#168402902
C2×#168398922
C2×#168398902
#214466172
#214466152
#214466132
#214466112
#214458032
#214458022
#214457982
#214455842
#214455802
C61×#17502
#2253361