Finite Group Databasebeta

← #29702240

Subgroups — #29702240

Order 15616.

992 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839841C211yesmaximal, characteristic, complemented
2C2×#16839839C211yesmaximal, characteristic, complemented
3C2×#16839835C211yesmaximal, characteristic, complemented
4C2×#16839787C211yesmaximal, characteristic, complemented
5#21449059C211yesmaximal, characteristic
6#21446617C211yesmaximal, characteristic, complemented
7#21446538C211yesmaximal, characteristic, complemented
8#21446432C211yesmaximal, characteristic, complemented
9#21446425C211yesmaximal, characteristic, complemented
10#21446115C211yesmaximal, characteristic, complemented
11#21446110C211yesmaximal, characteristic, complemented
12#21446003C211yesmaximal, characteristic, complemented
13#21446003C211yesmaximal, characteristic, complemented
14#21445588C211yesmaximal, characteristic, complemented
15C61×#1771C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×#14519734C2211yescharacteristic
24#16839841—24no—
25#16839839—24no—
26#16839835—24no—
27#16839787—24no—
28C2×C4⋊#92418C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C2×#14519706C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519689C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839694C411yescharacteristic
43#16839689C411yescharacteristic
44#16839684C411yescharacteristic
45#16839684C411yescharacteristic
46#16839680C411yescharacteristic
47#16839679C411yescharacteristic
48#16839679C411yescharacteristic
49#16839672C411yescharacteristic
50C4×#11758198C2211yescharacteristic
51C4×#11758198C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C2×C4×C8×C61C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×D244C2×C411yescharacteristic
64C22×D244C2×C411yescharacteristic
65C22×D244C2×C411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758189—22no—
70C2×#11758189—22no—
71C2×#11758189—22no—
72C2×#11758189—22no—
73C2×#11758189—22no—
74C2×#11758189—22no—
75C2×#11758189—41no—
76C2×#11758189—41no—
77C2×#11758189—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61—41no—
85C4×D244—22no—
86C4×D244—22no—
87C4×D244—22no—
88C4×D244—22no—
89C4×D244—22no—
90C4×D244—22no—
91#14519734—22no—
92#14519734—22no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C4⋊#92418—22no—
112C4⋊#92418—22no—
113C4⋊#92418—22no—
114#14519706—22no—
115#14519706—22no—
116#14519689—22no—
117#14519689—22no—
118#14519689—22no—
119#14519689—22no—
120#14519689—22no—
121#14519689—41no—
122#14519689—41no—
123#14519689D414yescomplemented
124C4×#92418—22no—
125#14519684C2×C411yescharacteristic
126#14519684C2×C411yescharacteristic
127#14519684C2×C411yescharacteristic
128#14519684C2×C411yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61D414yescomplemented
139#97×C61—22no—
140#97×C61—22no—
141C4×C8×C61—22no—
142#95×C61C2×C411yescharacteristic
143#95×C61C2×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C2411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C2×D244—22no—
160C2×D244—22no—
161C2×D244—22no—
162C2×D244—22no—
163C2×D244—41no—
164C2×D244—41no—
165C2×D244—41no—
166C2×D244—41no—
167C2×D244—41no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61C2×D412yes—
185C2×C4×D61#4112yes—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61C2×D412yes—
196C2×C8×C61C2×D412yes—
197C2×C8×C61C2×D412yes—
198C4⋊C4×C61—22no—
199C4⋊C4×C61—41no—
200C42×C61—21no—
201C42×C61—21no—
202C42×C61—21no—
203C42×C61—21no—
204C42×C61C2×D412yes—
205C42×C61#4112yes—
206#11758198—22no—
207#11758198—22no—
208#11758198—22no—
209#11758198—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—22no—
213#11758198—22no—
214#11758198—22no—
215#11758198—41no—
216#11758198—41no—
217#11758198—41no—
218C4⋊Dic61—22no—
219C4⋊Dic61—22no—
220C4⋊Dic61—22no—
221#11758196—22no—
222#11758196—22no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418C2×D412yes—
237#11758189—44no—
238#11758189—44no—
239#11758189—44no—
240C8×D61—44no—
241C23×C61C23×C411yescharacteristic
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61C4×D412yes—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61C4×D412yes—
279C2×C4×C61C4×D412yes—
280C2×C4×C61#13112yes—
281C2×C4×C61C22×D411yescharacteristic
282C2×C4×C61C22×D411yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61H(5,𝔽2)11yescharacteristic
286C2×C4×C612−1+411yescharacteristic
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61C4×D412yes—
302D244—44no—
303D244—44no—
304D244—44no—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—22no—
309C4×D61—41no—
310C4×D61—41no—
311C4×D61—41no—
312C4×D61—41no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C8×C61—22no—
318C8×C61—22no—
319C8×C61—22no—
320C8×C61—41no—
321#92418—22no—
322#92418—41no—
323#92418—41no—
324#92418—41no—
325#22994—611nomaximal, Sylow
326C22×C61C2×C4×D411yescharacteristic
327C22×C61C2×C4×D411yescharacteristic
328C22×C61#52011yescharacteristic
329C22×C61C2×#13111yescharacteristic
330C22×C61#56811yescharacteristic
331C22×C61#56811yescharacteristic
332C22×C61#56811yescharacteristic
333C2×D61—22no—
334C2×D61—22no—
335C2×D61—22no—
336C2×D61—41no—
337C2×D61—41no—
338C2×D61—41no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C4×C61—22no—
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—41no—
358C4×C61—41no—
359C4×C61—41no—
360C4×C61D4211yescharacteristic
361C4×C61#54711yescharacteristic
362C4×C61#54811yescharacteristic
363C4×C61#55311yescharacteristic
364Dic61—22no—
365Dic61—41no—
366Dic61—41no—
367Dic61—41no—
368Dic61—41no—
369C2×#436—611no—
370C2×#436—611no—
371C2×#435—611no—
372C2×#424—611no—
373#2392—611no—
374#1955—611no—
375#1939—611no—
376#1924—611no—
377#1923—611no—
378#1870—611no—
379#1869—611no—
380#1851—611no—
381#1851—611no—
382#1771D6111yescharacteristic, complemented
383#1750—611no—
384C2×C61#236111yescharacteristic
385C2×C61#293011yescharacteristic
386C2×C61#293011yescharacteristic
387C2×C61#293311yescharacteristic
388C2×C61#293511yescharacteristic
389C2×C61#299311yescharacteristic
390C2×C61#299511yescharacteristic
391D61—42no—
392D61—81no—
393D61—81no—
394C22×M16—611no—
395C22×M16—611no—
396C22×M16—611no—
397C23×C8—611no—
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C2×C4×D4—611no—
401C2×#117—611no—
402#436—1224no—
403#436—1224no—
404#435—1224no—
405#424—1224no—
406C2×C4⋊C8—611no—
407C2×C4⋊C8—611no—
408C2×C4⋊C8—611no—
409C2×C4⋊C8—611no—
410C2×C4⋊C8—611no—
411C2×C4⋊C8C2×D6111yescharacteristic
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C22⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419C2×C22⋊C8—611no—
420C2×#97C2×D6111yescharacteristic
421C2×#97C2×D6111yescharacteristic
422C2×C4×C8—611no—
423C2×C4×C8C2×D6111yescharacteristic
424#398—611no—
425#397—611no—
426#396—611no—
427#396—611no—
428#394—611no—
429#394—611no—
430#394—611no—
431#392—611no—
432C4×C4⋊C4C2×D6111yescharacteristic
433C4×C22⋊C4—611no—
434C4×C22⋊C4—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336C2×D6111yescharacteristic
440#336C2×D6111yescharacteristic
441C61#2299411yescharacteristic, complemented, Sylow
442C22×D4—611no—
443C22×D4—611no—
444C22×D4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—611no—
448C2×M16—1222no—
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—1222no—
452C2×M16—1222no—
453C2×M16—1222no—
454C2×M16—2441no—
455C2×M16—2441no—
456C2×M16—2441no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—1222no—
462C22×C8—1222no—
463C22×C8—2441no—
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6111yescharacteristic
468C4×D4—1222no—
469C4×D4—1222no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474#117—1222no—
475#117—1222no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4C4×D6111yescharacteristic
482C2×C4⋊C4C4×D6111yescharacteristic
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
495C2×C42—611no—
496C2×C42C22×D6111yescharacteristic
497C2×C42C22×D6111yescharacteristic
498C2×C42C22×D6111yescharacteristic
499C4⋊C8—1222no—
500C4⋊C8—1222no—
501C4⋊C8—1222no—
502C4⋊C8—1222no—
503C4⋊C8—1222no—
504C4⋊C8D24414yescomplemented
505C22⋊C8—614no—
506C22⋊C8—1222no—
507C22⋊C8—1222no—
508C22⋊C8—1222no—
509C22⋊C8—1222no—
510C22⋊C8—1222no—
511C22⋊C8—2441no—
512C22⋊C8—2441no—
513#97—22no—
514#97—22no—
515C4×C8—22no—
516C4×C8—1222no—
517#95—611no—
518#95—611no—
519#95—611no—
520#95—611no—
521#95C4×D6111yescharacteristic
522#95C4×D6111yescharacteristic
523C24—611no—
524C24—611no—
525C24—611no—
526C2×D4—1222no—
527C2×D4—1222no—
528C2×D4—1222no—
529C2×D4—1222no—
530C2×D4—2441no—
531C2×D4—2441no—
532C2×D4—2441no—
533C2×D4—2441no—
534C2×D4—2441no—
535C22×C4—611no—
536C22×C4—612no—
537C22×C4—612no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4C2×C4×D6111yescharacteristic
559C22×C4C2×C4×D6111yescharacteristic
560C22×C4C2×C4×D6111yescharacteristic
561C22×C4C2×C4×D6111yescharacteristic
562C22×C4C2×C4×D6111yescharacteristic
563C22×C4C2×C4×D6111yescharacteristic
564C22×C4C23×D6111yescharacteristic
565M16—2444no—
566M16—2444no—
567M16—2444no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—612no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—2444no—
590C2×C8C2×D24412yes—
591C2×C8C2×D24412yes—
592C2×C8D4×D6112yes—
593C4⋊C4—22no—
594C4⋊C4—41no—
595C4⋊C4—1222no—
596C4⋊C4—1222no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4—1222no—
600C22⋊C4—1222no—
601C22⋊C4—1222no—
602C22⋊C4—1222no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—2441no—
610C22⋊C4—2441no—
611C22⋊C4—2441no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—1221no—
617C42—1221no—
618C42C2×D24412yes—
619C42#1175822212yes—
620C23—612no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23—1221no—
626C23—1221no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23C22×C4×D6111yescharacteristic
642D4—2444no—
643D4—2444no—
644D4—2444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—612no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4C4×D24412yes—
688C2×C4C4×D24412yes—
689C2×C4#1451978512yes—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4C22×D24411yescharacteristic
692C2×C4#41×D6111yescharacteristic
693C2×C4C2×#1175822211yescharacteristic
694C2×C4#1451982311yescharacteristic
695C2×C4#1451982511yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—41no—
700C8—1222no—
701C8—2441no—
702C8—2441no—
703C8—2441no—
704C22—1222no—
705C22—1222no—
706C22—1222no—
707C22—2441no—
708C22—2441no—
709C22—2441no—
710C22—2441no—
711C22—2441no—
712C22—2441no—
713C22—2441no—
714C22—2441no—
715C22—2441no—
716C22—2441no—
717C22—2441no—
718C22—2441no—
719C22—2441no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22C4×D4×D6111yescharacteristic
726C22C2×C4×D24411yescharacteristic
727C22#1684024411yescharacteristic
728C22C2×#1451978511yescharacteristic
729C22#1684052711yescharacteristic
730C22#1684052711yescharacteristic
731C22#1684052811yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—1222no—
739C4—2441no—
740C4—2441no—
741C4—2441no—
742C4—2441no—
743C4D4×D24411yescharacteristic
744C4#1684041311yescharacteristic
745C4#1684042411yescharacteristic
746C4#1684045611yescharacteristic
747C2—4881no—
748C2—4881no—
749C2—2442no—
750C2#2144883711yescharacteristic
751C2#2145451711yescharacteristic
752C2#2145452411yescharacteristic
753C2#2145454511yescharacteristic
754C2#2145456511yescharacteristic
755C2#2145497111yescharacteristic
756C2#2145498811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1771C2
prime radical#16839672C4
cosocleC22×C4×C61C24
hypercenter#1771D61
hypocenterC61#22994
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
1. C2×#16839841C2semidirect
2. C2×#16839839C2semidirect
3. C2×#16839835C2semidirect
4. C2×#16839787C2semidirect
6. #21446617C2semidirect
7. #21446538C2semidirect
8. #21446432C2semidirect
9. #21446425C2semidirect
10. #21446115C2semidirect
11. #21446110C2semidirect
12. #21446003C2semidirect
13. #21446003C2semidirect
14. #21445588C2semidirect
15. C61×#1771C2semidirect
123. #14519689D4semidirect
138. C4⋊C8×C61D4semidirect
382. #1771D61semidirect
441. C61#22994semidirect
504. C4⋊C8D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168398412
C2×#168398392
C2×#168398352
C2×#168397872
#214490592
#214466172
#214465382
#214464322
#214464252
#214461152
#214461102
#214460032
#214455882
C61×#17712
#2299461