Finite Group Databasebeta

← #29686102

Subgroups — #29686102

Order 15616.

1096 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839841C211yesmaximal, characteristic, complemented
2C2×#16839835C211yesmaximal, characteristic, complemented
3C2×#16839835C211yesmaximal, characteristic, complemented
4C2×#16839714C211yesmaximal, characteristic, complemented
5C4×#14519752C211yesmaximal, characteristic
6#21446616C211yesmaximal, characteristic, complemented
7#21446543C211yesmaximal, characteristic, complemented
8#21446426C211yesmaximal, characteristic, complemented
9#21446426C211yesmaximal, characteristic, complemented
10#21446115C211yesmaximal, characteristic, complemented
11#21446115C211yesmaximal, characteristic, complemented
12#21445796C211yesmaximal, characteristic, complemented
13#21445604C211yesmaximal, characteristic, complemented
14C8×#11758198C211yesmaximal, characteristic, complemented
15C61×#1771C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519752C411yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic
24C2×C42×D61C2211yescharacteristic
25#16839841—24no—
26#16839835—24no—
27#16839835—24no—
28C2×C4⋊#92418C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519689C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39#16839714—24no—
40C2×#14519688C2211yescharacteristic
41C2×C8×Dic61C2211yescharacteristic
42C2×C8×Dic61C2211yescharacteristic
43#16839663C411yescharacteristic
44#16839661C411yescharacteristic
45#16839654C411yescharacteristic
46#16839654C411yescharacteristic
47#16839640C411yescharacteristic
48#16839640C411yescharacteristic
49#16839619C411yescharacteristic
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×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C2×#11758189—22no—
72C2×#11758189—22no—
73C2×#11758189—22no—
74C2×#11758189—22no—
75C2×#11758189—22no—
76C2×#11758189—22no—
77C2×#11758189—22no—
78C2×#11758189—22no—
79C2×#11758189D414yescomplemented
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C2×C8×D61—22no—
85C2×C8×D61—22no—
86C2×C8×D61—22no—
87#14519752—24no—
88C4×D244—22no—
89C4×D244—22no—
90C4×D244—22no—
91C4×D244—22no—
92C4×D244—22no—
93C4×D244—22no—
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×#11758198C2×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×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C42×D61—22no—
111C42×D61—22no—
112C4⋊#92418—22no—
113C4⋊#92418—22no—
114C4⋊#92418—22no—
115#14519689—22no—
116#14519689—22no—
117#14519689—22no—
118#14519689—22no—
119#14519689—22no—
120#14519689—22no—
121#14519689—22no—
122#14519689—22no—
123#14519688—22no—
124C8×Dic61—22no—
125C8×Dic61—22no—
126#14519684C2×C411yescharacteristic
127#14519684C2×C411yescharacteristic
128#14519684C2×C411yescharacteristic
129#14519684C2×C411yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C2×C42×C61C2311yescharacteristic
139C4⋊C8×C61—22no—
140#97×C61—22no—
141#97×C61D414yescomplemented
142C4×C8×C61—22no—
143#95×C61C2×C411yescharacteristic
144#95×C61C2×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C2411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C2×D244—22no—
161C2×D244—22no—
162C2×D244—22no—
163C2×D244—22no—
164C2×D244—22no—
165C2×D244—22no—
166C2×D244—41no—
167C2×D244—41no—
168C2×D244—41no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
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×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—41no—
190C2×C4×D61—41no—
191C2×C4×D61C2×D412yes—
192C2×C4×D61#4112yes—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61C2×D412yes—
202C2×C8×C61C2×D412yes—
203C2×C8×C61C2×D412yes—
204C2×C8×C61#4112yes—
205C4⋊C4×C61—22no—
206C4⋊C4×C61—41no—
207C42×C61—21no—
208C42×C61—21no—
209C42×C61—21no—
210C42×C61—21no—
211C42×C61C2×D412yes—
212C42×C61#4112yes—
213#11758198—22no—
214#11758198—22no—
215#11758198—22no—
216#11758198—22no—
217#11758198—22no—
218#11758198—22no—
219#11758198—22no—
220#11758198—22no—
221#11758198—22no—
222#11758198M1614yescomplemented
223C4⋊Dic61—22no—
224C4⋊Dic61—22no—
225C4⋊Dic61—22no—
226C4×Dic61—22no—
227C4×Dic61—22no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418C2×D412yes—
241C2×#92418#4112yes—
242#11758189—28no—
243#11758189—28no—
244#11758189—44no—
245C8×D61—44no—
246C23×C61C23×C411yescharacteristic
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×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61C4×D412yes—
267C22×D61C2×M1612yes—
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×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61C4×D412yes—
284C2×C4×C61C4×D412yes—
285C2×C4×C61C2×M1612yes—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
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×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61C4×D412yes—
305C2×Dic61C2×M1612yes—
306C2×Dic61#13112yes—
307D244—44no—
308D244—44no—
309D244—44no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—44no—
315C4×D61—44no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323C4×D61—41no—
324C8×C61—22no—
325C8×C61—41no—
326C8×C61—41no—
327C8×C61#12114yescomplemented
328#92418—22no—
329#92418—22no—
330#92418—41no—
331#92418—41no—
332#21490—611nomaximal, Sylow
333C22×C61C2×C4×D411yescharacteristic
334C22×C61C2×C4×D411yescharacteristic
335C22×C61C4×#4111yescharacteristic
336C22×C61C22×M1611yescharacteristic
337C22×C61C2×#13111yescharacteristic
338C22×C61#56811yescharacteristic
339C22×C61#56811yescharacteristic
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—22no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—41no—
367C4×C61C2×#12111yescharacteristic
368C4×C61#52511yescharacteristic
369C4×C61#52911yescharacteristic
370C4×C61#53211yescharacteristic
371Dic61—22no—
372Dic61—22no—
373Dic61—22no—
374Dic61—41no—
375Dic61—41no—
376C2×#436—611no—
377C2×#435—611no—
378C2×#435—611no—
379C2×C4×M16—611no—
380C4×#121—611no—
381#1955—611no—
382#1940—611no—
383#1923—611no—
384#1923—611no—
385#1870—611no—
386#1870—611no—
387#1797—611no—
388#1771D6111yescharacteristic, complemented
389#1753—611no—
390C8×C22⋊C4—611no—
391C2×C61C4×#12111yescharacteristic
392C2×C61#293311yescharacteristic
393C2×C61D4×M1611yescharacteristic
394C2×C61D4×M1611yescharacteristic
395C2×C61#293511yescharacteristic
396C2×C61#296511yescharacteristic
397C2×C61#296711yescharacteristic
398D61—42no—
399D61—42no—
400D61—81no—
401C22×M16—611no—
402C22×M16—611no—
403C22×M16—611no—
404C23×C8—611no—
405C2×#121—611no—
406C2×C4×D4—611no—
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C22×C42—611no—
410#436—1224no—
411#435—1224no—
412#435—1224no—
413C2×C4⋊C8—611no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8—611no—
416C2×C4⋊C8C2×D6111yescharacteristic
417C2×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419C2×C22⋊C8—611no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C4×M16—1224no—
426C2×#97—611no—
427C2×#97C2×D6111yescharacteristic
428C2×#97C2×D6111yescharacteristic
429C2×C4×C8—611no—
430C2×C4×C8—611no—
431C2×C4×C8C2×D6111yescharacteristic
432#390—611no—
433#389—611no—
434#388—611no—
435#388—611no—
436#386—611no—
437#386—611no—
438#380—611no—
439C4×C4⋊C4C2×D6111yescharacteristic
440C4×C22⋊C4—611no—
441C4×C22⋊C4—611no—
442#336—611no—
443#336—611no—
444#336—611no—
445#336—611no—
446#336C2×D6111yescharacteristic
447#336C2×D6111yescharacteristic
448C61#2149011yescharacteristic, complemented, Sylow
449C22×D4—611no—
450C22×D4—611no—
451C22×D4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C2×M16—614no—
458C2×M16—1222no—
459C2×M16—1222no—
460C2×M16—1222no—
461C2×M16—1222no—
462C2×M16—1222no—
463C2×M16—1222no—
464C2×M16—1222no—
465C2×M16—1222no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8—611no—
469C22×C8—611no—
470C22×C8—1222no—
471C22×C8—1222no—
472C22×C8—1222no—
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C22×C8C22×D6111yescharacteristic
476C22×C8C22×D6111yescharacteristic
477#121—1224no—
478C4×D4—1222no—
479C4×D4—1222no—
480C4×D4—1222no—
481C4×D4—1222no—
482C4×D4—1222no—
483C4×D4—1222no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4C4×D6111yescharacteristic
488C2×C4⋊C4C4×D6111yescharacteristic
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×C22⋊C4—611no—
496C2×C22⋊C4—611no—
497C2×C22⋊C4—611no—
498C2×C22⋊C4—611no—
499C2×C42—611no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—1222no—
503C2×C42—1222no—
504C2×C42C22×D6111yescharacteristic
505C2×C42C22×D6111yescharacteristic
506C2×C42C22×D6111yescharacteristic
507C4⋊C8—22no—
508C4⋊C8—1222no—
509C4⋊C8—1222no—
510C4⋊C8—1222no—
511C22⋊C8—1222no—
512C22⋊C8—1222no—
513C22⋊C8—1222no—
514C22⋊C8—1222no—
515C22⋊C8—1222no—
516C22⋊C8—1222no—
517C22⋊C8—1222no—
518C22⋊C8—1222no—
519#97—22no—
520#97—1222no—
521#97D24414yescomplemented
522C4×C8—22no—
523C4×C8—1222no—
524C4×C8—1222no—
525#95—611no—
526#95—611no—
527#95—611no—
528#95—611no—
529#95C4×D6111yescharacteristic
530#95C4×D6111yescharacteristic
531C24—611no—
532C24—611no—
533C24—611no—
534C2×D4—1222no—
535C2×D4—1222no—
536C2×D4—1222no—
537C2×D4—1222no—
538C2×D4—1222no—
539C2×D4—1222no—
540C2×D4—2441no—
541C2×D4—2441no—
542C2×D4—2441no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—612no—
547C22×C4—612no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—2441no—
571C22×C4—2441no—
572C22×C4C2×C4×D6111yescharacteristic
573C22×C4C2×C4×D6111yescharacteristic
574C22×C4C2×C4×D6111yescharacteristic
575C22×C4C2×C4×D6111yescharacteristic
576C22×C4C2×C4×D6111yescharacteristic
577C22×C4C2×C4×D6111yescharacteristic
578C22×C4C23×D6111yescharacteristic
579M16—1228no—
580M16—1228no—
581M16—2444no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—612no—
591C2×C8—612no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—2444no—
603C2×C8C2×D24412yes—
604C2×C8C2×D24412yes—
605C2×C8D4×D6112yes—
606C2×C8#1175822612yes—
607C4⋊C4—22no—
608C4⋊C4—41no—
609C4⋊C4—1222no—
610C4⋊C4—1222no—
611C4⋊C4—1222no—
612C22⋊C4—614no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—1222no—
621C22⋊C4—1222no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—1221no—
627C42—1221no—
628C42—1222no—
629C42—1222no—
630C42C2×D24412yes—
631C42#1175822212yes—
632C23—612no—
633C23—612no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
653C23C22×C4×D6111yescharacteristic
654D4—2444no—
655D4—2444no—
656D4—2444no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—612no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—2444no—
692C2×C4—2444no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4C4×D24412yes—
702C2×C4C4×D24412yes—
703C2×C4M16×D6112yes—
704C2×C4C2×D4×D6111yescharacteristic
705C2×C4C22×D24411yescharacteristic
706C2×C4#41×D6111yescharacteristic
707C2×C4#41×D6111yescharacteristic
708C2×C4C2×#1175822211yescharacteristic
709C2×C4C2×#1175822611yescharacteristic
710C8—22no—
711C8—41no—
712C8—41no—
713C8—1222no—
714C8—1222no—
715C8—2441no—
716C8—2441no—
717C8#1451975214yescomplemented
718C22—1222no—
719C22—1222no—
720C22—1222no—
721C22—1222no—
722C22—1222no—
723C22—1222no—
724C22—2441no—
725C22—2441no—
726C22—2441no—
727C22—2441no—
728C22—2441no—
729C22—2441no—
730C22—2441no—
731C22—2441no—
732C22—2441no—
733C22—2441no—
734C22—2441no—
735C22—2441no—
736C22—2441no—
737C22—2441no—
738C22—2441no—
739C22C4×D4×D6111yescharacteristic
740C22C2×C4×D24411yescharacteristic
741C22C4×#1175822611yescharacteristic
742C22C2×M16×D6111yescharacteristic
743C22#131×D6111yescharacteristic
744C22#1684052711yescharacteristic
745C22#1684052811yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—1222no—
753C4—1222no—
754C4—1222no—
755C4—2441no—
756C4—2441no—
757C4C2×#1451975211yescharacteristic
758C4#1684027411yescharacteristic
759C4#1684029911yescharacteristic
760C4#1684030911yescharacteristic
761C2—4881no—
762C2—2442no—
763C2—2442no—
764C2C4×#1451975211yescharacteristic
765C2#2145454711yescharacteristic
766C2#2145455211yescharacteristic
767C2M16×D24411yescharacteristic
768C2#2145456011yescharacteristic
769C2#2145478411yescharacteristic
770C2#2145480311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1771C2
prime radicalC2×#14519752C4
cosocleC22×C4×C61C24
hypercenter#1771D61
hypocenterC61#21490
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×#16839835C2semidirect
3. C2×#16839835C2semidirect
4. C2×#16839714C2semidirect
6. #21446616C2semidirect
7. #21446543C2semidirect
8. #21446426C2semidirect
9. #21446426C2semidirect
10. #21446115C2semidirect
11. #21446115C2semidirect
12. #21445796C2semidirect
13. #21445604C2semidirect
14. C8×#11758198C2semidirect
15. C61×#1771C2semidirect
79. C2×#11758189D4semidirect
141. #97×C61D4semidirect
222. #11758198M16semidirect
327. C8×C61#121semidirect
388. #1771D61semidirect
448. C61#21490semidirect
521. #97D244semidirect
717. C8#14519752semidirect

Maximal subgroups

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

subgroupindex
C2×#168398412
C2×#168398352
C2×#168397142
C4×#145197522
#214466162
#214465432
#214464262
#214461152
#214457962
#214456042
C8×#117581982
C61×#17712
#2149061