Finite Group Databasebeta

← #29696359

Subgroups — #29696359

Order 15616.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840412C211yesmaximal, characteristic
2C2×#16839830C211yesmaximal, characteristic, complemented
3#21448744C211yesmaximal, characteristic, complemented
4#21446790C211yesmaximal, characteristic, complemented
5#21446765C211yesmaximal, characteristic, complemented
6#21446254C211yesmaximal, characteristic, complemented
7#21446248C211yesmaximal, characteristic, complemented
8#21446138C211yesmaximal, characteristic, complemented
9#21445908C211yesmaximal, characteristic, complemented
10#21445906C211yesmaximal, characteristic, complemented
11#21445827C211yesmaximal, characteristic, complemented
12#21445646C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14C2×#16839524C211yesmaximal, characteristic, complemented
15C61×#1874C211yesmaximal, characteristic, complemented
16C22×#11758224—21no—
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19#16840412—24no—
20#16840412C418yescomplemented
21C2×#14519776C2211yescharacteristic
22C2×#14519759—21no—
23C2×#14519758—21no—
24C2×#14519754—21no—
25C2×#14519748C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31#16839830—24no—
32C2×#14519706C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519687C2211yescharacteristic
37#16839652—21no—
38#16839643—21no—
39#16839641—21no—
40#16839627C2211yescharacteristic
41#16839622C2211yescharacteristic
42#16839619C2211yescharacteristic
43C4⋊C4×Dic61C2211yescharacteristic
44C4×C22⋊Dic61—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×#121×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C2×#11758224—28no—
63C2×#11758224—44no—
64C2×#11758224—44no—
65C22×Dic122—21no—
66C22×C22⋊D61—21no—
67C22×C22⋊D61D411yescharacteristic
68C23×Dic61—21no—
69C23×Dic61—21no—
70C22×C4×D61—21no—
71C22×C4×D61C2311yescharacteristic
72C2×#11758189—22no—
73C2×#11758189—22no—
74C2×#11758189—41no—
75C22×#92418—22no—
76C22×#92418—22no—
77C22×#92418—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80#14519776—22no—
81#14519776C2×C414yescomplemented
82#14519759—28no—
83#14519758—28no—
84#14519754—28no—
85#14519748—22no—
86#14519748C2×C414yescomplemented
87D4×Dic61—22no—
88D4×Dic61C2×C414yescomplemented
89C4×C22⋊D61C2×C414yes—
90C4×C22⋊D61D414yes—
91#14519735—22no—
92#14519735—41no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61C2×C414yes—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196D411yescharacteristic
103C4⋊C4×D61—22no—
104C4⋊C4×D61C2×C414yescomplemented
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61D411yescharacteristic
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198D411yescharacteristic
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61C2311yescharacteristic
115#14519706—22no—
116#14519698—22no—
117#14519698—41no—
118#14519689—22no—
119#14519687—22no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125C22×D4×C61—21no—
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61—21no—
128C23×C4×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131#121×C61—22no—
132#121×C61C2×C414yes—
133C2×C4⋊C4×C61—22no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—41no—
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140#102×C61—22no—
141#102×C61—41no—
142C22⋊C8×C61—22no—
143C24×C61—21no—
144C24×C61C2×D411yescharacteristic
145C23×D61C2×D411yescharacteristic
146C2×D4×C61—24no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—42no—
153C2×D4×C61—42no—
154C2×D4×C61C22×C412yes—
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×C61—21no—
162C22×C4×C61—42no—
163C22×C4×C61—42no—
164C22×C4×C61—81no—
165C22×C4×C61C22×C412yes—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—24no—
172C2×C22⋊D61—42no—
173C2×C22⋊D61—42no—
174C2×C22⋊D61C22⋊C414yes—
175C22×Dic61—24no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—24no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—42no—
182C22×Dic61—42no—
183C22×Dic61—42no—
184C22×Dic61—42no—
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188#11758224—432no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—24no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61C22×C412yes—
197C2×C4×D61C2×D412yes—
198C2×Dic122—24no—
199C2×Dic122—42no—
200C2×Dic122—42no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61C22×C412yes—
213C4⋊C4×C61#4112yescomplemented
214C22⋊C4×C61—24no—
215C22⋊Dic61—24no—
216C22⋊Dic61—24no—
217C22⋊Dic61—42no—
218C22⋊Dic61C22⋊C414yes—
219#11758198—42no—
220#11758198—81no—
221#11758198C22⋊C414yes—
222C4⋊Dic61—24no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61C22×C412yes—
230C4⋊Dic61C22×C412yes—
231#11758196—24no—
232#11758196—24no—
233#11758196C22⋊C414yes—
234C4×Dic61—42no—
235C4×Dic61—81no—
236C4×Dic61C22×C412yes—
237C4×Dic61C2×D412yes—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—44no—
244C2×#92418#4112yescomplemented
245#11758189—44no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—22no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61C2×C22⋊C412yes—
258C23×C61AGL(1,ℤ/8)12yes—
259C23×C61AGL(1,ℤ/8)12yes—
260C23×C61C22×D411yescharacteristic
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61C2×C22⋊C412yes—
268D4×C61—22no—
269D4×C61—22no—
270D4×C61—48no—
271D4×C61—41no—
272D4×C61—41no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—84no—
289C2×C4×C61C2×C22⋊C412yes—
290C2×C4×C61C23×C411yescharacteristic
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C612−1+411yescharacteristic
296C22⋊D61—28no—
297C22⋊D61—48no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—48no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—48no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61C2×C22⋊C412yes—
319C2×Dic61C2×C22⋊C412yes—
320C2×Dic61C2×C22⋊C412yes—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—48no—
326Dic122—48no—
327C8×C61—41no—
328C8×C61—41no—
329#92418—22no—
330#92418—41no—
331#22495—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61#41814yes—
346C22×C61C22×C22⋊C411yescharacteristic
347C22×C61#54611yescharacteristic
348C22×C61#54711yescharacteristic
349C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C61#57711yescharacteristic
352C22×C61#57811yescharacteristic
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—41no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C4×C61—22no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61—81no—
364C4×C61C4×#4111yescharacteristic
365C4×C61#52011yescharacteristic
366C4×C61#54611yescharacteristic
367C4×C61#54711yescharacteristic
368Dic61—22no—
369Dic61—22no—
370Dic61—22no—
371Dic61—42no—
372Dic61—42no—
373Dic61—81no—
374Dic61—81no—
375C2×#547—611no—
376C2×#435—611no—
377#2352—611no—
378#1993—611no—
379#1987—611no—
380#1895—611no—
381#1893—611no—
382#1875—611no—
383#1874D6111yescharacteristic, complemented
384#1824—611no—
385#1823—611no—
386#1804—611no—
387#1762—611no—
388#1736—611no—
389C2×#340—611no—
390C2×C61—24no—
391C2×C61—82no—
392C2×C61#233911yescharacteristic
393C2×C61C2×#41811yescharacteristic
394C2×C61#289811yescharacteristic
395C2×C61#330611yescharacteristic
396C2×C61#330811yescharacteristic
397C2×C61#334311yescharacteristic
398C2×C61#334511yescharacteristic
399D61—42no—
400C22×#41—1221no—
401C22×M16—611no—
402C23×C8—611no—
403#547—618no—
404#547—1224no—
405C2×C4⋊Q8—611no—
406C2×#123—1221no—
407C2×#123—1221no—
408C2×C22⋊Q8—1221no—
409C2×#121—611no—
410C2×#121C2×D6111yescharacteristic
411C2×C4×D4—611no—
412C2×C4×D4—611no—
413C2×#117—611no—
414C22×C4⋊C4—611no—
415C22×C4⋊C4—611no—
416C22×C4⋊C4C2×D6111yescharacteristic
417#435—1224no—
418C2×C4⋊C8—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102C2×D6111yescharacteristic
422C2×#102C2×D6111yescharacteristic
423C2×C22⋊C8—611no—
424C2×C22⋊C8C2×D6111yescharacteristic
425C2×#97—611no—
426#388—1221no—
427#387—1221no—
428#386—1221no—
429#382—611no—
430#380—611no—
431#380—611no—
432C4×C4⋊C4—611no—
433C4×C22⋊C4—1221no—
434#340—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340C2×D6111yescharacteristic
445#340C2×D6111yescharacteristic
446C61#2249511yescharacteristic, complemented, Sylow
447C2×#41—1228no—
448C2×#41—2444no—
449C2×#41—2444no—
450C22×Q8—1221no—
451C22×D4—21no—
452C22×D4—611no—
453C22×D4—1221no—
454C22×D4C22×D6111yescharacteristic
455C23×C4—21no—
456C23×C4—611no—
457C23×C4—1221no—
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4C22×D6111yescharacteristic
461C2×M16—1222no—
462C2×M16—1222no—
463C2×M16—2441no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—1222no—
467C22×C8—1222no—
468C22×C8—2441no—
469C22×C8C22×D6111yescharacteristic
470C22×C8C22×D6111yescharacteristic
471C4⋊Q8—614no—
472C4⋊Q8—1222no—
473#123—1228no—
474#123—1228no—
475C22⋊Q8—1228no—
476#121—22no—
477#121—614no—
478#121—1222no—
479#121C4×D6114yes—
480C4×D4—614no—
481C4×D4—614no—
482C4×D4—614no—
483C4×D4—1222no—
484#117—1222no—
485#117—2441no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—614no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—614no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—1222no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1222no—
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C4⋊C4C22×D6111yescharacteristic
503C2×C4⋊C4C22×D6111yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C42—611no—
513C2×C42—1221no—
514C2×C42—1221no—
515C4⋊C8—1222no—
516#102—22no—
517#102—41no—
518#102—1222no—
519#102—2441no—
520C22⋊C8—22no—
521C22⋊C8—1222no—
522#97—1222no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528C24—21no—
529C24—611no—
530C24D4×D6111yescharacteristic
531#41—24432no—
532C2×Q8—1224no—
533C2×Q8—2442no—
534C2×Q8—2442no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—614no—
544C2×D4—1222no—
545C2×D4—1222no—
546C2×D4—1224no—
547C2×D4—2442no—
548C2×D4—2442no—
549C2×D4C2×C4×D6112yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—81no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—1224no—
566C22×C4—1224no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1224no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—2442no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4—2442no—
580C22×C4—2442no—
581C22×C4—2442no—
582C22×C4C2×C4×D6112yes—
583C22×C4D4×D6112yes—
584C22×C4D4×D6111yescharacteristic
585C22×C4C23×D6111yescharacteristic
586M16—2444no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—612no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—2444no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—42no—
605C4⋊C4—614no—
606C4⋊C4—612no—
607C4⋊C4—612no—
608C4⋊C4—1224no—
609C4⋊C4—1224no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1224no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4C2×C4×D6112yes—
618C4⋊C4#1175822412yescomplemented
619C22⋊C4—24no—
620C22⋊C4—614no—
621C22⋊C4—614no—
622C22⋊C4—1224no—
623C22⋊C4—1224no—
624C22⋊C4—4881no—
625C22⋊C4—2442no—
626C22⋊C4—2442no—
627C42—612no—
628C42—612no—
629C42—4881no—
630C42—2442no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—612no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23C22⋊C4×D6112yes—
650C23#1451980112yes—
651C23#1451980412yes—
652C23C2×D4×D6111yescharacteristic
653Q8—2448no—
654D4—22no—
655D4—22no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—1228no—
660D4—2448no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—84no—
677C2×C4—612no—
678C2×C4—612no—
679C2×C4—612no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—2448no—
693C2×C4—2448no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2448no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4C22⋊C4×D6112yes—
706C2×C4C22×C4×D6111yescharacteristic
707C2×C4C2×D4×D6111yescharacteristic
708C2×C4#41×D6111yescharacteristic
709C2×C4C2×#1175822411yescharacteristic
710C2×C4#1451982211yescharacteristic
711C2×C4#1451982411yescharacteristic
712C8—41no—
713C8—41no—
714C8—1222no—
715C8—2441no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—1222no—
730C22—1222no—
731C22—1222no—
732C22—2441no—
733C22—2441no—
734C22—2441no—
735C22—2441no—
736C22#1683976514yes—
737C22C2×C22⋊C4×D6111yescharacteristic
738C22#1684039911yescharacteristic
739C22#1684041011yescharacteristic
740C22C2×#1451980111yescharacteristic
741C22C2×#1451980411yescharacteristic
742C22#1684057211yescharacteristic
743C22#1684057811yescharacteristic
744C4—22no—
745C4—42no—
746C4—42no—
747C4—81no—
748C4—1222no—
749C4—1222no—
750C4—1222no—
751C4—4881no—
752C4—4881no—
753C4—2442no—
754C4—2442no—
755C4C4×#1175822411yescharacteristic
756C4#1684024111yescharacteristic
757C4#1684040111yescharacteristic
758C4#1684041211yescharacteristic
759C2—24no—
760C2—82no—
761C2—2442no—
762C2#2144864511yescharacteristic
763C2C2×#1683976511yescharacteristic
764C2#2145435011yescharacteristic
765C2#2145778411yescharacteristic
766C2#2145781411yescharacteristic
767C2#2145826311yescharacteristic
768C2#2145828711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1874C2
socleC23×C61C22×D4
prime radicalC2×#16840412C2
cosocleC22×C4×C61C24
hypercenter#1874D61
hypocenterC61#22495
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#16839830C2semidirect
3. #21448744C2semidirect
4. #21446790C2semidirect
5. #21446765C2semidirect
6. #21446254C2semidirect
7. #21446248C2semidirect
8. #21446138C2semidirect
9. #21445908C2semidirect
10. #21445906C2semidirect
11. #21445827C2semidirect
12. #21445646C2semidirect
13. #21445537C2semidirect
14. C2×#16839524C2semidirect
15. C61×#1874C2semidirect
20. #16840412C4semidirect
81. #14519776C2×C4semidirect
86. #14519748C2×C4semidirect
88. D4×Dic61C2×C4semidirect
104. C4⋊C4×D61C2×C4semidirect
213. C4⋊C4×C61#41semidirect
244. C2×#92418#41semidirect
383. #1874D61semidirect
446. C61#22495semidirect
618. C4⋊C4#11758224semidirect

Maximal subgroups

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

subgroupindex
C2×#168404122
C2×#168398302
#214487442
#214467902
#214467652
#214462542
#214462482
#214461382
#214459082
#214459062
#214458272
#214456462
#214455372
C2×#168395242
C61×#18742
#2249561