Finite Group Databasebeta

← #29700414

Subgroups — #29700414

Order 15616.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839911C211yesmaximal, characteristic
2C2×#16839765C211yesmaximal, characteristic
3#21448842C211yesmaximal, characteristic, complemented
4D4×#11758198C211yesmaximal, characteristic
5#21446670C211yesmaximal, characteristic, complemented
6#21446516C211yesmaximal, characteristic, complemented
7#21446438C211yesmaximal, characteristic, complemented
8#21446249C211yesmaximal, characteristic, complemented
9#21446174C211yesmaximal, characteristic, complemented
10#21446155C211yesmaximal, characteristic, complemented
11#21446080C211yesmaximal, characteristic, complemented
12#21446015C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445604C211yesmaximal, characteristic, complemented
15C2×C61×#440C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C2×#14519753C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22C22×#11758198—21no—
23#16839911C418yescomplemented
24C2×#14519708C2211yescharacteristic, complemented
25#16839765—24no—
26C2×#14519701C2211yescharacteristic, complemented
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic, complemented
34#16839669C2211yescharacteristic, complemented
35#16839664C2211yescharacteristic
36#16839663C2211yescharacteristic
37#16839660C2211yescharacteristic, complemented
38#16839653—21no—
39#16839652—21no—
40#16839643—21no—
41#16839641—21no—
42#16839639—21no—
43#16839619C2211yescharacteristic
44#16839617—21no—
45C4⋊C4×Dic61C2211yescharacteristic, complemented
46C4×#11758196—21no—
47C4×#11758198C2211yescharacteristic
48#16839525C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C22×SD16×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic, complemented
56C2×C4×D4×C61C2211yescharacteristic
57C61×#440—24no—
58C2×#107×C61C2211yescharacteristic, complemented
59C2×#103×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C2×D4×D61—22no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—41no—
69C2×D4×D61—41no—
70C2×D4×D61C2×C414yes—
71C23×Dic61—21no—
72C22×C4×D61C2311yescharacteristic
73C2×#11758201—41no—
74C2×#11758201—41no—
75C2×#11758201C2×C414yescomplemented
76C2×#11758189—22no—
77C2×#11758189—22no—
78C2×#11758189—41no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81#14519753—22no—
82#14519753C2×C414yescomplemented
83D4×Dic61—22no—
84D4×Dic61—41no—
85#14519735—22no—
86#14519735—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—44no—
101C2×#11758198D411yescharacteristic
102C2×#11758198D411yescharacteristic
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61C2311yescharacteristic
106#14519708—41no—
107#14519701—41no—
108#14519699—22no—
109#14519699C2×C414yescomplemented
110#14519698—22no—
111#14519698C2×C414yes—
112#14519697—22no—
113#14519689C2×C414yescomplemented
114C8×Dic61—41no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684D411yescharacteristic
121#14519684D411yescharacteristic
122C22×Q8×C61C2311yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C2×SD16×C61—22no—
126C2×SD16×C61—22no—
127C2×SD16×C61C2×C414yes—
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C4×Q8×C61—22no—
131C4×Q8×C61—41no—
132C4×D4×C61—22no—
133C4×D4×C61—41no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139C2×C42×C61C2311yescharacteristic
140#107×C61—22no—
141#103×C61—22no—
142#102×C61D414yes—
143#97×C61—22no—
144C24×C61—21no—
145C23×D61—21no—
146C23×D61—24no—
147C23×D61—42no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—81no—
152C23×D61—81no—
153C23×D61C2×D411yescharacteristic
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61C22×C412yes—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61C22×C412yes—
164C2×D4×C61C2×D412yes—
165C2×D4×C61#4112yes—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—42no—
170C22×C4×C61—42no—
171C22×C4×C61—81no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2411yescharacteristic
175C2×C22⋊D61—24no—
176C2×C22⋊D61—42no—
177C2×C22⋊D61—42no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—42no—
182C22×Dic61—42no—
183C22×Dic61—81no—
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187D4×D61—28no—
188D4×D61—44no—
189D4×D61—44no—
190D4×D61—44no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244C22×C412yes—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61C22×C412yes—
202C2×C4×D61#4112yes—
203SD16×C61—28no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61C22×C412yes—
209C2×C8×C61C2×D412yes—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—42no—
214C4⋊C4×C61C2×D412yes—
215C22⋊C4×C61—42no—
216C42×C61—21no—
217C42×C61—21no—
218C42×C61—42no—
219C22⋊Dic61—42no—
220#11758201—44no—
221#11758198—24no—
222#11758198—22no—
223#11758198—41no—
224#11758198—42no—
225#11758198—42no—
226#11758198—42no—
227#11758198—42no—
228#11758198—81no—
229#11758198—81no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61C22×C412yes—
236#11758196—24no—
237#11758196—42no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—42no—
241C4×Dic61—42no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418C22×C412yes—
248#11758189—44no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61C22×D411yescharacteristic
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—22no—
264C22×D61—48no—
265C22×D61—48no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—84no—
273C22×D61—84no—
274C22×D61—84no—
275C22×D61—84no—
276C22×D61—84no—
277C22×D61C4×D412yes—
278Q8×C61—22no—
279Q8×C61—22no—
280Q8×C61—41no—
281Q8×C61—41no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61C4×D414yes—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—84no—
302C2×C4×C61C23×C411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C22⋊D61—48no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—22no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—84no—
326C2×Dic61C4×D412yes—
327C2×Dic61AGL(1,ℤ/8)12yes—
328D244—22no—
329D244—22no—
330D244—41no—
331D244—41no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C8×C61—22no—
337C8×C61—22no—
338#92418—22no—
339#92418—41no—
340#22864—611nomaximal, Sylow
341C22×C61—24no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61C2×C4×D411yescharacteristic
349C22×C61D4211yescharacteristic
350C22×C61#54611yescharacteristic
351C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C61#57511yescharacteristic
353C22×C61#57711yescharacteristic
354C22×C61#57711yescharacteristic
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—816no—
366C2×D61—81no—
367C2×D61—81no—
368C2×D61—81no—
369C2×D61—81no—
370C4×C61—42no—
371C4×C61—41no—
372C4×C61—42no—
373C4×C61—41no—
374C4×C61—81no—
375C4×C61C2×C4×D411yescharacteristic
376C4×C61#51811yescharacteristic
377C4×C61#54611yescharacteristic
378C4×C61#55111yescharacteristic
379Dic61—22no—
380Dic61—22no—
381Dic61—42no—
382Dic61—41no—
383Dic61—81no—
384Dic61—81no—
385C2×#450—611no—
386C2×#440D6111yescharacteristic, complemented
387C2×#418—611no—
388#2362—611no—
389D4×C22⋊C4—611no—
390#1968—611no—
391#1936—611no—
392#1925—611no—
393#1894—611no—
394#1880—611no—
395#1877—611no—
396#1864—611no—
397#1854—611no—
398C4×#102—611no—
399#1753—611no—
400C2×C61—44no—
401C2×C61#235811yescharacteristic
402C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
403C2×C61#294911yescharacteristic
404C2×C61#327211yescharacteristic
405C2×C61#327511yescharacteristic
406C2×C61#331011yescharacteristic
407C2×C61#331111yescharacteristic
408D61—42no—
409D61—82no—
410C23×D4—611no—
411C22×SD16—611no—
412C22×SD16C2×D6111yescharacteristic
413C22×M16—611no—
414C2×C22⋊Q8—611no—
415C2×C4×Q8C2×D6111yescharacteristic, complemented
416C2×C4×D4—611no—
417C2×C4×D4C2×D6111yescharacteristic
418C2×#117—611no—
419C22×C22⋊C4—1221no—
420#450—618no—
421#440—24no—
422C2×#107C2×D6111yescharacteristic, complemented
423C2×#106—611no—
424#418—1224no—
425C2×#103—611no—
426C2×#103C2×D6111yescharacteristic, complemented
427C2×#102—611no—
428C2×#102—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102C2×D6111yescharacteristic
433C2×C22⋊C8—611no—
434C2×#97C2×D6111yescharacteristic, complemented
435C2×C4×C8—611no—
436#391—611no—
437#390—611no—
438#390—611no—
439#389—611no—
440#388—1221no—
441#388—1221no—
442#387—1221no—
443#386—1221no—
444#386—1221no—
445#380—611no—
446#379—1221no—
447C4×C4⋊C4—611no—
448C4×C4⋊C4—1221no—
449C4×C22⋊C4—611no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#336—611no—
455#336—611no—
456C61#2286411yescharacteristic, complemented, Sylow
457C25—1221no—
458C22×Q8C22×D6111yescharacteristic
459C22×D4—614no—
460C22×D4—611no—
461C22×D4—1222no—
462C22×D4—1221no—
463C22×D4—1222no—
464C22×D4—1222no—
465C22×D4—2441no—
466C22×D4—2441no—
467C22×D4C22×D6111yescharacteristic
468C23×C4—21no—
469C23×C4—611no—
470C23×C4—1221no—
471C2×SD16—22no—
472C2×SD16—22no—
473C2×SD16—614no—
474C2×SD16—2441no—
475C2×SD16—2441no—
476C2×SD16C4×D6114yes—
477C2×M16—1222no—
478C2×M16—1222no—
479C2×M16—2441no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C22⋊Q8—614no—
485C22⋊Q8—1222no—
486C4×Q8—22no—
487C4×Q8—41no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—1222no—
491C4×D4—2441no—
492#117—1222no—
493#117—2441no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4C22×D6111yescharacteristic
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—611no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—2444no—
514C2×C42—21no—
515C2×C42—611no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42C22×D6111yescharacteristic
519#107—22no—
520#106—2441no—
521#103—22no—
522#103—2441no—
523#102—614no—
524#102—614no—
525#102—1222no—
526#102—1222no—
527#102—1222no—
528#102C22⋊D6114yes—
529C22⋊C8—614no—
530#97—22no—
531C4×C8—2441no—
532#95—611no—
533#95—611no—
534#95—1221no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—21no—
540C24—611no—
541C24—1224no—
542C24—1221no—
543C24—4881no—
544C24—4881no—
545C24—2442no—
546C24—2442no—
547C24—2442no—
548C24—2442no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8C2×C4×D6112yes—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—612no—
559C2×D4—1224no—
560C2×D4—1228no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—2444no—
567C2×D4—2444no—
568C2×D4—2444no—
569C2×D4—2442no—
570C2×D4—2442no—
571C2×D4C2×C4×D6112yes—
572C2×D4#1175822212yes—
573C2×D4C2×C22⋊D6112yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—611no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—4881no—
593C22×C4—2442no—
594C22×C4—2442no—
595C22×C4D4×D6111yescharacteristic
596C22×C4D4×D6111yescharacteristic
597C22×C4C23×D6111yescharacteristic
598SD16—28no—
599SD16—2444no—
600M16—2444no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—612no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8C2×C4×D6112yes—
612C2×C8C2×C22⋊D6112yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—612no—
618C4⋊C4—1224no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—2442no—
625C4⋊C4C2×C22⋊D6112yes—
626C22⋊C4—42no—
627C22⋊C4—1222no—
628C22⋊C4—1224no—
629C22⋊C4—4881no—
630C22⋊C4—4881no—
631C22⋊C4—2441no—
632C22⋊C4—2442no—
633C22⋊C4—2442no—
634C22⋊C4—2442no—
635C22⋊C4—2442no—
636C22⋊C4—2442no—
637C42—21no—
638C42—21no—
639C42—42no—
640C42—1221no—
641C42—1221no—
642C42—2442no—
643C42—2442no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—612no—
652C23—1221no—
653C23—1221no—
654C23—1221no—
655C23—1221no—
656C23—1221no—
657C23—1221no—
658C23—1222no—
659C23—4884no—
660C23—4884no—
661C23—4884no—
662C23—4884no—
663C23—4884no—
664C23—2448no—
665C23—2448no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23—2441no—
670C23—2441no—
671C23—2441no—
672C23C2×D4×D6111yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—41no—
676Q8—41no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—1222no—
681D4—1222no—
682D4—2448no—
683D4—2441no—
684D4—2441no—
685D4C4×C22⋊D6114yes—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—84no—
702C2×C4—612no—
703C2×C4—612no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—4884no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4C22×C4×D6111yescharacteristic
726C2×C4C22×C22⋊D6111yescharacteristic
727C2×C4#41×D6111yescharacteristic
728C2×C4C2×#1175822211yescharacteristic
729C2×C4#1451982211yescharacteristic
730C2×C4#1451982311yescharacteristic
731C8—22no—
732C8—22no—
733C8—1222no—
734C8—2441no—
735C22—24no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—1222no—
743C22—1222no—
744C22—1222no—
745C22—48816no—
746C22—4881no—
747C22—4881no—
748C22—4881no—
749C22—4881no—
750C22—2442no—
751C22—2442no—
752C22—2442no—
753C22—2441no—
754C22—2441no—
755C22—2441no—
756C22—2441no—
757C22C4×D4×D6111yescharacteristic
758C22D4×C22⋊D6111yescharacteristic
759C22#1684040811yescharacteristic
760C22AGL(1,ℤ/8)×D6111yescharacteristic
761C22#1684056111yescharacteristic
762C22#1684057111yescharacteristic
763C22#1684057211yescharacteristic
764C4—41no—
765C4—42no—
766C4—41no—
767C4—42no—
768C4—81no—
769C4—1222no—
770C4—1222no—
771C4—4881no—
772C4—4881no—
773C4—2442no—
774C4—2441no—
775C4C2×C4×C22⋊D6111yescharacteristic
776C4#1684023411yescharacteristic
777C4#1684040011yescharacteristic
778C4#1684044111yescharacteristic
779C2—44no—
780C2—4882no—
781C2—2442no—
782C2#2144879611yescharacteristic
783C2#2145462411yescharacteristic
784C2#2145467511yescharacteristic
785C2#2145741311yescharacteristic
786C2#2145744411yescharacteristic
787C2#2145784511yescharacteristic
788C2#2145786011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenterC2×#440D61
hypocenterC61#22864
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
3. #21448842C2semidirect
5. #21446670C2semidirect
6. #21446516C2semidirect
7. #21446438C2semidirect
8. #21446249C2semidirect
9. #21446174C2semidirect
10. #21446155C2semidirect
11. #21446080C2semidirect
12. #21446015C2semidirect
13. #102×Dic61C2semidirect
14. #21445604C2semidirect
15. C2×C61×#440C2semidirect
23. #16839911C4semidirect
24. C2×#14519708C22semidirect
26. C2×#14519701C22semidirect
33. C2×C8×Dic61C22semidirect
34. #16839669C22semidirect
37. #16839660C22semidirect
45. C4⋊C4×Dic61C22semidirect
48. #16839525C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
53. #16839516C22semidirect
55. C2×C4×Q8×C61C22semidirect
58. C2×#107×C61C22semidirect
59. C2×#103×C61C22semidirect
61. C2×#97×C61C22semidirect
75. C2×#11758201C2×C4semidirect
82. #14519753C2×C4semidirect
109. #14519699C2×C4semidirect
113. #14519689C2×C4semidirect
386. C2×#440D61semidirect
415. C2×C4×Q8C2×D61semidirect
422. C2×#107C2×D61semidirect
426. C2×#103C2×D61semidirect
434. C2×#97C2×D61semidirect
456. C61#22864semidirect

Maximal subgroups

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

subgroupindex
C2×#168399112
C2×#168397652
#214488422
D4×#117581982
#214466702
#214465162
#214464382
#214462492
#214461742
#214461552
#214460802
#214460152
#102×Dic612
#214456042
C2×C61×#4402
#2286461