Finite Group Databasebeta

← #29723747

Subgroups — #29723747

Order 15616.

1232 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839894C211yesmaximal, characteristic
2#21449327C211yesmaximal, characteristic, complemented
3D4×#11758198C211yesmaximal, characteristic, complemented
4#21447344C211yesmaximal, characteristic, complemented
5#21447243C211yesmaximal, characteristic, complemented
6#21447128C211yesmaximal, characteristic, complemented
7#21446999C211yesmaximal, characteristic, complemented
8#21446502C211yesmaximal, characteristic, complemented
9#21446425C211yesmaximal, characteristic, complemented
10#21446169C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446066C211yesmaximal, characteristic, complemented
13#21445817C211yesmaximal, characteristic, complemented
14#21445748C211yesmaximal, characteristic, complemented
15C2×C4×D8×C61C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519760—21no—
19C2×#14519748C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C22×#11758198—21no—
22#16839894—24no—
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519706C2211yescharacteristic, complemented
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic, complemented
30C2×#14519697C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33#16839690—21no—
34#16839677—21no—
35#16839665C2211yescharacteristic, complemented
36#16839664C2211yescharacteristic
37#16839663C2211yescharacteristic
38#16839660C2211yescharacteristic, complemented
39#16839641—21no—
40#16839639—21no—
41#16839635—21no—
42#16839631C2211yescharacteristic, complemented
43#16839619C2211yescharacteristic
44#16839619C2211yescharacteristic
45#16839617—21no—
46C4×#11758198C2211yescharacteristic
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C22×D8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic, complemented
56C4×D8×C61—24no—
57C2×#107×C61C2211yescharacteristic, complemented
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic, complemented
60C2×C4×C8×C61C2211yescharacteristic, complemented
61C24×D61—21no—
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C2×D4×D61—22no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—41no—
70C2×D4×D61—41no—
71C23×Dic61—21no—
72C22×C4×D61C2311yescharacteristic
73C2×#11758199—22no—
74C2×#11758199—22no—
75C2×#11758199—41no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78#14519760—44no—
79#14519748—22no—
80#14519748—41no—
81D4×Dic61—22no—
82D4×Dic61—41no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—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—44no—
100C2×#11758198D411yescharacteristic
101C2×#11758198D411yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103#14519710—41no—
104#14519706—41no—
105#14519699—22no—
106#14519699—22no—
107#14519698—22no—
108#14519698—22no—
109#14519698—41no—
110#14519697—41no—
111#14519689—22no—
112#14519689—41no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684D411yescharacteristic
117#14519684D411yescharacteristic
118C22×D4×C61C2311yescharacteristic
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61—21no—
121C23×C4×C61—21no—
122C2×D8×C61—22no—
123C2×D8×C61—22no—
124C2×D8×C61D414yes—
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129C4×D4×C61—41no—
130C4×D4×C61—41no—
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C42×C61C2311yescharacteristic
136#107×C61—22no—
137#102×C61—22no—
138#102×C61—22no—
139C4×C8×C61—22no—
140C24×C61—21no—
141C24×C61—21no—
142C23×D61—21no—
143C23×D61—24no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61—42no—
147C23×D61—42no—
148C23×D61—81no—
149C23×D61—81no—
150C23×D61C2×D411yescharacteristic
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61C2×D412yes—
160C2×D4×C61C2×D412yes—
161C2×D4×C61#4112yes—
162C2×D4×C61#4112yes—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—42no—
166C22×C4×C61—42no—
167C22×C4×C61—42no—
168C22×C4×C61—42no—
169C22×C4×C61—81no—
170C22×C4×C61—81no—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—24no—
175C2×C22⋊D61—42no—
176C2×C22⋊D61—42no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—81no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—42no—
184C22×Dic61—42no—
185C22×Dic61—81no—
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189D4×D61—44no—
190D4×D61—44no—
191D4×D61—44no—
192D4×D61—44no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244#4112yes—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205D8×C61—28no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61C2×D412yes—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C42×C61—21no—
219C42×C61—21no—
220C22⋊Dic61—42no—
221C22⋊Dic61—42no—
222C22⋊Dic61—42no—
223C22⋊Dic61—42no—
224#11758199—44no—
225#11758198—41no—
226#11758198—42no—
227#11758198—42no—
228#11758198—42no—
229#11758198—42no—
230#11758198—81no—
231#11758198—81no—
232#11758198D814yescomplemented
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239#11758196—42no—
240#11758196—42no—
241#11758196—81no—
242C4×Dic61—21no—
243C4×Dic61—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61C22×D411yescharacteristic
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—22no—
272C22×D61—48no—
273C22×D61—48no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—84no—
281C22×D61—84no—
282C22×D61—84no—
283C22×D61—84no—
284C22×D61—84no—
285C22×D61C2×D812yes—
286D4×C61—22no—
287D4×C61—22no—
288D4×C61—22no—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61#12314yescomplemented
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—84no—
306C2×C4×C61—84no—
307C2×C4×C61C2×D812yes—
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C22⋊D61—48no—
315C22⋊D61—84no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—84no—
334C2×Dic61C2×D812yes—
335D244—22no—
336D244—22no—
337D244—41no—
338D244—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343C8×C61—22no—
344C8×C61—41no—
345#92418—41no—
346#92418—41no—
347#24893—611nomaximal, Sylow
348C22×C61—24no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61#52511yescharacteristic
363C22×C61D4211yescharacteristic
364C22×C61#54611yescharacteristic
365C22×C61C22×D811yescharacteristic
366C22×C61#57511yescharacteristic
367C22×C61#57611yescharacteristic
368C22×C61#57711yescharacteristic
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—816no—
380C2×D61—81no—
381C2×D61—81no—
382C2×D61—81no—
383C2×D61—81no—
384C4×C61—22no—
385C4×C61—41no—
386C4×C61—81no—
387C4×C61—81no—
388C4×C61C2×#12311yescharacteristic
389C4×C61#53811yescharacteristic
390C4×C61#54611yescharacteristic
391C4×C61#55111yescharacteristic
392Dic61—22no—
393Dic61—41no—
394Dic61—41no—
395Dic61—81no—
396Dic61—81no—
397Dic61—81no—
398C2×#447—611no—
399C2×C4×D8D6111yescharacteristic, complemented
400#2422—611no—
401D4×C22⋊C4—611no—
402#2093—611no—
403#2075—611no—
404#2054—611no—
405#2033—611no—
406#1934—611no—
407#1923—611no—
408#1879—611no—
409#1879—611no—
410#1862—611no—
411#1802—611no—
412#1786—611no—
413C2×C61—44no—
414C2×C61—82no—
415C2×C61#241811yescharacteristic
416C2×C61#310011yescharacteristic
417C2×C61#311811yescharacteristic
418C2×C61#326711yescharacteristic
419C2×C61D4×D811yescharacteristic
420C2×C61#329411yescharacteristic
421C2×C61#332211yescharacteristic
422D61—42no—
423D61—82no—
424C23×D4—611no—
425C22×D8—611no—
426C22×D8C2×D6111yescharacteristic
427C2×#123—1221no—
428C2×#121—611no—
429C2×C4×D4—611no—
430C2×C4×D4C2×D6111yescharacteristic
431C2×C4×D4C2×D6111yescharacteristic, complemented
432C22×C22⋊C4—1221no—
433#447—1224no—
434C4×D8—24no—
435C2×#107—611no—
436C2×#107C2×D6111yescharacteristic, complemented
437C2×C4⋊C8—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×#102C2×D6111yescharacteristic
445C2×#102C2×D6111yescharacteristic, complemented
446C2×C22⋊C8—611no—
447C2×C22⋊C8—611no—
448C2×C4×C8C2×D6111yescharacteristic, complemented
449#397—1221no—
450#394—1221no—
451#390—611no—
452#390—611no—
453#390—611no—
454#389—611no—
455#386—1221no—
456#386—1221no—
457#385—1221no—
458#384—611no—
459#380—611no—
460#380—611no—
461#379—1221no—
462C4×C22⋊C4—611no—
463#340—611no—
464#340—611no—
465#340—611no—
466#340—611no—
467#336—611no—
468#336—611no—
469C61#2489311yescharacteristic, complemented, Sylow
470C25—1221no—
471C22×D4—611no—
472C22×D4—1221no—
473C22×D4—1222no—
474C22×D4—1222no—
475C22×D4—1222no—
476C22×D4—1222no—
477C22×D4—1221no—
478C22×D4—2441no—
479C22×D4—2441no—
480C22×D4C22×D6111yescharacteristic
481C22×D4C22×D6111yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—611no—
485C23×C4—1221no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—1222no—
489C2×D8—1222no—
490C2×D8—2441no—
491C2×D8C22⋊D6114yes—
492C22×C8—611no—
493C22×C8—611no—
494C22×C8C22×D6111yescharacteristic
495C22×C8C22×D6111yescharacteristic
496#123—2444no—
497#121—1222no—
498#121—2441no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—41no—
502C4×D4—41no—
503C4×D4—1222no—
504C4×D4—2441no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—2444no—
528C2×C42—611no—
529C2×C42C22×D6111yescharacteristic
530#107—22no—
531#107—2441no—
532C4⋊C8—2441no—
533#102—22no—
534#102—22no—
535#102—1222no—
536#102—1222no—
537#102—1222no—
538#102—1222no—
539#102—2441no—
540#102—2441no—
541C22⋊C8—1222no—
542C22⋊C8—2441no—
543C4×C8—22no—
544#95—611no—
545#95—611no—
546#95—1221no—
547#95—1221no—
548#95—1221no—
549C24—21no—
550C24—21no—
551C24—611no—
552C24—1224no—
553C24—1221no—
554C24—4881no—
555C24—4881no—
556C24—2442no—
557C24—2442no—
558C24—2442no—
559C24—2442no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—612no—
569C2×D4—1224no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4—4881no—
576C2×D4—2442no—
577C2×D4—2442no—
578C2×D4—2444no—
579C2×D4—2444no—
580C2×D4—2444no—
581C2×D4—2442no—
582C2×D4—2442no—
583C2×D4—2444no—
584C2×D4#1175822212yes—
585C2×D4#1175822212yes—
586C2×D4C2×C22⋊D6112yes—
587C2×D4C2×C22⋊D6112yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—4881no—
609C22×C4—2442no—
610C22×C4—2442no—
611C22×C4D4×D6111yescharacteristic
612C22×C4D4×D6111yescharacteristic
613C22×C4C23×D6111yescharacteristic
614D8—28no—
615D8—2444no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8C2×C22⋊D6112yes—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—4881no—
639C4⋊C4—2442no—
640C4⋊C4—2442no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—614no—
644C22⋊C4—4881no—
645C22⋊C4—4881no—
646C22⋊C4—2441no—
647C22⋊C4—2442no—
648C22⋊C4—2442no—
649C22⋊C4—2442no—
650C22⋊C4—2442no—
651C22⋊C4—2442no—
652C22⋊C4—2442no—
653C22⋊C4—2442no—
654C22⋊C4—2442no—
655C42—21no—
656C42—21no—
657C42—1221no—
658C42—1221no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—612no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1222no—
681C23—4884no—
682C23—4884no—
683C23—4884no—
684C23—4884no—
685C23—4884no—
686C23—2448no—
687C23—2448no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691C23—2441no—
692C23—2441no—
693C23—2441no—
694C23C2×D4×D6111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—41no—
701D4—41no—
702D4—1222no—
703D4—1222no—
704D4—4884no—
705D4—2448no—
706D4—2441no—
707D4—2441no—
708D4#1451976014yescomplemented
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—84no—
721C2×C4—84no—
722C2×C4—612no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—4884no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4D8×D6112yes—
746C2×C4C22×C22⋊D6111yescharacteristic
747C2×C4#41×D6111yescharacteristic
748C2×C4C2×#1175822211yescharacteristic
749C2×C4C2×#1175822211yescharacteristic
750C2×C4#1451982211yescharacteristic
751C2×C4#1451982311yescharacteristic
752C8—22no—
753C8—41no—
754C8—2441no—
755C8—2441no—
756C22—24no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—1222no—
771C22—1222no—
772C22—1222no—
773C22—48816no—
774C22—4881no—
775C22—4881no—
776C22—4881no—
777C22—4881no—
778C22—2442no—
779C22—2442no—
780C22—2442no—
781C22—2441no—
782C22—2441no—
783C22—2441no—
784C22—2441no—
785C22#1684027111yescharacteristic
786C22D4×C22⋊D6111yescharacteristic
787C22#1684040811yescharacteristic
788C22C2×D8×D6111yescharacteristic
789C22#1684055911yescharacteristic
790C22#1684056311yescharacteristic
791C22#1684056911yescharacteristic
792C4—22no—
793C4—41no—
794C4—81no—
795C4—81no—
796C4—1222no—
797C4—4881no—
798C4—4881no—
799C4—4881no—
800C4—2441no—
801C4—2441no—
802C4C2×#1451976011yescharacteristic
803C4#1684034511yescharacteristic
804C4#1684040011yescharacteristic
805C4#1684044111yescharacteristic
806C2—44no—
807C2—82no—
808C2—4882no—
809C2—2442no—
810C2#2144927511yescharacteristic
811C2#2145581711yescharacteristic
812C2#2145599911yescharacteristic
813C2#2145734411yescharacteristic
814C2D8×C22⋊D6111yescharacteristic
815C2#2145763411yescharacteristic
816C2#2145802511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C4×D8×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
hypercenterC2×C4×D8D61
hypocenterC61#24893
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. #21449327C2semidirect
3. D4×#11758198C2semidirect
4. #21447344C2semidirect
5. #21447243C2semidirect
6. #21447128C2semidirect
7. #21446999C2semidirect
8. #21446502C2semidirect
9. #21446425C2semidirect
10. #21446169C2semidirect
11. #21446167C2semidirect
12. #21446066C2semidirect
13. #21445817C2semidirect
14. #21445748C2semidirect
15. C2×C4×D8×C61C2semidirect
23. C2×#14519710C22semidirect
24. C2×#14519706C22semidirect
29. C2×#14519698C22semidirect
35. #16839665C22semidirect
38. #16839660C22semidirect
42. #16839631C22semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839517C22semidirect
52. #16839516C22semidirect
55. C2×C4×D4×C61C22semidirect
57. C2×#107×C61C22semidirect
59. C2×#102×C61C22semidirect
60. C2×C4×C8×C61C22semidirect
232. #11758198D8semidirect
293. D4×C61#123semidirect
399. C2×C4×D8D61semidirect
431. C2×C4×D4C2×D61semidirect
436. C2×#107C2×D61semidirect
445. C2×#102C2×D61semidirect
448. C2×C4×C8C2×D61semidirect
469. C61#24893semidirect
708. D4#14519760semidirect

Maximal subgroups

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

subgroupindex
C2×#168398942
#214493272
D4×#117581982
#214473442
#214472432
#214471282
#214469992
#214465022
#214464252
#214461692
#214461672
#214460662
#214458172
#214457482
C2×C4×D8×C612
#2489361