Finite Group Databasebeta

← #29727461

Subgroups — #29727461

Order 15616.

1186 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839962C211yesmaximal, characteristic, complemented
2C2×#16839901C211yesmaximal, characteristic, complemented
3C2×#16839901C211yesmaximal, characteristic, complemented
4C2×C4×#11758201C211yesmaximal, characteristic, complemented
5#21449407C211yesmaximal, characteristic
6#21447200C211yesmaximal, characteristic, complemented
7#21447008C211yesmaximal, characteristic, complemented
8#21447008C211yesmaximal, characteristic, complemented
9#21446906C211yesmaximal, characteristic, complemented
10#21446676C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic, complemented
12#21446174C211yesmaximal, characteristic, complemented
13#21446156C211yesmaximal, characteristic, complemented
14#21446087C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C2×#14519774C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×#14519750—21no—
24C2×C4×D244C2211yescharacteristic
25#16839962—24no—
26#16839901—24no—
27#16839901—24no—
28C4×#11758201—24no—
29C2×#14519708C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C4×#92418C2211yescharacteristic
43#16839680—21no—
44#16839671—21no—
45#16839664C2211yescharacteristic
46#16839660C2211yescharacteristic
47#16839640—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C23×Q8×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C61×#391—21no—
56C61×#391—21no—
57C61×#391C2211yescharacteristic
58C61×#391C2211yescharacteristic
59C61×#380—21no—
60C61×#380C2211yescharacteristic
61C4×C22⋊C4×C61—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C22×D244—21no—
64C22×D244—21no—
65C22×D244C2311yescharacteristic
66C22×D244C2311yescharacteristic
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C22×C4×D61—21no—
70C2×#11758201—22no—
71C2×#11758201—22no—
72C2×#11758201—22no—
73C2×#11758201—22no—
74C2×#11758201—22no—
75C2×#11758201—22no—
76C2×#11758201—22no—
77C2×#11758201—22no—
78C2×#11758201—22no—
79C2×#11758201—41no—
80C2×#11758201—41no—
81C2×#11758201D414yescomplemented
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86#14519774—22no—
87#14519774—41no—
88#14519751—22no—
89#14519751—22no—
90#14519751—41no—
91#14519751—41no—
92#14519750—44no—
93C4×D244—22no—
94C4×D244—41no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103#14519708—22no—
104#14519708—41no—
105C4⋊#92418—22no—
106#14519701—22no—
107#14519701—22no—
108#14519701—22no—
109#14519701D414yescomplemented
110#14519697—22no—
111#14519697—22no—
112#14519697—22no—
113#14519697—41no—
114C22⋊#92418—22no—
115C22⋊#92418—22no—
116C4×#92418—22no—
117#14519684—21no—
118C22×Q8×C61—22no—
119C22×Q8×C61—22no—
120C22×Q8×C61—21no—
121C22×Q8×C61—22no—
122C22×Q8×C61—22no—
123C22×Q8×C61—41no—
124C22×Q8×C61—41no—
125C22×Q8×C61C2311yescharacteristic
126C22×Q8×C61C2311yescharacteristic
127C23×C4×C61—21no—
128C23×C4×C61C2311yescharacteristic
129C4×Q8×C61—22no—
130C4×Q8×C61—22no—
131C4×Q8×C61—41no—
132C4×Q8×C61—41no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61D411yescharacteristic
139C2×C22⋊C4×C61D411yescharacteristic
140C2×C42×C61—21no—
141C2×C42×C61—21no—
142C2×C42×C61C2311yescharacteristic
143C2×C42×C61C2311yescharacteristic
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61—21no—
149#95×C61D411yescharacteristic
150#95×C61D411yescharacteristic
151C24×C61C2×D411yescharacteristic
152C23×D61—21no—
153C23×D61—21no—
154C2×Q8×C61—24no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—42no—
164C2×Q8×C61—42no—
165C2×Q8×C61—44no—
166C2×Q8×C61—44no—
167C2×Q8×C61—44no—
168C2×Q8×C61—44no—
169C2×Q8×C61C2×D412yes—
170C2×Q8×C61C2×D412yes—
171C2×Q8×C61#4112yes—
172C2×Q8×C61#4112yes—
173C22×C4×C61—21no—
174C22×C4×C61—24no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—42no—
185C22×C4×C61—42no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2411yescharacteristic
192C2×C22⋊D61—42no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—81no—
197C2×C22⋊D61—81no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—42no—
212C2×D244—42no—
213C2×D244—42no—
214C2×D244—42no—
215C2×D244—81no—
216C2×D244—81no—
217C2×D244C2×D412yes—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—81no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—42no—
226C4⋊C4×C61—42no—
227C22⋊C4×C61—41no—
228C22⋊C4×C61—42no—
229C22⋊C4×C61SD1614yescomplemented
230C42×C61—21no—
231C42×C61—21no—
232C42×C61—21no—
233C42×C61—21no—
234C42×C61—42no—
235C42×C61—42no—
236#11758201—28no—
237#11758201—44no—
238#11758201—44no—
239#11758201—44no—
240#11758198—42no—
241#11758198—42no—
242#11758198—42no—
243#11758198—42no—
244#11758198—81no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61C2×D412yes—
249#11758196—42no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418C2×D412yes—
261C2×#92418C2×D412yes—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61C2×SD1612yes—
269C23×C61C22×D411yescharacteristic
270C22×D61—22no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284Q8×C61—22no—
285Q8×C61—22no—
286Q8×C61—22no—
287Q8×C61—22no—
288Q8×C61—22no—
289Q8×C61—48no—
290Q8×C61—41no—
291Q8×C61—41no—
292Q8×C61#12114yescomplemented
293C2×C4×C61—22no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—22no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—48no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61C2×SD1612yes—
324C2×C4×C61C2×SD1612yes—
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C2×#4111yescharacteristic
328C2×C4×C61C2×#4111yescharacteristic
329C2×C4×C61H(5,𝔽2)11yescharacteristic
330C2×C4×C61H(5,𝔽2)11yescharacteristic
331C22⋊D61—84no—
332C22⋊D61—84no—
333C2×Dic61—22no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339D244—22no—
340D244—22no—
341D244—41no—
342D244—41no—
343D244—41no—
344D244—41no—
345D244—41no—
346D244—41no—
347D244—84no—
348D244—84no—
349C4×D61—84no—
350#92418—22no—
351#92418—22no—
352#92418—41no—
353#92418—41no—
354#25153—611nomaximal, Sylow
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61#52511yescharacteristic
363C22×C61D4211yescharacteristic
364C22×C61D4211yescharacteristic
365C22×C61C22×SD1611yescharacteristic
366C22×C61#57511yescharacteristic
367C22×C61#57711yescharacteristic
368C22×C61#57711yescharacteristic
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C2×D61—81no—
377C2×D61—81no—
378C2×D61—81no—
379C2×D61—81no—
380C2×D61—81no—
381C2×D61—81no—
382C2×D61—81no—
383C4×C61—24no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—41no—
387C4×C61—42no—
388C4×C61—41no—
389C4×C61—41no—
390C4×C61—81no—
391C4×C61—81no—
392C4×C61C2×#12111yescharacteristic
393C4×C61#53811yescharacteristic
394C4×C61#54611yescharacteristic
395C4×C61#54611yescharacteristic
396Dic61—42no—
397Dic61—81no—
398C2×#460—611no—
399C2×#448—611no—
400C2×#448—611no—
401C2×C4×SD16—611no—
402#2428—611no—
403Q8×C22⋊C4D6111yescharacteristic, complemented
404#2066—611no—
405#2034—611no—
406#2034—611no—
407#2014—611no—
408#1968—611no—
409#1923—611no—
410#1880—611no—
411#1877—611no—
412#1865—611no—
413C2×C61—42no—
414C2×C61#242411yescharacteristic
415C2×C61#310311yescharacteristic
416C2×C61#312611yescharacteristic
417C2×C61#327111yescharacteristic
418C2×C61#327511yescharacteristic
419C2×C61D4×SD1611yescharacteristic
420C2×C61D4×SD1611yescharacteristic
421D61—82no—
422D61—161no—
423C23×Q8C2×D6111yescharacteristic
424C22×SD16—611no—
425C22×SD16—611no—
426C22×SD16—611no—
427C22×SD16—611no—
428C2×#127—611no—
429C2×#121—611no—
430C2×#121—611no—
431C2×#121—1221no—
432C2×C4×Q8C2×D6111yescharacteristic
433C2×C4×Q8C2×D6111yescharacteristic
434C2×C4×D4—611no—
435#460—1224no—
436#448—1224no—
437#448—1224no—
438C4×SD16—1224no—
439C2×#106—611no—
440C2×#106—611no—
441C2×C4⋊C8—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#103—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×C22⋊C8—611no—
451C2×C22⋊C8—611no—
452C2×C4×C8—611no—
453#394—1221no—
454#392—1221no—
455#391—21no—
456#391—21no—
457#391C2×D6111yescharacteristic
458#391C2×D6111yescharacteristic
459#390—611no—
460#389—611no—
461#386—1221no—
462#380—21no—
463#380C2×D6111yescharacteristic
464C4×C22⋊C4—21no—
465C4×C22⋊C4C2×D6111yescharacteristic
466#340—611no—
467#340—611no—
468#336—611no—
469#336—611no—
470C61#2515311yescharacteristic, complemented, Sylow
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—21no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8—41no—
477C22×Q8—41no—
478C22×Q8C22×D6111yescharacteristic
479C22×Q8C22×D6111yescharacteristic
480C22×D4—611no—
481C22×D4—611no—
482C22×D4—1221no—
483C22×D4—1221no—
484C22×D4—1221no—
485C22×D4—1221no—
486C23×C4—21no—
487C23×C4—1221no—
488C23×C4C22×D6111yescharacteristic
489C2×SD16—614no—
490C2×SD16—1222no—
491C2×SD16—1222no—
492C2×SD16—1222no—
493C2×SD16—1222no—
494C2×SD16—1222no—
495C2×SD16—1222no—
496C2×SD16—1222no—
497C2×SD16—1222no—
498C2×SD16—1222no—
499C2×SD16—2441no—
500C2×SD16—2441no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—611no—
505#127—1222no—
506#127—2441no—
507#121—1222no—
508#121—1222no—
509#121—2441no—
510#121—2441no—
511#121—2444no—
512C4×Q8—22no—
513C4×Q8—22no—
514C4×Q8—41no—
515C4×Q8—41no—
516C4×D4—1222no—
517C4×D4—2441no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C4⋊C4C22×D6111yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4C22⋊D6111yescharacteristic
532C2×C22⋊C4C22⋊D6111yescharacteristic
533C2×C42—21no—
534C2×C42—21no—
535C2×C42C22×D6111yescharacteristic
536C2×C42C22×D6111yescharacteristic
537#106—1222no—
538#106—2441no—
539C4⋊C8—1222no—
540#103—614no—
541#103—1222no—
542#103—1222no—
543#103—1222no—
544#102—1222no—
545#102—1222no—
546#102—1222no—
547#102—2441no—
548C22⋊C8—1222no—
549C22⋊C8—1222no—
550C4×C8—1222no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—1221no—
557#95C22⋊D6111yescharacteristic
558#95C22⋊D6111yescharacteristic
559C24—1221no—
560C24—1221no—
561C24C2×C22⋊D6111yescharacteristic
562C2×Q8—24no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8#1175822212yes—
578C2×Q8#1175822212yes—
579C2×Q8D4×D6112yes—
580C2×Q8D4×D6112yes—
581C2×D4—612no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—4881no—
594C2×D4—4881no—
595C2×D4—4881no—
596C2×D4—4881no—
597C2×D4—2442no—
598C2×D4—2442no—
599C2×D4—2442no—
600C2×D4—2442no—
601C2×D4—2442no—
602C2×D4—2442no—
603C2×D4—2442no—
604C2×D4—2442no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—4881no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4C2×C22⋊D6111yescharacteristic
624C22×C4C2×C22⋊D6111yescharacteristic
625C22×C4C2×C22⋊D6111yescharacteristic
626C22×C4C2×C22⋊D6111yescharacteristic
627C22×C4C2×C22⋊D6111yescharacteristic
628C22×C4C23×D6111yescharacteristic
629SD16—1228no—
630SD16—2444no—
631SD16—2444no—
632SD16—2444no—
633C2×C8—612no—
634C2×C8—612no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—612no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—2442no—
656C22⋊C4—41no—
657C22⋊C4—42no—
658C22⋊C4—4881no—
659C22⋊C4—2442no—
660C22⋊C4—2442no—
661C22⋊C4—2442no—
662C22⋊C4—2442no—
663C22⋊C4#1175820114yescomplemented
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—42no—
669C42—42no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—1222no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23C2×#1175820112yes—
691C23C22×C22⋊D6111yescharacteristic
692Q8—22no—
693Q8—22no—
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—48no—
698Q8—41no—
699Q8—41no—
700Q8#1451975014yescomplemented
701D4—1222no—
702D4—1222no—
703D4—4884no—
704D4—4884no—
705D4—4884no—
706D4—4884no—
707D4—2441no—
708D4—2441no—
709D4—2441no—
710D4—2441no—
711D4—2441no—
712D4—2441no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—48no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—1222no—
744C2×C4—4884no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4C2×#1175820112yes—
751C2×C4C2×#1175820112yes—
752C2×C4C2×D4×D6111yescharacteristic
753C2×C4C2×D4×D6111yescharacteristic
754C2×C4C2×#1175822211yescharacteristic
755C2×C4C2×#1175822211yescharacteristic
756C2×C4#1451982211yescharacteristic
757C2×C4#1451982211yescharacteristic
758C8—1222no—
759C8—1222no—
760C8—2441no—
761C8—2441no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—4881no—
770C22—4881no—
771C22—4881no—
772C22—4881no—
773C22—4881no—
774C22—4881no—
775C22—4881no—
776C22—4881no—
777C22—4881no—
778C22—4881no—
779C22—4881no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22#1684027311yescharacteristic
784C22D4×C22⋊D6111yescharacteristic
785C22D4×C22⋊D6111yescharacteristic
786C22C22×#1175820111yescharacteristic
787C22#1684056011yescharacteristic
788C22#1684057011yescharacteristic
789C22#1684057011yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—41no—
794C4—41no—
795C4—42no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—4881no—
800C4—2442no—
801C4C2×#1451975011yescharacteristic
802C4#1684035011yescharacteristic
803C4#1684040211yescharacteristic
804C4#1684040211yescharacteristic
805C2—42no—
806C2—9761no—
807C2—4882no—
808C2#2144935511yescharacteristic
809C2#2145585011yescharacteristic
810C2#2145611011yescharacteristic
811C2#2145740511yescharacteristic
812C2#2145745111yescharacteristic
813C2D4×#1175820111yescharacteristic
814C2D4×#1175820111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingQ8×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radical#21449407C2
hypercenterQ8×C22⋊C4D61
hypocenterC61#25153
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16839962C2semidirect
2. C2×#16839901C2semidirect
3. C2×#16839901C2semidirect
4. C2×C4×#11758201C2semidirect
6. #21447200C2semidirect
7. #21447008C2semidirect
8. #21447008C2semidirect
9. #21446906C2semidirect
10. #21446676C2semidirect
11. #21446427C2semidirect
12. #21446174C2semidirect
13. #21446156C2semidirect
14. #21446087C2semidirect
15. Q8×C22⋊C4×C61C2semidirect
81. C2×#11758201D4semidirect
109. #14519701D4semidirect
229. C22⋊C4×C61SD16semidirect
292. Q8×C61#121semidirect
403. Q8×C22⋊C4D61semidirect
470. C61#25153semidirect
663. C22⋊C4#11758201semidirect
700. Q8#14519750semidirect

Maximal subgroups

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

subgroupindex
C2×#168399622
C2×#168399012
C2×C4×#117582012
#214494072
#214472002
#214470082
#214469062
#214466762
#214464272
#214461742
#214461562
#214460872
Q8×C22⋊C4×C612
#2515361