Finite Group Databasebeta

← #29727458

Subgroups — #29727458

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×#16839959C211yesmaximal, characteristic, complemented
2C2×#16839900C211yesmaximal, characteristic, complemented
3C2×#16839900C211yesmaximal, characteristic, complemented
4C2×C4×#11758200C211yesmaximal, characteristic, complemented
5C22⋊C4×Dic122C211yesmaximal, characteristic, complemented
6#21447197C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21447005C211yesmaximal, characteristic, complemented
9#21446907C211yesmaximal, characteristic, complemented
10#21446672C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic, complemented
12#21446177C211yesmaximal, characteristic, complemented
13#21446153C211yesmaximal, characteristic, complemented
14#21446086C211yesmaximal, characteristic, complemented
15C61×#2428C211yesmaximal, characteristic
16C23×Dic122C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23#16839959—24no—
24#16839900—24no—
25#16839900—24no—
26C4×#11758200—24no—
27C2×#14519708C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C4×#92418C2211yescharacteristic
41#16839668C2211yescharacteristic
42#16839668C2211yescharacteristic
43#16839666—21no—
44#16839666—21no—
45#16839622C2211yescharacteristic
46#16839620—21no—
47C22⋊C4×Dic61—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×#127×C61C2211yescharacteristic
53C2×#121×C61—21no—
54C2×#121×C61C2211yescharacteristic
55C2×#121×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C61×#394—21no—
58C61×#392—21no—
59C61×#390C2211yescharacteristic
60C61×#389C2211yescharacteristic
61C61×#386—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122—22no—
65C22×Dic122—22no—
66C22×Dic122—22no—
67C22×Dic122—22no—
68C22×Dic122—41no—
69C22×Dic122—41no—
70C22×Dic122C2311yescharacteristic
71C22×Dic122C2311yescharacteristic
72C23×Dic61—21no—
73C2×#11758200—22no—
74C2×#11758200—22no—
75C2×#11758200—22no—
76C2×#11758200—22no—
77C2×#11758200—22no—
78C2×#11758200—22no—
79C2×#11758200—22no—
80C2×#11758200—22no—
81C2×#11758200—22no—
82C2×#11758200—41no—
83C2×#11758200—41no—
84C2×#11758200D414yescomplemented
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C4×Dic122—22no—
90C4×Dic122—22no—
91C4×Dic122—41no—
92C4×Dic122—41no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100#14519708—22no—
101#14519708—41no—
102C4⋊#92418—22no—
103#14519700—22no—
104#14519700—22no—
105#14519700—22no—
106#14519700D414yescomplemented
107#14519698—22no—
108#14519698—22no—
109#14519698—22no—
110#14519698—41no—
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113C4×#92418—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×D4×C61—21no—
120C22×D4×C61—21no—
121C22×D4×C61—21no—
122C22×D4×C61—21no—
123C22×D4×C61C2311yescharacteristic
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61—21no—
126C23×C4×C61C2311yescharacteristic
127#127×C61—22no—
128#127×C61—41no—
129#121×C61—22no—
130#121×C61—22no—
131#121×C61—41no—
132#121×C61—41no—
133#121×C61—44no—
134C4×D4×C61—22no—
135C4×D4×C61—41no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148#95×C61—21no—
149#95×C61D411yescharacteristic
150#95×C61D411yescharacteristic
151C24×C61—21no—
152C24×C61—21no—
153C24×C61C2×D411yescharacteristic
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—42no—
166C2×D4×C61—42no—
167C2×D4×C61—42no—
168C2×D4×C61—42no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61—81no—
174C2×D4×C61—81no—
175C2×D4×C61—81no—
176C2×D4×C61—81no—
177C2×D4×C61C2×D412yes—
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—21no—
185C22×C4×C61—21no—
186C22×C4×C61—42no—
187C22×C4×C61—42no—
188C22×C4×C61—81no—
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2411yescharacteristic
195C22×Dic61—21no—
196C22×Dic61—24no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—42no—
201C22×Dic61—42no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—24no—
210C2×Dic122—21no—
211C2×Dic122—44no—
212C2×Dic122—44no—
213C2×Dic122—44no—
214C2×Dic122—42no—
215C2×Dic122—42no—
216C2×Dic122—44no—
217C2×Dic122C2×D412yes—
218C2×Dic122C2×D412yes—
219C2×Dic122#4112yes—
220C2×Dic122#4112yes—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—42no—
225C4⋊C4×C61C2×D412yes—
226C22⋊C4×C61—41no—
227C22⋊C4×C61—42no—
228C22⋊C4×C61—42no—
229C22⋊C4×C61—42no—
230C22⋊C4×C61—42no—
231C22⋊C4×C61—81no—
232C22⋊C4×C61SD1614yescomplemented
233C42×C61—21no—
234C42×C61—21no—
235C42×C61—21no—
236C42×C61—21no—
237C22⋊Dic61—42no—
238#11758200—28no—
239#11758200—44no—
240#11758200—44no—
241#11758200—44no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246#11758196—42no—
247#11758196—42no—
248C4×Dic61—42no—
249C4×Dic61—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×C61—22no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61C2×SD1612yes—
283C23×C61C22×D411yescharacteristic
284D4×C61—22no—
285D4×C61—22no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61—41no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61—84no—
293D4×C61—84no—
294D4×C61—84no—
295D4×C61—84no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—22no—
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—41no—
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—84no—
320C2×C4×C61C2×SD1612yes—
321C2×C4×C61C2×SD1612yes—
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4111yescharacteristic
325C2×C4×C61C2×#4111yescharacteristic
326C2×C4×C61H(5,𝔽2)11yescharacteristic
327C2×C4×C61H(5,𝔽2)11yescharacteristic
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—48no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341Dic122—22no—
342Dic122—22no—
343Dic122—22no—
344Dic122—22no—
345Dic122—22no—
346Dic122—48no—
347Dic122—41no—
348Dic122—41no—
349Dic122#12114yescomplemented
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—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61—81no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61#52511yescharacteristic
377C22×C61D4211yescharacteristic
378C22×C61D4211yescharacteristic
379C22×C61C22×SD1611yescharacteristic
380C22×C61#57511yescharacteristic
381C22×C61#57711yescharacteristic
382C22×C61#57711yescharacteristic
383C4×C61—22no—
384C4×C61—22no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61—42no—
389C4×C61—81no—
390C4×C61C2×#12111yescharacteristic
391C4×C61#53811yescharacteristic
392C4×C61#54611yescharacteristic
393C4×C61#54611yescharacteristic
394Dic61—24no—
395Dic61—42no—
396Dic61—81no—
397Dic61—81no—
398C2×#460—611no—
399C2×#448—611no—
400C2×#448—611no—
401C2×C4×SD16—611no—
402#2428D6111yescharacteristic
403Q8×C22⋊C4—611no—
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—82no—
415C2×C61—161no—
416C2×C61#242411yescharacteristic
417C2×C61#310311yescharacteristic
418C2×C61#312611yescharacteristic
419C2×C61#327111yescharacteristic
420C2×C61#327511yescharacteristic
421C2×C61D4×SD1611yescharacteristic
422C2×C61D4×SD1611yescharacteristic
423C23×Q8—611no—
424C22×SD16—611no—
425C22×SD16—611no—
426C22×SD16—611no—
427C22×SD16—611no—
428C2×#127C2×D6111yescharacteristic
429C2×#121—21no—
430C2×#121C2×D6111yescharacteristic
431C2×#121C2×D6111yescharacteristic
432C2×C4×Q8—611no—
433C2×C4×Q8—611no—
434C2×C4×D4C2×D6111yescharacteristic
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—21no—
454#392—21no—
455#391—611no—
456#391—611no—
457#391—1221no—
458#391—1221no—
459#390C2×D6111yescharacteristic
460#389C2×D6111yescharacteristic
461#386—21no—
462#380—611no—
463#380—1221no—
464C4×C22⋊C4—1221no—
465C4×C22⋊C4C2×D6111yescharacteristic
466#340—611no—
467#340—611no—
468#336—611no—
469#336—611no—
470C61#2515311yescharacteristic, complemented, Sylow
471C22×Q8—611no—
472C22×Q8—611no—
473C22×Q8—1222no—
474C22×Q8—1222no—
475C22×Q8—1222no—
476C22×Q8—1222no—
477C22×Q8—1221no—
478C22×Q8—2441no—
479C22×Q8—2441no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4C22×D6111yescharacteristic
485C22×D4C22×D6111yescharacteristic
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—22no—
506#127—41no—
507#121—22no—
508#121—22no—
509#121—41no—
510#121—41no—
511#121—44no—
512C4×Q8—1222no—
513C4×Q8—1222no—
514C4×Q8—2441no—
515C4×Q8—2441no—
516C4×D4—22no—
517C4×D4—41no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C4⋊C4C22×D6111yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4C22⋊D6111yescharacteristic
532C2×C22⋊C4C22⋊D6111yescharacteristic
533C2×C42—1221no—
534C2×C42—1221no—
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—1221no—
553#95—1221no—
554#95—1221no—
555#95—1221no—
556#95—1221no—
557#95C22⋊D6111yescharacteristic
558#95C22⋊D6111yescharacteristic
559C24—21no—
560C24—21no—
561C24C2×C22⋊D6111yescharacteristic
562C2×Q8—612no—
563C2×Q8—612no—
564C2×Q8—612no—
565C2×Q8—612no—
566C2×Q8—1224no—
567C2×Q8—1221no—
568C2×Q8—1221no—
569C2×Q8—1221no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—2442no—
576C2×Q8—2442no—
577C2×Q8—2444no—
578C2×Q8—2444no—
579C2×Q8—2444no—
580C2×Q8—2444no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4D4×D6112yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—81no—
616C22×C4—1221no—
617C22×C4—1224no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
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—42no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—2442no—
654C4⋊C4—2442no—
655C4⋊C4D4×D6112yes—
656C22⋊C4—41no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—81no—
662C22⋊C4—2442no—
663C22⋊C4#1175820014yescomplemented
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—2442no—
669C42—2442no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23C2×#1175820012yes—
691C23C22×C22⋊D6111yescharacteristic
692Q8—614no—
693Q8—1222no—
694Q8—1222no—
695Q8—1222no—
696Q8—1222no—
697Q8—1222no—
698Q8—2448no—
699Q8—2441no—
700Q8—2441no—
701D4—22no—
702D4—22no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—84no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—2448no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4C2×#1175820012yes—
751C2×C4C2×#1175820012yes—
752C2×C4C2×D4×D6111yescharacteristic
753C2×C4C2×D4×D6111yescharacteristic
754C2×C4#41×D6111yescharacteristic
755C2×C4#41×D6111yescharacteristic
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—42no—
770C22—42no—
771C22—42no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22#1684026911yescharacteristic
784C22D4×C22⋊D6111yescharacteristic
785C22D4×C22⋊D6111yescharacteristic
786C22C22×#1175820011yescharacteristic
787C22#1684056011yescharacteristic
788C22#1684057311yescharacteristic
789C22#1684057311yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—42no—
794C4—41no—
795C4—41no—
796C4—81no—
797C4—1224no—
798C4—4881no—
799C4—4881no—
800C4—2442no—
801C4#121×D6111yescharacteristic
802C4#1684034411yescharacteristic
803C4#1684040111yescharacteristic
804C4#1684040911yescharacteristic
805C2—42no—
806C2—82no—
807C2—161no—
808C2#2144935211yescharacteristic
809C2#2145584611yescharacteristic
810C2#2145610511yescharacteristic
811C2#2145740011yescharacteristic
812C2#2145744611yescharacteristic
813C2D4×#1175820011yescharacteristic
814C2D4×#1175820011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2428C2
socleC23×C61C22×D4
hypercenter#2428D61
hypocenterC61#25153
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2428

Complements

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

NH ≅ G/Ntype
1. C2×#16839959C2semidirect
2. C2×#16839900C2semidirect
3. C2×#16839900C2semidirect
4. C2×C4×#11758200C2semidirect
5. C22⋊C4×Dic122C2semidirect
6. #21447197C2semidirect
7. #21447005C2semidirect
8. #21447005C2semidirect
9. #21446907C2semidirect
10. #21446672C2semidirect
11. #21446427C2semidirect
12. #21446177C2semidirect
13. #21446153C2semidirect
14. #21446086C2semidirect
84. C2×#11758200D4semidirect
106. #14519700D4semidirect
232. C22⋊C4×C61SD16semidirect
349. Dic122#121semidirect
470. C61#25153semidirect
663. C22⋊C4#11758200semidirect

Maximal subgroups

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

subgroupindex
C2×#168399592
C2×#168399002
C2×C4×#117582002
C22⋊C4×Dic1222
#214471972
#214470052
#214469072
#214466722
#214464272
#214461772
#214461532
#214460862
C61×#24282
#2515361