Finite Group Databasebeta

← #29727833

Subgroups — #29727833

Order 15616.

1134 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839974C211yesmaximal, characteristic, complemented
2C2×#16839922C211yesmaximal, characteristic, complemented
3C2×#16839905C211yesmaximal, characteristic
4C2×#16839860C211yesmaximal, characteristic, complemented
5#21448650C211yesmaximal, characteristic, complemented
6#21447211C211yesmaximal, characteristic, complemented
7#21447019C211yesmaximal, characteristic, complemented
8#21446998C211yesmaximal, characteristic, complemented
9#21446913C211yesmaximal, characteristic, complemented
10#21446699C211yesmaximal, characteristic, complemented
11#21446434C211yesmaximal, characteristic, complemented
12#21446170C211yesmaximal, characteristic, complemented
13#21446160C211yesmaximal, characteristic, complemented
14#21446065C211yesmaximal, characteristic, complemented
15C61×#2426C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23#16839974—24no—
24#16839922—24no—
25#16839905—24no—
26#16839860—24no—
27C2×#14519710C2211yescharacteristic
28C2×#14519710C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519688C2211yescharacteristic
41#16839668C2211yescharacteristic
42#16839668C2211yescharacteristic
43#16839638—21no—
44#16839638—21no—
45#16839624—21no—
46#16839622C2211yescharacteristic
47#95×D61—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×#124×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×#121×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C61×#396—21no—
57C61×#394—21no—
58C61×#390—21no—
59C61×#390C2211yescharacteristic
60C61×#389C2211yescharacteristic
61C61×#388—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C22×Dic122C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C2×#11758202—22no—
76C2×#11758202—22no—
77C2×#11758202—41no—
78C2×#11758200—22no—
79C2×#11758200—22no—
80C2×#11758200—41no—
81C2×#11758201—22no—
82C2×#11758201—22no—
83C2×#11758201D414yescomplemented
84C2×#11758199—22no—
85C2×#11758199—22no—
86C2×#11758199—22no—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C4×D244—22no—
92C4×D244—22no—
93C4×D244—41no—
94C4×D244—41no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100#14519710—22no—
101#14519710—41no—
102C4⋊#92418—22no—
103#14519701—22no—
104#14519701—22no—
105#14519700—22no—
106#14519700—22no—
107#14519698—22no—
108#14519698—41no—
109#14519697—22no—
110#14519697D414yes—
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113#14519688—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×Q8×C61C2311yescharacteristic
120C22×D4×C61—21no—
121C22×D4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123#124×C61—22no—
124#124×C61—41no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—41no—
127#121×C61—22no—
128#121×C61—41no—
129C4×Q8×C61—22no—
130C4×Q8×C61—41no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146C2×C42×C61C2311yescharacteristic
147#95×C61—21no—
148#95×C61D411yescharacteristic
149#95×C61D411yescharacteristic
150C24×C61—21no—
151C24×C61C2×D411yescharacteristic
152C23×D61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61C2×D412yes—
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—81no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61—24no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—42no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189#11758222—44no—
190#11758222—44no—
191#11758222—44no—
192#11758222—44no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244C2×D412yes—
197C2×D244C2×D412yes—
198C2×D244#4112yes—
199C2×C4×D61—24no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—81no—
207C2×C4×D61—81no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122#4112yes—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—42no—
218C4⋊C4×C61—42no—
219C4⋊C4×C61—81no—
220C4⋊C4×C61C2×D412yes—
221C22⋊C4×C61—41no—
222C22⋊C4×C61—41no—
223C22⋊C4×C61—42no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—42no—
227C22⋊C4×C61—42no—
228C22⋊C4×C61—81no—
229C42×C61—21no—
230C42×C61—21no—
231C42×C61—21no—
232C42×C61—21no—
233C42×C61—42no—
234C22⋊Dic61—81no—
235#11758202—44no—
236#11758201—28no—
237#11758200—44no—
238#11758199—44no—
239#11758198—42no—
240#11758198—42no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418C2×D412yes—
256C2×#92418C2×D412yes—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61C22×D411yescharacteristic
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279Q8×C61—22no—
280Q8×C61—22no—
281Q8×C61—41no—
282Q8×C61—41no—
283D4×C61—41no—
284D4×C61—41no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—84no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
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—21no—
304C2×C4×C61—21no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
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×C61C22×D411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C22⋊D61—48no—
323C2×Dic61—22no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332D244—22no—
333D244—22no—
334D244—22no—
335D244#12114yes—
336C4×D61—48no—
337C4×D61—84no—
338C4×D61—84no—
339Dic122—22no—
340Dic122—22no—
341Dic122—41no—
342Dic122—41no—
343#92418—22no—
344#92418—22no—
345#92418—41no—
346#92418—41no—
347#25178—611nomaximal, Sylow
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61#52511yescharacteristic
363C22×C61D4211yescharacteristic
364C22×C61D4211yescharacteristic
365C22×C61#57511yescharacteristic
366C22×C61#57511yescharacteristic
367C22×C61#57611yescharacteristic
368C22×C61#57811yescharacteristic
369C2×D61—24no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C4×C61—41no—
377C4×C61—42no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—41no—
381C4×C61—41no—
382C4×C61—42no—
383C4×C61—81no—
384C4×C61C2×#12111yescharacteristic
385C4×C61#53811yescharacteristic
386C4×C61#54611yescharacteristic
387C4×C61#54611yescharacteristic
388Dic61—42no—
389Dic61—81no—
390Dic61—81no—
391C2×#463—611no—
392C2×#452—611no—
393C2×#449—611no—
394C2×#440—611no—
395#2426D6111yescharacteristic, complemented
396#2339—611no—
397#2068—611no—
398#2036—611no—
399#2033—611no—
400#2015—611no—
401#1973—611no—
402#1924—611no—
403#1879—611no—
404#1878—611no—
405#1862—611no—
406C2×C61—81no—
407C2×C61—161no—
408C2×C61#242411yescharacteristic
409C2×C61#311111yescharacteristic
410C2×C61#312411yescharacteristic
411C2×C61#326811yescharacteristic
412C2×C61#326911yescharacteristic
413C2×C61#326911yescharacteristic
414C2×C61#327311yescharacteristic
415D61—44no—
416C22×#41—611no—
417C22×Q16—611no—
418C22×SD16—611no—
419C22×SD16—611no—
420C22×D8—611no—
421C2×#124C2×D6111yescharacteristic
422C2×C22⋊Q8C2×D6111yescharacteristic
423C2×#121C2×D6111yescharacteristic
424C2×C4×Q8C2×D6111yescharacteristic
425C2×C4×D4—611no—
426C2×C4×D4—611no—
427#463—1224no—
428#452—1224no—
429#449—1224no—
430#440—1224no—
431C2×#107—611no—
432C2×#107—611no—
433C2×C4⋊C8—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×#97—611no—
445#396—21no—
446#394—21no—
447#391—611no—
448#391—611no—
449#390—21no—
450#390C2×D6111yescharacteristic
451#389C2×D6111yescharacteristic
452#388—21no—
453#386—1221no—
454#386—1221no—
455#381—1221no—
456#380—611no—
457C4×C22⋊C4C2×D6111yescharacteristic
458C2×#95—1221no—
459#340—611no—
460#340—611no—
461#336—611no—
462#336—611no—
463C61#2517811yescharacteristic, complemented, Sylow
464C2×#41—1222no—
465C2×#41—1222no—
466C2×#41—1222no—
467C2×#41—1222no—
468C2×#41—2441no—
469C2×#41—2441no—
470C22×Q8—611no—
471C22×Q8C22×D6111yescharacteristic
472C22×D4—21no—
473C22×D4—611no—
474C22×D4—1221no—
475C22×D4C22×D6111yescharacteristic
476C23×C4—1221no—
477C23×C4—1221no—
478C23×C4—1221no—
479C23×C4C22×D6111yescharacteristic
480C2×Q16—1222no—
481C2×Q16—1222no—
482C2×Q16—2441no—
483C2×SD16—614no—
484C2×SD16—1222no—
485C2×SD16—1222no—
486C2×SD16—1222no—
487C2×SD16—1222no—
488C2×SD16—2441no—
489C2×D8—1222no—
490C2×D8—1222no—
491C2×D8—1222no—
492C22×C8—611no—
493C22×C8—611no—
494C22×C8—611no—
495C22×C8—611no—
496#124—22no—
497#124—41no—
498C22⋊Q8—22no—
499C22⋊Q8—41no—
500#121—22no—
501#121—41no—
502C4×Q8—22no—
503C4×Q8—41no—
504C4×D4—1222no—
505C4×D4—1222no—
506C4×D4—2441no—
507C4×D4—2441no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4C22⋊D6111yescharacteristic
525C2×C22⋊C4C22⋊D6111yescharacteristic
526C2×C42—21no—
527C2×C42C22×D6111yescharacteristic
528C2×C42C22×D6111yescharacteristic
529#107—1222no—
530#107—2441no—
531C4⋊C8—1222no—
532#103—1222no—
533#103—1222no—
534#103—1222no—
535#103—1222no—
536#102—614no—
537#102—1222no—
538#102—1222no—
539#102—2441no—
540C22⋊C8—1222no—
541C22⋊C8—1222no—
542#97—1222no—
543#95—21no—
544#95—1221no—
545#95—1221no—
546#95—1221no—
547#95—1221no—
548#95—1221no—
549#95C22⋊D6111yescharacteristic
550#95C22⋊D6111yescharacteristic
551C24—21no—
552C24—1221no—
553C24C2×C22⋊D6111yescharacteristic
554#41—2444no—
555#41—2444no—
556#41—2444no—
557#41—2444no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—612no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×Q8—1221no—
567C2×Q8—1221no—
568C2×Q8—1221no—
569C2×Q8D4×D6112yes—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4—612no—
580C2×D4—612no—
581C2×D4—612no—
582C2×D4—1224no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—2442no—
587C2×D4—2442no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—1224no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—4881no—
602C22×C4—4881no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4—2442no—
608C22×C4—2442no—
609C22×C4C2×C22⋊D6111yescharacteristic
610C22×C4C2×C22⋊D6111yescharacteristic
611C22×C4C2×C22⋊D6111yescharacteristic
612C22×C4C2×C22⋊D6111yescharacteristic
613C22×C4C2×C22⋊D6111yescharacteristic
614C22×C4C23×D6111yescharacteristic
615Q16—2444no—
616SD16—1228no—
617SD16—2444no—
618D8—2444no—
619C2×C8—612no—
620C2×C8—612no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—81no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4D4×D6112yes—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—81no—
650C22⋊C4—4881no—
651C22⋊C4—2442no—
652C22⋊C4—2442no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—42no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23C22×C22⋊D6111yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—41no—
683Q8—41no—
684Q8—1222no—
685Q8—1222no—
686Q8—2441no—
687Q8—2441no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—84no—
693D4—614no—
694D4—1222no—
695D4—1222no—
696D4—1222no—
697D4—2448no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—1222no—
727C2×C4—4884no—
728C2×C4—4884no—
729C2×C4—2448no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4C2×D4×D6111yescharacteristic
739C2×C4C2×D4×D6111yescharacteristic
740C2×C4#41×D6111yescharacteristic
741C2×C4#41×D6111yescharacteristic
742C2×C4#1451982211yescharacteristic
743C2×C4#1451982211yescharacteristic
744C8—1222no—
745C8—1222no—
746C8—2441no—
747C8—2441no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—1224no—
763C22—2442no—
764C22—2442no—
765C22—2442no—
766C22—2442no—
767C22—2442no—
768C22—2442no—
769C22#1684026911yescharacteristic
770C22D4×C22⋊D6111yescharacteristic
771C22D4×C22⋊D6111yescharacteristic
772C22#1684056011yescharacteristic
773C22#1684056011yescharacteristic
774C22#1684056511yescharacteristic
775C22#1684057711yescharacteristic
776C4—41no—
777C4—42no—
778C4—41no—
779C4—42no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—81no—
784C4—4881no—
785C4—4881no—
786C4—2442no—
787C4#121×D6111yescharacteristic
788C4#1684034411yescharacteristic
789C4#1684040111yescharacteristic
790C4#1684040911yescharacteristic
791C2—81no—
792C2—161no—
793C2—2444no—
794C2#2144935211yescharacteristic
795C2#2145592211yescharacteristic
796C2#2145607511yescharacteristic
797C2#2145736011yescharacteristic
798C2#2145737511yescharacteristic
799C2#2145737511yescharacteristic
800C2#2145742611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2426C2
socleC23×C61C22×D4
prime radicalC2×#16839905C2
hypercenter#2426D61
hypocenterC61#25178
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2426

Complements

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

NH ≅ G/Ntype
1. C2×#16839974C2semidirect
2. C2×#16839922C2semidirect
4. C2×#16839860C2semidirect
5. #21448650C2semidirect
6. #21447211C2semidirect
7. #21447019C2semidirect
8. #21446998C2semidirect
9. #21446913C2semidirect
10. #21446699C2semidirect
11. #21446434C2semidirect
12. #21446170C2semidirect
13. #21446160C2semidirect
14. #21446065C2semidirect
15. C61×#2426C2semidirect
83. C2×#11758201D4semidirect
395. #2426D61semidirect
463. C61#25178semidirect

Maximal subgroups

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

subgroupindex
C2×#168399742
C2×#168399222
C2×#168399052
C2×#168398602
#214486502
#214472112
#214470192
#214469982
#214469132
#214466992
#214464342
#214461702
#214461602
#214460652
C61×#24262
#2517861