Finite Group Databasebeta

← #29727803

Subgroups — #29727803

Order 15616.

1262 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839964C211yesmaximal, characteristic, complemented
2C2×#16839912C211yesmaximal, characteristic
3C2×#16839912C211yesmaximal, characteristic
4C2×#16839860C211yesmaximal, characteristic, complemented
5C22⋊C4×D244C211yesmaximal, characteristic
6#21447204C211yesmaximal, characteristic, complemented
7#21447019C211yesmaximal, characteristic, complemented
8#21447019C211yesmaximal, characteristic, complemented
9#21446902C211yesmaximal, characteristic, complemented
10#21446703C211yesmaximal, characteristic, complemented
11#21446434C211yesmaximal, characteristic, complemented
12#21446174C211yesmaximal, characteristic, complemented
13#21446156C211yesmaximal, characteristic, complemented
14#21446065C211yesmaximal, characteristic, complemented
15C61×#2429C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×C22⋊C4×D61—21no—
24#16839964—24no—
25#16839912—24no—
26#16839912—24no—
27#16839860—24no—
28C2×#14519710C2211yescharacteristic, complemented
29C2×#14519710C2211yescharacteristic, complemented
30C2×C4⋊#92418C2211yescharacteristic, complemented
31C2×#14519701C2211yescharacteristic, complemented
32C2×#14519701C2211yescharacteristic, complemented
33C2×#14519701C2211yescharacteristic, complemented
34C2×#14519701C2211yescharacteristic, complemented
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×#14519688C2211yescharacteristic, complemented
42#16839664C2211yescharacteristic
43#16839664C2211yescharacteristic
44#16839640—21no—
45#16839640—21no—
46#16839622C2211yescharacteristic
47#16839617—21no—
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C2×C4⋊Q8×C61C2211yescharacteristic, complemented
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic, complemented
56C61×#398—21no—
57C61×#396—21no—
58C61×#391C2211yescharacteristic, complemented
59C61×#389—21no—
60C61×#389C2211yescharacteristic, complemented
61C61×#388—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C24×D61—21no—
64C22×D244—21no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—22no—
69C22×D244—41no—
70C22×D244—41no—
71C22×D244C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C2×#11758201—22no—
76C2×#11758201—22no—
77C2×#11758201—22no—
78C2×#11758201—22no—
79C2×#11758201—22no—
80C2×#11758201—22no—
81C2×#11758201—22no—
82C2×#11758201—22no—
83C2×#11758201—22no—
84C2×#11758201—41no—
85C2×#11758201—41no—
86C2×#11758201D414yes—
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—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C22⋊C4×D61—44no—
105#14519710—22no—
106#14519710—41no—
107C4⋊#92418—22no—
108#14519701—22no—
109#14519701—22no—
110#14519701—22no—
111#14519701—41no—
112#14519697—22no—
113#14519697—22no—
114#14519697—22no—
115#14519697D414yes—
116C22⋊#92418—22no—
117C22⋊#92418—22no—
118#14519688—22no—
119#14519684—21no—
120C22×Q8×C61C2311yescharacteristic
121C22×Q8×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C4⋊Q8×C61—22no—
124C4⋊Q8×C61—41no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—22no—
127C22⋊Q8×C61—41no—
128C22⋊Q8×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×C61—21no—
135C2×C4⋊C4×C61—21no—
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×C61D411yescharacteristic
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C42×C61—21no—
144C2×C42×C61C2311yescharacteristic
145C2×C42×C61C2311yescharacteristic
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—
154C23×D61—24no—
155C23×D61—42no—
156C23×D61—42no—
157C23×D61—42no—
158C23×D61—42no—
159C23×D61—81no—
160C23×D61—81no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61C2×D412yes—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
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×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C22×Dic61—21no—
190C22×Dic61—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—24no—
199C2×D244—21no—
200C2×D244—44no—
201C2×D244—44no—
202C2×D244—44no—
203C2×D244—42no—
204C2×D244—42no—
205C2×D244—44no—
206C2×D244C2×D412yes—
207C2×D244C2×D412yes—
208C2×D244#4112yes—
209C2×D244#4112yes—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61—81no—
215C2×C4×D61—81no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—42no—
220C4⋊C4×C61—42no—
221C4⋊C4×C61—42no—
222C4⋊C4×C61—42no—
223C4⋊C4×C61—42no—
224C4⋊C4×C61—42no—
225C4⋊C4×C61C2×D412yes—
226C22⋊C4×C61—22no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—42no—
229C22⋊C4×C61—42no—
230C42×C61—21no—
231C42×C61—21no—
232C42×C61—21no—
233C42×C61—21no—
234C42×C61—42no—
235C22⋊Dic61—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—
245#11758198—81no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
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#13712yes—
269C23×C61C22×D411yescharacteristic
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—48no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—48no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61—84no—
291Q8×C61—22no—
292Q8×C61—22no—
293Q8×C61—41no—
294Q8×C61—41no—
295Q8×C61—41no—
296Q8×C61—41no—
297Q8×C61—41no—
298Q8×C61—41no—
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—22no—
306C2×C4×C61—22no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
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×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61AGL(1,ℤ/8)12yes—
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C2×C4×C61C2×#4111yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342D244—22no—
343D244—22no—
344D244—22no—
345D244—22no—
346D244—22no—
347D244—48no—
348D244—41no—
349D244—41no—
350D244#12114yes—
351C4×D61—84no—
352C4×D61—84no—
353#92418—22no—
354#92418—22no—
355#92418—41no—
356#92418—41no—
357#25176—611nomaximal, Sylow
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61#52511yescharacteristic
366C22×C61D4211yescharacteristic
367C22×C61D4211yescharacteristic
368C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C61C2×#13711yescharacteristic
370C22×C61#57711yescharacteristic
371C22×C61#57711yescharacteristic
372C2×D61—24no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—816no—
383C2×D61—81no—
384C2×D61—81no—
385C2×D61—81no—
386C2×D61—81no—
387C4×C61—22no—
388C4×C61—41no—
389C4×C61—42no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61—42no—
394C4×C61—81no—
395C4×C61—81no—
396C4×C61C2×#12111yescharacteristic
397C4×C61#53811yescharacteristic
398C4×C61#54611yescharacteristic
399C4×C61#54611yescharacteristic
400Dic61—81no—
401Dic61—81no—
402C2×#461—611no—
403C2×#450—611no—
404C2×#450—611no—
405C2×#440—611no—
406#2429D6111yescharacteristic, complemented
407D4×C22⋊C4—611no—
408#2067—611no—
409#2036—611no—
410#2036—611no—
411#2013—611no—
412#1973—611no—
413#1924—611no—
414#1880—611no—
415#1877—611no—
416#1862—611no—
417C2×C61—42no—
418C2×C61#242411yescharacteristic
419C2×C61#311011yescharacteristic
420C2×C61#312311yescharacteristic
421C2×C61#326511yescharacteristic
422C2×C61#326611yescharacteristic
423C2×C61#326611yescharacteristic
424C2×C61#327211yescharacteristic
425D61—44no—
426D61—82no—
427C23×D4—611no—
428C22×SD16—611no—
429C22×SD16—611no—
430C22×SD16—611no—
431C22×SD16—611no—
432C2×C4⋊Q8C2×D6111yescharacteristic, complemented
433C2×C22⋊Q8C2×D6111yescharacteristic
434C2×C22⋊Q8C2×D6111yescharacteristic
435C2×C4×Q8C2×D6111yescharacteristic, complemented
436C2×C4×D4—611no—
437C2×C4×D4—611no—
438C22×C22⋊C4—1221no—
439#461—1224no—
440#450—1224no—
441#450—1224no—
442#440—1224no—
443C2×#107—611no—
444C2×#107—611no—
445C2×C4⋊C8—611no—
446C2×#103—611no—
447C2×#103—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×#97—611no—
457#398—21no—
458#396—21no—
459#391C2×D6111yescharacteristic, complemented
460#390—611no—
461#390—611no—
462#389—21no—
463#389C2×D6111yescharacteristic, complemented
464#388—21no—
465#386—1221no—
466#386—1221no—
467#380—611no—
468#379—1221no—
469C4×C22⋊C4C2×D6111yescharacteristic
470#340—611no—
471#340—611no—
472#336—611no—
473#336—611no—
474C61#2517611yescharacteristic, complemented, Sylow
475C25—1221no—
476C22×Q8C22×D6111yescharacteristic
477C22×Q8C22×D6111yescharacteristic
478C22×D4—611no—
479C22×D4—611no—
480C22×D4—1222no—
481C22×D4—1222no—
482C22×D4—1222no—
483C22×D4—1222no—
484C22×D4—1221no—
485C22×D4—2441no—
486C22×D4—2441no—
487C23×C4—1221no—
488C23×C4—1221no—
489C23×C4C22×D6111yescharacteristic
490C2×SD16—614no—
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—1222no—
500C2×SD16—2441no—
501C2×SD16—2441no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—611no—
506C4⋊Q8—22no—
507C4⋊Q8—41no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—41no—
511C22⋊Q8—41no—
512C4×Q8—22no—
513C4×Q8—41no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4—2441no—
517C4×D4—2441no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—2444no—
538C2×C22⋊C4C22⋊D6111yescharacteristic
539C2×C22⋊C4C22⋊D6111yescharacteristic
540C2×C42—21no—
541C2×C42C22×D6111yescharacteristic
542C2×C42C22×D6111yescharacteristic
543#107—1222no—
544#107—2441no—
545C4⋊C8—1222no—
546#103—1222no—
547#103—1222no—
548#103—1222no—
549#103—2441no—
550#102—614no—
551#102—1222no—
552#102—1222no—
553#102—1222no—
554C22⋊C8—1222no—
555C22⋊C8—1222no—
556#97—1222no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95—1221no—
561#95C22⋊D6111yescharacteristic
562#95C22⋊D6111yescharacteristic
563C24—1224no—
564C24—1221no—
565C24—1221no—
566C24—4881no—
567C24—4881no—
568C24—2442no—
569C24—2442no—
570C24—2442no—
571C24—2442no—
572C24C2×C22⋊D6111yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8D4×D6112yes—
585C2×D4—612no—
586C2×D4—612no—
587C2×D4—612no—
588C2×D4—612no—
589C2×D4—1224no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—2442no—
599C2×D4—2442no—
600C2×D4—2444no—
601C2×D4—2444no—
602C2×D4—2444no—
603C2×D4—2444no—
604C22×C4—21no—
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—21no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—4881no—
617C22×C4—4881no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4C2×C22⋊D6111yescharacteristic
623C22×C4C2×C22⋊D6111yescharacteristic
624C22×C4C2×C22⋊D6111yescharacteristic
625C22×C4C2×C22⋊D6111yescharacteristic
626C22×C4C2×C22⋊D6111yescharacteristic
627C22×C4C23×D6111yescharacteristic
628SD16—1228no—
629SD16—2444no—
630SD16—2444no—
631SD16—2444no—
632C2×C8—612no—
633C2×C8—612no—
634C2×C8—1221no—
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—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4D4×D6112yes—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—4881no—
663C22⋊C4—4881no—
664C22⋊C4—2442no—
665C22⋊C4—2442no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C22⋊C4—2442no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—42no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—1222no—
681C23—1222no—
682C23—1222no—
683C23—1222no—
684C23—4884no—
685C23—4884no—
686C23—4884no—
687C23—4884no—
688C23—4884no—
689C23—2448no—
690C23—2448no—
691C23—2441no—
692C23—2441no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23#1451980812yes—
702C23C22×C22⋊D6111yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—614no—
712D4—1222no—
713D4—1222no—
714D4—1222no—
715D4—1222no—
716D4—1222no—
717D4—2448no—
718D4—2441no—
719D4—2441no—
720C2×C4—21no—
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—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—4884no—
751C2×C4—4884no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4#1451980212yes—
759C2×C4C2×D4×D6111yescharacteristic
760C2×C4C2×D4×D6111yescharacteristic
761C2×C4#41×D6111yescharacteristic
762C2×C4#41×D6111yescharacteristic
763C2×C4#1451982211yescharacteristic
764C2×C4#1451982211yescharacteristic
765C8—1222no—
766C8—1222no—
767C8—2441no—
768C8—2441no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—1224no—
777C22—48816no—
778C22—4881no—
779C22—4881no—
780C22—4881no—
781C22—4881no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22—2442no—
791C22#1684026911yescharacteristic
792C22D4×C22⋊D6111yescharacteristic
793C22D4×C22⋊D6111yescharacteristic
794C22C2×#1451980211yescharacteristic
795C22C2×#1451980811yescharacteristic
796C22#1684057011yescharacteristic
797C22#1684057011yescharacteristic
798C4—22no—
799C4—41no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—41no—
805C4—81no—
806C4—81no—
807C4—4881no—
808C4—4881no—
809C4#121×D6111yescharacteristic
810C4#1684034411yescharacteristic
811C4#1684040111yescharacteristic
812C4#1684040911yescharacteristic
813C2—42no—
814C2—4882no—
815C2—2444no—
816C2#2144935211yescharacteristic
817C2#2145591411yescharacteristic
818C2#2145606611yescharacteristic
819C2#2145731511yescharacteristic
820C2#2145733011yescharacteristic
821C2#2145733011yescharacteristic
822C2#2145741911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2429C2
socleC23×C61C22×D4
prime radicalC23×D244C22
hypercenter#2429D61
hypocenterC61#25176
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2429

Complements

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

NH ≅ G/Ntype
1. C2×#16839964C2semidirect
4. C2×#16839860C2semidirect
6. #21447204C2semidirect
7. #21447019C2semidirect
8. #21447019C2semidirect
9. #21446902C2semidirect
10. #21446703C2semidirect
11. #21446434C2semidirect
12. #21446174C2semidirect
13. #21446156C2semidirect
14. #21446065C2semidirect
15. C61×#2429C2semidirect
28. C2×#14519710C22semidirect
29. C2×#14519710C22semidirect
30. C2×C4⋊#92418C22semidirect
31. C2×#14519701C22semidirect
32. C2×#14519701C22semidirect
33. C2×#14519701C22semidirect
34. C2×#14519701C22semidirect
41. C2×#14519688C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
52. C2×C4⋊Q8×C61C22semidirect
55. C2×C4×Q8×C61C22semidirect
58. C61×#391C22semidirect
60. C61×#389C22semidirect
406. #2429D61semidirect
432. C2×C4⋊Q8C2×D61semidirect
435. C2×C4×Q8C2×D61semidirect
459. #391C2×D61semidirect
463. #389C2×D61semidirect
474. C61#25176semidirect

Maximal subgroups

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

subgroupindex
C2×#168399642
C2×#168399122
C2×#168398602
C22⋊C4×D2442
#214472042
#214470192
#214469022
#214467032
#214464342
#214461742
#214461562
#214460652
C61×#24292
#2517661