Finite Group Databasebeta

← #29727503

Subgroups — #29727503

Order 15616.

1268 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×C4×#11758201C211yesmaximal, characteristic, complemented
5C22⋊C4×D244C211yesmaximal, characteristic
6#21447190C211yesmaximal, characteristic, complemented
7#21447012C211yesmaximal, characteristic, complemented
8#21447012C211yesmaximal, characteristic, complemented
9#21446902C211yesmaximal, characteristic, complemented
10#21446676C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic, complemented
12#21446174C211yesmaximal, characteristic, complemented
13#21446156C211yesmaximal, characteristic, complemented
14#21446079C211yesmaximal, 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—
27C4×#11758201—24no—
28C2×#14519708C2211yescharacteristic, complemented
29C2×#14519708C2211yescharacteristic, 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×C4×#92418C2211yescharacteristic, 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#14519708—22no—
106#14519708—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—
118C4×#92418—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—41no—
227C22⋊C4×C61—42no—
228C22⋊C4×C61—42no—
229C22⋊C4×C61SD1614yescomplemented
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×C61C2×SD1612yes—
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—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
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—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×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61C2×SD1612yes—
329C2×C4×C61C2×SD1612yes—
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#25156—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×C61C22×SD1611yescharacteristic
369C22×C61#57511yescharacteristic
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—22no—
389C4×C61—41no—
390C4×C61—42no—
391C4×C61—41no—
392C4×C61—42no—
393C4×C61—41no—
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×C4×SD16—611no—
406#2429D6111yescharacteristic, complemented
407D4×C22⋊C4—611no—
408#2065—611no—
409#2035—611no—
410#2035—611no—
411#2013—611no—
412#1968—611no—
413#1923—611no—
414#1880—611no—
415#1877—611no—
416#1864—611no—
417C2×C61—42no—
418C2×C61#242411yescharacteristic
419C2×C61#310111yescharacteristic
420C2×C61#312311yescharacteristic
421C2×C61#326711yescharacteristic
422C2×C61#327511yescharacteristic
423C2×C61D4×SD1611yescharacteristic
424C2×C61D4×SD1611yescharacteristic
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—
442C4×SD16—1224no—
443C2×#106—611no—
444C2×#106—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×C4×C8—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#2515611yescharacteristic, 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#106—1222no—
544#106—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—
556C4×C8—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—41no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—4881no—
662C22⋊C4—4881no—
663C22⋊C4—2442no—
664C22⋊C4—2442no—
665C22⋊C4—2442no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C22⋊C4#1175820114yescomplemented
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—
701C23C2×#1175820112yes—
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—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
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—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—4884no—
750C2×C4—4884no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4C2×#1175820112yes—
758C2×C4C2×#1175820112yes—
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
794C22C22×#1175820111yescharacteristic
795C22#1684056011yescharacteristic
796C22#1684057011yescharacteristic
797C22#1684057011yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
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#2145582311yescharacteristic
818C2#2145606611yescharacteristic
819C2#2145734511yescharacteristic
820C2#2145745111yescharacteristic
821C2D4×#1175820111yescharacteristic
822C2D4×#1175820111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2429C2
socleC23×C61C22×D4
prime radicalC23×D244C22
hypercenter#2429D61
hypocenterC61#25156
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×C4×#11758201C2semidirect
6. #21447190C2semidirect
7. #21447012C2semidirect
8. #21447012C2semidirect
9. #21446902C2semidirect
10. #21446676C2semidirect
11. #21446427C2semidirect
12. #21446174C2semidirect
13. #21446156C2semidirect
14. #21446079C2semidirect
15. C61×#2429C2semidirect
28. C2×#14519708C22semidirect
29. C2×#14519708C22semidirect
30. C2×C4⋊#92418C22semidirect
31. C2×#14519701C22semidirect
32. C2×#14519701C22semidirect
33. C2×#14519701C22semidirect
34. C2×#14519701C22semidirect
41. C2×C4×#92418C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
52. C2×C4⋊Q8×C61C22semidirect
55. C2×C4×Q8×C61C22semidirect
58. C61×#391C22semidirect
60. C61×#389C22semidirect
229. C22⋊C4×C61SD16semidirect
406. #2429D61semidirect
432. C2×C4⋊Q8C2×D61semidirect
435. C2×C4×Q8C2×D61semidirect
459. #391C2×D61semidirect
463. #389C2×D61semidirect
474. C61#25156semidirect
668. C22⋊C4#11758201semidirect

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×C4×#117582012
C22⋊C4×D2442
#214471902
#214470122
#214469022
#214466762
#214464272
#214461742
#214461562
#214460792
C61×#24292
#2515661