Finite Group Databasebeta

← #29731081

Subgroups — #29731081

Order 15616.

1104 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×#16840136C211yesmaximal, characteristic, complemented
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839993C211yesmaximal, characteristic, complemented
4C2×C4×#11758201C211yesmaximal, characteristic, complemented
5#21449407C211yesmaximal, characteristic
6#21447062C211yesmaximal, characteristic, complemented
7#21447053C211yesmaximal, characteristic, complemented
8#21446820C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446676C211yesmaximal, characteristic, complemented
11#21446544C211yesmaximal, characteristic, complemented
12#21446174C211yesmaximal, characteristic, complemented
13#21446156C211yesmaximal, characteristic, complemented
14C22⋊C4×#92418C211yesmaximal, characteristic, complemented
15C61×#2429C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C23×#92418C2211yescharacteristic
21C2×#14519774C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519750—21no—
25C2×C4×D244C2211yescharacteristic
26#16840136—24no—
27#16839993—24no—
28#16839993—24no—
29C4×#11758201—24no—
30C2×#14519708C2211yescharacteristic
31C2×#14519708C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C4×#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
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C61×#398—21no—
57C61×#396—21no—
58C61×#391C2211yescharacteristic
59C61×#389—21no—
60C61×#389C2211yescharacteristic
61C61×#388—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×#92418—22no—
83C22×#92418—22no—
84C22×#92418—22no—
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89#14519774—22no—
90#14519774—41no—
91#14519751—22no—
92#14519751—22no—
93#14519751—41no—
94#14519751—41no—
95#14519750—44no—
96C4×D244—22no—
97C4×D244—41no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106#14519708—22no—
107#14519708D414yescomplemented
108#14519701—22no—
109#14519701—22no—
110#14519701—22no—
111#14519701—41no—
112#14519697—22no—
113#14519697—22no—
114#14519697—22no—
115#14519697—41no—
116C22⋊#92418—22no—
117C4×#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—
154C2×Q8×C61—21no—
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—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61C2×D412yes—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
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×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2411yescharacteristic
182C2×C22⋊D61—42no—
183C2×C22⋊D61—42no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—42no—
186C2×C22⋊D61—81no—
187C2×C22⋊D61—81no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—42no—
202C2×D244—42no—
203C2×D244—42no—
204C2×D244—42no—
205C2×D244—81no—
206C2×D244—81no—
207C2×D244C2×D412yes—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—81no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—42no—
215C4⋊C4×C61—42no—
216C4⋊C4×C61—42no—
217C4⋊C4×C61—42no—
218C4⋊C4×C61—42no—
219C4⋊C4×C61—42no—
220C4⋊C4×C61C2×D412yes—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—42no—
223C22⋊C4×C61—42no—
224C22⋊C4×C61SD1614yescomplemented
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61—42no—
230#11758201—28no—
231#11758201—44no—
232#11758201—44no—
233#11758201—44no—
234#11758198—42no—
235#11758198—42no—
236#11758198—42no—
237#11758198—42no—
238#11758198—81no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61C2×D412yes—
243#11758196—42no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—44no—
253C2×#92418C2×D412yes—
254C2×#92418C2×D412yes—
255C2×#92418#4112yes—
256C2×#92418#4112yes—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61C2×SD1612yes—
264C23×C61C22×D411yescharacteristic
265C22×D61—22no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279Q8×C61—22no—
280Q8×C61—22no—
281Q8×C61—41no—
282Q8×C61—41no—
283Q8×C61—41no—
284Q8×C61—41no—
285Q8×C61—41no—
286Q8×C61—41no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
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×C61C2×SD1612yes—
316C2×C4×C61C2×SD1612yes—
317C2×C4×C61#13512yes—
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C2×C4×C61H(5,𝔽2)11yescharacteristic
324C22⋊D61—84no—
325C22⋊D61—84no—
326C2×Dic61—22no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332D244—22no—
333D244—22no—
334D244—41no—
335D244—41no—
336D244—41no—
337D244—41no—
338D244—41no—
339D244—41no—
340D244—84no—
341D244—84no—
342C4×D61—84no—
343#92418—22no—
344#92418—41no—
345#92418—41no—
346#92418#12114yescomplemented
347#25410—611nomaximal, Sylow
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61#53211yescharacteristic
356C22×C61D4211yescharacteristic
357C22×C61D4211yescharacteristic
358C22×C61C22×SD1611yescharacteristic
359C22×C61C2×#13511yescharacteristic
360C22×C61#57711yescharacteristic
361C22×C61#57711yescharacteristic
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—81no—
366C2×D61—81no—
367C2×D61—81no—
368C2×D61—81no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C4×C61—22no—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—41no—
380C4×C61—42no—
381C4×C61—41no—
382C4×C61—42no—
383C4×C61—81no—
384C4×C61—81no—
385C4×C61C2×#12111yescharacteristic
386C4×C61#54011yescharacteristic
387C4×C61#54611yescharacteristic
388C4×C61#55011yescharacteristic
389Dic61—42no—
390Dic61—81no—
391C2×#492—611no—
392C2×#465—611no—
393C2×#465—611no—
394C2×C4×SD16—611no—
395#2429D6111yescharacteristic, complemented
396#2428—611no—
397#2043—611no—
398#2041—611no—
399#2000—611no—
400#2000—611no—
401#1968—611no—
402#1941—611no—
403#1880—611no—
404#1877—611no—
405C8×C22⋊C4—611no—
406C2×C61—42no—
407C2×C61#242811yescharacteristic
408C2×C61#316711yescharacteristic
409C2×C61#317411yescharacteristic
410C2×C61D4×SD1611yescharacteristic
411C2×C61D4×SD1611yescharacteristic
412C2×C61#328211yescharacteristic
413C2×C61#328411yescharacteristic
414D61—82no—
415D61—161no—
416C22×SD16—611no—
417C22×SD16—611no—
418C22×SD16—611no—
419C22×SD16—611no—
420C23×C8—611no—
421C2×C4⋊Q8C2×D6111yescharacteristic
422C2×#127—611no—
423C2×C22⋊Q8C2×D6111yescharacteristic
424C2×C22⋊Q8C2×D6111yescharacteristic
425C2×#121—611no—
426C2×#121—611no—
427C2×#121—1221no—
428C2×C4×Q8C2×D6111yescharacteristic
429C2×C4×D4—611no—
430#492—1224no—
431#465—1224no—
432#465—1224no—
433C4×SD16—1224no—
434C2×#106—611no—
435C2×#106—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×C22⋊C8—611no—
445C2×C4×C8—611no—
446C2×C4×C8—611no—
447#398—21no—
448#396—21no—
449#394—1221no—
450#392—1221no—
451#391C2×D6111yescharacteristic
452#390—611no—
453#389—21no—
454#389—611no—
455#389C2×D6111yescharacteristic
456#388—21no—
457#386—1221no—
458C4×C22⋊C4C2×D6111yescharacteristic
459#340—611no—
460#340—611no—
461#336—611no—
462#336—611no—
463C61#2541011yescharacteristic, complemented, Sylow
464C22×Q8C22×D6111yescharacteristic
465C22×Q8C22×D6111yescharacteristic
466C22×D4—611no—
467C22×D4—611no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1221no—
472C23×C4—1221no—
473C23×C4C22×D6111yescharacteristic
474C2×SD16—614no—
475C2×SD16—1222no—
476C2×SD16—1222no—
477C2×SD16—1222no—
478C2×SD16—1222no—
479C2×SD16—1222no—
480C2×SD16—1222no—
481C2×SD16—1222no—
482C2×SD16—1222no—
483C2×SD16—1222no—
484C2×SD16—2441no—
485C2×SD16—2441no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8—611no—
489C22×C8—611no—
490C22×C8—1222no—
491C22×C8—1222no—
492C22×C8—1222no—
493C4⋊Q8—22no—
494C4⋊Q8—41no—
495#127—1222no—
496#127—2441no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—41no—
500C22⋊Q8—41no—
501#121—1222no—
502#121—1222no—
503#121—2441no—
504#121—2441no—
505#121—2444no—
506C4×Q8—22no—
507C4×Q8—41no—
508C4×D4—1222no—
509C4×D4—2441no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4C22⋊D6111yescharacteristic
529C2×C22⋊C4C22⋊D6111yescharacteristic
530C2×C42—21no—
531C2×C42C22×D6111yescharacteristic
532C2×C42C22×D6111yescharacteristic
533#106—614no—
534#106—1222no—
535#103—1222no—
536#103—1222no—
537#103—1222no—
538#103—2441no—
539#102—1222no—
540#102—1222no—
541#102—1222no—
542#102—2441no—
543C22⋊C8—1222no—
544C4×C8—1222no—
545C4×C8—1222no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—1221no—
550#95C22⋊D6111yescharacteristic
551#95C22⋊D6111yescharacteristic
552C24—1221no—
553C24—1221no—
554C24C2×C22⋊D6111yescharacteristic
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8D4×D6112yes—
567C2×D4—612no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—4881no—
580C2×D4—4881no—
581C2×D4—4881no—
582C2×D4—4881no—
583C2×D4—2442no—
584C2×D4—2442no—
585C2×D4—2442no—
586C2×D4—2442no—
587C2×D4—2442no—
588C2×D4—2442no—
589C2×D4—2442no—
590C2×D4—2442no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—4881no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4C2×C22⋊D6111yescharacteristic
607C22×C4C2×C22⋊D6111yescharacteristic
608C22×C4C2×C22⋊D6111yescharacteristic
609C22×C4C2×C22⋊D6111yescharacteristic
610C22×C4C2×C22⋊D6111yescharacteristic
611C22×C4C23×D6111yescharacteristic
612SD16—1228no—
613SD16—2444no—
614SD16—2444no—
615SD16—2444no—
616C2×C8—612no—
617C2×C8—612no—
618C2×C8—612no—
619C2×C8—612no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—2444no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—612no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—2442no—
643C4⋊C4D4×D6112yes—
644C22⋊C4—22no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—4881no—
648C22⋊C4—2442no—
649C22⋊C4—2442no—
650C22⋊C4—2442no—
651C22⋊C4—2442no—
652C22⋊C4#1175820114yescomplemented
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—42no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—1222no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23—2441no—
670C23—2441no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23C2×#1175820112yes—
679C23C22×C22⋊D6111yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688D4—1222no—
689D4—1222no—
690D4—4884no—
691D4—4884no—
692D4—4884no—
693D4—4884no—
694D4—2441no—
695D4—2441no—
696D4—2441no—
697D4—2441no—
698D4—2441no—
699D4—2441no—
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—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
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—41no—
727C2×C4—41no—
728C2×C4—1222no—
729C2×C4—4884no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4C2×#1175820112yes—
736C2×C4C2×#1175820112yes—
737C2×C4#1451979712yes—
738C2×C4C2×D4×D6111yescharacteristic
739C2×C4C2×D4×D6111yescharacteristic
740C2×C4#41×D6111yescharacteristic
741C2×C4#41×D6111yescharacteristic
742C2×C4#1451982211yescharacteristic
743C2×C4#1451982211yescharacteristic
744C8—614no—
745C8—1222no—
746C8—2441no—
747C8—2441no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—4881no—
756C22—4881no—
757C22—4881no—
758C22—4881no—
759C22—4881no—
760C22—4881no—
761C22—4881no—
762C22—4881no—
763C22—4881no—
764C22—4881no—
765C22—4881no—
766C22—2442no—
767C22—2442no—
768C22—2442no—
769C22#1684030811yescharacteristic
770C22D4×C22⋊D6111yescharacteristic
771C22D4×C22⋊D6111yescharacteristic
772C22C22×#1175820111yescharacteristic
773C22C2×#1451979711yescharacteristic
774C22#1684057011yescharacteristic
775C22#1684057011yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—41no—
780C4—42no—
781C4—41no—
782C4—42no—
783C4—81no—
784C4—81no—
785C4—4881no—
786C4—2442no—
787C4#121×D6111yescharacteristic
788C4#1684036211yescharacteristic
789C4#1684040111yescharacteristic
790C4#1684043011yescharacteristic
791C2—42no—
792C2—9761no—
793C2—4882no—
794C2#2144940411yescharacteristic
795C2#2145637911yescharacteristic
796C2#2145644811yescharacteristic
797C2D4×#1175820111yescharacteristic
798C2D4×#1175820111yescharacteristic
799C2#2145752711yescharacteristic
800C2#2145754511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2429C2
socleC23×C61C22×D4
prime radical#21449407C2
hypercenter#2429D61
hypocenterC61#25410
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×#16840136C2semidirect
2. C2×#16839993C2semidirect
3. C2×#16839993C2semidirect
4. C2×C4×#11758201C2semidirect
6. #21447062C2semidirect
7. #21447053C2semidirect
8. #21446820C2semidirect
9. #21446820C2semidirect
10. #21446676C2semidirect
11. #21446544C2semidirect
12. #21446174C2semidirect
13. #21446156C2semidirect
14. C22⋊C4×#92418C2semidirect
15. C61×#2429C2semidirect
81. C2×#11758201D4semidirect
107. #14519708D4semidirect
224. C22⋊C4×C61SD16semidirect
346. #92418#121semidirect
395. #2429D61semidirect
463. C61#25410semidirect
652. C22⋊C4#11758201semidirect

Maximal subgroups

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

subgroupindex
C2×#168401362
C2×#168399932
C2×C4×#117582012
#214494072
#214470622
#214470532
#214468202
#214466762
#214465442
#214461742
#214461562
C22⋊C4×#924182
C61×#24292
#2541061