Finite Group Databasebeta

← #29731088

Subgroups — #29731088

Order 15616.

1052 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840144C211yesmaximal, characteristic, complemented
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839989C211yesmaximal, characteristic, complemented
4C2×C4×#11758201C211yesmaximal, characteristic, complemented
5#21449396C211yesmaximal, characteristic, complemented
6#21447060C211yesmaximal, characteristic, complemented
7#21447055C211yesmaximal, characteristic, complemented
8#21446827C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic
10#21446672C211yesmaximal, characteristic, complemented
11#21446544C211yesmaximal, characteristic, complemented
12#21446170C211yesmaximal, characteristic, complemented
13#21446160C211yesmaximal, characteristic, complemented
14C22⋊C4×#92418C211yesmaximal, characteristic, complemented
15C61×#2426C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C23×#92418C2211yescharacteristic
21C2×#14519765C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25#16840144—24no—
26#16839993—24no—
27#16839989—24no—
28C4×#11758201—24no—
29C2×#14519708C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C4×#92418C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839691—21no—
43#16839677—21no—
44#16839668C2211yescharacteristic
45#16839660C2211yescharacteristic
46#16839638—21no—
47#16839621—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
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—41no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—22no—
73C2×#11758201—22no—
74C2×#11758201—22no—
75C2×#11758201D414yescomplemented
76C2×#11758199—22no—
77C2×#11758199—22no—
78C2×#11758199—41no—
79C22×#92418—22no—
80C22×#92418—22no—
81C22×#92418—22no—
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86#14519765—22no—
87#14519765—41no—
88#14519756—22no—
89#14519756—41no—
90#14519751—22no—
91#14519751—41no—
92C4×D244—22no—
93C4×D244—41no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103#14519708—22no—
104#14519708D414yescomplemented
105#14519701—22no—
106#14519701—22no—
107#14519700—22no—
108#14519700—41no—
109#14519698—22no—
110#14519698—41no—
111#14519697—22no—
112#14519697—22no—
113C22⋊#92418—22no—
114C4×#92418—22no—
115C4×#92418—22no—
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—42no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—81no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244C2×D412yes—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—81no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61—81no—
210C4⋊C4×C61C2×D412yes—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—81no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—21no—
223C42×C61—42no—
224C22⋊Dic61—42no—
225#11758202—44no—
226#11758201—28no—
227#11758200—44no—
228#11758199—44no—
229#11758198—42no—
230#11758198—42no—
231#11758198—42no—
232#11758198—42no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61C2×D412yes—
237#11758196—42no—
238#11758196—81no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—44no—
248C2×#92418C2×D412yes—
249C2×#92418C2×D412yes—
250C2×#92418#4112yes—
251C2×#92418#4112yes—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61#13512yes—
266C23×C61C22×D411yescharacteristic
267C22×D61—22no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274Q8×C61—22no—
275Q8×C61—22no—
276Q8×C61—41no—
277Q8×C61—41no—
278D4×C61—41no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—84no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
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#13512yes—
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C2×C4×C61H(5,𝔽2)11yescharacteristic
317C22⋊D61—84no—
318C2×Dic61—22no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327D244—22no—
328D244—22no—
329D244—41no—
330D244—41no—
331C4×D61—84no—
332Dic122—41no—
333Dic122—41no—
334Dic122—41no—
335Dic122—41no—
336#92418—22no—
337#92418—41no—
338#92418—41no—
339#92418#12114yes—
340#25411—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61#53211yescharacteristic
356C22×C61D4211yescharacteristic
357C22×C61D4211yescharacteristic
358C22×C61C2×#13511yescharacteristic
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—
369C4×C61—22no—
370C4×C61—41no—
371C4×C61—42no—
372C4×C61—41no—
373C4×C61—41no—
374C4×C61—42no—
375C4×C61—41no—
376C4×C61—81no—
377C4×C61C2×#12111yescharacteristic
378C4×C61#54011yescharacteristic
379C4×C61#54611yescharacteristic
380C4×C61#55011yescharacteristic
381Dic61—42no—
382Dic61—81no—
383Dic61—81no—
384C2×#495—611no—
385C2×#465—611no—
386C2×#465—611no—
387C2×C4×SD16—611no—
388#2427—611no—
389#2426D6111yescharacteristic, complemented
390#2042—611no—
391#2042—611no—
392#2001—611no—
393#1999—611no—
394#1968—611no—
395#1941—611no—
396#1879—611no—
397#1878—611no—
398C8×C22⋊C4—611no—
399C2×C61—42no—
400C2×C61—161no—
401C2×C61#242811yescharacteristic
402C2×C61#316811yescharacteristic
403C2×C61#317311yescharacteristic
404C2×C61#328211yescharacteristic
405C2×C61#328211yescharacteristic
406C2×C61#328211yescharacteristic
407C2×C61#328411yescharacteristic
408D61—82no—
409C22×Q16—611no—
410C22×SD16—611no—
411C22×SD16—611no—
412C22×D8—611no—
413C23×C8—611no—
414C2×#124—611no—
415C2×#124C2×D6111yescharacteristic
416C2×C22⋊Q8—611no—
417C2×C22⋊Q8C2×D6111yescharacteristic
418C2×#121—611no—
419C2×#121C2×D6111yescharacteristic
420C2×C4×Q8C2×D6111yescharacteristic
421C2×C4×D4—611no—
422#495—1224no—
423#465—1224no—
424#465—1224no—
425C4×SD16—1224no—
426C2×#106—611no—
427C2×#106—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#103—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×C22⋊C8—611no—
437C2×C4×C8—611no—
438C2×C4×C8—611no—
439#397—1221no—
440#396—21no—
441#394—21no—
442#394—1221no—
443#391—611no—
444#390—21no—
445#390C2×D6111yescharacteristic
446#389—611no—
447#389C2×D6111yescharacteristic
448#388—21no—
449#386—1221no—
450#380—1221no—
451C4×C22⋊C4C2×D6111yescharacteristic
452#340—611no—
453#340—611no—
454#336—611no—
455#336—611no—
456C61#2541111yescharacteristic, complemented, Sylow
457C22×Q8—611no—
458C22×Q8C22×D6111yescharacteristic
459C22×D4—21no—
460C22×D4—611no—
461C22×D4—1221no—
462C22×D4C22×D6111yescharacteristic
463C23×C4—1221no—
464C23×C4C22×D6111yescharacteristic
465C2×Q16—1222no—
466C2×Q16—1222no—
467C2×Q16—2441no—
468C2×SD16—614no—
469C2×SD16—1222no—
470C2×SD16—1222no—
471C2×SD16—1222no—
472C2×SD16—1222no—
473C2×SD16—1222no—
474C2×D8—1222no—
475C2×D8—1222no—
476C2×D8—2441no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—611no—
480C22×C8—611no—
481C22×C8—1222no—
482C22×C8—1222no—
483C22×C8—1222no—
484#124—22no—
485#124—41no—
486#124—1222no—
487#124—2441no—
488C22⋊Q8—22no—
489C22⋊Q8—41no—
490C22⋊Q8—1222no—
491C22⋊Q8—2441no—
492#121—22no—
493#121—41no—
494#121—1222no—
495#121—2441no—
496C4×Q8—22no—
497C4×Q8—41no—
498C4×D4—1222no—
499C4×D4—2441no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C4⋊C4C22×D6111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4C22⋊D6111yescharacteristic
521C2×C22⋊C4C22⋊D6111yescharacteristic
522C2×C42—21no—
523C2×C42C22×D6111yescharacteristic
524C2×C42C22×D6111yescharacteristic
525#106—614no—
526#106—1222no—
527#103—1222no—
528#103—1222no—
529#103—1222no—
530#103—2441no—
531#102—1222no—
532#102—1222no—
533#102—1222no—
534#102—2441no—
535C22⋊C8—1222no—
536C4×C8—1222no—
537C4×C8—1222no—
538#95—21no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542#95C22⋊D6111yescharacteristic
543#95C22⋊D6111yescharacteristic
544C24—21no—
545C24—1221no—
546C24C2×C22⋊D6111yescharacteristic
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8D4×D6112yes—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—612no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—4881no—
575C2×D4—2442no—
576C2×D4—2442no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—4881no—
590C22×C4—2442no—
591C22×C4—2442no—
592C22×C4C2×C22⋊D6111yescharacteristic
593C22×C4C2×C22⋊D6111yescharacteristic
594C22×C4C2×C22⋊D6111yescharacteristic
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C23×D6111yescharacteristic
598Q16—2444no—
599SD16—1228no—
600SD16—2444no—
601D8—2444no—
602C2×C8—612no—
603C2×C8—612no—
604C2×C8—612no—
605C2×C8—612no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—2444no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—81no—
621C4⋊C4—612no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—4881no—
626C4⋊C4—2442no—
627C4⋊C4D4×D6112yes—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—81no—
636C22⋊C4—2442no—
637C22⋊C4—2442no—
638C22⋊C4—2442no—
639C22⋊C4—2442no—
640C22⋊C4—2442no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—1222no—
660C23—2441no—
661C23—2441no—
662C23—2441no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23#1451979712yes—
667C23C22×C22⋊D6111yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672Q8—2441no—
673Q8—2441no—
674Q8—2441no—
675Q8—2441no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—84no—
681D4—1222no—
682D4—1222no—
683D4—4884no—
684D4—2441no—
685D4—2441no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—1222no—
714C2×C4—4884no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4#1451979712yes—
724C2×C4C2×D4×D6111yescharacteristic
725C2×C4C2×D4×D6111yescharacteristic
726C2×C4#41×D6111yescharacteristic
727C2×C4#41×D6111yescharacteristic
728C2×C4#1451982211yescharacteristic
729C2×C4#1451982211yescharacteristic
730C8—614no—
731C8—1222no—
732C8—2441no—
733C8—2441no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—4881no—
749C22—4881no—
750C22—4881no—
751C22—4881no—
752C22—2442no—
753C22—2442no—
754C22—2442no—
755C22#1684030811yescharacteristic
756C22D4×C22⋊D6111yescharacteristic
757C22D4×C22⋊D6111yescharacteristic
758C22C2×#1451979711yescharacteristic
759C22C2×#1451979711yescharacteristic
760C22#1684057011yescharacteristic
761C22#1684057311yescharacteristic
762C4—22no—
763C4—41no—
764C4—42no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—42no—
769C4—81no—
770C4—4881no—
771C4—4881no—
772C4—2442no—
773C4#121×D6111yescharacteristic
774C4#1684036211yescharacteristic
775C4#1684040111yescharacteristic
776C4#1684043011yescharacteristic
777C2—42no—
778C2—161no—
779C2—4882no—
780C2#2144940411yescharacteristic
781C2#2145638311yescharacteristic
782C2#2145643011yescharacteristic
783C2#2145752211yescharacteristic
784C2#2145752711yescharacteristic
785C2#2145752711yescharacteristic
786C2#2145754911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2426C2
socleC23×C61C22×D4
prime radical#21446815C2
hypercenter#2426D61
hypocenterC61#25411
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×#16840144C2semidirect
2. C2×#16839993C2semidirect
3. C2×#16839989C2semidirect
4. C2×C4×#11758201C2semidirect
5. #21449396C2semidirect
6. #21447060C2semidirect
7. #21447055C2semidirect
8. #21446827C2semidirect
10. #21446672C2semidirect
11. #21446544C2semidirect
12. #21446170C2semidirect
13. #21446160C2semidirect
14. C22⋊C4×#92418C2semidirect
15. C61×#2426C2semidirect
75. C2×#11758201D4semidirect
104. #14519708D4semidirect
389. #2426D61semidirect
456. C61#25411semidirect

Maximal subgroups

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

subgroupindex
C2×#168401442
C2×#168399932
C2×#168399892
C2×C4×#117582012
#214493962
#214470602
#214470552
#214468272
#214468152
#214466722
#214465442
#214461702
#214461602
C22⋊C4×#924182
C61×#24262
#2541161