Finite Group Databasebeta

← #29748237

Subgroups — #29748237

Order 15616.

804 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450182C211yesmaximal, characteristic
2#21448844C211yesmaximal, characteristic, complemented
3#21447137C211yesmaximal, characteristic, complemented
4#21447023C211yesmaximal, characteristic, complemented
5#21446961C211yesmaximal, characteristic, complemented
6#21446824C211yesmaximal, characteristic
7#21446766C211yesmaximal, characteristic, complemented
8#21446502C211yesmaximal, characteristic, complemented
9#21446440C211yesmaximal, characteristic, complemented
10#21446391C211yesmaximal, characteristic, complemented
11#21446173C211yesmaximal, characteristic, complemented
12#21446139C211yesmaximal, characteristic
13#21445915C211yesmaximal, characteristic, complemented
14C4×#14519702C211yesmaximal, characteristic, complemented
15C61×#1923C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18C2×#14519763—21no—
19C2×#14519756C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×#14519736C2211yescharacteristic
23C2×#14519711C2211yescharacteristic
24C2×#14519702C2211yescharacteristic
25C2×#14519702C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30#16839678—21no—
31#16839675—21no—
32#16839668C2211yescharacteristic
33#16839664C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839656—21no—
37#16839654—21no—
38#16839650—21no—
39#16839644—21no—
40#16839622C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43#16839613—21no—
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C22⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122—21no—
60C22×Dic122C2311yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C2×#11758190—22no—
64C2×#11758190—41no—
65C2×#11758190—41no—
66#14519777—22no—
67#14519777—41no—
68#14519763—44no—
69#14519756—22no—
70#14519756—22no—
71#14519751—22no—
72#14519751—41no—
73C4×Dic122—22no—
74C4×Dic122—41no—
75#14519736—22no—
76#14519736—41no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99#14519711—22no—
100#14519702—22no—
101#14519702—22no—
102#14519702—41no—
103#14519699—22no—
104#14519699—22no—
105#14519699—41no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112C23×C4×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C2×C22⋊C4×C61D411yescharacteristic
118C2×C22⋊C4×C61D411yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121C4⋊C8×C61—41no—
122C22⋊C8×C61—41no—
123C22⋊C8×C61—41no—
124C4×C8×C61—41no—
125#95×C61D411yescharacteristic
126#95×C61D411yescharacteristic
127C24×C61C2×D411yescharacteristic
128C23×D61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2411yescharacteristic
141C2×C22⋊D61—42no—
142C2×C22⋊D61—42no—
143C2×C22⋊D61—81no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—42no—
163C2×Dic122—42no—
164C2×Dic122—81no—
165C2×Dic122#4112yes—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C22⋊C4×C61—22no—
179C22⋊C4×C61—22no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—21no—
183C42×C61—21no—
184C22⋊Dic61—24no—
185C22⋊Dic61—42no—
186C22⋊Dic61—42no—
187#11758198—42no—
188#11758198—42no—
189#11758198—42no—
190#11758198—42no—
191#11758198—81no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—42no—
202C4⋊Dic61#4112yes—
203C4⋊Dic61#4112yes—
204C4⋊Dic61#4112yes—
205#11758196—24no—
206#11758196—42no—
207#11758196—42no—
208C4×Dic61—42no—
209C4×Dic61—42no—
210C4×Dic61—42no—
211C4×Dic61—42no—
212#11758190—44no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61C22×D411yescharacteristic
221C22×D61—41no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61—41no—
226C22×D61—41no—
227C22×D61—41no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61#13512yes—
246C2×C4×C61AGL(1,ℤ/8)12yes—
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61H(5,𝔽2)11yescharacteristic
252C2×C4×C61H(5,𝔽2)11yescharacteristic
253C22⋊D61—84no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275D244—41no—
276D244—41no—
277D244—41no—
278D244—41no—
279Dic122—22no—
280Dic122—22no—
281Dic122—41no—
282Dic122—41no—
283Dic122—84no—
284C8×C61—41no—
285C8×C61—41no—
286C8×C61—41no—
287C8×C61—41no—
288#26733—611nomaximal, Sylow
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61#52511yescharacteristic
297C22×C61#54611yescharacteristic
298C22×C61#54611yescharacteristic
299C22×C61C2×#13511yescharacteristic
300C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C61#57711yescharacteristic
302C22×C61#57811yescharacteristic
303C2×D61—81no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—81no—
307C2×D61—81no—
308C2×D61—81no—
309C2×D61—81no—
310C4×C61—22no—
311C4×C61—22no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61#52911yescharacteristic
316C4×C61#53811yescharacteristic
317C4×C61#55511yescharacteristic
318C4×C61#55911yescharacteristic
319Dic61—42no—
320Dic61—42no—
321Dic61—42no—
322Dic61—42no—
323Dic61—81no—
324Dic61—81no—
325Dic61—81no—
326#2491—611no—
327#2362—611no—
328#2055—611no—
329#2036—611no—
330#2024—611no—
331#2000—611no—
332#1987—611no—
333#1934—611no—
334#1925—611no—
335#1923D6111yescharacteristic, complemented
336#1918—611no—
337#1880—611no—
338#1875—611no—
339#1825—611no—
340C4×#103—611no—
341C2×C61—81no—
342C2×C61#245911yescharacteristic
343C2×C61#310611yescharacteristic
344C2×C61#312111yescharacteristic
345C2×C61#330011yescharacteristic
346C2×C61#330311yescharacteristic
347C2×C61#330811yescharacteristic
348C2×C61#332411yescharacteristic
349D61—161no—
350C22×SD16—611no—
351C2×C4⋊Q8—611no—
352C2×#124—1221no—
353C2×C22⋊Q8—611no—
354C2×#121—611no—
355C2×C4×Q8—611no—
356C2×#117—611no—
357C2×#107—611no—
358C2×C4⋊C8C2×D6111yescharacteristic
359C2×#103—611no—
360C2×#103—611no—
361C2×#103—611no—
362C2×#102—611no—
363C2×#102—611no—
364C2×#102—611no—
365C2×C22⋊C8C2×D6111yescharacteristic
366C2×C22⋊C8C2×D6111yescharacteristic
367C2×C4×C8C2×D6111yescharacteristic
368#394—1221no—
369#393—1221no—
370#391—611no—
371#390—611no—
372#390—611no—
373#389—611no—
374#388—1221no—
375#388—1221no—
376#388—1221no—
377#387—1221no—
378#380—611no—
379C4×C4⋊C4—611no—
380C4×C4⋊C4—611no—
381C4×C4⋊C4—1221no—
382C4×C22⋊C4C2×D6111yescharacteristic
383#340—611no—
384#340—611no—
385#340—611no—
386#340—611no—
387#340—611no—
388#340—611no—
389#340—611no—
390#340—611no—
391#336C2×D6111yescharacteristic
392#336C2×D6111yescharacteristic
393C61#2673311yescharacteristic, complemented, Sylow
394C22×Q8—611no—
395C22×Q8—1221no—
396C22×D4—611no—
397C22×D4—1221no—
398C23×C4C22×D6111yescharacteristic
399C2×SD16—1222no—
400C2×SD16—2441no—
401C2×SD16—2441no—
402C22×C8C22×D6111yescharacteristic
403C22×C8C22×D6111yescharacteristic
404C22×C8C22×D6111yescharacteristic
405C22×C8C22×D6111yescharacteristic
406C4⋊Q8—1222no—
407C4⋊Q8—2441no—
408#124—2444no—
409C22⋊Q8—1222no—
410C22⋊Q8—1222no—
411#121—1222no—
412#121—2441no—
413C4×Q8—1222no—
414C4×Q8—2441no—
415#117—1222no—
416#117—2441no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4D24411yescharacteristic
436C2×C22⋊C4D24411yescharacteristic
437C2×C42—1221no—
438C2×C42—1221no—
439C2×C42—1221no—
440C2×C42—1221no—
441C2×C42C22×D6111yescharacteristic
442C2×C42C22×D6111yescharacteristic
443#107—1222no—
444C4⋊C8—41no—
445#103—1222no—
446#103—1222no—
447#103—2441no—
448#102—1222no—
449#102—1222no—
450#102—2441no—
451C22⋊C8—41no—
452C22⋊C8—41no—
453C4×C8—41no—
454#95—1221no—
455#95—1221no—
456#95—1221no—
457#95—1221no—
458#95—1221no—
459#95—1221no—
460#95D24411yescharacteristic
461#95D24411yescharacteristic
462C24—1221no—
463C24C2×D24411yescharacteristic
464C2×Q8—612no—
465C2×Q8—1221no—
466C2×Q8—1221no—
467C2×Q8—1221no—
468C2×Q8—1221no—
469C2×Q8—1221no—
470C2×Q8—4881no—
471C2×Q8—2442no—
472C2×Q8—2442no—
473C2×D4—1221no—
474C2×D4—1221no—
475C2×D4—1221no—
476C2×D4—1221no—
477C2×D4—1221no—
478C2×D4—1221no—
479C2×D4—4881no—
480C2×D4—2442no—
481C2×D4—2442no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4C2×D24411yescharacteristic
496C22×C4C2×D24411yescharacteristic
497C22×C4C2×D24411yescharacteristic
498C22×C4C2×D24411yescharacteristic
499C22×C4C2×D24411yescharacteristic
500C22×C4C23×D6111yescharacteristic
501SD16—2444no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C4⋊C4—612no—
515C4⋊C4—612no—
516C4⋊C4—612no—
517C4⋊C4—1224no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—2442no—
528C4⋊C4—2442no—
529C4⋊C4—2442no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—1224no—
533C22⋊C4—4881no—
534C22⋊C4—2442no—
535C22⋊C4—2442no—
536C22⋊C4—2442no—
537C22⋊C4—2442no—
538C22⋊C4—2442no—
539C22⋊C4—2442no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—2442no—
545C42—2442no—
546C42—2442no—
547C42—2442no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—2441no—
556C23—2441no—
557C23—2441no—
558C23—2441no—
559C23—2441no—
560C23—2441no—
561C23—2441no—
562C23C22×D24411yescharacteristic
563Q8—1222no—
564Q8—1222no—
565Q8—4884no—
566Q8—2441no—
567Q8—2441no—
568D4—4884no—
569D4—2441no—
570D4—2441no—
571D4—2441no—
572D4—2441no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—1222no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4#1451979912yes—
612C2×C4#1451980512yes—
613C2×C4#41×D6111yescharacteristic
614C2×C4#41×D6111yescharacteristic
615C2×C4#41×D6111yescharacteristic
616C2×C4#41×D6111yescharacteristic
617C2×C4#1451982211yescharacteristic
618C2×C4#1451982211yescharacteristic
619C8—41no—
620C8—41no—
621C8—41no—
622C8—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—4881no—
631C22—4881no—
632C22—4881no—
633C22—4881no—
634C22—4881no—
635C22—4881no—
636C22—4881no—
637C22#1684027411yescharacteristic
638C22#1684040711yescharacteristic
639C22#1684040711yescharacteristic
640C22C2×#1451979911yescharacteristic
641C22C2×#1451980511yescharacteristic
642C22#1684057411yescharacteristic
643C22#1684057911yescharacteristic
644C4—22no—
645C4—22no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—4881no—
650C4—4881no—
651C4—4881no—
652C4—2442no—
653C4—2442no—
654C4—2442no—
655C4—2442no—
656C4#1684029511yescharacteristic
657C4#1684034411yescharacteristic
658C4#1684047411yescharacteristic
659C4#1684049611yescharacteristic
660C2—81no—
661C2—9761no—
662C2#2144975411yescharacteristic
663C2#2145588011yescharacteristic
664C2#2145605011yescharacteristic
665C2#2145770811yescharacteristic
666C2#2145774811yescharacteristic
667C2#2145781211yescharacteristic
668C2#2145805111yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1923C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#1923D61
hypocenterC61#26733
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #21448844C2semidirect
3. #21447137C2semidirect
4. #21447023C2semidirect
5. #21446961C2semidirect
7. #21446766C2semidirect
8. #21446502C2semidirect
9. #21446440C2semidirect
10. #21446391C2semidirect
11. #21446173C2semidirect
13. #21445915C2semidirect
14. C4×#14519702C2semidirect
15. C61×#1923C2semidirect
335. #1923D61semidirect
393. C61#26733semidirect

Maximal subgroups

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

subgroupindex
#214501822
#214488442
#214471372
#214470232
#214469612
#214468242
#214467662
#214465022
#214464402
#214463912
#214461732
#214461392
#214459152
C4×#145197022
C61×#19232
#2673361