Finite Group Databasebeta

← #29779644

Subgroups — #29779644

Order 15616.

842 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451654C211yesmaximal, characteristic, complemented
2#21448410C211yesmaximal, characteristic
3#21447230C211yesmaximal, characteristic, complemented
4#21447226C211yesmaximal, characteristic, complemented
5#21446968C211yesmaximal, characteristic, complemented
6#21446964C211yesmaximal, characteristic, complemented
7#21446516C211yesmaximal, characteristic, complemented
8#21446501C211yesmaximal, characteristic, complemented
9#21446498C211yesmaximal, characteristic, complemented
10#21445908C211yesmaximal, characteristic, complemented
11#21445904C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic
13#21445758C211yesmaximal, characteristic
14#21445588C211yesmaximal, characteristic, complemented
15C61×#1935C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×#14519734C2211yescharacteristic
19C2×C4⋊C4×D61C2211yescharacteristic
20C2×#14519701C2211yescharacteristic
21C2×#14519701C2211yescharacteristic
22C2×#14519699C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519697C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×C4×#92418C2211yescharacteristic
29#16839696—21no—
30#16839693—21no—
31#16839686—21no—
32#16839684—21no—
33#16839669C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839663C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839640—21no—
38#16839640—21no—
39#16839631C2211yescharacteristic
40#16839621—21no—
41#16839621—21no—
42#16839619C2211yescharacteristic
43#16839619C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#103×C61C2211yescharacteristic
53C2×#103×C61C2211yescharacteristic
54C2×#97×C61C2211yescharacteristic
55C61×#391C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C2×#11758226—22no—
60C2×#11758226—22no—
61C2×#11758226—22no—
62C2×#11758226—22no—
63C2×#11758226—41no—
64C2×#11758226—41no—
65C22×D244—21no—
66C22×D244C2311yescharacteristic
67C22×C4×D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519768—41no—
73#14519768—41no—
74#14519734—41no—
75#14519734—41no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196D411yescharacteristic
86C2×#11758196D411yescharacteristic
87C4⋊C4×D61—22no—
88C4⋊C4×D61—22no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198D411yescharacteristic
96C2×#11758198D411yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98#14519701—22no—
99#14519701—41no—
100#14519699—22no—
101#14519699—41no—
102#14519697—22no—
103#14519697—41no—
104#14519689—22no—
105#14519689—22no—
106C4×#92418—41no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112C22×Q8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120#103×C61—22no—
121#103×C61—41no—
122#97×C61—41no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126C23×D61—21no—
127C23×D61C2×D411yescharacteristic
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61#4112yes—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2411yescharacteristic
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61C2×D411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147#11758226—44no—
148#11758226—44no—
149#11758226—44no—
150#11758226—44no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—24no—
156C2×D244—21no—
157C2×D244—42no—
158C2×D244—42no—
159C2×D244#4112yes—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—24no—
165C2×C4×D61—42no—
166C2×C4×D61—42no—
167C2×C4×D61—42no—
168C2×C4×D61—81no—
169C2×C4×D61—81no—
170C2×C4×D61#4112yes—
171C2×C4×D61#4112yes—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—81no—
185C42×C61—21no—
186C42×C61—21no—
187#11758198—41no—
188#11758198—41no—
189#11758198—81no—
190#11758198—81no—
191#11758198—81no—
192#11758198—81no—
193#11758198—81no—
194#11758198—81no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—42no—
202#11758196—41no—
203#11758196—41no—
204#11758196—42no—
205#11758196—42no—
206#11758196—81no—
207#11758196—81no—
208#11758196—81no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C23×C61C22×D411yescharacteristic
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—22no—
225C22×D61—41no—
226C22×D61—41no—
227C22×D61—41no—
228C22×D61—41no—
229C22×D61—41no—
230C22×D61—41no—
231C22×D61#12412yes—
232Q8×C61—22no—
233Q8×C61—22no—
234Q8×C61—41no—
235Q8×C61—41no—
236C2×C4×C61—22no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61C2×#4111yescharacteristic
255C2×C4×C61C2×#4111yescharacteristic
256C2×C4×C61C2×#4111yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61H(5,𝔽2)11yescharacteristic
259C2×C4×C61H(5,𝔽2)11yescharacteristic
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61#12412yes—
278D244—22no—
279D244—22no—
280D244—48no—
281D244—41no—
282D244—41no—
283C4×D61—22no—
284C4×D61—22no—
285C4×D61—22no—
286C4×D61—22no—
287C4×D61—48no—
288C4×D61—84no—
289C8×C61—41no—
290C8×C61—41no—
291#92418—41no—
292#92418—41no—
293#29119—611nomaximal, Sylow
294C22×C61#52511yescharacteristic
295C22×C61C2×#12411yescharacteristic
296C22×C61#53411yescharacteristic
297C22×C61#57611yescharacteristic
298C22×C61#57711yescharacteristic
299C22×C61#57711yescharacteristic
300C22×C61#57811yescharacteristic
301C2×D61—22no—
302C2×D61—22no—
303C2×D61—22no—
304C2×D61—41no—
305C2×D61—41no—
306C2×D61—41no—
307C2×D61—41no—
308C2×D61—42no—
309C2×D61—42no—
310C2×D61—42no—
311C2×D61—81no—
312C2×D61—81no—
313C2×D61—81no—
314C2×D61—81no—
315C4×C61—42no—
316C4×C61—41no—
317C4×C61—41no—
318C4×C61—81no—
319C4×C61—81no—
320C4×C61—81no—
321C4×C61#55111yescharacteristic
322C4×C61#55111yescharacteristic
323C4×C61#55111yescharacteristic
324C4×C61#55111yescharacteristic
325Dic61—22no—
326Dic61—41no—
327Dic61—41no—
328Dic61—81no—
329Dic61—81no—
330Dic61—81no—
331#2629—611no—
332#2311—611no—
333#2072—611no—
334#2071—611no—
335#2026—611no—
336#2025—611no—
337#1936—611no—
338#1935D6111yescharacteristic, complemented
339#1934—611no—
340#1933—611no—
341#1824—611no—
342#1823—611no—
343#1788—611no—
344#1788—611no—
345#1750—611no—
346C2×C61#256111yescharacteristic
347C2×C61#311911yescharacteristic
348C2×C61#312011yescharacteristic
349C2×C61#313611yescharacteristic
350C2×C61#313711yescharacteristic
351C2×C61#320311yescharacteristic
352C2×C61#320411yescharacteristic
353D61—42no—
354D61—82no—
355C22×#41—611no—
356C2×#125—611no—
357C2×#117—611no—
358C22×C4⋊C4—611no—
359C2×#103—611no—
360C2×#103—611no—
361C2×#103C2×D6111yescharacteristic
362C2×#103C2×D6111yescharacteristic
363C2×#102—611no—
364C2×#102—611no—
365C2×#102—611no—
366C2×#102—611no—
367C2×C22⋊C8—611no—
368C2×C22⋊C8—611no—
369C2×#97C2×D6111yescharacteristic
370C2×C4×C8—611no—
371#398—1221no—
372#398—1221no—
373#396—1221no—
374#396—1221no—
375#391—611no—
376#391C2×D6111yescharacteristic
377#390—611no—
378#390—611no—
379#389—611no—
380#389C2×D6111yescharacteristic
381#386—1221no—
382#386—1221no—
383#384—611no—
384#380—611no—
385#380—611no—
386#380—1221no—
387#380—1221no—
388#340—611no—
389#340—611no—
390#340—611no—
391#340—611no—
392#340—611no—
393#340—611no—
394#340C2×D6111yescharacteristic
395#340C2×D6111yescharacteristic
396#336—611no—
397#336—611no—
398C61#2911911yescharacteristic, complemented, Sylow
399C2×#41—1222no—
400C2×#41—1222no—
401C2×#41—1222no—
402C2×#41—1222no—
403C2×#41—2441no—
404C2×#41—2441no—
405C22×Q8C22×D6111yescharacteristic
406C22×D4—611no—
407C22×D4—1221no—
408C23×C4—611no—
409C23×C4—1221no—
410C23×C4—1221no—
411C22×C8—611no—
412C22×C8—611no—
413C22×C8C22×D6111yescharacteristic
414C22×C8C22×D6111yescharacteristic
415#125—2441no—
416#125—2441no—
417#117—2441no—
418#117—2441no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—1222no—
426C2×C4⋊C4—1222no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4C22×D6111yescharacteristic
434C2×C4⋊C4C22×D6111yescharacteristic
435C2×C4⋊C4C22×D6111yescharacteristic
436C2×C22⋊C4—611no—
437C2×C22⋊C4—611no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1221no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4—1221no—
443C2×C22⋊C4—1221no—
444C2×C42—611no—
445C2×C42C22×D6111yescharacteristic
446#103—22no—
447#103—41no—
448#103—1222no—
449#103—2441no—
450#102—1222no—
451#102—1222no—
452#102—2441no—
453#102—2441no—
454C22⋊C8—1222no—
455C22⋊C8—1222no—
456#97—41no—
457C4×C8—2441no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—1221no—
462#95—1221no—
463#95—1221no—
464#95—1221no—
465#95—1221no—
466C24—611no—
467C24—1221no—
468#41—2444no—
469#41—2444no—
470#41—2444no—
471#41—2444no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8#1175822212yes—
478C2×D4—612no—
479C2×D4—1224no—
480C2×D4—1221no—
481C2×D4—1221no—
482C2×D4—1221no—
483C2×D4—1221no—
484C2×D4—1221no—
485C2×D4—2442no—
486C2×D4—2442no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—611no—
492C22×C4—612no—
493C22×C4—612no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—1224no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—4881no—
505C22×C4—4881no—
506C22×C4—2442no—
507C22×C4—2442no—
508C22×C4—2442no—
509C22×C4D4×D6111yescharacteristic
510C22×C4D4×D6111yescharacteristic
511C22×C4C23×D6111yescharacteristic
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—81no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—4881no—
538C4⋊C4—4881no—
539C4⋊C4—4881no—
540C4⋊C4—2441no—
541C4⋊C4—2441no—
542C4⋊C4—2442no—
543C4⋊C4—2442no—
544C4⋊C4—2442no—
545C22⋊C4—4881no—
546C22⋊C4—4881no—
547C22⋊C4—4881no—
548C22⋊C4—4881no—
549C22⋊C4—4881no—
550C22⋊C4—4881no—
551C22⋊C4—2441no—
552C22⋊C4—2441no—
553C42—21no—
554C42—21no—
555C42—1221no—
556C42—1221no—
557C23—612no—
558C23—1221no—
559C23—1221no—
560C23—1221no—
561C23—1221no—
562C23—1221no—
563C23—1221no—
564C23—1222no—
565C23—2441no—
566C23—2441no—
567C23—2441no—
568C23—2441no—
569C23—2441no—
570C23—2441no—
571C23C2×D4×D6111yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576D4—1222no—
577D4—1222no—
578D4—2448no—
579D4—2441no—
580D4—2441no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—612no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1222no—
603C2×C4—1222no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—4884no—
613C2×C4—2448no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4#41×D6111yescharacteristic
624C2×C4#41×D6111yescharacteristic
625C2×C4#41×D6111yescharacteristic
626C2×C4C2×#1175822211yescharacteristic
627C2×C4#1451982211yescharacteristic
628C2×C4#1451982311yescharacteristic
629C8—41no—
630C8—41no—
631C8—2441no—
632C8—2441no—
633C22—1222no—
634C22—1222no—
635C22—1222no—
636C22—4881no—
637C22—4881no—
638C22—4881no—
639C22—4881no—
640C22—2442no—
641C22—2442no—
642C22—2442no—
643C22—2441no—
644C22—2441no—
645C22—2441no—
646C22—2441no—
647C22#1684027111yescharacteristic
648C22#124×D6111yescharacteristic
649C22#1684032011yescharacteristic
650C22#1684056611yescharacteristic
651C22#1684057111yescharacteristic
652C22#1684057111yescharacteristic
653C22#1684057811yescharacteristic
654C4—41no—
655C4—41no—
656C4—42no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—1222no—
661C4—4881no—
662C4—4881no—
663C4—4881no—
664C4—2441no—
665C4—2441no—
666C4#1684043611yescharacteristic
667C4#1684043711yescharacteristic
668C4#1684044011yescharacteristic
669C4#1684044111yescharacteristic
670C2—4882no—
671C2—2442no—
672C2#2145097511yescharacteristic
673C2#2145601611yescharacteristic
674C2#2145603111yescharacteristic
675C2#2145617011yescharacteristic
676C2#2145618511yescharacteristic
677C2#2145671711yescharacteristic
678C2#2145672611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1935C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
hypercenter#1935D61
hypocenterC61#29119
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
1. #21451654C2semidirect
3. #21447230C2semidirect
4. #21447226C2semidirect
5. #21446968C2semidirect
6. #21446964C2semidirect
7. #21446516C2semidirect
8. #21446501C2semidirect
9. #21446498C2semidirect
10. #21445908C2semidirect
11. #21445904C2semidirect
14. #21445588C2semidirect
15. C61×#1935C2semidirect
338. #1935D61semidirect
398. C61#29119semidirect

Maximal subgroups

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

subgroupindex
#214516542
#214484102
#214472302
#214472262
#214469682
#214469642
#214465162
#214465012
#214464982
#214459082
#214459042
#214457582
#214455882
C61×#19352
#2911961