Finite Group Databasebeta

← #29689598

Subgroups — #29689598

Order 15616.

1170 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840292C211yesmaximal, characteristic
2C2×#16839812C211yesmaximal, characteristic, complemented
3C22×#14519706C211yesmaximal, characteristic, complemented
4#21446753C212yesmaximal, complemented
5#21446611C212yesmaximal, complemented
6#21446112C211yesmaximal, characteristic, complemented
7#21446111C211yesmaximal, characteristic, complemented
8#21446109C211yesmaximal, characteristic, complemented
9#21445802C212yesmaximal, complemented
10#21445801C212yesmaximal, complemented
11C61×#1869C211yesmaximal, characteristic, complemented
12C23×#92418C2211yescharacteristic
13#16840292—24no—
14#16840292—24no—
15C2×#14519772C411yescharacteristic
16C2×#14519770C411yescharacteristic
17C2×#14519767C411yescharacteristic
18C2×#14519763C411yescharacteristic
19C2×#14519761C411yescharacteristic
20C2×#14519758C411yescharacteristic
21C2×#14519754C411yescharacteristic
22C2×#14519749C411yescharacteristic
23C2×C4×Dic122C2211yescharacteristic
24C2×C4×C22⋊D61C2211yescharacteristic
25C2×C4×C22⋊D61C2211yescharacteristic
26C2×#14519736C2211yescharacteristic
27C2×#14519734C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29#16839812—24no—
30C2×#14519706—24no—
31C2×#14519706C2212yes—
32C2×#14519706C2212yes—
33C2×#14519706C2212yes—
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2212yes—
36C2×#14519689C2212yes—
37C2×#14519689C2212yes—
38C2×C8×Dic61C2212yes—
39#16839517C2212yes—
40#16839516C2212yes—
41#16839516C2212yes—
42C23×C8×C61C2211yescharacteristic
43C2×C4×D4×C61C2211yescharacteristic
44C2×C22⋊C8×C61C2211yescharacteristic
45C2×C22⋊C8×C61C2212yes—
46C61×#336C2212yes—
47C22×Dic122C2×C411yescharacteristic
48C22×C22⋊D61C2×C411yescharacteristic
49C22×C22⋊D61C2×C411yescharacteristic
50C23×Dic61C2×C411yescharacteristic
51C23×Dic61C2×C411yescharacteristic
52C22×C4×D61C2311yescharacteristic
53C22×#92418—22no—
54C22×#92418—42no—
55C22×#92418C2312yes—
56C22×#92418C2312yes—
57#14519772—24no—
58#14519770—24no—
59#14519767—24no—
60#14519763—24no—
61#14519761—24no—
62#14519758—24no—
63#14519754—24no—
64#14519749—24no—
65C4×Dic122—22no—
66C4×Dic122—22no—
67C4×C22⋊D61—22no—
68C4×C22⋊D61—22no—
69C4×C22⋊D61—22no—
70C4×C22⋊D61—22no—
71#14519736—22no—
72#14519736—22no—
73#14519734—22no—
74#14519734—22no—
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×C4⋊Dic61C2×C411yescharacteristic
77C2×C4⋊Dic61C2×C411yescharacteristic
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×#11758196C2×C411yescharacteristic
82C2×#11758196C2×C411yescharacteristic
83C2×#11758196C2×C411yescharacteristic
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×C22⋊Dic61C2×C411yescharacteristic
86C2×C22⋊Dic61C2×C411yescharacteristic
87C2×C22⋊Dic61C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61D414yes—
95C2×C4×Dic61D414yes—
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99#14519706—24no—
100#14519706—24no—
101#14519706—24no—
102C22⋊#92418—22no—
103C22⋊#92418—42no—
104#14519689—42no—
105#14519689—42no—
106C8×Dic61—24no—
107C22×D4×C61C2×C411yescharacteristic
108C23×C4×C61C2311yescharacteristic
109C23×C4×C61C2311yescharacteristic
110C22×C8×C61—22no—
111C22×C8×C61—42no—
112C22×C8×C61C2312yes—
113C22×C8×C61C2312yes—
114C4×D4×C61—22no—
115C4×D4×C61—22no—
116C2×C4⋊C4×C61C2×C411yescharacteristic
117C2×C22⋊C4×C61C2×C411yescharacteristic
118C2×C22⋊C4×C61C2×C411yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C22⋊C8×C61—22no—
121C22⋊C8×C61—42no—
122C24×C61C22×C411yescharacteristic
123C24×C61C22×C411yescharacteristic
124C23×D61C22×C411yescharacteristic
125C2×D4×C61—22no—
126C2×D4×C61—22no—
127C2×D4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C2×D412yes—
139C22×C4×C61C2×D412yes—
140C22×C4×C61C2411yescharacteristic
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—24no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—24no—
149C22×Dic61C22⋊C414yes—
150C22×Dic61C22⋊C414yes—
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×Dic122—22no—
163C2×Dic122—24no—
164C2×C8×C61—22no—
165C2×C8×C61—22no—
166C2×C8×C61—22no—
167C2×C8×C61—22no—
168C2×C8×C61—22no—
169C2×C8×C61—22no—
170C2×C8×C61—44no—
171C4⋊C4×C61—22no—
172C22⋊C4×C61—22no—
173C22⋊C4×C61—22no—
174C42×C61—21no—
175C42×C61—21no—
176C22⋊Dic61—22no—
177C22⋊Dic61—22no—
178C22⋊Dic61—22no—
179C22⋊Dic61—22no—
180#11758198—22no—
181#11758198—22no—
182#11758198—22no—
183#11758198—22no—
184C4⋊Dic61—22no—
185C4⋊Dic61—22no—
186C4⋊Dic61—22no—
187#11758196—22no—
188#11758196—22no—
189#11758196—22no—
190#11758196—22no—
191#11758196—22no—
192#11758196—22no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61C22⋊C414yes—
196C4×Dic61C22⋊C414yes—
197C4×Dic61C2×D412yes—
198C4×Dic61C2×D412yes—
199C4×Dic61C2×D412yes—
200C4×Dic61C2×D412yes—
201C2×#92418—22no—
202C2×#92418—22no—
203C2×#92418—22no—
204C2×#92418—22no—
205C2×#92418—22no—
206C2×#92418—22no—
207C2×#92418—44no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—21no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61C2×C22⋊C412yes—
216C23×C61#13112yes—
217C23×C61#13112yes—
218C23×C61C23×C411yescharacteristic
219C22×D61—21no—
220C22×D61—22no—
221C22×D61—22no—
222C22×D61—21no—
223C22×D61—21no—
224D4×C61—44no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—24no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—42no—
239C2×C4×C61C2×C22⋊C412yes—
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61H(5,𝔽2)12yes—
243C2×C4×C612−1+412yes—
244C22⋊D61—44no—
245C22⋊D61—44no—
246C2×Dic61—22no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—28no—
252C2×Dic61—28no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61C2×C22⋊C412yes—
261C2×Dic61C2×C22⋊C412yes—
262C2×Dic61C2×C22⋊C412yes—
263C2×Dic61C2×C22⋊C412yes—
264C2×Dic61#13114yes—
265C4×D61—41no—
266C4×D61—41no—
267C4×D61—42no—
268Dic122—44no—
269C8×C61—42no—
270C8×C61—42no—
271#92418—42no—
272#92418—42no—
273#21848—611nomaximal, Sylow
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—24no—
277C22×C61—24no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—42no—
282C22×C61—42no—
283C22×C61#40814yes—
284C22×C61C22×C22⋊C411yescharacteristic
285C22×C61#52012yes—
286C22×C61C2×#13112yes—
287C22×C61C2×#13111yescharacteristic
288C22×C61C2×#13111yescharacteristic
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—42no—
293C2×D61—42no—
294C4×C61—22no—
295C4×C61—41no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61#53511yescharacteristic
299C4×C61#53611yescharacteristic
300C4×C61#53712yes—
301Dic61—22no—
302Dic61—22no—
303Dic61—22no—
304Dic61—41no—
305Dic61—41no—
306Dic61—41no—
307Dic61#40814yes—
308C2×#529—611no—
309C2×#431—611no—
310C22×C4⋊C8—611no—
311#1984—612no—
312#1954—612no—
313#1869—611no—
314#1869—611no—
315#1869—611no—
316#1869D6111yescharacteristic, complemented
317#1798—612no—
318#1798—612no—
319C2×C61—24no—
320C2×C61—81no—
321C2×C61#231111yescharacteristic
322C2×C61C2×#40811yescharacteristic
323C2×C61C2×#40811yescharacteristic
324C2×C61#299412yes—
325C2×C61#299412yes—
326D61—81no—
327C23×C8—611no—
328C23×C8C2×D6111yescharacteristic
329#529—1224no—
330#529—1224no—
331C2×#126—611no—
332C2×#126—611no—
333C2×#125—611no—
334C2×#124—611no—
335C2×#123—611no—
336C2×#123—611no—
337C2×C22⋊Q8—611no—
338C2×#121—611no—
339C2×C4×Q8—611no—
340C2×C4×D4—611no—
341C2×C4×D4—611no—
342C2×C4×D4C2×D6111yescharacteristic
343C2×#117—611no—
344C2×#117—611no—
345C22×C42—611no—
346#431—1224no—
347C2×C4⋊C8—612no—
348C2×C4⋊C8—612no—
349C2×C4⋊C8—612no—
350C2×C4⋊C8—1224no—
351C2×C22⋊C8—611no—
352C2×C22⋊C8—612no—
353C2×C22⋊C8—612no—
354C2×C22⋊C8—612no—
355C2×C22⋊C8C2×D6111yescharacteristic
356C2×C22⋊C8C2×D6112yes—
357C2×C4×C8—612no—
358#336—612no—
359#336—612no—
360#336—612no—
361#336C2×D6112yes—
362C61#2184811yescharacteristic, complemented, Sylow
363C22×Q8—611no—
364C22×D4—611no—
365C22×D4—611no—
366C22×D4C4×D6111yescharacteristic
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4C22×D6111yescharacteristic
371C23×C4C22×D6111yescharacteristic
372C22×C8—22no—
373C22×C8—42no—
374C22×C8—612no—
375C22×C8—612no—
376C22×C8—1222no—
377C22×C8—2442no—
378C22×C8C22×D6112yes—
379C22×C8C22×D6112yes—
380#126—1224no—
381#126—1224no—
382#125—1224no—
383#124—1224no—
384#123—1224no—
385#123—1224no—
386C22⋊Q8—1224no—
387#121—1224no—
388C4×Q8—1222no—
389C4×Q8—1222no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—1222no—
393C4×D4—1222no—
394C4×D4—1222no—
395C4×D4—1222no—
396#117—1222no—
397#117—1222no—
398#117—1222no—
399#117—1222no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4C4×D6111yescharacteristic
410C2×C22⋊C4—611no—
411C2×C22⋊C4—611no—
412C2×C22⋊C4—611no—
413C2×C22⋊C4—611no—
414C2×C22⋊C4—611no—
415C2×C22⋊C4—611no—
416C2×C22⋊C4—611no—
417C2×C22⋊C4—611no—
418C2×C22⋊C4C4×D6111yescharacteristic
419C2×C22⋊C4C4×D6111yescharacteristic
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—614no—
423C2×C42—614no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42C22×D6111yescharacteristic
428C4⋊C8—1224no—
429C4⋊C8—1224no—
430C4⋊C8—1224no—
431C22⋊C8—22no—
432C22⋊C8—42no—
433C22⋊C8—1222no—
434C22⋊C8—2442no—
435C22⋊C8—2442no—
436C22⋊C8—2442no—
437C4×C8—1224no—
438C24—611no—
439C24C2×C4×D6111yescharacteristic
440C24C2×C4×D6111yescharacteristic
441C2×Q8—1222no—
442C2×Q8—1224no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—1222no—
447C2×D4—1224no—
448C2×D4—1222no—
449C2×D4—1222no—
450C2×D4—1222no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—614no—
462C22×C4—614no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—1224no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4C2×C4×D6111yescharacteristic
474C22×C4C2×C4×D6111yescharacteristic
475C22×C4C2×C4×D6111yescharacteristic
476C22×C4C2×C4×D6111yescharacteristic
477C22×C4D4×D6112yes—
478C22×C4D4×D6112yes—
479C22×C4C23×D6111yescharacteristic
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—44no—
487C2×C8—1222no—
488C2×C8—1222no—
489C2×C8—1222no—
490C2×C8—1222no—
491C2×C8—1222no—
492C2×C8—1222no—
493C2×C8—2444no—
494C4⋊C4—22no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—1222no—
507C22⋊C4—1222no—
508C22⋊C4—1222no—
509C22⋊C4—1222no—
510C22⋊C4—1222no—
511C22⋊C4—1222no—
512C22⋊C4—1222no—
513C22⋊C4—1222no—
514C42—21no—
515C42—21no—
516C42—612no—
517C42—612no—
518C42—612no—
519C42—612no—
520C42—614no—
521C42—614no—
522C42—1221no—
523C42—1221no—
524C23—22no—
525C23—22no—
526C23—21no—
527C23—22no—
528C23—22no—
529C23—21no—
530C23—21no—
531C23—1221no—
532C23—1222no—
533C23—1222no—
534C23—1221no—
535C23—1221no—
536C23C22⋊C4×D6112yes—
537C23#1451978312yes—
538C23#1451978512yes—
539C23C22×C4×D6111yescharacteristic
540Q8—2444no—
541D4—44no—
542D4—2444no—
543D4—2444no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—612no—
559C2×C4—614no—
560C2×C4—612no—
561C2×C4—612no—
562C2×C4—612no—
563C2×C4—1228no—
564C2×C4—1228no—
565C2×C4—1222no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2442no—
580C2×C4C22⋊C4×D6112yes—
581C2×C4C2×D4×D6111yescharacteristic
582C2×C4C2×D4×D6111yescharacteristic
583C2×C4#1451982212yes—
584C2×C4#1451982412yes—
585C8—42no—
586C8—42no—
587C8—2442no—
588C8—2442no—
589C22—24no—
590C22—24no—
591C22—22no—
592C22—22no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—2442no—
599C22—2442no—
600C22—2441no—
601C22—2441no—
602C22—2441no—
603C22#1683972714yes—
604C22C2×C22⋊C4×D6111yescharacteristic
605C22#1684024112yes—
606C22#131×D6112yes—
607C22C2×#1451978311yescharacteristic
608C22C2×#1451978511yescharacteristic
609C4—22no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—614no—
614C4—1222no—
615C4—1222no—
616C4—1222no—
617C4—2441no—
618C4—2441no—
619C4—2441no—
620C4#1684032711yescharacteristic
621C4#1684033411yescharacteristic
622C4#1684033912yes—
623C2—24no—
624C2—81no—
625C2—4881no—
626C2#2144840611yescharacteristic
627C2#408×D6111yescharacteristic
628C2C2×#1683972711yescharacteristic
629C2#2145497212yes—
630C2#2145497612yes—
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1869C2
prime radicalC2×#14519749C4
cosocleC22×C4×C61C24
hypercenter#1869D61
hypocenterC61#21848
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. C2×#16839812C2semidirect
3. C22×#14519706C2semidirect
4. #21446753C2semidirect
5. #21446611C2semidirect
6. #21446112C2semidirect
7. #21446111C2semidirect
8. #21446109C2semidirect
9. #21445802C2semidirect
10. #21445801C2semidirect
11. C61×#1869C2semidirect
316. #1869D61semidirect
362. C61#21848semidirect

Maximal subgroups

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

subgroupindex
C2×#168402922
C2×#168398122
C22×#145197062
#214467532
#214466112
#214461122
#214461112
#214461092
#214458022
#214458012
C61×#18692
#2184861