Finite Group Databasebeta

← #29734433

Subgroups — #29734433

Order 15616.

1096 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840367C211yesmaximal, characteristic
2C2×#16840168C211yesmaximal, characteristic, complemented
3C2×#16840110C211yesmaximal, characteristic, complemented
4#21447008C212yesmaximal, complemented
5#21447001C212yesmaximal, complemented
6#21446783C211yesmaximal, characteristic, complemented
7#21446642C211yesmaximal, characteristic, complemented
8#21446079C212yesmaximal, complemented
9#21446065C212yesmaximal, complemented
10#21445585C211yesmaximal, characteristic, complemented
11C61×#2628C211yesmaximal, characteristic, complemented
12#16840367—24no—
13#16840367—24no—
14C2×#14519774C2211yescharacteristic
15C2×#14519769C2211yescharacteristic
16C2×#14519762—21no—
17C2×#14519762—21no—
18C2×#14519751C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×#14519750—21no—
21C2×#14519750—21no—
22C2×C4×D244C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic
24#16840168—24no—
25#16840110—24no—
26C2×#14519710C2212yes—
27C2×#14519708C2212yes—
28C2×#14519697C2212yes—
29C2×#14519697C2212yes—
30C2×#14519697C2212yes—
31C2×#14519697C2212yes—
32C2×C22⋊#92418C2212yes—
33C2×#14519688C2211yescharacteristic
34C2×C4×#92418C2211yescharacteristic
35#16839524C2212yes—
36#16839524C2212yes—
37#16839517C2212yes—
38C2×C4⋊Q8×C61C2211yescharacteristic
39C2×#117×C61C2211yescharacteristic
40C61×#400—21no—
41C61×#399—21no—
42C61×#395—21no—
43C61×#393—21no—
44C61×#389C2212yes—
45C61×#382C2211yescharacteristic
46C61×#380C2212yes—
47C22×D244—21no—
48C22×D244—21no—
49C22×D244C2311yescharacteristic
50C22×D244C2311yescharacteristic
51C22×C22⋊D61—21no—
52C22×C22⋊D61—21no—
53C22×C4×D61—21no—
54C22×C4×D61—21no—
55C22×#92418C2312yes—
56C22×#92418C2312yes—
57#14519774—22no—
58#14519774D414yes—
59#14519769—22no—
60#14519769D414yes—
61#14519762—28no—
62#14519762—28no—
63#14519751—22no—
64#14519751—22no—
65#14519751—22no—
66#14519751—22no—
67#14519750—28no—
68#14519750—28no—
69C4×D244—22no—
70C4×D244—22no—
71C4×D244—22no—
72C4×D244—22no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81#14519710—24no—
82#14519708—24no—
83#14519697—24no—
84#14519697—24no—
85#14519697—24no—
86#14519697—24no—
87C22⋊#92418—24no—
88#14519688—22no—
89C4×#92418—22no—
90C22×Q8×C61—21no—
91C23×C4×C61C2311yescharacteristic
92C4⋊Q8×C61—22no—
93C4⋊Q8×C61—22no—
94#117×C61—22no—
95#117×C61—22no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61D411yescharacteristic
99C2×C4⋊C4×C61D411yescharacteristic
100C2×C4⋊C4×C61C2312yes—
101C2×C4⋊C4×C61C2312yes—
102C2×C22⋊C4×C61—22no—
103C2×C22⋊C4×C61D411yescharacteristic
104C2×C22⋊C4×C61D411yescharacteristic
105C2×C42×C61C2311yescharacteristic
106C2×C42×C61C2311yescharacteristic
107#95×C61—22no—
108#95×C61—21no—
109#95×C61—21no—
110#95×C61—22no—
111C24×C61C2×D411yescharacteristic
112C23×D61—21no—
113C23×D61—21no—
114C2×Q8×C61—42no—
115C2×Q8×C61—82no—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2411yescharacteristic
128C2×C22⋊D61—24no—
129C2×C22⋊D61—24no—
130C2×C22⋊D61—82no—
131C2×C22⋊D61—82no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C2×D244—22no—
135C2×D244—22no—
136C2×D244—22no—
137C2×D244—22no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244—24no—
141C2×D244—24no—
142C2×D244—82no—
143C2×D244—82no—
144C2×D244C2×D412yes—
145C2×D244C2×D412yes—
146C2×C4×D61—24no—
147C2×C4×D61—24no—
148C2×C4×D61—82no—
149C2×C4×D61—82no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—22no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—42no—
157C4⋊C4×C61—82no—
158C22⋊C4×C61—22no—
159C22⋊C4×C61—22no—
160C22⋊C4×C61—82no—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61C2×D412yes—
164C42×C61C2×D412yes—
165#11758198—24no—
166#11758198—24no—
167#11758198—24no—
168#11758198—24no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61C2×D412yes—
172C4⋊Dic61C2×D412yes—
173#11758196—24no—
174#11758196—24no—
175C2×#92418—22no—
176C2×#92418—22no—
177C2×#92418—22no—
178C2×#92418—22no—
179C2×#92418—22no—
180C2×#92418#4114yes—
181C23×C61—21no—
182C23×C61—21no—
183C23×C61—21no—
184C23×C61—22no—
185C23×C61—22no—
186C23×C61C22×D411yescharacteristic
187C22×D61—22no—
188C22×D61—22no—
189C22×D61—41no—
190C22×D61—41no—
191C22×D61—41no—
192C22×D61—41no—
193C22×D61—42no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—42no—
197Q8×C61—84no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—42no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61#12012yes—
216C2×C4×C61#12012yes—
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C2×#4112yes—
220C2×C4×C612−1+412yes—
221C22⋊D61—84no—
222C22⋊D61—84no—
223C2×Dic61—22no—
224C2×Dic61—22no—
225C2×Dic61—42no—
226C2×Dic61—42no—
227D244—24no—
228D244—24no—
229D244—42no—
230D244—42no—
231D244—84no—
232D244—84no—
233C4×D61—84no—
234C4×D61—84no—
235#92418—24no—
236#92418—42no—
237#25685—611nomaximal, Sylow
238C22×C61—42no—
239C22×C61—41no—
240C22×C61—42no—
241C22×C61—41no—
242C22×C61—41no—
243C22×C61C2×#12011yescharacteristic
244C22×C61#53211yescharacteristic
245C22×C61#53611yescharacteristic
246C22×C61#57612yes—
247C22×C61#57712yes—
248C2×D61—42no—
249C2×D61—42no—
250C2×D61—42no—
251C2×D61—42no—
252C2×D61—42no—
253C2×D61—42no—
254C2×D61—82no—
255C2×D61—82no—
256C2×D61—82no—
257C2×D61—82no—
258C4×C61—22no—
259C4×C61—22no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—82no—
264C4×C61—82no—
265C4×C61#54712yes—
266C4×C61#54812yes—
267Dic61—42no—
268Dic61—42no—
269C2×#540—611no—
270C2×#501—611no—
271C2×#486—611no—
272#2628D6111yescharacteristic, complemented
273#2034—612no—
274#2033—612no—
275#1991—611no—
276#1961—611no—
277#1864—612no—
278#1862—612no—
279#1750—611no—
280C2×C61—81no—
281C2×C61#243211yescharacteristic
282C2×C61#300811yescharacteristic
283C2×C61#300911yescharacteristic
284C2×C61#317912yes—
285C2×C61#324112yes—
286D61—82no—
287D61—82no—
288#540—1224no—
289#540—1224no—
290C2×C4⋊Q8C2×D6111yescharacteristic
291C2×#127—611no—
292C2×#125—611no—
293C2×#123—1221no—
294C2×#123—1221no—
295C2×#121—611no—
296C2×#121—611no—
297C2×#121—1221no—
298C2×#121—1221no—
299C2×C4×D4—611no—
300C2×C4×D4—611no—
301C2×#117C2×D6111yescharacteristic
302#501—1224no—
303#486—1224no—
304C2×#107—612no—
305C2×#106—612no—
306C2×#102—612no—
307C2×#102—612no—
308C2×#102—612no—
309C2×#102—612no—
310C2×C22⋊C8—612no—
311C2×#97—611no—
312C2×C4×C8—611no—
313#400—21no—
314#399—21no—
315#395—21no—
316#393—21no—
317#389C2×D6112yes—
318#382C2×D6111yescharacteristic
319#380C2×D6112yes—
320#340—612no—
321#340—612no—
322#336—612no—
323C61#2568511yescharacteristic, complemented, Sylow
324C22×Q8—21no—
325C22×D4—611no—
326C22×D4—611no—
327C22×D4—1221no—
328C22×D4—1221no—
329C22×D4—1221no—
330C22×D4—1221no—
331C23×C4—1221no—
332C23×C4—1221no—
333C23×C4C22×D6111yescharacteristic
334C22×C8—612no—
335C22×C8—612no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338#127—614no—
339#127—1222no—
340#125—614no—
341#125—1222no—
342#123—1228no—
343#123—1228no—
344#121—1228no—
345#121—1228no—
346#121—1222no—
347#121—1222no—
348#121—1222no—
349#121—1222no—
350C4×D4—1222no—
351C4×D4—1222no—
352C4×D4—1222no—
353C4×D4—1222no—
354#117—22no—
355#117—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—611no—
359C2×C4⋊C4—611no—
360C2×C4⋊C4—1221no—
361C2×C4⋊C4—1221no—
362C2×C4⋊C4C22⋊D6111yescharacteristic
363C2×C4⋊C4C22⋊D6111yescharacteristic
364C2×C4⋊C4C22×D6112yes—
365C2×C4⋊C4C22×D6112yes—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—1221no—
368C2×C22⋊C4—1221no—
369C2×C22⋊C4—1221no—
370C2×C22⋊C4—1221no—
371C2×C22⋊C4C22⋊D6111yescharacteristic
372C2×C22⋊C4C22⋊D6111yescharacteristic
373C2×C42C22×D6111yescharacteristic
374C2×C42C22×D6111yescharacteristic
375#107—1224no—
376#106—1224no—
377#102—1224no—
378#102—1224no—
379#102—1224no—
380#102—1224no—
381C22⋊C8—1224no—
382#97—1222no—
383C4×C8—1222no—
384#95—22no—
385#95—21no—
386#95—21no—
387#95—22no—
388C24—1221no—
389C24—1221no—
390C24C2×C22⋊D6111yescharacteristic
391C2×Q8—42no—
392C2×Q8—82no—
393C2×D4—612no—
394C2×D4—612no—
395C2×D4—1224no—
396C2×D4—1224no—
397C2×D4—1221no—
398C2×D4—1221no—
399C2×D4—1222no—
400C2×D4—1222no—
401C2×D4—1222no—
402C2×D4—1222no—
403C2×D4—1224no—
404C2×D4—1224no—
405C2×D4—4882no—
406C2×D4—4882no—
407C2×D4—4882no—
408C2×D4—4882no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—1224no—
416C22×C4—1224no—
417C22×C4—1221no—
418C22×C4—1221no—
419C22×C4—4882no—
420C22×C4—4882no—
421C22×C4C2×C22⋊D6111yescharacteristic
422C22×C4C2×C22⋊D6111yescharacteristic
423C22×C4C2×C22⋊D6111yescharacteristic
424C22×C4C2×C22⋊D6111yescharacteristic
425C22×C4C2×C22⋊D6111yescharacteristic
426C22×C4C23×D6111yescharacteristic
427C2×C8—614no—
428C2×C8—1222no—
429C2×C8—1222no—
430C2×C8—1222no—
431C2×C8—1222no—
432C2×C8—1222no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—42no—
440C4⋊C4—82no—
441C4⋊C4—612no—
442C4⋊C4—612no—
443C4⋊C4—1221no—
444C4⋊C4—1221no—
445C4⋊C4—1224no—
446C4⋊C4—1224no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—82no—
450C22⋊C4—1224no—
451C22⋊C4—1224no—
452C22⋊C4—1224no—
453C22⋊C4—1224no—
454C42—21no—
455C42—21no—
456C42D4×D6112yes—
457C42D4×D6112yes—
458C23—21no—
459C23—21no—
460C23—22no—
461C23—22no—
462C23—21no—
463C23—1222no—
464C23—1222no—
465C23—2441no—
466C23—2441no—
467C23—2442no—
468C23—2442no—
469C23—2442no—
470C23—2442no—
471C23—2441no—
472C23—2441no—
473C23C22×C22⋊D6111yescharacteristic
474Q8—84no—
475D4—1224no—
476D4—1224no—
477D4—4884no—
478D4—4884no—
479D4—4884no—
480D4—4884no—
481D4—2442no—
482D4—2442no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—1222no—
501C2×C4—1222no—
502C2×C4—4884no—
503C2×C4—4884no—
504C2×C4—2442no—
505C2×C4—2442no—
506C2×C4#1451974512yes—
507C2×C4#1451974512yes—
508C2×C4C2×D4×D6111yescharacteristic
509C2×C4C2×D4×D6111yescharacteristic
510C2×C4#41×D6112yes—
511C2×C4#1451982512yes—
512C8—1224no—
513C8—2442no—
514C22—42no—
515C22—42no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22—4882no—
520C22—4882no—
521C22—4882no—
522C22—4882no—
523C22—2442no—
524C22—2442no—
525C22—2442no—
526C22—2442no—
527C22—2442no—
528C22—2442no—
529C22C2×#1451974511yescharacteristic
530C22#1684030811yescharacteristic
531C22#1684033611yescharacteristic
532C22#1684056512yes—
533C22#1684057012yes—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—82no—
540C4—82no—
541C4—2442no—
542C4—2442no—
543C4#1684041412yes—
544C4#1684042212yes—
545C2—81no—
546C2—4882no—
547C2—4882no—
548C2#2144944811yescharacteristic
549C2#2145508511yescharacteristic
550C2#2145509411yescharacteristic
551C2#2145649612yes—
552C2#2145707212yes—
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2628C2
socleC23×C61C22×D4
prime radicalC2×#16840367C2
hypercenter#2628D61
hypocenterC61#25685
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
2. C2×#16840168C2semidirect
3. C2×#16840110C2semidirect
4. #21447008C2semidirect
5. #21447001C2semidirect
6. #21446783C2semidirect
7. #21446642C2semidirect
8. #21446079C2semidirect
9. #21446065C2semidirect
10. #21445585C2semidirect
11. C61×#2628C2semidirect
272. #2628D61semidirect
323. C61#25685semidirect

Maximal subgroups

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

subgroupindex
C2×#168403672
C2×#168401682
C2×#168401102
#214470082
#214470012
#214467832
#214466422
#214460792
#214460652
#214455852
C61×#26282
#2568561