Finite Group Databasebeta

← #29651438

Subgroups — #29651438

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454827C212yesmaximal, complemented
2C4×#14519796C211yesmaximal, characteristic
3#21444717C211yesmaximal, characteristic, complemented
4#21444715C211yesmaximal, characteristic, complemented
5#21444655C212yesmaximal, complemented
6#21444652C212yesmaximal, complemented
7D8×#92418C211yesmaximal, characteristic, complemented
8#21444581C211yesmaximal, characteristic, complemented
9#21444250C212yesmaximal, complemented
10C8×#11758189C211yesmaximal, characteristic, complemented
11C8×D8×C61C211yesmaximal, characteristic, complemented
12C2×#14519796C411yescharacteristic
13C4×#11758224C2212yes—
14#16839892C2212yes—
15#16839889C2212yes—
16C4×Dic244C2211yescharacteristic
17#16839856C411yescharacteristic
18#16839853C412yes—
19C4×#11758200C2212yes—
20D8×Dic61C411yescharacteristic
21#16839833—22no—
22#16839830—22no—
23D4×#92418C2212yes—
24#16839818C2212yes—
25#16839816—22no—
26#16839813C2211yescharacteristic
27#16839799C411yescharacteristic
28#16839755C412yes—
29C4×#11758189C2211yescharacteristic
30C2×#14519687—22no—
31C4×C8×D61C2211yescharacteristic
32#16839515C2211yescharacteristic
33#16839512C2212yes—
34#16839494C2212yes—
35#16839492C2212yes—
36D4⋊#92418C2212yes—
37#16839484C2211yescharacteristic
38#16839483C2211yescharacteristic
39C8×#92418C2211yescharacteristic
40C4×D8×C61C2211yescharacteristic
41C8×D4×C61C2212yes—
42C61×#335C2211yescharacteristic
43C61×D4⋊C8C2212yes—
44C82×C61C2211yescharacteristic
45C2×#11758224C2×C412yes—
46#14519796—24no—
47C2×Dic244C2×C411yescharacteristic
48C2×#11758200C2×C412yes—
49C2×#11758189D411yescharacteristic
50C2×#11758189D411yescharacteristic
51C22×#92418—22no—
52C2×C8×D61C2×C411yescharacteristic
53C2×C8×D61C2×C411yescharacteristic
54C4×Dic122C2312yes—
55#14519742C2×C412yes—
56D4×Dic61C2×C412yes—
57C4×C22⋊D61—22no—
58#14519737—22no—
59#14519735C2×C412yes—
60#14519733—22no—
61C2×C4×Dic61—22no—
62C42×D61C2311yescharacteristic
63#14519711C2×C411yescharacteristic
64#14519708C2×C412yes—
65C4⋊#92418C2312yes—
66#14519706—22no—
67#14519706—21no—
68#14519706—22no—
69#14519702C2×C412yes—
70#14519700C2×C412yes—
71#14519698C2×C412yes—
72C22⋊#92418—22no—
73#14519689—22no—
74#14519689—21no—
75#14519687—22no—
76#14519687—22no—
77#14519687—22no—
78#14519687D411yescharacteristic
79#14519687D411yescharacteristic
80C4×#92418C2311yescharacteristic
81C4×#92418C2311yescharacteristic
82C4×#92418C2311yescharacteristic
83C8×Dic61C2×C411yescharacteristic
84C8×Dic61C2×C411yescharacteristic
85C2×D8×C61C2×C411yescharacteristic
86C22×C8×C61—22no—
87C4×D4×C61C2312yes—
88#107×C61C2×C411yescharacteristic
89C4⋊C8×C61C2312yes—
90#102×C61C2×C412yes—
91C22⋊C8×C61—22no—
92C4×C8×C61C2311yescharacteristic
93C4×C8×C61C2311yescharacteristic
94C4×C8×C61C2311yescharacteristic
95C2×D4×C61C22×C412yes—
96C22×C4×C61—22no—
97C2×C22⋊D61—22no—
98C22×Dic61—22no—
99C22×Dic61—22no—
100#11758224—24no—
101#11758224—42no—
102C2×C4×D61C22×C411yescharacteristic
103C2×C4×D61C2×D411yescharacteristic
104C2×C4×D61#4111yescharacteristic
105C2×Dic122C22×C412yes—
106D8×C61M1614yescomplemented
107C2×C8×C61—22no—
108C2×C8×C61—21no—
109C2×C8×C61—44no—
110C2×C8×C61C22×C411yescharacteristic
111C2×C8×C61C22×C411yescharacteristic
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61C2×D411yescharacteristic
114C4⋊C4×C61C22×C412yes—
115C22⋊C4×C61—22no—
116C42×C61C2411yescharacteristic
117C22⋊Dic61—22no—
118#11758200—24no—
119#11758198—22no—
120C4⋊Dic61C22×C412yes—
121#11758196—22no—
122#11758196—22no—
123C4×Dic61—22no—
124C4×Dic61—22no—
125C4×Dic61—22no—
126C4×Dic61C22×C411yescharacteristic
127C4×Dic61C2×D411yescharacteristic
128C4×Dic61#4111yescharacteristic
129C2×#92418—22no—
130C2×#92418—21no—
131C2×#92418—44no—
132C2×#92418C22×C411yescharacteristic
133C2×#92418C22×C411yescharacteristic
134C2×#92418C2×D411yescharacteristic
135C2×#92418C2×D411yescharacteristic
136Dic244—22no—
137#11758189—22no—
138#11758189—22no—
139C8×D61—22no—
140C8×D61—41no—
141C23×C61—22no—
142C22×D61C4×D411yescharacteristic
143D4×C61—22no—
144D4×C61C2×M1614yes—
145C2×C4×C61—22no—
146C2×C4×C61—42no—
147C2×C4×C61—42no—
148C2×C4×C61C23×C411yescharacteristic
149C2×C4×C61C22×D411yescharacteristic
150C2×C4×C61C2×#4111yescharacteristic
151C22⋊D61—44no—
152C2×Dic61—22no—
153C2×Dic61—22no—
154C2×Dic61—44no—
155C2×Dic61—82no—
156C2×Dic61C4×D411yescharacteristic
157C2×Dic61C4×D411yescharacteristic
158C2×Dic61C4×D411yescharacteristic
159C4×D61—21no—
160C4×D61—21no—
161C4×D61—21no—
162C4×D61—21no—
163C4×D61—41no—
164Dic122—22no—
165Dic122—22no—
166C8×C61—21no—
167C8×C61—21no—
168C8×C61—41no—
169C8×C61—42no—
170C8×C61C2×M1612yes—
171C8×C61#13512yescomplemented
172#92418—21no—
173#92418—21no—
174#92418—21no—
175#92418—41no—
176#92418—42no—
177#92418#13512yescomplemented
178#18035—611nomaximal, Sylow
179C22×C61—24no—
180C22×C61—42no—
181C22×C61—42no—
182C22×C61C2×C4×D411yescharacteristic
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—21no—
186C4×C61—21no—
187C4×C61—42no—
188C4×C61C22×M1611yescharacteristic
189C4×C61#56811yescharacteristic
190C4×C61C2×#13511yescharacteristic
191C4×C61C2×#13511yescharacteristic
192Dic61—21no—
193Dic61—21no—
194Dic61—21no—
195Dic61—42no—
196Dic61—42no—
197#2970—612no—
198C4×#135—611no—
199#1591—611no—
200#1591—611no—
201#1582—612no—
202#1582—612no—
203C8×D8—611no—
204C8×D8D6111yescharacteristic, complemented
205#1568—611no—
206#1488—612no—
207C8×M16—611no—
208C2×C61—44no—
209C2×C61D4×M1611yescharacteristic
210C2×C61C4×#13511yescharacteristic
211C2×C61#295711yescharacteristic
212D61—41no—
213C2×#135—611no—
214C4×#41—612no—
215#446—612no—
216#446—612no—
217C4×Q16—611no—
218C4×Q16—611no—
219C4×SD16—612no—
220C4×SD16—612no—
221C4×D8—611no—
222C4×D8C2×D6111yescharacteristic
223#435—1222no—
224#435—1222no—
225C8×D4—612no—
226C8×D4C2×D6112yes—
227#432—612no—
228#432—1222no—
229#431—611no—
230#427—611no—
231#416—612no—
232C4×M16—611no—
233C2×#97—1222no—
234C2×C4×C8—611no—
235#335—611no—
236#335C2×D6111yescharacteristic
237#334—612no—
238Q8⋊C8—612no—
239Q8⋊C8—612no—
240D4⋊C8—612no—
241D4⋊C8C2×D6112yes—
242#322—611no—
243#322—611no—
244C82—611no—
245C82C2×D6111yescharacteristic
246C61#1803511yescharacteristic, complemented, Sylow
247C2×#41—612no—
248#135—1224no—
249C2×Q16—611no—
250C2×SD16—612no—
251C2×D8C4×D6111yescharacteristic
252C2×M16—611no—
253C2×M16—611no—
254C22×C8—22no—
255C22×C8—611no—
256C22×C8—611no—
257C22×C8—1222no—
258C4×Q8—612no—
259C4×Q8—612no—
260C4×D4—612no—
261C4×D4—1222no—
262C4×D4—1222no—
263C4×D4C22×D6112yes—
264#117—612no—
265#117—1222no—
266C2×C42—611no—
267C2×C42—1222no—
268#107—611no—
269#107C4×D6111yescharacteristic
270#106—612no—
271C4⋊C8—612no—
272C4⋊C8—1221no—
273C4⋊C8—1222no—
274C4⋊C8—1222no—
275C4⋊C8C22×D6112yes—
276#103—612no—
277#103—612no—
278#102—612no—
279#102C4×D6112yes—
280C22⋊C8—22no—
281C22⋊C8—1221no—
282C22⋊C8—1222no—
283C22⋊C8—1222no—
284#97—611no—
285#97—611no—
286#97—1222no—
287#97—1222no—
288#97—1222no—
289C4×C8—611no—
290C4×C8—611no—
291C4×C8—611no—
292C4×C8—611no—
293C4×C8—611no—
294C4×C8C22×D6111yescharacteristic
295C4×C8C22×D6111yescharacteristic
296C4×C8C22×D6111yescharacteristic
297#41—1224no—
298#41—2442no—
299C2×Q8—612no—
300C2×D4—1222no—
301C2×D4C2×C4×D6112yes—
302C22×C4—22no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—1222no—
307C22×C4—1222no—
308Q16—1222no—
309SD16—1224no—
310D8#1175818914yescomplemented
311M16—1222no—
312M16—1222no—
313C2×C8—22no—
314C2×C8—21no—
315C2×C8—44no—
316C2×C8—611no—
317C2×C8—611no—
318C2×C8—611no—
319C2×C8—611no—
320C2×C8—1222no—
321C2×C8—1222no—
322C2×C8—1221no—
323C2×C8—2441no—
324C2×C8—2444no—
325C2×C8C2×C4×D6111yescharacteristic
326C2×C8C2×C4×D6111yescharacteristic
327C2×C8D4×D6111yescharacteristic
328C2×C8D4×D6111yescharacteristic
329C4⋊C4—612no—
330C4⋊C4—1222no—
331C4⋊C4—1222no—
332C4⋊C4C2×C4×D6112yes—
333C22⋊C4—22no—
334C22⋊C4—1222no—
335C22⋊C4—1222no—
336C42—611no—
337C42—611no—
338C42—611no—
339C42—1222no—
340C42—1222no—
341C42—1222no—
342C42C23×D6111yescharacteristic
343C23—22no—
344C23—611no—
345Q8—1222no—
346Q8—1222no—
347D4—22no—
348D4—2444no—
349D4C2×#1175818914yes—
350C2×C4—22no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1222no—
361C2×C4—1222no—
362C2×C4—4882no—
363C2×C4—2441no—
364C2×C4—2444no—
365C2×C4C22×C4×D6111yescharacteristic
366C2×C4C2×D4×D6111yescharacteristic
367C2×C4#41×D6111yescharacteristic
368C8—21no—
369C8—21no—
370C8—41no—
371C8—42no—
372C8—612no—
373C8—1221no—
374C8—1221no—
375C8—1221no—
376C8—2441no—
377C8—2442no—
378C8C2×#1175818912yes—
379C8#1451979612yescomplemented
380C22—24no—
381C22—42no—
382C22—42no—
383C22—1221no—
384C22—1221no—
385C22—1221no—
386C22C4×D4×D6111yescharacteristic
387C4—21no—
388C4—42no—
389C4—1221no—
390C4—1221no—
391C4—1221no—
392C4—2442no—
393C4—2442no—
394C4C22×#1175818911yescharacteristic
395C4#1684052711yescharacteristic
396C4#135×D6111yescharacteristic
397C4C2×#1451979611yescharacteristic
398C2—44no—
399C2—2441no—
400C2D4×#1175818911yescharacteristic
401C2C4×#1451979611yescharacteristic
402C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC8×D8×C61C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519796C4
cosocleC42×C61C24
hypercenterC8×D8D61
hypocenterC61#18035
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
1. #21454827C2semidirect
3. #21444717C2semidirect
4. #21444715C2semidirect
5. #21444655C2semidirect
6. #21444652C2semidirect
7. D8×#92418C2semidirect
8. #21444581C2semidirect
9. #21444250C2semidirect
10. C8×#11758189C2semidirect
11. C8×D8×C61C2semidirect
106. D8×C61M16semidirect
171. C8×C61#135semidirect
177. #92418#135semidirect
204. C8×D8D61semidirect
246. C61#18035semidirect
310. D8#11758189semidirect
379. C8#14519796semidirect

Maximal subgroups

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

subgroupindex
#214548272
C4×#145197962
#214447172
#214447152
#214446552
#214446522
D8×#924182
#214445812
#214442502
C8×#117581892
C8×D8×C612
#1803561