Finite Group Databasebeta

← #29593449

Subgroups — #29593449

Order 15616.

384 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic244C211yesmaximal, characteristic, complemented
2#21448074C211yesmaximal, characteristic, complemented
3#21447856C211yesmaximal, characteristic, complemented
4#21443867C211yesmaximal, characteristic, complemented
5#21443782C211yesmaximal, characteristic, complemented
6D4⋊#11758185C211yesmaximal, characteristic, complemented
7C61×#1667C211yesmaximal, characteristic
8C22×Dic244—21no—
9D4×Dic122—21no—
10C2×#14519721—22no—
11C2×#14519721—21no—
12#16840142C2211yescharacteristic
13#16840003—21no—
14#16839973—21no—
15#16839920—22no—
16C4×Dic244C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839563—21no—
19C4×#11758185C2211yescharacteristic
20C61×#493C2211yescharacteristic
21C61×#459—21no—
22C8×D4×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic
24C61×#331—21no—
25C22×Dic122—22no—
26C2×Dic244—22no—
27C2×Dic244—21no—
28C2×Dic244—42no—
29C2×Dic244—42no—
30C2×Dic244D411yescharacteristic
31C2×Dic244D412yes—
32#14519777—21no—
33#14519776—41no—
34#14519756—22no—
35#14519754—42no—
36C4×Dic122—21no—
37D4×Dic61—41no—
38#14519721—44no—
39#14519721—42no—
40C2×#11758185—21no—
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519702—22no—
44#14519702—21no—
45C2×D8×C61—21no—
46C2×D8×C61—21no—
47C2×D8×C61—41no—
48C22×C8×C61—21no—
49#127×C61—21no—
50C4×D4×C61D411yescharacteristic
51C4⋊C8×C61—21no—
52C4⋊C8×C61D411yescharacteristic
53#102×C61—41no—
54C22⋊C8×C61—21no—
55C4×C8×C61C2311yescharacteristic
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C2×D4×C61D811yescharacteristic
60C22×C4×C61—21no—
61C22×Dic61—42no—
62C2×Dic122—21no—
63C2×Dic122—22no—
64C2×Dic122—44no—
65C2×Dic122—42no—
66C2×Dic122—82no—
67D8×C61—42no—
68D8×C61—41no—
69D8×C61—41no—
70D8×C61—82no—
71C2×C8×C61—21no—
72C2×C8×C61—41no—
73C2×C8×C61—41no—
74C2×C8×C61—41no—
75C2×C8×C61C2×D411yescharacteristic
76C2×C8×C61C2×D411yescharacteristic
77C4⋊C4×C61D811yescharacteristic
78C22⋊C4×C61—21no—
79C42×C61C2×D411yescharacteristic
80C22⋊Dic61—42no—
81C4⋊Dic61—21no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84#11758196—42no—
85#11758196—41no—
86C4×Dic61—41no—
87Dic244—21no—
88Dic244—42no—
89Dic244—44no—
90Dic244—41no—
91Dic244—41no—
92Dic244D812yescomplemented
93#11758185—22no—
94#11758185—41no—
95C23×C61—21no—
96C23×C61—81no—
97D4×C61—21no—
98D4×C61—81no—
99D4×C61—81no—
100D4×C61—81no—
101D4×C61—81no—
102D4×C61—161no—
103D4×C61SD3212yescomplemented
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61#12011yescharacteristic
108C2×C4×C61C2×D811yescharacteristic
109C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—42no—
113C2×Dic61—84no—
114Dic122—22no—
115Dic122—41no—
116Dic122—42no—
117Dic122—42no—
118Dic122—84no—
119C8×C61—21no—
120C8×C61—41no—
121C8×C61—81no—
122C8×C61C2×D811yescharacteristic
123C8×C61AGL(1,ℤ/8)11yescharacteristic
124#12318—611nomaximal, Sylow
125C22×C61—22no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61—161no—
129C22×C61—161no—
130C22×C61—161no—
131C22×C61#44711yescharacteristic
132C4×C61—21no—
133C4×C61—41no—
134C4×C61#44711yescharacteristic
135C4×C61#45311yescharacteristic
136C4×C61C2×SD3211yescharacteristic
137C4×C61#51011yescharacteristic
138Dic61—42no—
139Dic61—82no—
140Dic61—81no—
141D4×Q16—611no—
142#2248—611no—
143#2207—611no—
144#1667D6111yescharacteristic
145#1362—611no—
146#1332—611no—
147D4⋊C16—611no—
148C2×C61—42no—
149C2×C61—321no—
150C2×C61#161911yescharacteristic
151C2×C61#218511yescharacteristic
152C2×C61#219311yescharacteristic
153C22×Q16—1221no—
154D4×Q8—1221no—
155C2×SD32—1221no—
156C2×SD32—1222no—
157#494—611no—
158#493C2×D6111yescharacteristic
159#467—1221no—
160#462—1221no—
161#459—21no—
162#451—1222no—
163C4×Q16—611no—
164C8×D4C2×D6111yescharacteristic
165C4⋊C16—611no—
166#357—1221no—
167C4×C16—611no—
168#335C2×D6111yescharacteristic
169#331—21no—
170C61#1231811yescharacteristic, complemented, Sylow
171C22×Q8—1222no—
172C2×Q16—611no—
173C2×Q16—612no—
174C2×Q16—1222no—
175C2×Q16—1221no—
176C2×Q16—2442no—
177C2×Q16—2442no—
178C2×D8—21no—
179C2×D8—21no—
180C2×D8—41no—
181C22×C8—21no—
182C4⋊Q8—1221no—
183C4⋊Q8—2441no—
184#127—21no—
185C22⋊Q8—1222no—
186C22⋊Q8—2442no—
187C4×Q8—1221no—
188C4×D4—2441no—
189C4×D4C22⋊D6111yescharacteristic
190SD32—2444no—
191SD32—2442no—
192C2×C16—1221no—
193C2×C16—1221no—
194#107—611no—
195C4⋊C8—21no—
196C4⋊C8C22⋊D6111yescharacteristic
197#103—1222no—
198#103—1221no—
199#102—41no—
200C22⋊C8—21no—
201C4×C8C22×D6111yescharacteristic
202C2×Q8—1221no—
203C2×Q8—1222no—
204C2×Q8—4882no—
205C2×Q8—2442no—
206C2×Q8—2444no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4#1175819911yescharacteristic
211C22×C4—21no—
212C22×C4—2442no—
213Q16—612no—
214Q16—1221no—
215Q16—2442no—
216Q16—2444no—
217Q16—2441no—
218Q16—2441no—
219D8—42no—
220D8—41no—
221D8—41no—
222D8—82no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8D4×D6111yescharacteristic
228C2×C8D4×D6111yescharacteristic
229C4⋊C4—1221no—
230C4⋊C4—2442no—
231C4⋊C4—2441no—
232C4⋊C4—2441no—
233C4⋊C4—2441no—
234C4⋊C4#1175819911yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—2442no—
237C42—2441no—
238C42C2×C22⋊D6111yescharacteristic
239C16—1222no—
240C16—2441no—
241C23—21no—
242C23—81no—
243Q8—1222no—
244Q8—4884no—
245Q8—2442no—
246Q8—2442no—
247Q8—2441no—
248D4—21no—
249D4—81no—
250D4—81no—
251D4—81no—
252D4—81no—
253D4—161no—
254D4#1451972112yescomplemented
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—4884no—
259C2×C4—2441no—
260C2×C4—2442no—
261C2×C4—2441no—
262C2×C4#1451974511yescharacteristic
263C2×C4C2×#1175819911yescharacteristic
264C2×C4#1451980211yescharacteristic
265C8—21no—
266C8—41no—
267C8—81no—
268C8D8×D6111yescharacteristic
269C8#1451980111yescharacteristic
270C22—22no—
271C22—41no—
272C22—41no—
273C22—161no—
274C22—161no—
275C22—161no—
276C22#1683989511yescharacteristic
277C4—21no—
278C4—41no—
279C4—4882no—
280C4—4881no—
281C4—2442no—
282C4#1683989411yescharacteristic
283C4#1683992811yescharacteristic
284C4C2×#1451972111yescharacteristic
285C4#1684020211yescharacteristic
286C2—42no—
287C2—321no—
288C2#2144487211yescharacteristic
289C2#2144773511yescharacteristic
290C2#2144778111yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
Fitting, prime radicalC61×#1667C2
socleC22×C61#447
hypercenter#1667D61
hypocenterC61#12318
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1667

Complements

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

NH ≅ G/Ntype
1. D4×Dic244C2semidirect
2. #21448074C2semidirect
3. #21447856C2semidirect
4. #21443867C2semidirect
5. #21443782C2semidirect
6. D4⋊#11758185C2semidirect
92. Dic244D8semidirect
103. D4×C61SD32semidirect
170. C61#12318semidirect
254. D4#14519721semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2442
#214480742
#214478562
#214438672
#214437822
D4⋊#117581852
C61×#16672
#1231861