Finite Group Databasebeta

← #30604533

Subgroups — #30604533

Order 15616.

430 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 106 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
1#21462179C211yesmaximal, characteristic, complemented
2#21462178C211yesmaximal, characteristic, complemented
3#21460770C212yesmaximal, complemented
4D4⋊#11758187C212yesmaximal, complemented
5C8×D4×D61C211yesmaximal, characteristic
6#16840683—21no—
7C4⋊#11758187C2212yescomplemented
8#16840657—21no—
9#16840657—21no—
10#16840648—21no—
11C4×#11758187C2212yescomplemented
12C22×C8×D61—21no—
13C4×D4×D61C411yescharacteristic
14C8×D244C411yescharacteristic
15D4×#92418C2211yescharacteristic
16#16839827C2211yescharacteristic
17C8×C22⋊D61—21no—
18#16839825—21no—
19C4⋊C8×D61C411yescharacteristic
20C22⋊C8×D61—21no—
21C4×C8×D61C2211yescharacteristic
22C8×D4×C61C411yescharacteristic
23C2×#11758187—22no—
24C2×#11758187—22no—
25C2×D4×D61C811yescharacteristic
26C22×C4×D61—21no—
27C22×#92418—21no—
28C2×C8×D61—21no—
29C2×C8×D61—21no—
30C2×C8×D61—21no—
31C2×C8×D61—44no—
32C2×C8×D61D411yescharacteristic
33C2×C8×D61D411yescharacteristic
34C4×D244C2×C411yescharacteristic
35D4×Dic61C811yescharacteristic
36#14519739C811yescharacteristic
37C4×C22⋊D61—21no—
38#14519737—21no—
39C4⋊C4×D61C811yescharacteristic
40C22⋊C4×D61—21no—
41C42×D61C2×C411yescharacteristic
42C4⋊#92418C2×C411yescharacteristic
43#14519706—21no—
44C22⋊#92418—21no—
45#14519689—21no—
46#14519689—21no—
47C4×#92418C2311yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61D411yescharacteristic
50C22×C8×C61—21no—
51C4×D4×C61C2×C411yescharacteristic
52C4⋊C8×C61C2×C411yescharacteristic
53C22⋊C8×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C23×D61—21no—
56C2×D4×C61C2×C811yescharacteristic
57C22×C4×C61—21no—
58C2×C22⋊D61—21no—
59C22×Dic61—21no—
60D4×D61—22no—
61D4×D61C1614yescomplemented
62C2×D244C2×C811yescharacteristic
63C2×C4×D61—21no—
64C2×C4×D61—21no—
65C2×C4×D61—21no—
66C2×C4×D61—42no—
67C2×C4×D61—42no—
68C2×C4×D61C22⋊C411yescharacteristic
69C2×C4×D61C2×C811yescharacteristic
70C2×C4×D61M1611yescharacteristic
71C2×C8×C61—21no—
72C2×C8×C61—42no—
73C2×C8×C61C22⋊C411yescharacteristic
74C2×C8×C61C22⋊C411yescharacteristic
75C4⋊C4×C61C2×C811yescharacteristic
76C22⋊C4×C61—21no—
77C42×C61C22×C411yescharacteristic
78C22⋊Dic61—21no—
79#11758198—21no—
80#11758198—21no—
81C4⋊Dic61C2×C811yescharacteristic
82#11758196—21no—
83C4×Dic61C22⋊C411yescharacteristic
84C4×Dic61C2×C811yescharacteristic
85C4×Dic61M1611yescharacteristic
86C2×#92418—21no—
87C2×#92418—42no—
88C2×#92418C2×D411yescharacteristic
89C2×#92418C2×D411yescharacteristic
90C8×D61—22no—
91C8×D61—41no—
92C8×D61—42no—
93C8×D61—42no—
94C8×D61—42no—
95#11758187—42no—
96#11758187—42no—
97C23×C61—21no—
98C22×D61—21no—
99C22×D61—24no—
100C22×D61—42no—
101C22×D61—42no—
102C22×D61C22⋊C811yescharacteristic
103D4×C61—21no—
104D4×C61C2×C1612yes—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61C2×C22⋊C411yescharacteristic
109C2×C4×C61C22×C811yescharacteristic
110C2×C4×C61C2×M1611yescharacteristic
111C22⋊D61—24no—
112C2×Dic61—21no—
113C2×Dic61—42no—
114C2×Dic61C22⋊C811yescharacteristic
115C2×Dic61C22⋊C811yescharacteristic
116C2×Dic61C22⋊C811yescharacteristic
117D244—21no—
118D244C2×C1612yes—
119C4×D61—21no—
120C4×D61—21no—
121C4×D61—41no—
122C4×D61—42no—
123C4×D61—42no—
124C4×D61—41no—
125C4×D61—41no—
126C4×D61C2×C1612yes—
127C4×D61M3212yes—
128C8×C61—21no—
129C8×C61—21no—
130C8×C61—41no—
131#92418—21no—
132#92418—41no—
133#92418AGL(1,ℤ/8)12yes—
134#11629—611nomaximal, Sylow
135C22×C61—22no—
136C22×C61—41no—
137C22×C61—41no—
138C22×C61C2×C22⋊C811yescharacteristic
139C2×D61—21no—
140C2×D61—21no—
141C2×D61—22no—
142C2×D61—48no—
143C2×D61—41no—
144C2×D61—41no—
145C2×D61C22⋊C1612yes—
146C4×C61—21no—
147C4×C61—41no—
148C4×C61#41811yescharacteristic
149C4×C61#42111yescharacteristic
150C4×C61C22×C1611yescharacteristic
151C4×C61C2×M3211yescharacteristic
152Dic61—21no—
153Dic61—21no—
154Dic61—41no—
155Dic61C22⋊C1612yes—
156C2×C8×D4—611no—
157#2162—611no—
158#2162—611no—
159D4⋊C16—612no—
160D4⋊C16—612no—
161C2×C61—42no—
162C2×C61#147811yescharacteristic
163C2×C61C2×C22⋊C1611yescharacteristic
164C2×C61#211711yescharacteristic
165D61—22no—
166D61—42no—
167C23×C8—1221no—
168C2×C4×D4—611no—
169C8×D4—611no—
170C8×D4—611no—
171C8×D4—611no—
172C8×D4—1221no—
173C8×D4—1221no—
174C8×D4#692311yescharacteristic
175C2×C4⋊C8—611no—
176C2×C22⋊C8—1221no—
177C2×C4×C8—611no—
178C4⋊C16—612no—
179C4⋊C16—1221no—
180C22⋊C16—1221no—
181C22⋊C16—1221no—
182C4×C16—612no—
183C4×C16—1221no—
184C61#1162911yescharacteristic, complemented, Sylow
185C22×D4—611no—
186C23×C4—1221no—
187C22×C8—21no—
188C22×C8—611no—
189C22×C8—611no—
190C22×C8—1221no—
191C22×C8—1221no—
192C22×C8—1221no—
193C22×C8—1221no—
194C22×C8—2444no—
195C4×D4—611no—
196C4×D4—611no—
197C4×D4—611no—
198C4×D4—1221no—
199C4×D4—1221no—
200C4×D4C2×#692311yescharacteristic
201C2×C4⋊C4—611no—
202C2×C22⋊C4—1221no—
203C2×C42—611no—
204C2×C16—1222no—
205C2×C16—1222no—
206C4⋊C8—611no—
207C4⋊C8—1221no—
208C4⋊C8C2×#692311yescharacteristic
209C22⋊C8—21no—
210C22⋊C8—1221no—
211C22⋊C8—1221no—
212C22⋊C8—1221no—
213C4×C8—611no—
214C4×C8—611no—
215C4×C8—611no—
216C4×C8C2×#692311yescharacteristic
217C24—1221no—
218C2×D4—614no—
219C2×D4—611no—
220C2×D4—1222no—
221C2×D4—1221no—
222C2×D4D61⋊C811yescharacteristic
223C22×C4—21no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4—2442no—
232C22×C4—2442no—
233C2×C8—21no—
234C2×C8—42no—
235C2×C8—611no—
236C2×C8—611no—
237C2×C8—1222no—
238C2×C8—1221no—
239C2×C8—2441no—
240C2×C8—2442no—
241C2×C8—2442no—
242C2×C8—2442no—
243C2×C8—2442no—
244C2×C8C22⋊#692311yescharacteristic
245C2×C8C22⋊#692311yescharacteristic
246C4⋊C4—611no—
247C4⋊C4—1221no—
248C4⋊C4D61⋊C811yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—1221no—
251C22⋊C4—1221no—
252C22⋊C4—1221no—
253C42—611no—
254C42—611no—
255C42—611no—
256C42C22×#692311yescharacteristic
257C16—2442no—
258C16—2442no—
259C23—21no—
260C23—611no—
261C23—1224no—
262C23—1221no—
263C23—2442no—
264C23—2442no—
265D4—21no—
266D4—612no—
267D4—1224no—
268D4—1221no—
269D4D61⋊C1612yes—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—611no—
274C2×C4—612no—
275C2×C4—612no—
276C2×C4—611no—
277C2×C4—611no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—2441no—
282C2×C4—2442no—
283C2×C4—2442no—
284C2×C4—2442no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4C2×C22⋊#692311yescharacteristic
288C2×C4C2×D61⋊C811yescharacteristic
289C2×C4D61⋊M1611yescharacteristic
290C8—21no—
291C8—21no—
292C8—41no—
293C8—612no—
294C8—1221no—
295C8—2441no—
296C22—22no—
297C22—41no—
298C22—41no—
299C22—612no—
300C22—1221no—
301C22—1221no—
302C22—1222no—
303C22—2448no—
304C22—2441no—
305C22—2441no—
306C22D61⋊(C22⋊C8)11yescharacteristic
307C4—21no—
308C4—41no—
309C4—612no—
310C4—1221no—
311C4—1221no—
312C4—2441no—
313C4#1684075411yescharacteristic
314C4#1684075911yescharacteristic
315C4C2×D61⋊C1611yescharacteristic
316C4D61⋊M3211yescharacteristic
317C2—42no—
318C2—1222no—
319C2—2442no—
320C2#2146111911yescharacteristic
321C2D61⋊(C22⋊C16)11yescharacteristic
322C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC4×C61C22×C16
FrattiniC42C22×#6923
FittingC8×D4×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC2×D4×D61C8
cosocleC4×#92418C23
hypercenterC8×D4#6923
hypocenterC61#11629
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #21462179C2semidirect
2. #21462178C2semidirect
3. #21460770C2semidirect
4. D4⋊#11758187C2semidirect
7. C4⋊#11758187C22semidirect
11. C4×#11758187C22semidirect
61. D4×D61C16semidirect
184. C61#11629semidirect

Maximal subgroups

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

subgroupindex
#214621792
#214621782
#214607702
D4⋊#117581872
C8×D4×D612
#1162961