Finite Group Databasebeta

← #30604375

Subgroups — #30604375

Order 15616.

450 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 110 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#21462152C211yesmaximal, characteristic, complemented
2C4×#14519852C211yesmaximal, characteristic, complemented
3#21460770C212yesmaximal, complemented
4D4⋊#11758187C212yesmaximal, complemented
5C8×D4×D61C211yesmaximal, characteristic
6C2×#14519852—21no—
7C2×#14519852—21no—
8#16840683—21no—
9C4⋊#11758187C2212yescomplemented
10#16840651—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
23#14519852—24no—
24#14519852—42no—
25C2×#11758187—22no—
26C2×#11758187—22no—
27C2×D4×D61C811yescharacteristic
28C22×C4×D61—21no—
29C22×#92418—21no—
30C2×C8×D61—21no—
31C2×C8×D61—21no—
32C2×C8×D61—21no—
33C2×C8×D61—42no—
34C2×C8×D61—42no—
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C4×D244C2×C411yescharacteristic
38D4×Dic61C811yescharacteristic
39#14519739C811yescharacteristic
40C4×C22⋊D61—21no—
41#14519737—21no—
42C4⋊C4×D61C811yescharacteristic
43C22⋊C4×D61—21no—
44C42×D61C2×C411yescharacteristic
45C4⋊#92418C2×C411yescharacteristic
46#14519706—21no—
47C22⋊#92418—21no—
48#14519689—21no—
49#14519689—21no—
50C4×#92418C2311yescharacteristic
51C8×Dic61D411yescharacteristic
52C8×Dic61D411yescharacteristic
53C22×C8×C61—21no—
54C4×D4×C61C2×C411yescharacteristic
55C4⋊C8×C61C2×C411yescharacteristic
56C22⋊C8×C61—21no—
57C4×C8×C61C2×C411yescharacteristic
58C23×D61—21no—
59C2×D4×C61C2×C811yescharacteristic
60C22×C4×C61—21no—
61C2×C22⋊D61—21no—
62C22×Dic61—21no—
63D4×D61—22no—
64D4×D61—22no—
65C2×D244C2×C811yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—42no—
70C2×C4×D61—42no—
71C2×C4×D61C22⋊C411yescharacteristic
72C2×C4×D61C2×C811yescharacteristic
73C2×C4×D61M1611yescharacteristic
74C2×C8×C61—21no—
75C2×C8×C61—42no—
76C2×C8×C61C22⋊C411yescharacteristic
77C2×C8×C61C22⋊C411yescharacteristic
78C4⋊C4×C61C2×C811yescharacteristic
79C22⋊C4×C61—21no—
80C42×C61C22×C411yescharacteristic
81C22⋊Dic61—21no—
82#11758198—21no—
83#11758198—21no—
84C4⋊Dic61C2×C811yescharacteristic
85#11758196—21no—
86C4×Dic61C22⋊C411yescharacteristic
87C4×Dic61C2×C811yescharacteristic
88C4×Dic61M1611yescharacteristic
89C2×#92418—21no—
90C2×#92418—41no—
91C2×#92418—41no—
92C2×#92418C2×D411yescharacteristic
93C2×#92418C2×D411yescharacteristic
94C8×D61—22no—
95C8×D61—42no—
96C8×D61—42no—
97C8×D61—41no—
98C8×D61—41no—
99C8×D61D812yes—
100C8×D61SD1612yes—
101#11758187—24no—
102#11758187—42no—
103C23×C61—21no—
104C22×D61—24no—
105C22×D61—21no—
106C22×D61—42no—
107C22×D61—42no—
108C22×D61C22⋊C811yescharacteristic
109D4×C61—21no—
110D4×C61M3212yescomplemented
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61C2×C22⋊C411yescharacteristic
115C2×C4×C61C22×C811yescharacteristic
116C2×C4×C61C2×M1611yescharacteristic
117C22⋊D61—24no—
118C2×Dic61—21no—
119C2×Dic61—42no—
120C2×Dic61C22⋊C811yescharacteristic
121C2×Dic61C22⋊C811yescharacteristic
122C2×Dic61C22⋊C811yescharacteristic
123D244—21no—
124D244M3212yescomplemented
125C4×D61—21no—
126C4×D61—21no—
127C4×D61—41no—
128C4×D61—42no—
129C4×D61—41no—
130C4×D61—41no—
131C4×D61—42no—
132C4×D61#10212yes—
133C4×D61#10412yes—
134C8×C61—21no—
135C8×C61—41no—
136C8×C61#10212yes—
137#92418—21no—
138#92418—41no—
139#92418C2×D811yescharacteristic
140#92418C2×SD1611yescharacteristic
141#11583—611nomaximal, Sylow
142C22×C61—22no—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61C2×C22⋊C811yescharacteristic
146C2×D61—21no—
147C2×D61—21no—
148C2×D61—22no—
149C2×D61—48no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61D4⋊C812yes—
153C4×C61—21no—
154C4×C61—41no—
155C4×C61C2×#10211yescharacteristic
156C4×C61C2×#10411yescharacteristic
157C4×C61C2×M3211yescharacteristic
158C4×C61C2×M3211yescharacteristic
159Dic61—21no—
160Dic61—21no—
161Dic61—41no—
162Dic61D4⋊C812yes—
163C2×C8×D4—611no—
164#2150—611no—
165C4×M32—611no—
166D4⋊C16—612no—
167D4⋊C16—612no—
168C2×C61—42no—
169C2×C61C2×D4⋊C811yescharacteristic
170C2×C61#211211yescharacteristic
171C2×C61#211711yescharacteristic
172D61—22no—
173D61—42no—
174C23×C8—1221no—
175C2×C4×D4—611no—
176C2×M32—1221no—
177C2×M32—1221no—
178C8×D4—611no—
179C8×D4—611no—
180C8×D4—611no—
181C8×D4—1221no—
182C8×D4—1221no—
183C8×D4#692311yescharacteristic
184C2×C4⋊C8—611no—
185C2×C22⋊C8—1221no—
186C2×C4×C8—611no—
187C4⋊C16—612no—
188C4⋊C16—1221no—
189#346—1221no—
190C4×C16—612no—
191C61#1158311yescharacteristic, complemented, Sylow
192C22×D4—611no—
193C23×C4—1221no—
194C22×C8—21no—
195C22×C8—611no—
196C22×C8—611no—
197C22×C8—1221no—
198C22×C8—1221no—
199C22×C8—1221no—
200C22×C8—1221no—
201C22×C8—2442no—
202C22×C8—2442no—
203C4×D4—611no—
204C4×D4—611no—
205C4×D4—611no—
206C4×D4—1221no—
207C4×D4—1221no—
208C4×D4C2×#692311yescharacteristic
209C2×C4⋊C4—611no—
210C2×C22⋊C4—1221no—
211C2×C42—611no—
212M32—1224no—
213M32—2442no—
214C2×C16—1222no—
215C2×C16—1222no—
216C4⋊C8—611no—
217C4⋊C8—1221no—
218C4⋊C8C2×#692311yescharacteristic
219C22⋊C8—21no—
220C22⋊C8—1221no—
221C22⋊C8—1221no—
222C22⋊C8—1221no—
223C4×C8—611no—
224C4×C8—611no—
225C4×C8—611no—
226C4×C8C2×#692311yescharacteristic
227C24—1221no—
228C2×D4—611no—
229C2×D4—1221no—
230C2×D4—1222no—
231C2×D4—1222no—
232C2×D4D61⋊C811yescharacteristic
233C22×C4—21no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4—2442no—
242C22×C4—2442no—
243C2×C8—21no—
244C2×C8—42no—
245C2×C8—611no—
246C2×C8—612no—
247C2×C8—612no—
248C2×C8—611no—
249C2×C8—1222no—
250C2×C8—1221no—
251C2×C8—2441no—
252C2×C8—2441no—
253C2×C8—2442no—
254C2×C8—2441no—
255C2×C8—2441no—
256C2×C8—2442no—
257C2×C8C22⋊#692311yescharacteristic
258C2×C8C22⋊#692311yescharacteristic
259C4⋊C4—611no—
260C4⋊C4—1221no—
261C4⋊C4D61⋊C811yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C22⋊C4—1221no—
266C42—611no—
267C42—611no—
268C42—611no—
269C42C22×#692311yescharacteristic
270C16—1224no—
271C16—2442no—
272C23—21no—
273C23—611no—
274C23—1224no—
275C23—1221no—
276C23—2442no—
277C23—2442no—
278D4—21no—
279D4—612no—
280D4—1224no—
281D4—1221no—
282D4#1451985212yescomplemented
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—611no—
287C2×C4—612no—
288C2×C4—612no—
289C2×C4—611no—
290C2×C4—611no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—2441no—
295C2×C4—2442no—
296C2×C4—2442no—
297C2×C4—2442no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4C2×C22⋊#692311yescharacteristic
301C2×C4C2×D61⋊C811yescharacteristic
302C2×C4D61⋊M1611yescharacteristic
303C8—21no—
304C8—41no—
305C8—611no—
306C8—611no—
307C8—1221no—
308C8—2441no—
309C8#1451983912yes—
310C22—22no—
311C22—41no—
312C22—41no—
313C22—612no—
314C22—1221no—
315C22—1221no—
316C22—1222no—
317C22—2448no—
318C22—2441no—
319C22—2441no—
320C22D61⋊(C22⋊C8)11yescharacteristic
321C4—21no—
322C4—41no—
323C4—612no—
324C4—1221no—
325C4—1221no—
326C4—2441no—
327C4C2×#1451983911yescharacteristic
328C4D61⋊#10411yescharacteristic
329C4D61⋊M3211yescharacteristic
330C4C2×#1451985211yescharacteristic
331C2—42no—
332C2—1222no—
333C2—2442no—
334C2D61⋊(D4⋊C8)11yescharacteristic
335C2#2146204711yescharacteristic
336C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC8×D4×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC2×D4×D61C8
cosocleC4×#92418C23
hypercenterC8×D4#6923
hypocenterC61#11583
LCSG ▷ C2×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. #21462152C2semidirect
2. C4×#14519852C2semidirect
3. #21460770C2semidirect
4. D4⋊#11758187C2semidirect
9. C4⋊#11758187C22semidirect
11. C4×#11758187C22semidirect
110. D4×C61M32semidirect
124. D244M32semidirect
191. C61#11583semidirect
282. D4#14519852semidirect

Maximal subgroups

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

subgroupindex
#214621522
C4×#145198522
#214607702
D4⋊#117581872
C8×D4×D612
#1158361