Finite Group Databasebeta

← #30604475

Subgroups — #30604475

Order 15616.

326 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 92 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
2C4×#14519852C211yesmaximal, characteristic, complemented
3Q8⋊#11758187C212yesmaximal, complemented
4#21460770C212yesmaximal, complemented
5#21454793C211yesmaximal, characteristic
6C2×#14519852—21no—
7C4⋊#11758187C2212yes—
8#16840657—21no—
9#16840651—21no—
10#16840648—21no—
11C4×#11758187C2212yes—
12#16840299C411yescharacteristic
13Q8×#92418C2211yescharacteristic
14#16839841C411yescharacteristic
15#16839835—21no—
16#16839827—21no—
17#16839827C2211yescharacteristic
18#16839822—21no—
19#16839818C411yescharacteristic
20#16839719—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#446C411yescharacteristic
23#14519852—24no—
24C2×#11758187—22no—
25C2×#11758187—22no—
26C2×#11758189—21no—
27C2×C8×D61—21no—
28C2×C8×D61D411yescharacteristic
29C2×C8×D61D411yescharacteristic
30#14519772—21no—
31#14519768C811yescharacteristic
32#14519766C811yescharacteristic
33#14519762—21no—
34#14519753C811yescharacteristic
35#14519752C811yescharacteristic
36C4×D244—21no—
37C4×D244C2×C411yescharacteristic
38#14519734—21no—
39C42×D61C2×C411yescharacteristic
40C4⋊#92418—21no—
41C4⋊#92418C2×C411yescharacteristic
42#14519689—21no—
43#14519689—21no—
44#14519689—21no—
45#14519687—21no—
46C4×#92418—21no—
47C4×#92418C2311yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61D411yescharacteristic
50C4×Q8×C61C2×C411yescharacteristic
51C4⋊C8×C61—21no—
52C4⋊C8×C61C2×C411yescharacteristic
53#97×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×Q8×C61C2×C811yescharacteristic
56C2×D244—21no—
57C2×D244C2×C811yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61C22⋊C411yescharacteristic
60C2×C4×D61C2×C811yescharacteristic
61C2×C4×D61M1611yescharacteristic
62C2×C8×C61—21no—
63C2×C8×C61C22⋊C411yescharacteristic
64C2×C8×C61C22⋊C411yescharacteristic
65C4⋊C4×C61—21no—
66C4⋊C4×C61C2×C811yescharacteristic
67C42×C61—21no—
68C42×C61C22×C411yescharacteristic
69#11758198—21no—
70#11758198—21no—
71#11758198—21no—
72#11758198—21no—
73#11758198—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61C2×C811yescharacteristic
76#11758196—21no—
77#11758196—21no—
78C4×Dic61C22⋊C411yescharacteristic
79C4×Dic61C2×C811yescharacteristic
80C4×Dic61M1611yescharacteristic
81C2×#92418—21no—
82C2×#92418C2×D411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84#11758189—42no—
85C8×D61—22no—
86C8×D61—22no—
87C8×D61—42no—
88#11758187—24no—
89#11758187—42no—
90C22×D61—21no—
91C22×D61C22⋊C811yescharacteristic
92Q8×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61C22×C811yescharacteristic
97C2×C4×C61C2×M1611yescharacteristic
98C2×Dic61—21no—
99C2×Dic61C22⋊C811yescharacteristic
100C2×Dic61C22⋊C811yescharacteristic
101C2×Dic61C22⋊C811yescharacteristic
102D244—22no—
103D244—42no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—22no—
107C4×D61—41no—
108C4×D61—41no—
109C4×D61—41no—
110C8×C61—21no—
111C8×C61—41no—
112C8×C61#10412yes—
113#92418—21no—
114#92418—41no—
115#92418#13512yes—
116#11614—611nomaximal, Sylow
117C22×C61C2×C22⋊C811yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61—21no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—41no—
124C4×C61—21no—
125C4×C61—41no—
126C4×C61—41no—
127C4×C61#41611yescharacteristic
128C4×C61C2×#10411yescharacteristic
129C4×C61#50412yes—
130Dic61—21no—
131Dic61—21no—
132Dic61—21no—
133Dic61—41no—
134#2966—611no—
135#2162—611no—
136C4×M32—611no—
137Q8⋊C16—612no—
138D4⋊C16—612no—
139C2×C61#147611yescharacteristic
140C2×C61#211311yescharacteristic
141C2×C61#211711yescharacteristic
142D61—41no—
143D61—81no—
144#529—611no—
145C2×M32—1221no—
146#446#692311yescharacteristic
147C8×Q8—611no—
148#436—611no—
149#435—1221no—
150C8×D4—611no—
151C8×D4—1221no—
152#433—1221no—
153#432—611no—
154#405—1221no—
155C2×C4×C8—611no—
156C4⋊C16—612no—
157C22⋊C16—1221no—
158#346—1221no—
159C4×C16—612no—
160C4×C16—1221no—
161C61#1161411yescharacteristic, complemented, Sylow
162C2×M16—1221no—
163C22×C8—611no—
164C22×C8—611no—
165C22×C8—1221no—
166#126—1221no—
167#125—611no—
168#124—611no—
169#123—1221no—
170C22⋊Q8—611no—
171#121—611no—
172C4×Q8C2×#692311yescharacteristic
173C4×D4—611no—
174C4×D4—1221no—
175#117—1221no—
176C2×C42—611no—
177M32—1224no—
178C2×C16—1222no—
179C2×C16—1222no—
180C4⋊C8—21no—
181C4⋊C8—611no—
182C4⋊C8—1221no—
183C4⋊C8C2×#692311yescharacteristic
184C22⋊C8—1221no—
185C22⋊C8—1221no—
186C22⋊C8—1221no—
187#97—21no—
188#97—1221no—
189C4×C8—611no—
190C4×C8—611no—
191C4×C8—611no—
192C4×C8—1221no—
193C4×C8C2×#692311yescharacteristic
194C2×Q8D61⋊C811yescharacteristic
195C2×D4—611no—
196C2×D4—1221no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—1221no—
201M16—2442no—
202C2×C8—21no—
203C2×C8—611no—
204C2×C8—611no—
205C2×C8—1222no—
206C2×C8—1222no—
207C2×C8—1221no—
208C2×C8—2442no—
209C2×C8C22⋊#692311yescharacteristic
210C2×C8C22⋊#692311yescharacteristic
211C4⋊C4—21no—
212C4⋊C4—611no—
213C4⋊C4—1221no—
214C4⋊C4—1221no—
215C4⋊C4—1221no—
216C4⋊C4D61⋊C811yescharacteristic
217C22⋊C4—1221no—
218C22⋊C4—1221no—
219C22⋊C4—1221no—
220C22⋊C4—1221no—
221C22⋊C4—1221no—
222C42—21no—
223C42—611no—
224C42—611no—
225C42—611no—
226C42C22×#692311yescharacteristic
227C16—1224no—
228C16—2442no—
229C23—611no—
230C23—1221no—
231Q8—22no—
232D4—1222no—
233D4—2442no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—611no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1222no—
242C2×C4—1221no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4C2×C22⋊#692311yescharacteristic
247C2×C4C2×D61⋊C811yescharacteristic
248C2×C4D61⋊M1611yescharacteristic
249C8—21no—
250C8—41no—
251C8—612no—
252C8—1221no—
253C8—2441no—
254C8#1451984212yes—
255C22—1221no—
256C22—1221no—
257C22—1221no—
258C22—2441no—
259C22—2441no—
260C22—2441no—
261C22D61⋊(C22⋊C8)11yescharacteristic
262C4—21no—
263C4—41no—
264C4—41no—
265C4—1221no—
266C4—1221no—
267C4—1221no—
268C4—2441no—
269C4#1684075211yescharacteristic
270C4C2×#1451984211yescharacteristic
271C4#1684082112yes—
272C2—4881no—
273C2—2441no—
274C2#2146111311yescharacteristic
275C2#2146205011yescharacteristic
276C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC61×#446C4
socleC22×C61C2×C22⋊C8
prime radical#14519752C8
cosocleC4×#92418C23
hypercenter#446#6923
hypocenterC61#11614
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #21462179C2semidirect
2. C4×#14519852C2semidirect
3. Q8⋊#11758187C2semidirect
4. #21460770C2semidirect
161. C61#11614semidirect

Maximal subgroups

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

subgroupindex
#214621792
C4×#145198522
Q8⋊#117581872
#214607702
#214547932
#1161461