Finite Group Databasebeta

← #30603933

Subgroups — #30603933

Order 15616.

320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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#21462181C211yesmaximal, characteristic, complemented
2#21462177C211yesmaximal, characteristic, complemented
3#21460756C212yesmaximal, complemented
4#21460739C212yesmaximal
5C2×#16839820C211yesmaximal, characteristic
6#16840683—21no—
7#16840683—21no—
8C22⋊#11758187C2212yes—
9C22⋊#11758187C2212yes—
10#16840651—21no—
11#16840648—21no—
12C2×#14519736C411yescharacteristic
13#16839820—21no—
14#16839820—21no—
15#16839820—21no—
16#16839820—21no—
17C2×#14519706C411yescharacteristic
18C2×#14519706C2211yescharacteristic
19C2×C22⋊#92418C2211yescharacteristic
20C2×#14519687C411yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C2×C22⋊C8×C61C411yescharacteristic
23C2×#11758187—22no—
24C2×#11758187—22no—
25C22×#92418C2×C411yescharacteristic
26C22×#92418C2311yescharacteristic
27#14519736—21no—
28#14519736—21no—
29#14519736—21no—
30#14519736—21no—
31C2×C4⋊Dic61C811yescharacteristic
32C2×C4⋊Dic61C811yescharacteristic
33C2×C22⋊Dic61C811yescharacteristic
34C2×C22⋊Dic61C811yescharacteristic
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61C2×C411yescharacteristic
37#14519706—21no—
38#14519706—21no—
39#14519706—21no—
40#14519706—21no—
41C22⋊#92418—21no—
42C22⋊#92418—21no—
43#14519687—21no—
44#14519687—21no—
45C8×Dic61D411yescharacteristic
46C8×Dic61D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C23×C4×C61C2×C411yescharacteristic
50C22×C8×C61C2×C411yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52C22⋊C8×C61—21no—
53C22⋊C8×C61—21no—
54C24×C61C2×C811yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61C2×C811yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61C2×C811yescharacteristic
62C22×Dic61C2×C811yescharacteristic
63C22×Dic61C2×C811yescharacteristic
64C22×Dic61C2×C811yescharacteristic
65C2×C8×C61—21no—
66C2×C8×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61C22⋊C411yescharacteristic
69C2×C8×C61C22⋊C411yescharacteristic
70C22⋊Dic61—21no—
71C22⋊Dic61—21no—
72C22⋊Dic61—21no—
73C22⋊Dic61—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61—21no—
76C4⋊Dic61—21no—
77C4⋊Dic61—21no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61C22⋊C411yescharacteristic
81C4×Dic61C22⋊C411yescharacteristic
82C4×Dic61M1611yescharacteristic
83C4×Dic61M1611yescharacteristic
84C2×#92418—21no—
85C2×#92418—41no—
86C2×#92418—41no—
87C2×#92418C2×D411yescharacteristic
88C2×#92418C2×D411yescharacteristic
89#11758187—42no—
90#11758187—42no—
91C23×C61—21no—
92C23×C61—22no—
93C23×C61—41no—
94C23×C61—41no—
95C23×C61C22×C811yescharacteristic
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—42no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61C2×C22⋊C411yescharacteristic
104C2×C4×C61C2×M1611yescharacteristic
105C2×Dic61—22no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—22no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61C22⋊C811yescharacteristic
112C2×Dic61C22⋊C811yescharacteristic
113C2×Dic61C22⋊C811yescharacteristic
114C2×Dic61C22⋊C811yescharacteristic
115C8×C61—21no—
116C8×C61—21no—
117C8×C61—41no—
118#92418—21no—
119#92418—21no—
120#92418—41no—
121#11461—611nomaximal, Sylow
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—82no—
128C22×C61C2×C22⋊C811yescharacteristic
129C22×C61#50412yes—
130C4×C61—21no—
131C4×C61—41no—
132C4×C61#41011yescharacteristic
133C4×C61#41311yescharacteristic
134Dic61—21no—
135Dic61—21no—
136Dic61—21no—
137Dic61—21no—
138Dic61—41no—
139Dic61—41no—
140C2×#433—611no—
141#2163—611no—
142#2162—611no—
143#1322—612no—
144#1314—612no—
145C2×C61—22no—
146C2×C61—81no—
147C2×C61#145811yescharacteristic
148C2×C61#211311yescharacteristic
149C2×C61#211511yescharacteristic
150C2×#117—611no—
151#433—1221no—
152#433—1221no—
153#433—1221no—
154#433—1221no—
155C2×C4⋊C8—611no—
156C2×C4⋊C8—611no—
157C2×C22⋊C8—611no—
158C2×C22⋊C8#692311yescharacteristic
159C2×#97—611no—
160C2×C4×C8—611no—
161C4⋊C16—1221no—
162C4⋊C16—1221no—
163C22⋊C16—612no—
164C22⋊C16—612no—
165#346—1221no—
166C4×C16—1221no—
167C61#1146111yescharacteristic, complemented, Sylow
168C23×C4C2×#692311yescharacteristic
169C22×C8—611no—
170C22×C8—611no—
171C22×C8C2×#692311yescharacteristic
172C22×C8C2×#692311yescharacteristic
173#117—1221no—
174#117—1221no—
175#117—1221no—
176#117—1221no—
177C2×C4⋊C4—611no—
178C2×C4⋊C4—611no—
179C2×C22⋊C4—611no—
180C2×C22⋊C4—611no—
181C2×C42—611no—
182C2×C42—611no—
183C2×C16—1222no—
184C2×C16—1222no—
185C4⋊C8—1221no—
186C4⋊C8—1221no—
187C4⋊C8—1221no—
188C4⋊C8—1221no—
189C22⋊C8—21no—
190C22⋊C8—21no—
191C22⋊C8—1221no—
192C22⋊C8—1221no—
193#97—1221no—
194#97—1221no—
195C4×C8—611no—
196C4×C8—611no—
197C4×C8—611no—
198C4×C8—611no—
199C24D61⋊C811yescharacteristic
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4D61⋊C811yescharacteristic
209C22×C4C22×#692311yescharacteristic
210C2×C8—21no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—611no—
214C2×C8—611no—
215C2×C8—1221no—
216C2×C8—2441no—
217C2×C8—2441no—
218C2×C8C22⋊#692311yescharacteristic
219C2×C8C22⋊#692311yescharacteristic
220C4⋊C4—1221no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4—1221no—
224C22⋊C4—1221no—
225C22⋊C4—1221no—
226C22⋊C4—1221no—
227C22⋊C4—1221no—
228C42—611no—
229C42—611no—
230C42—611no—
231C42—611no—
232C42—1221no—
233C42—1221no—
234C16—2442no—
235C16—2442no—
236C23—21no—
237C23—22no—
238C23—41no—
239C23—41no—
240C23C2×D61⋊C811yescharacteristic
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—611no—
251C2×C4—611no—
252C2×C4—1222no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1222no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4C2×C22⋊#692311yescharacteristic
259C2×C4D61⋊M1611yescharacteristic
260C8—21no—
261C8—21no—
262C8—41no—
263C8—1221no—
264C8—1221no—
265C8—2441no—
266C22—21no—
267C22—21no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—82no—
272C22D61⋊(C22⋊C8)11yescharacteristic
273C22#1684082112yes—
274C4—21no—
275C4—41no—
276C4—1221no—
277C4—1221no—
278C4—1221no—
279C4—1221no—
280C4—2441no—
281C4—2441no—
282C4#1684074211yescharacteristic
283C4#1684074911yescharacteristic
284C2—22no—
285C2—81no—
286C2#2146105111yescharacteristic
287C2#2146205011yescharacteristic
288C2#2146205611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC24×C61C2×C8
cosocleC22×#92418C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#11461
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #21462181C2semidirect
2. #21462177C2semidirect
3. #21460756C2semidirect
167. C61#11461semidirect

Maximal subgroups

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

subgroupindex
#214621812
#214621772
#214607562
#214607392
C2×#168398202
#1146161