Finite Group Databasebeta

← #30603935

Subgroups — #30603935

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#21460755C212yesmaximal, complemented
4#21460740C212yesmaximal
5C2×#16839822C211yesmaximal, characteristic
6#16840683—21no—
7#16840683—21no—
8C22⋊#11758187C2212yes—
9C22⋊#11758187C2212yes—
10#16840651—21no—
11#16840648—21no—
12C2×#14519734C411yescharacteristic
13#16839822—21no—
14#16839822—21no—
15#16839822—21no—
16#16839822—21no—
17C2×C4⋊#92418C2211yescharacteristic
18C2×#14519689C411yescharacteristic
19C2×#14519689C2211yescharacteristic
20C2×#14519687C411yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C2×C4⋊C8×C61C411yescharacteristic
23C2×#11758187—22no—
24C2×#11758187—22no—
25C22×C4×D61C2×C411yescharacteristic
26C22×#92418C2×C411yescharacteristic
27C22×#92418C2311yescharacteristic
28#14519734—21no—
29#14519734—21no—
30#14519734—21no—
31#14519734—21no—
32C2×#11758196C811yescharacteristic
33C2×#11758196C811yescharacteristic
34C2×#11758198C811yescharacteristic
35C2×#11758198C811yescharacteristic
36C2×C4×Dic61C2×C411yescharacteristic
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39#14519689—21no—
40#14519689—21no—
41#14519689—21no—
42#14519689—21no—
43#14519687—21no—
44#14519687—21no—
45C8×Dic61D411yescharacteristic
46C8×Dic61D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C22×C8×C61C2×C411yescharacteristic
50C22×C8×C61C2×C411yescharacteristic
51C2×C42×C61C2×C411yescharacteristic
52C4⋊C8×C61—21no—
53C4⋊C8×C61—21no—
54C23×D61C2×C811yescharacteristic
55C22×C4×C61C2×C811yescharacteristic
56C22×C4×C61C2×C811yescharacteristic
57C22×C4×C61C22×C411yescharacteristic
58C22×Dic61C2×C811yescharacteristic
59C22×Dic61C2×C811yescharacteristic
60C22×Dic61C2×C811yescharacteristic
61C2×C4×D61—21no—
62C2×C4×D61—21no—
63C2×C4×D61—41no—
64C2×C4×D61—41no—
65C2×C8×C61—21no—
66C2×C8×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61C22⋊C411yescharacteristic
69C2×C8×C61C22⋊C411yescharacteristic
70C42×C61—21no—
71C42×C61—21no—
72#11758198—21no—
73#11758198—21no—
74#11758198—21no—
75#11758198—21no—
76#11758196—21no—
77#11758196—21no—
78#11758196—21no—
79#11758196—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×C61C22×C811yescharacteristic
92C22×D61—21no—
93C22×D61—22no—
94C22×D61—41no—
95C22×D61—41no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—22no—
101C2×C4×C61—41no—
102C2×C4×C61C2×C22⋊C411yescharacteristic
103C2×C4×C61C2×M1611yescharacteristic
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61C22⋊C811yescharacteristic
109C2×Dic61C22⋊C811yescharacteristic
110C2×Dic61C22⋊C811yescharacteristic
111C2×Dic61C22⋊C811yescharacteristic
112C4×D61—42no—
113C4×D61—41no—
114C4×D61—41no—
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×C61C2×C22⋊C811yescharacteristic
125C22×C61#50412yes—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—82no—
130C4×C61—21no—
131C4×C61—41no—
132C4×C61—41no—
133C4×C61#41011yescharacteristic
134C4×C61#41311yescharacteristic
135Dic61—21no—
136Dic61—21no—
137Dic61—21no—
138Dic61—21no—
139Dic61—41no—
140C2×#433—611no—
141#2163—611no—
142#2162—611no—
143#1322—612no—
144#1314—612no—
145C2×C61—22no—
146C2×C61#145811yescharacteristic
147C2×C61#211311yescharacteristic
148C2×C61#211511yescharacteristic
149D61—81no—
150C2×#117—611no—
151#433—1221no—
152#433—1221no—
153#433—1221no—
154#433—1221no—
155C2×C4⋊C8—611no—
156C2×C4⋊C8#692311yescharacteristic
157C2×C22⋊C8—611no—
158C2×C22⋊C8—611no—
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×C4—611no—
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×C42C2×#692311yescharacteristic
183C2×C16—1222no—
184C2×C16—1222no—
185C4⋊C8—21no—
186C4⋊C8—21no—
187C4⋊C8—1221no—
188C4⋊C8—1221no—
189C22⋊C8—1221no—
190C22⋊C8—1221no—
191C22⋊C8—1221no—
192C22⋊C8—1221no—
193#97—1221no—
194#97—1221no—
195C4×C8—611no—
196C4×C8—611no—
197C4×C8—611no—
198C4×C8—611no—
199C24—611no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—1221no—
204C22×C4—1221no—
205C22×C4—2441no—
206C22×C4—2441no—
207C22×C4D61⋊C811yescharacteristic
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—21no—
229C42—21no—
230C42—611no—
231C42—611no—
232C42—611no—
233C42—611no—
234C16—2442no—
235C16—2442no—
236C23—1222no—
237C23—1221no—
238C23—2441no—
239C23—2441no—
240C23C2×D61⋊C811yescharacteristic
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—611no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—611no—
251C2×C4—1222no—
252C2×C4—1221no—
253C2×C4—2442no—
254C2×C4—2441no—
255C2×C4—2441no—
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—4882no—
269C22—2441no—
270C22—2441no—
271C22—2441no—
272C22D61⋊(C22⋊C8)11yescharacteristic
273C22#1684082112yes—
274C4—21no—
275C4—41no—
276C4—41no—
277C4—1221no—
278C4—1221no—
279C4—1221no—
280C4—1221no—
281C4—2441no—
282C4#1684074311yescharacteristic
283C4#1684074911yescharacteristic
284C2—22no—
285C2—4881no—
286C2#2146105311yescharacteristic
287C2#2146205011yescharacteristic
288C2#2146205611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4⋊C8×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC23×D61C2×C8
cosocleC22×#92418C23
hypercenterC2×C4⋊C8#6923
hypocenterC61#11461
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #21462181C2semidirect
2. #21462177C2semidirect
3. #21460755C2semidirect
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
#214607552
#214607402
C2×#168398222
#1146161