Finite Group Databasebeta

← #11797369

Subgroups — #11797369

Order 1152.

303 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 303 conjugacy classes of subgroups — too many to draw. Only its 98 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#10590692C211yesmaximal, characteristic
2#10589368C211yesmaximal, characteristic, complemented
3C3×(C2×D3)⋊C16C211yesmaximal, characteristic
4C3×Dic3⋊C16C211yesmaximal, characteristic, complemented
5Dic3⋊(C3⋊C16)C211yesmaximal, characteristic, complemented
6(C2×D3)⋊(C3⋊C16)C211yesmaximal, characteristic
7#10589102C211yesmaximal, characteristic, complemented
8#69276—31nomaximal
9#69094—31nomaximal
10C2×C3×D3×C8C2211yescharacteristic
11#63855C411yescharacteristic
12C2×#3711C411yescharacteristic
13C2×C32×C16C2211yescharacteristic
14C8×C3⋊Dic3C2211yescharacteristic
15C2×C3⋊(C3⋊C16)C2211yescharacteristic
16C3×C8×Dic3C2211yescharacteristic
17C2×C3×C3⋊C16C2211yescharacteristic
18C2×C3×C3⋊C16C2211yescharacteristic
19#63555C411yescharacteristic
20#63554C411yescharacteristic
21#5101—31no—
22#4689—31no—
23C3×C4⋊C16—31no—
24C3×C22⋊C16—31no—
25#4549—31no—
26(C2×D3)⋊C16—31no—
27(C2×D3)⋊C16D311yescharacteristic
28#4502—31no—
29#4502—31no—
30#4502—61no—
31Dic3⋊C16—31no—
32Dic3⋊C16D311yescharacteristic, complemented
33Dic3×C16—31no—
34Dic3×C16—31no—
35C4⋊(C3⋊C16)—31no—
36C2×C3×C4×D3C2×C411yescharacteristic
37C2×C32×C8C2311yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
40C3×C4×Dic3C2×C411yescharacteristic
41C2×C3×C3⋊C8C2×C411yescharacteristic
42C2×C3×C3⋊C8C2×C411yescharacteristic
43C3×D3×C8—21no—
44C3×D3×C8—21no—
45Dic3⋊Dic3C811yescharacteristic
46Dic3⋊Dic3C811yescharacteristic
47(C2×D3)⋊Dic3C811yescharacteristic
48(C2×D3)⋊Dic3C811yescharacteristic
49#3711—22no—
50C32×C16—21no—
51C3⋊(C3⋊C16)—21no—
52C3×C3⋊C16—21no—
53C3×C3⋊C16—21no—
54#2164—91noSylow
55C22×C3×C8—31no—
56#926—31no—
57C2×#208—31no—
58C2×ΓL(1,𝔽25)—31no—
59C2×D3×C8C2×D311yescharacteristic
60#872—31no—
61C2×C3×C16—21no—
62C2×C3×C16—31no—
63C2×C3×C16—31no—
64C2×C3×C16C2×D311yescharacteristic
65C2×C3×C16C2×D311yescharacteristic
66C3×C4×C8—31no—
67#815—31no—
68#815—31no—
69#815—31no—
70C8×Dic3—31no—
71C8×Dic3—31no—
72C8×Dic3—61no—
73C8×Dic3C2×D311yescharacteristic
74C2×C3⋊C16—31no—
75C2×C3⋊C16—31no—
76C2×C3⋊C16—61no—
77C2×C3⋊C16C2×D311yescharacteristic
78C2×C3⋊C16C2×D311yescharacteristic
79#803—31no—
80C22×C3×D3C2×C811yescharacteristic
81C2×C32×C4C22×C411yescharacteristic
82C2×C3⋊Dic3C2×C811yescharacteristic
83C2×C3⋊Dic3C2×C811yescharacteristic
84C2×C3×Dic3C2×C811yescharacteristic
85C2×C3×Dic3C2×C811yescharacteristic
86C2×C3×Dic3C2×C811yescharacteristic
87C3×C4×D3—21no—
88C3×C4×D3—21no—
89C32×C8#4111yescharacteristic
90C32×C8#4111yescharacteristic
91C3⋊(C3⋊C8)M1612yes—
92C3×C3⋊C8—21no—
93C3×C3⋊C8—21no—
94#405—91no—
95C4⋊C16—31no—
96C4⋊C16—91no—
97C22⋊C16—31no—
98C22⋊C16—91no—
99#346—91no—
100C4×C16—91no—
101C22×C3×C4—31no—
102C2×C4×D3C4×D311yescharacteristic
103C2×C3×C8—21no—
104C2×C3×C8—31no—
105C2×C3×C8—31no—
106C2×C3×C8—61no—
107C2×C3×C8—61no—
108C2×C3×C8C22×D311yescharacteristic
109C2×C3×C8C22×D311yescharacteristic
110C3×C42—31no—
111#217—31no—
112#217—31no—
113(C2×D3)⋊C4—31no—
114(C2×D3)⋊C4—31no—
115C4⋊Dic3—31no—
116C4⋊Dic3—31no—
117Dic3⋊C4—31no—
118Dic3⋊C4—31no—
119C4×Dic3—31no—
120C4×Dic3—31no—
121C4×Dic3—61no—
122C4×Dic3C4×D311yescharacteristic
123#208—62no—
124C2×C3⋊C8—31no—
125C2×C3⋊C8—31no—
126C2×C3⋊C8—61no—
127C2×C3⋊C8C4×D311yescharacteristic
128C2×C3⋊C8C4×D311yescharacteristic
129ΓL(1,𝔽25)—62no—
130D3×C8—21no—
131D3×C8—21no—
132C3×C16—22no—
133C3×C16—21no—
134C3×C16—21no—
135C3×C16—61no—
136C3×C16—61no—
137C3⋊C16—21no—
138C3⋊C16—21no—
139C3⋊C16—62no—
140C3⋊C16—61no—
141C3⋊C16—61no—
142C22×C32C22×C811yescharacteristic
143C2×C3×D3—21no—
144C2×C3×D3—21no—
145C2×C3×D3—21no—
146C32×C4#11711yescharacteristic
147C32×C4C2×M1611yescharacteristic
148C3⋊Dic3—21no—
149C3⋊Dic3—21no—
150C3×Dic3—21no—
151C3×Dic3—21no—
152C3×Dic3—21no—
153C2×M16—91no—
154C22×C8—31no—
155#117—91no—
156C2×C16—31no—
157C2×C16—31no—
158C2×C16—91no—
159C2×C16D3211yescharacteristic
160#97—91no—
161#97—91no—
162C4×C8—31no—
163C4×C8—91no—
164C23×C3—31no—
165C22×D3D3×C811yescharacteristic
166C2×C3×C4—21no—
167C2×C3×C4—31no—
168C2×C3×C4—31no—
169C2×C3×C4—31no—
170C2×C3×C4—61no—
171C2×C3×C4—61no—
172C2×C3×C4C2×C4×D311yescharacteristic
173C2×C3×C4C2×C4×D311yescharacteristic
174C2×Dic3—31no—
175C2×Dic3—31no—
176C2×Dic3—31no—
177C2×Dic3—31no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3D3×C811yescharacteristic
181C2×Dic3D3×C811yescharacteristic
182C2×Dic3D3×C811yescharacteristic
183C4×D3—21no—
184C4×D3—21no—
185C3×C8—21no—
186C3×C8—21no—
187C3×C8—61no—
188C3×C8—61no—
189C3×C8#23711yescharacteristic
190C3×C8#23711yescharacteristic
191C3×C8#23711yescharacteristic
192C3×C8#23911yescharacteristic
193C3⋊C8—21no—
194C3⋊C8—21no—
195C3⋊C8—32no—
196C3⋊C8—32no—
197C3⋊C8—62no—
198C2×C32#43111yescharacteristic
199C2×C32#50411yescharacteristic
200C2×C32#50411yescharacteristic
201C3×D3—41no—
202C22×C4—31no—
203M16—182no—
204C2×C8—31no—
205C2×C8—31no—
206C2×C8—61no—
207C2×C8—61no—
208C2×C8—91no—
209C2×C8C2×D3211yescharacteristic
210C4⋊C4—91no—
211C4⋊C4—91no—
212C22⋊C4—91no—
213C22⋊C4—91no—
214C42—31no—
215C42—91no—
216C16—21no—
217C16—61no—
218C16—61no—
219C16—181no—
220C22×C3—21no—
221C22×C3—61no—
222C22×C3—61no—
223C22×C3—61no—
224C22×C3C2×D3×C811yescharacteristic
225C22×C3C2×D3×C811yescharacteristic
226C2×D3—21no—
227C2×D3—21no—
228C2×D3—21no—
229C3×C4—21no—
230C3×C4—21no—
231C3×C4—61no—
232C3×C4—61no—
233C3×C4—61no—
234C3×C4#87711yescharacteristic
235C3×C4#89211yescharacteristic
236C3×C4D3×M1611yescharacteristic
237C3×C4D3×M1611yescharacteristic
238Dic3—21no—
239Dic3—21no—
240Dic3—21no—
241Dic3—61no—
242Dic3—61no—
243Dic3—61no—
244Dic3—61no—
245Dic3—121no—
246Dic3—121no—
247C32#216411yescharacteristic, complemented, Sylow
248C23—31no—
249C2×C4—31no—
250C2×C4—31no—
251C2×C4—31no—
252C2×C4—61no—
253C2×C4—61no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4C4×D3211yescharacteristic
257C8—61no—
258C8—61no—
259C8—92no—
260C8#379611yescharacteristic
261C8#380511yescharacteristic
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—121no—
266C2×C3#471811yescharacteristic
267C2×C3#483311yescharacteristic
268C2×C3#490111yescharacteristic
269C2×C3#490111yescharacteristic
270C2×C3#490711yescharacteristic
271C2×C3#490711yescharacteristic
272D3—41no—
273C22—61no—
274C22—61no—
275C22—61no—
276C22D32×C811yescharacteristic
277C4—61no—
278C4—61no—
279C4—61no—
280C4—181no—
281C4—181no—
282C4#6379111yescharacteristic
283C4#6387811yescharacteristic
284C3—21no—
285C3#6909411yescharacteristic, complemented
286C3#6927611yescharacteristic, complemented
287C2—121no—
288C2#1059022811yescharacteristic
289C2#1059022811yescharacteristic
290C2#1059065611yescharacteristic
subgroupG/H
center, FrattiniC2×C8C2×D32
commutator, socleC22×C32C22×C8
FittingC2×C32×C16C22
prime radicalC22×C3×D3C2×C8
cosocleC2×C32×C8C23
hypercenterC2×C16D32
hypocenterC32#2164
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
2. #10589368C2semidirect
4. C3×Dic3⋊C16C2semidirect
5. Dic3⋊(C3⋊C16)C2semidirect
7. #10589102C2semidirect
32. Dic3⋊C16D3semidirect
247. C32#2164semidirect
285. C3#69094semidirect
286. C3#69276semidirect

Maximal subgroups

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

subgroupindex
#105906922
#105893682
C3×(C2×D3)⋊C162
C3×Dic3⋊C162
Dic3⋊(C3⋊C16)2
(C2×D3)⋊(C3⋊C16)2
#105891022
#692763
#690943