Finite Group Databasebeta

← #11796895

Subgroups — #11796895

Order 1152.

478 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×#63797C211yesmaximal, characteristic
2#10593762C211yesmaximal, characteristic, complemented
3#10590913C211yesmaximal, characteristic, complemented
4#10590065C214yesmaximal, complemented
5C2×#3802—21no—
6C2×C8×C3⋊D3C2211yescharacteristic
7C2×C3×D24—21no—
8C2×#3713C2212yes—
9#63818—21no—
10#63797—21no—
11#63797—21no—
12#63797C412yes—
13#63797C412yes—
14#63773C2212yescomplemented
15#63765—21no—
16#63764—21no—
17C3×#819—21no—
18#63578C2212yescomplemented
19C2×D3×D8—61no—
20D3×#108—61no—
21C22×D32—41no—
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C3×D12—22no—
24C2×#625—41no—
25#3802—22no—
26#3802—22no—
27#3802—41no—
28#3802—41no—
29C2×C32×C8D411yescharacteristic
30C2×C3⋊(C3⋊C8)C2311yescharacteristic
31C8×C3⋊D3C2×C411yescharacteristic
32C8×C3⋊D3C2×C411yescharacteristic
33C8×C3⋊D3D411yescharacteristic
34C8×C3⋊D3D411yescharacteristic
35C3×#208—22no—
36C3×D24—22no—
37C3×D24—22no—
38#3713—22no—
39#3713C2×C414yes—
40#3712—41no—
41#3710—41no—
42#3708—22no—
43C2×#361—91nomaximal, Sylow
44C2×D3×D4—62no—
45C2×C3×D8—61no—
46C2×#213—62no—
47D3×D8—62no—
48D3×D8—62no—
49D3×D8—62no—
50D3×D8—62no—
51D3×M16—62no—
52C2×D24—21no—
53C2×D3×C8—61no—
54C2×D3×C8—61no—
55C3×#108—61no—
56#822—62no—
57#819—21no—
58C22×C3⋊D3SD1611yescharacteristic
59C22×C3×D3—42no—
60C2×D32—42no—
61C2×D32—42no—
62C2×D32—84no—
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3SD1611yescharacteristic
65C4×C3⋊D3C22⋊C411yescharacteristic
66C4×C3⋊D3C22⋊C411yescharacteristic
67C4×C3⋊D3D811yescharacteristic
68C4×C3⋊D3D811yescharacteristic
69C3×D12—24no—
70C3×D12—42no—
71#625—42no—
72#625—42no—
73C32×C8C22⋊C411yescharacteristic
74C32×C8C22⋊C411yescharacteristic
75C3⋊(C3⋊C8)C22×C411yescharacteristic
76C3⋊(C3⋊C8)C2×D411yescharacteristic
77C3×C3⋊C8—42no—
78C22×D8—91no—
79C2×M32—91no—
80C2×#108—91no—
81#361—94no—
82C23×D3—122no—
83C2×C3×D4—62no—
84C2×#67—122no—
85D3×D4—64no—
86D3×D4—64no—
87D3×D4—122no—
88D3×D4—122no—
89C2×D12—22no—
90C2×C4×D3—61no—
91C2×C4×D3—61no—
92C3×D8—62no—
93C3×D8—62no—
94C3×M16—62no—
95C2×C3×C8—21no—
96C2×C3×C8—21no—
97#213—64no—
98#213—64no—
99#208—22no—
100C2×C3⋊C8—61no—
101C2×C3⋊C8—61no—
102D24—22no—
103D24—22no—
104ΓL(1,𝔽25)—122no—
105D3×C8—61no—
106D3×C8—61no—
107D3×C8—61no—
108D3×C8—61no—
109D3×C8—61no—
110D3×C8—61no—
111D3×C8—61no—
112D3×C8—61no—
113D3×C8—122no—
114C22×C32C2×SD1611yescharacteristic
115C2×C3⋊D3—22no—
116C2×C3⋊D3#10211yescharacteristic
117C2×C3⋊D3#10211yescharacteristic
118C2×C3×D3—44no—
119C2×C3×D3—84no—
120D32—84no—
121D32—84no—
122C32×C4C2×C22⋊C411yescharacteristic
123C32×C4C2×D811yescharacteristic
124C3⋊Dic3#10211yescharacteristic
125C3⋊Dic3#10211yescharacteristic
126C22×D4—181no—
127C2×D8—61no—
128C2×D8—92no—
129C2×D8—92no—
130C2×D8—92no—
131C2×D8—181no—
132C2×D8—181no—
133C2×M16—181no—
134C22×C8—91no—
135M32—92no—
136M32—181no—
137C2×C16—181no—
138#108—61no—
139#108—92no—
140C23×C3—122no—
141C22×D3—42no—
142C22×D3—61no—
143C22×D3—61no—
144C22×D3—124no—
145C22×D3—124no—
146C22×D3—248no—
147C3×D4—64no—
148C3×D4—122no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151#67—124no—
152#67—124no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155D12—24no—
156D12—42no—
157C4×D3—61no—
158C4×D3—61no—
159C4×D3—61no—
160C4×D3—61no—
161C4×D3—61no—
162C4×D3—61no—
163C4×D3—61no—
164C4×D3—61no—
165C3×C8—21no—
166C3×C8—21no—
167C3×C8—21no—
168C3×C8—21no—
169C3×C8—122no—
170C3⋊C8—42no—
171C3⋊C8—61no—
172C3⋊C8—61no—
173C3⋊C8—61no—
174C3⋊C8—61no—
175C2×C32—21no—
176C2×C32C2×#10211yescharacteristic
177C3⋊D3—21no—
178C3⋊D3#36112yescomplemented
179C3×D3—84no—
180C24—361no—
181C2×D4—62no—
182C2×D4—182no—
183C2×D4—182no—
184C2×D4—361no—
185C2×D4—361no—
186C2×D4—361no—
187C22×C4—91no—
188D8—62no—
189D8—62no—
190D8—94no—
191D8—182no—
192M16—62no—
193M16—361no—
194C2×C8—91no—
195C2×C8—91no—
196C2×C8—91no—
197C2×C8—91no—
198C2×C8—91no—
199C2×C8—361no—
200C2×C8GO+(4,𝔽2)11yescharacteristic
201C16—182no—
202C22×C3—21no—
203C22×C3—21no—
204C22×C3—124no—
205C22×C3—244no—
206C2×D3—44no—
207C2×D3—61no—
208C2×D3—61no—
209C2×D3—61no—
210C2×D3—61no—
211C2×D3—64no—
212C2×D3—84no—
213C2×D3—122no—
214C2×D3—248no—
215C2×D3—248no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—21no—
220Dic3—61no—
221Dic3—61no—
222Dic3—61no—
223Dic3—61no—
224C32C2×#36111yescharacteristic, complemented, Sylow
225C23—91no—
226C23—122no—
227C23—362no—
228C23—362no—
229C23—724no—
230D4—64no—
231D4—122no—
232D4—362no—
233D4—362no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—91no—
238C2×C4—91no—
239C2×C4C2×GO+(4,𝔽2)11yescharacteristic
240C8—91no—
241C8—91no—
242C8—122no—
243C8D32⋊C411yescharacteristic
244C8D32⋊C411yescharacteristic
245C2×C3—22no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—41no—
249C2×C3—244no—
250D3—62no—
251D3—62no—
252D3—62no—
253D3—84no—
254D3—121no—
255C22—91no—
256C22—91no—
257C22—124no—
258C22—182no—
259C22—244no—
260C22—724no—
261C22—724no—
262C22#6422711yescharacteristic
263C4—91no—
264C4—91no—
265C4#6422511yescharacteristic
266C4C2×D32⋊C411yescharacteristic
267C3—21no—
268C3—21no—
269C2—21no—
270C2—92no—
271C2—181no—
272C2—244no—
273C2#1059336511yescharacteristic
subgroupG/H
centerC2#10593365
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×#102
prime radicalC2×#63797C2
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32C2×#361
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10593762C2semidirect
3. #10590913C2semidirect
4. #10590065C2semidirect
14. #63773C22semidirect
18. #63578C22semidirect
178. C3⋊D3#361semidirect
224. C32C2×#361semidirect

Maximal subgroups

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

subgroupindex
C2×#637972
#105937622
#105909132
#105900652
C2×#3619