Finite Group Databasebeta

← #11775886

Subgroups — #11775886

Order 1152.

484 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 55 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#10593972C211yesmaximal, characteristic
2#10593731C211yesmaximal, characteristic, complemented
3#10590322C211yesmaximal, characteristic, complemented
4#10590035C214yesmaximal, complemented
5C2×#3798C412yes—
6C42×C3⋊D3C2211yescharacteristic
7C3×C4×D12—21no—
8#63919C411yescharacteristic
9#63916—21no—
10#63915C2212yes—
11#63914C411yescharacteristic
12#63912—21no—
13C4×#625—21no—
14C2×#3710—21no—
15#63779—21no—
16#63778—21no—
17#63777C2212yes—
18C3×#803—21no—
19#63555C2212yes—
20#5548—61no—
21D3×#97—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×D12—21no—
26C2×C3×C4×D3—22no—
27C2×#627C2×C412yes—
28C2×#626—22no—
29C2×#625—21no—
30C2×#625C2×C412yes—
31#3798—44no—
32C2×#622—22no—
33C32×C42D411yescharacteristic
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C3×(C2×D3)⋊C4—22no—
38C3×C4⋊Dic3—21no—
39C2×C3×C3⋊C8—22no—
40#3724—21no—
41(C2×D3)⋊Dic3—22no—
42#3710—24no—
43#1530—91nomaximal, Sylow
44C2×#235—62no—
45C3×C4×D4—61no—
46#940—61no—
47#938—61no—
48C4×#67—62no—
49C2×D3×C8—62no—
50#895—61no—
51#888—61no—
52#885—62no—
53#884—62no—
54C4×D12—21no—
55C42×D3—61no—
56C42×D3—61no—
57C3×#97—61no—
58#815—62no—
59#803—21no—
60C22×C3⋊D3C22⋊C411yescharacteristic
61C22×C3×D3—22no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22×C411yescharacteristic
67C2×C3⋊Dic3C2×D411yescharacteristic
68C4×C3⋊D3—22no—
69C4×C3⋊D3—22no—
70C4×C3⋊D3—41no—
71C2×C3×Dic3—22no—
72C3×D12—42no—
73C3×C4×D3—44no—
74#627—42no—
75#626—44no—
76#625—42no—
77#625—42no—
78#622—42no—
79C3×C3⋊C8—24no—
80#532—91no—
81#432—91no—
82C2×#97—91no—
83#329—94no—
84C2×C3×D4—61no—
85C22×C3×C4—62no—
86C2×#67—62no—
87C2×#67—62no—
88C2×#67—62no—
89#235—128no—
90C2×D12—21no—
91C2×D12—62no—
92C2×C4×D3—22no—
93C2×C4×D3—61no—
94C2×C4×D3—61no—
95C2×C4×D3—61no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×Dic6—62no—
100C2×C3×C8—62no—
101C3×C4⋊C4—61no—
102C3×C22⋊C4—62no—
103C3×C42—21no—
104C3×C42—21no—
105#217—62no—
106(C2×D3)⋊C4—22no—
107(C2×D3)⋊C4—62no—
108C4⋊Dic3—21no—
109Dic3⋊C4—62no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C2×C3⋊C8—22no—
117D3×C8—68no—
118C22×C32C2×C22⋊C411yescharacteristic
119C2×C3⋊D3—21no—
120C2×C3⋊D3—21no—
121C2×C3⋊D3#10012yes—
122C2×C3×D3—42no—
123C2×C3×D3—42no—
124C2×C3×D3—42no—
125C32×C4—21no—
126C32×C4—21no—
127C32×C4—21no—
128C3⋊Dic3—21no—
129C3⋊Dic3—21no—
130C3⋊Dic3#10412yes—
131C3×Dic3—42no—
132C2×#41—92no—
133C22×C8—181no—
134C4⋊Q8—91no—
135#127—91no—
136#124—92no—
137#121—181no—
138#121—181no—
139C4×D4—61no—
140C4×D4—181no—
141C2×C42—91no—
142C4⋊C8—181no—
143C22⋊C8—181no—
144#97—61no—
145#97—92no—
146#97—92no—
147C23×C3—62no—
148C22×D3—22no—
149C22×D3—61no—
150C22×D3—61no—
151C3×D4—122no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—62no—
159C2×C3×C4—124no—
160#67—124no—
161#67—124no—
162#67—124no—
163C2×Dic3—22no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170D12—42no—
171D12—124no—
172C4×D3—44no—
173C4×D3—64no—
174C4×D3—64no—
175C4×D3—122no—
176C4×D3—122no—
177C4×D3—122no—
178C4×D3—122no—
179Dic6—124no—
180C3×C8—64no—
181C3⋊C8—24no—
182C2×C32C2×#10011yescharacteristic
183C2×C32C2×#10411yescharacteristic
184C2×C32#42111yescharacteristic
185C3⋊D3—22no—
186C3×D3—82no—
187#41—364no—
188C2×Q8—92no—
189C2×D4—61no—
190C2×D4—92no—
191C2×D4—182no—
192C2×D4—181no—
193C22×C4—62no—
194C22×C4—91no—
195C22×C4—91no—
196C22×C4—91no—
197C2×C8—62no—
198C2×C8—184no—
199C2×C8—182no—
200C4⋊C4—61no—
201C4⋊C4—181no—
202C22⋊C4—62no—
203C22⋊C4—182no—
204C42—91no—
205C42—91no—
206C42—91no—
207C42GO+(4,𝔽2)11yescharacteristic
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—122no—
211C22×C3—122no—
212C22×C3—122no—
213C2×D3—42no—
214C2×D3—42no—
215C2×D3—42no—
216C2×D3—62no—
217C2×D3—62no—
218C2×D3—62no—
219C2×D3—62no—
220C2×D3—121no—
221C2×D3—121no—
222C3×C4—22no—
223C3×C4—22no—
224C3×C4—22no—
225C3×C4—41no—
226C3×C4—41no—
227C3×C4—41no—
228C3×C4—122no—
229Dic3—42no—
230Dic3—62no—
231Dic3—62no—
232Dic3—62no—
233Dic3—121no—
234Dic3—121no—
235Dic3—121no—
236C32#153011yescharacteristic, complemented, Sylow
237C23—62no—
238C23—91no—
239Q8—362no—
240D4—122no—
241D4—362no—
242D4—364no—
243D4—362no—
244C2×C4—62no—
245C2×C4—91no—
246C2×C4—91no—
247C2×C4—91no—
248C2×C4—124no—
249C2×C4—182no—
250C2×C4—182no—
251C2×C4—361no—
252C2×C4D32⋊C411yescharacteristic
253C2×C4D32⋊C411yescharacteristic
254C2×C4C2×GO+(4,𝔽2)11yescharacteristic
255C8—64no—
256C8—362no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—242no—
264D3—64no—
265D3—82no—
266D3—122no—
267C22—92no—
268C22—122no—
269C22—122no—
270C22—122no—
271C22—181no—
272C22—181no—
273C22C2×D32⋊C411yescharacteristic
274C4—21no—
275C4—21no—
276C4—21no—
277C4—92no—
278C4—122no—
279C4—181no—
280C4—181no—
281C3—21no—
282C3—21no—
283C2—182no—
284C2—242no—
285C2#1059331211yescharacteristic
286C2#1059332311yescharacteristic
287C2#1059338011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593972C2
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1530
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593731C2semidirect
3. #10590322C2semidirect
4. #10590035C2semidirect
236. C32#1530semidirect

Maximal subgroups

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

subgroupindex
#105939722
#105937312
#105903222
#105900352
#15309