Finite Group Databasebeta

← #11787807

Subgroups — #11787807

Order 1152.

690 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 68 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#10596642C211yesmaximal, characteristic
2C3⋊D3×#124C211yesmaximal, characteristic
3#10593829C212yesmaximal, complemented
4#10593825C211yesmaximal, characteristic
5#10590151C212yesmaximal, complemented
6C2×Q8×C3⋊D3C2211yescharacteristic
7C2×D4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157—22no—
9D4×#157—24no—
10#64286C2212yes—
11#64283C2212yes—
12C32×#124C411yescharacteristic, complemented
13#64156C411yescharacteristic, complemented
14#64145C411yescharacteristic, complemented
15#64094—22no—
16C22⋊C4×C3⋊D3—22no—
17#64084C411yescharacteristic, complemented
18C42×C3⋊D3C2211yescharacteristic
19#63788—22no—
20#63784—24no—
21D3×#124—62no—
22C23×C3⋊D3D412yes—
23C22×#157—24no—
24C2×C32×Q8C2×C411yescharacteristic, complemented
25C2×C32×D4C2×C411yescharacteristic
26C2×#638D412yes—
27Q8×C3⋊D3—22no—
28Q8×C3⋊D3—22no—
29D4×C3⋊D3—22no—
30D4×C3⋊D3—22no—
31C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3C2311yescharacteristic
35C2×#634—21no—
36C2×#634C2×C411yescharacteristic, complemented
37C22⋊#157—24no—
38C22⋊#157—22no—
39#3792—22no—
40C4⋊#157D414yes—
41C4×#157—22no—
42#3788—22no—
43#3787—22no—
44C32×C22⋊C4—22no—
45C32×C42C2×C411yescharacteristic, complemented
46#3757—22no—
47#3752—22no—
48#3752—22no—
49C4×C3⋊Dic3—21no—
50C4×C3⋊Dic3C2×C411yescharacteristic, complemented
51#1885—91nomaximal, Sylow
52C2×D3×Q8—62no—
53C2×D3×D4—62no—
54C3×#124—22no—
55#947—62no—
56#936—62no—
57#885—68no—
58D3×C22⋊C4—68no—
59#875—62no—
60C42×D3—62no—
61C23×C32C22⋊C412yes—
62C22×C3⋊D3—22no—
63C22×C3⋊D3—22no—
64C22×C3⋊D3—44no—
65C22×C3⋊D3C22⋊C412yes—
66C22×C3⋊D3C2×D411yescharacteristic
67C2×#157—24no—
68C2×#157—84no—
69C32×Q8—22no—
70C32×D4—22no—
71C2×C32×C4—21no—
72C2×C32×C4—21no—
73C2×C32×C4C22×C411yescharacteristic
74#638—24no—
75C2×C3⋊Dic3—21no—
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3C2×D411yescharacteristic
78C4⋊(C3⋊D3)—22no—
79C4×C3⋊D3—42no—
80C4×C3⋊D3—41no—
81C4×C3⋊D3—41no—
82C4×C3⋊D3C2×D412yes—
83C4×C3⋊D3#4112yes—
84#634—22no—
85#634—42no—
86#622—42no—
87C2×#124—91no—
88#518—91no—
89#419—92no—
90C2×#100—91no—
91#339—92no—
92C23×D3—64no—
93C2×C3×Q8—22no—
94C2×C3×D4—22no—
95C2×#67—64no—
96D3×Q8—124no—
97D3×Q8—124no—
98D3×D4—124no—
99D3×D4—124no—
100C2×D12—62no—
101C2×C4×D3—62no—
102C2×C4×D3—64no—
103C2×C4×D3—64no—
104C2×Dic6—62no—
105C2×Dic6—64no—
106C3×C22⋊C4—28no—
107C3×C42—22no—
108#217—68no—
109(C2×D3)⋊C4—68no—
110(C2×D3)⋊C4—68no—
111C4×Dic3—62no—
112C4×Dic3—64no—
113C22×C32—22no—
114C22×C32—42no—
115C22×C32C2×C22⋊C411yescharacteristic
116C2×C3⋊D3—22no—
117C2×C3⋊D3—22no—
118C2×C3⋊D3—42no—
119C2×C3⋊D3—44no—
120C2×C3⋊D3—82no—
121C2×C3⋊D3#12011yescharacteristic
122C2×C3⋊D3#12311yescharacteristic
123#157—44no—
124C32×C4—41no—
125C32×C4—41no—
126C32×C4C4×D412yes—
127C3⋊Dic3—41no—
128C3⋊Dic3—41no—
129C3⋊Dic3#12112yes—
130C22×Q8—91no—
131C22×D4—91no—
132C2×M16—92no—
133#124—91no—
134#124—91no—
135#124—91no—
136#124—182no—
137#124#15711yescharacteristic, complemented
138C4×D4—184no—
139#117—92no—
140C2×C22⋊C4—182no—
141C2×C22⋊C4—182no—
142C2×C42—91no—
143#103—184no—
144#100—182no—
145C23×C3—24no—
146C22×D3—62no—
147C22×D3—64no—
148C22×D3—124no—
149C22×D3—124no—
150C22×D3—1216no—
151C3×Q8—44no—
152C3×D4—44no—
153C2×C3×C4—24no—
154C2×C3×C4—24no—
155C2×C3×C4—22no—
156#67—128no—
157C2×Dic3—62no—
158C2×Dic3—64no—
159C2×Dic3—64no—
160D12—124no—
161C4×D3—64no—
162C4×D3—64no—
163C4×D3—128no—
164C4×D3—124no—
165C4×D3—124no—
166Dic6—124no—
167Dic6—128no—
168C2×C32—21no—
169C2×C32—42no—
170C2×C32#38611yescharacteristic
171C3⋊D3—21no—
172C3⋊D3—42no—
173C3⋊D3#45512yes—
174C24—92no—
175C2×Q8—91no—
176C2×Q8—181no—
177C2×Q8—182no—
178C2×Q8—182no—
179C2×Q8C2×#15711yescharacteristic, complemented
180C2×D4—92no—
181C2×D4—91no—
182C2×D4—182no—
183C2×D4—182no—
184C2×D4C2×#15711yescharacteristic
185C22×C4—91no—
186C22×C4—181no—
187C22×C4—181no—
188C22×C4—184no—
189M16—182no—
190M16—182no—
191C2×C8—182no—
192C4⋊C4—94no—
193C22⋊C4—22no—
194C22⋊C4—182no—
195C22⋊C4—182no—
196C22⋊C4—182no—
197C22⋊C4—184no—
198C22⋊C4—182no—
199C42—91no—
200C42—181no—
201C42—182no—
202C42C2×#15711yescharacteristic, complemented
203C22×C3—22no—
204C22×C3—44no—
205C22×C3—48no—
206C2×D3—62no—
207C2×D3—62no—
208C2×D3—68no—
209C2×D3—124no—
210C2×D3—128no—
211C2×D3—248no—
212C2×D3—248no—
213C3×C4—24no—
214C3×C4—44no—
215C3×C4—44no—
216Dic3—64no—
217Dic3—124no—
218Dic3—124no—
219C32#188511yescharacteristic, complemented, Sylow
220C23—91no—
221C23—92no—
222C23—182no—
223C23—182no—
224C23—364no—
225C23C22⋊#15712yes—
226Q8—22no—
227Q8—182no—
228Q8—362no—
229D4—22no—
230D4—184no—
231D4—182no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—91no—
235C2×C4—92no—
236C2×C4—92no—
237C2×C4—184no—
238C2×C4—181no—
239C2×C4—181no—
240C2×C4—361no—
241C2×C4—361no—
242C2×C4—362no—
243C2×C4—724no—
244C2×C4C22×#15711yescharacteristic
245C8—362no—
246C2×C3—24no—
247C2×C3—22no—
248C2×C3—84no—
249D3—64no—
250D3—64no—
251D3—244no—
252C22—22no—
253C22—42no—
254C22—91no—
255C22—91no—
256C22—182no—
257C22—182no—
258C22—362no—
259C22—364no—
260C22—722no—
261C22C2×C22⋊#15711yescharacteristic
262C4—41no—
263C4—41no—
264C4—92no—
265C4—361no—
266C4—364no—
267C4—361no—
268C4D4×#15712yes—
269C3—22no—
270C2—21no—
271C2—42no—
272C2—92no—
273C2—181no—
274C2—362no—
275C2#1059382611yescharacteristic
subgroupG/H
centerC2#10593826
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#124C4
socleC2×C32#386
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C4×C3⋊D3C23
hypercenter#124#157
hypocenterC32#1885
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
3. #10593829C2semidirect
5. #10590151C2semidirect
12. C32×#124C4semidirect
13. #64156C4semidirect
14. #64145C4semidirect
17. #64084C4semidirect
24. C2×C32×Q8C2×C4semidirect
36. C2×#634C2×C4semidirect
45. C32×C42C2×C4semidirect
50. C4×C3⋊Dic3C2×C4semidirect
137. #124#157semidirect
179. C2×Q8C2×#157semidirect
202. C42C2×#157semidirect
219. C32#1885semidirect

Maximal subgroups

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

subgroupindex
#105966422
C3⋊D3×#1242
#105938292
#105938252
#105901512
#18859