Finite Group Databasebeta

← #11785847

Subgroups — #11785847

Order 1152.

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

normal subgroups only

This group has 636 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
1C3⋊D3×#117C211yesmaximal, characteristic
2C4×C22⋊#157C211yesmaximal, characteristic
3#10593803C211yesmaximal, characteristic
4#10590164C212yesmaximal, complemented
5#10590164C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157—21no—
8C2×C4×#157C2212yes—
9C2×#3788C2212yes—
10C32×#117C411yescharacteristic, complemented
11#64135C411yescharacteristic, complemented
12#64101C2211yescharacteristic
13#64101C2211yescharacteristic
14C4⋊C4×C3⋊D3C411yescharacteristic, complemented
15C4⋊C4×C3⋊D3C411yescharacteristic, complemented
16C22⋊C4×C3⋊D3—21no—
17#64086—21no—
18#64081—21no—
19C42×C3⋊D3—21no—
20C22⋊#622—21no—
21#63781—21no—
22#63778—21no—
23D3×#117—62no—
24C23×C3⋊D3D411yescharacteristic
25C22×#157—22no—
26C22×C32×C4C2×C411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C2×C4×C3⋊D3—24no—
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3C2311yescharacteristic
35C22⋊#157—24no—
36C2×#622—22no—
37C4×#157—24no—
38#3788—24no—
39C32×C4⋊C4C2×C411yescharacteristic
40C32×C4⋊C4C2×C411yescharacteristic
41C32×C22⋊C4—21no—
42C32×C42—21no—
43#3757—21no—
44#3752—21no—
45#3752—21no—
46C4⋊(C3⋊Dic3)C2×C411yescharacteristic
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48#3750—21no—
49#3750—21no—
50C4×C3⋊Dic3—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3—21no—
53#1826—91nomaximal, Sylow
54C22×C4×D3—62no—
55C3×#117—22no—
56#926—62no—
57#892—62no—
58#892—62no—
59D3×C4⋊C4—62no—
60D3×C4⋊C4—62no—
61D3×C22⋊C4—64no—
62#877—64no—
63#872—64no—
64C42×D3—64no—
65C23×C32C22⋊C411yescharacteristic
66C22×C3⋊D3—22no—
67C22×C3⋊D3—22no—
68C22×C3⋊D3—41no—
69C22×C3⋊D3C22⋊C411yescharacteristic
70C22×C3⋊D3C2×D411yescharacteristic
71C2×#157—24no—
72C2×#157—42no—
73C2×#157—42no—
74C2×C32×C4—22no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C22×C411yescharacteristic
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C2×D411yescharacteristic
84C4×C3⋊D3—22no—
85C4×C3⋊D3—22no—
86C4×C3⋊D3—22no—
87C4×C3⋊D3—42no—
88C4×C3⋊D3—42no—
89C4×C3⋊D3#4114yes—
90#622—42no—
91C2×#117—91no—
92#407—91no—
93C4×C22⋊C4—91no—
94#339—92no—
95#339—92no—
96C23×D3—62no—
97C22×C3×C4—22no—
98C22×Dic3—62no—
99C2×C4×D3—62no—
100C2×C4×D3—62no—
101C2×C4×D3—62no—
102C2×C4×D3—62no—
103C2×C4×D3—616no—
104C2×C4×D3—64no—
105C2×C4×D3—64no—
106C3×C4⋊C4—22no—
107C3×C4⋊C4—22no—
108C3×C22⋊C4—24no—
109C3×C42—24no—
110#217—64no—
111(C2×D3)⋊C4—64no—
112(C2×D3)⋊C4—64no—
113C4⋊Dic3—62no—
114C4⋊Dic3—62no—
115Dic3⋊C4—64no—
116Dic3⋊C4—64no—
117C4×Dic3—64no—
118C4×Dic3—64no—
119C4×Dic3—64no—
120C22×C32—21no—
121C22×C32—21no—
122C22×C32—21no—
123C22×C32C2×C22⋊C411yescharacteristic
124C2×C3⋊D3—21no—
125C2×C3⋊D3—21no—
126C2×C3⋊D3—21no—
127C2×C3⋊D3—21no—
128C2×C3⋊D3—44no—
129C2×C3⋊D3#10412yes—
130C2×C3⋊D3#12312yes—
131#157—44no—
132C32×C4—21no—
133C32×C4—41no—
134C32×C4—41no—
135C32×C4#11712yes—
136C3⋊Dic3—21no—
137C3⋊Dic3—41no—
138C3⋊Dic3—41no—
139C3⋊Dic3#12312yes—
140C23×C4—91no—
141C2×M16—92no—
142#117—91no—
143#117—91no—
144#117—91no—
145#117—181no—
146#117—181no—
147#117#15711yescharacteristic, complemented
148C2×C4⋊C4—91no—
149C2×C4⋊C4—91no—
150C2×C22⋊C4—181no—
151C2×C22⋊C4—181no—
152C2×C42—92no—
153C2×C42—181no—
154C22⋊C8—181no—
155C22⋊C8—181no—
156#95—181no—
157C23×C3—22no—
158C22×D3—62no—
159C22×D3—62no—
160C22×D3—68no—
161C22×D3—124no—
162C22×D3—124no—
163C2×C3×C4—28no—
164C2×C3×C4—24no—
165C2×C3×C4—24no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168C2×Dic3—62no—
169C2×Dic3—62no—
170C2×Dic3—68no—
171C2×Dic3—64no—
172C2×Dic3—64no—
173C4×D3—68no—
174C4×D3—68no—
175C4×D3—68no—
176C4×D3—68no—
177C4×D3—128no—
178C4×D3—128no—
179C2×C32—41no—
180C2×C32#38111yescharacteristic
181C2×C32C2×#10411yescharacteristic
182C2×C32#42111yescharacteristic
183C3⋊D3—22no—
184C3⋊D3—22no—
185C24—91no—
186C22×C4—91no—
187C22×C4—91no—
188C22×C4—91no—
189C22×C4—91no—
190C22×C4—91no—
191C22×C4—184no—
192C22×C4—181no—
193C22×C4—181no—
194C22×C4—182no—
195C22×C4C2×#15711yescharacteristic
196M16—184no—
197C2×C8—182no—
198C4⋊C4—91no—
199C4⋊C4—91no—
200C4⋊C4—181no—
201C4⋊C4—181no—
202C4⋊C4C2×#15711yescharacteristic
203C4⋊C4C2×#15711yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—181no—
206C22⋊C4—181no—
207C22⋊C4—184no—
208C22⋊C4—181no—
209C42—21no—
210C42—181no—
211C42—181no—
212C42—184no—
213C42—181no—
214C22×C3—24no—
215C22×C3—22no—
216C22×C3—42no—
217C22×C3—42no—
218C2×D3—64no—
219C2×D3—64no—
220C2×D3—64no—
221C2×D3—64no—
222C2×D3—122no—
223C2×D3—122no—
224C2×D3—1216no—
225C3×C4—24no—
226C3×C4—24no—
227C3×C4—44no—
228C3×C4—44no—
229Dic3—64no—
230Dic3—64no—
231Dic3—124no—
232Dic3—124no—
233C32#182611yescharacteristic, complemented, Sylow
234C23—91no—
235C23—91no—
236C23—182no—
237C23—182no—
238C23—361no—
239C23C22⋊#15711yescharacteristic
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—91no—
244C2×C4—94no—
245C2×C4—91no—
246C2×C4—182no—
247C2×C4—182no—
248C2×C4—182no—
249C2×C4—182no—
250C2×C4—184no—
251C2×C4—181no—
252C2×C4—181no—
253C2×C4—362no—
254C2×C4—362no—
255C2×C4—362no—
256C2×C4—362no—
257C2×C4C22⋊#15711yescharacteristic
258C2×C4C22×#15711yescharacteristic
259C8—362no—
260C2×C3—22no—
261C2×C3—22no—
262C2×C3—22no—
263C2×C3—44no—
264D3—68no—
265D3—124no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—92no—
270C22—92no—
271C22—181no—
272C22—181no—
273C22—181no—
274C22—181no—
275C22—364no—
276C22C2×C22⋊#15711yescharacteristic
277C4—21no—
278C4—41no—
279C4—41no—
280C4—92no—
281C4—181no—
282C4—364no—
283C4—361no—
284C4—361no—
285C4#6428612yes—
286C3—22no—
287C2—41no—
288C2—182no—
289C2—182no—
290C2#1059381111yescharacteristic
291C2#1059383911yescharacteristic
292C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#117C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenter#117#157
hypocenterC32#1826
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10590164C2semidirect
5. #10590164C2semidirect
10. C32×#117C4semidirect
11. #64135C4semidirect
14. C4⋊C4×C3⋊D3C4semidirect
15. C4⋊C4×C3⋊D3C4semidirect
147. #117#157semidirect
233. C32#1826semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
C4×C22⋊#1572
#105938032
#105901642
#18269