Finite Group Databasebeta

← #11858783

Subgroups — #11858783

Order 1152.

742 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 742 conjugacy classes of subgroups — too many to draw. Only its 162 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
2#10593800C212yesmaximal
3#10593753C214yesmaximal, complemented
4#10593744C214yesmaximal, complemented
5#10593726C212yesmaximal, complemented
6#10593723C211yesmaximal, characteristic, complemented
7C4×#3787C211yesmaximal, characteristic, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×#3787C2212yes—
10C2×#3787C2212yes—
11C32×#117C411yescharacteristic
12#64135C411yescharacteristic
13#64101C2212yes—
14C4⋊C4×C3⋊D3C412yes—
15C22⋊C4×C3⋊D3C412yes—
16#64086C2212yes—
17#64081C411yescharacteristic
18#64081C411yescharacteristic
19C42×C3⋊D3C2211yescharacteristic
20C42×C3⋊D3C2211yescharacteristic
21C22⋊#622C2214yes—
22#63779C2214yescomplemented
23#63778C2214yes—
24#63777C2214yescomplemented
25C4⋊#622C2214yescomplemented
26C4×#622C2214yescomplemented
27D3×#117—62no—
28C23×C3⋊D3C2×C411yescharacteristic
29C22×C32×C4C2×C411yescharacteristic
30C22×C3⋊Dic3C2311yescharacteristic
31C2×C4×C3⋊D3—24no—
32C2×C4×C3⋊D3C2×C412yes—
33C2×C4×C3⋊D3C2×C412yes—
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×C4×C3⋊D3C2311yescharacteristic
38C2×#622C2314yes—
39C2×#622C2314yes—
40#3787—24no—
41#3787—24no—
42C32×C4⋊C4C2×C412yes—
43C32×C22⋊C4C2×C412yes—
44C32×C42C2×C411yescharacteristic
45C32×C42C2×C411yescharacteristic
46#3757C2×C412yes—
47#3752C2×C412yes—
48#3752C2×C412yes—
49C4⋊(C3⋊Dic3)C2×C412yes—
50#3750C2×C412yes—
51#3750C2×C412yes—
52C4×C3⋊Dic3C2×C411yescharacteristic
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3C2312yes—
55C4×C3⋊Dic3C2312yes—
56C2×#433—91nomaximal, Sylow
57C22×C4×D3—62no—
58C3×#117—22no—
59#926—62no—
60#892—64no—
61D3×C4⋊C4—64no—
62D3×C22⋊C4—64no—
63#877—64no—
64#872—62no—
65#872—62no—
66C42×D3—62no—
67C42×D3—62no—
68C23×C32C22×C411yescharacteristic
69C22×C3⋊D3—22no—
70C22×C3⋊D3—24no—
71C22×C3⋊D3C22×C411yescharacteristic
72C22×C3⋊D3C22×C411yescharacteristic
73C2×C32×C4—22no—
74C2×C32×C4C22×C412yes—
75C2×C32×C4C22×C412yes—
76C2×C32×C4C22×C411yescharacteristic
77C2×C32×C4C22×C411yescharacteristic
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3C22×C412yes—
80C2×C3⋊Dic3C22×C412yes—
81C2×C3⋊Dic3C22×C411yescharacteristic
82C2×C3⋊Dic3C2411yescharacteristic
83C4×C3⋊D3—22no—
84C4×C3⋊D3—22no—
85C4×C3⋊D3—22no—
86C4×C3⋊D3—24no—
87C4×C3⋊D3—24no—
88C4×C3⋊D3#4114yes—
89#622—24no—
90#622—24no—
91C2×#117—91no—
92#433—94no—
93#433—94no—
94C2×C4⋊C8—92no—
95C2×C22⋊C8—92no—
96C2×#97—91no—
97C2×C4×C8—91no—
98C23×D3—62no—
99C22×C3×C4—22no—
100C22×Dic3—62no—
101C2×C4×D3—62no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—64no—
106C2×C4×D3—64no—
107C2×C4×D3—616no—
108C3×C4⋊C4—24no—
109C3×C22⋊C4—24no—
110C3×C42—22no—
111C3×C42—22no—
112#217—64no—
113(C2×D3)⋊C4—64no—
114(C2×D3)⋊C4—64no—
115C4⋊Dic3—64no—
116Dic3⋊C4—64no—
117Dic3⋊C4—64no—
118C4×Dic3—62no—
119C4×Dic3—62no—
120C4×Dic3—64no—
121C4×Dic3—64no—
122C22×C32—21no—
123C22×C32—22no—
124C22×C32C23×C411yescharacteristic
125C2×C3⋊D3—21no—
126C2×C3⋊D3—22no—
127C2×C3⋊D3—44no—
128C2×C3⋊D3#11712yes—
129C2×C3⋊D3#13114yes—
130C32×C4—21no—
131C32×C4—22no—
132C32×C4—22no—
133C32×C4#11712yes—
134C3⋊Dic3—21no—
135C3⋊Dic3—22no—
136C3⋊Dic3—22no—
137C3⋊Dic3C2×#4112yes—
138C23×C4—91no—
139C22×C8—92no—
140C22×C8—92no—
141#117—91no—
142#117—92no—
143#117—92no—
144#117—91no—
145#117—91no—
146#117#15711yescharacteristic
147C2×C4⋊C4—92no—
148C2×C22⋊C4—92no—
149C2×C42—91no—
150C2×C42—91no—
151C4⋊C8—94no—
152C4⋊C8—94no—
153C22⋊C8—94no—
154C22⋊C8—94no—
155#97—94no—
156C4×C8—94no—
157C23×C3—22no—
158C22×D3—62no—
159C22×D3—62no—
160C22×D3—68no—
161C22×D3—128no—
162C2×C3×C4—28no—
163C2×C3×C4—22no—
164C2×C3×C4—24no—
165C2×C3×C4—24no—
166C2×C3×C4—22no—
167C2×Dic3—62no—
168C2×Dic3—62no—
169C2×Dic3—64no—
170C2×Dic3—64no—
171C2×Dic3—68no—
172C4×D3—68no—
173C4×D3—68no—
174C4×D3—68no—
175C4×D3—68no—
176C4×D3—128no—
177C4×D3—128no—
178C2×C32—41no—
179C2×C32C2×#11711yescharacteristic
180C2×C32C2×#13112yes—
181C3⋊D3—41no—
182C3⋊D3#43314yescomplemented
183C24—91no—
184C22×C4—91no—
185C22×C4—91no—
186C22×C4—91no—
187C22×C4—92no—
188C22×C4—92no—
189C22×C4—91no—
190C22×C4—91no—
191C22×C4—184no—
192C22×C4C2×#15711yescharacteristic
193C2×C8—94no—
194C2×C8—94no—
195C2×C8—184no—
196C2×C8—184no—
197C4⋊C4—92no—
198C4⋊C4—92no—
199C4⋊C4—92no—
200C4⋊C4C2×#15712yes—
201C22⋊C4—92no—
202C22⋊C4—92no—
203C22⋊C4—92no—
204C22⋊C4C2×#15712yes—
205C42—92no—
206C42—92no—
207C42—91no—
208C42—91no—
209C42C2×#15711yescharacteristic
210C42C2×#15711yescharacteristic
211C22×C3—24no—
212C22×C3—22no—
213C22×C3—44no—
214C2×D3—64no—
215C2×D3—68no—
216C2×D3—64no—
217C2×D3—124no—
218C2×D3—1216no—
219C3×C4—24no—
220C3×C4—24no—
221C3×C4—44no—
222C3×C4—44no—
223Dic3—64no—
224Dic3—64no—
225Dic3—124no—
226Dic3—124no—
227C32C2×#43311yescharacteristic, complemented, Sylow
228C23—91no—
229C23—91no—
230C23—182no—
231C23—184no—
232C23C22×#15711yescharacteristic
233C2×C4—22no—
234C2×C4—91no—
235C2×C4—94no—
236C2×C4—92no—
237C2×C4—92no—
238C2×C4—91no—
239C2×C4—182no—
240C2×C4—182no—
241C2×C4—184no—
242C2×C4—184no—
243C2×C4—182no—
244C2×C4—182no—
245C2×C4C22×#15712yes—
246C2×C4C22×#15712yes—
247C2×C4C22×#15711yescharacteristic
248C2×C4C22×#15711yescharacteristic
249C8—184no—
250C8—184no—
251C2×C3—22no—
252C2×C3—24no—
253C2×C3—44no—
254D3—68no—
255D3—124no—
256C22—21no—
257C22—22no—
258C22—92no—
259C22—94no—
260C22—181no—
261C22—182no—
262C22—364no—
263C22C23×#15711yescharacteristic
264C4—21no—
265C4—22no—
266C4—22no—
267C4—92no—
268C4—181no—
269C4—182no—
270C4—182no—
271C4#6428612yes—
272C3—22no—
273C2—41no—
274C2—94no—
275C2—361no—
276C2C2×#6428611yescharacteristic
277C2#1059664712yes—
subgroupG/H
centerC2×C4C22×#157
commutator, socleC22×C32C23×C4
FrattiniC22C23×#157
FittingC32×#117C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C3⋊Dic3C24
hypercenter#117#157
hypocenterC32C2×#433
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #10593753C2semidirect
4. #10593744C2semidirect
5. #10593726C2semidirect
6. #10593723C2semidirect
7. C4×#3787C2semidirect
22. #63779C22semidirect
24. #63777C22semidirect
25. C4⋊#622C22semidirect
26. C4×#622C22semidirect
182. C3⋊D3#433semidirect
227. C32C2×#433semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
#105938002
#105937532
#105937442
#105937262
#105937232
C4×#37872
C2×#4339