Finite Group Databasebeta

← #11858869

Subgroups — #11858869

Order 1152.

722 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 154 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#10593803C212yesmaximal
3#10593753C214yesmaximal, complemented
4#10593744C214yesmaximal, complemented
5#10593729C211yesmaximal, characteristic, complemented
6#10593728C211yesmaximal, characteristic, complemented
7C4×#3788C212yesmaximal, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×#3788C2212yes—
10C2×#3788C2212yes—
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—22no—
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3C2×C411yescharacteristic
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3C2×C412yes—
36C2×C4×C3⋊D3C2×C412yes—
37C2×C4×C3⋊D3C2311yescharacteristic
38C2×C4×C3⋊D3C2311yescharacteristic
39C2×#622C2314yes—
40C2×#622C2314yes—
41#3788—24no—
42#3788—24no—
43C32×C4⋊C4C2×C412yes—
44C32×C22⋊C4C2×C412yes—
45C32×C42C2×C411yescharacteristic
46C32×C42C2×C411yescharacteristic
47#3757C2×C412yes—
48#3752C2×C412yes—
49#3752C2×C412yes—
50C4⋊(C3⋊Dic3)C2×C412yes—
51#3750C2×C412yes—
52#3750C2×C412yes—
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3C2×C411yescharacteristic
55C4×C3⋊Dic3C2312yes—
56C4×C3⋊Dic3C2312yes—
57#2921—91nomaximal, Sylow
58C22×C4×D3—62no—
59C3×#117—22no—
60#926—62no—
61#892—64no—
62D3×C4⋊C4—64no—
63D3×C22⋊C4—64no—
64#877—64no—
65#872—62no—
66#872—62no—
67C42×D3—62no—
68C42×D3—62no—
69C23×C32C22×C411yescharacteristic
70C22×C3⋊D3—22no—
71C22×C3⋊D3—42no—
72C22×C3⋊D3C22×C411yescharacteristic
73C22×C3⋊D3C22×C411yescharacteristic
74C2×C32×C4—22no—
75C2×C32×C4C22×C412yes—
76C2×C32×C4C22×C412yes—
77C2×C32×C4C22×C411yescharacteristic
78C2×C32×C4C22×C411yescharacteristic
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3C22×C412yes—
82C2×C3⋊Dic3C22×C412yes—
83C2×C3⋊Dic3C22×C411yescharacteristic
84C2×C3⋊Dic3C2411yescharacteristic
85C4×C3⋊D3—22no—
86C4×C3⋊D3—22no—
87C4×C3⋊D3—21no—
88C4×C3⋊D3—21no—
89C4×C3⋊D3—42no—
90C4×C3⋊D3—42no—
91C4×C3⋊D3#4112yes—
92C4×C3⋊D3#4112yes—
93#622—24no—
94#622—24no—
95C2×#117—91no—
96#433—94no—
97#433—94no—
98#423—91no—
99#423—91no—
100#407—92no—
101C4×M16—92no—
102C23×D3—62no—
103C22×C3×C4—22no—
104C22×Dic3—62no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×C4×D3—62no—
108C2×C4×D3—62no—
109C2×C4×D3—64no—
110C2×C4×D3—64no—
111C2×C4×D3—68no—
112C2×C4×D3—68no—
113C3×C4⋊C4—24no—
114C3×C22⋊C4—24no—
115C3×C42—22no—
116C3×C42—22no—
117#217—64no—
118(C2×D3)⋊C4—64no—
119(C2×D3)⋊C4—64no—
120C4⋊Dic3—64no—
121Dic3⋊C4—64no—
122Dic3⋊C4—64no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C4×Dic3—64no—
126C4×Dic3—64no—
127C22×C32—21no—
128C22×C32—22no—
129C22×C32C23×C411yescharacteristic
130C2×C3⋊D3—22no—
131C2×C3⋊D3—21no—
132C2×C3⋊D3—22no—
133C2×C3⋊D3—44no—
134C2×C3⋊D3#11712yes—
135C32×C4—21no—
136C32×C4—22no—
137C32×C4—22no—
138C32×C4#11712yes—
139C3⋊Dic3—21no—
140C3⋊Dic3—22no—
141C3⋊Dic3—22no—
142C3⋊Dic3C2×#4111yescharacteristic
143C3⋊Dic3C2×#4111yescharacteristic
144C23×C4—91no—
145C2×M16—92no—
146C2×M16—92no—
147#117—91no—
148#117—92no—
149#117—92no—
150#117—91no—
151#117—91no—
152#117#15711yescharacteristic
153C2×C4⋊C4—92no—
154C2×C22⋊C4—92no—
155C2×C42—91no—
156C2×C42—91no—
157C4⋊C8—94no—
158C4⋊C8—94no—
159C22⋊C8—94no—
160C22⋊C8—94no—
161#97—94no—
162C4×C8—94no—
163C23×C3—22no—
164C22×D3—62no—
165C22×D3—62no—
166C22×D3—68no—
167C22×D3—128no—
168C2×C3×C4—28no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—24no—
172C2×C3×C4—24no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—64no—
176C2×Dic3—64no—
177C2×Dic3—64no—
178C2×Dic3—64no—
179C4×D3—64no—
180C4×D3—64no—
181C4×D3—64no—
182C4×D3—64no—
183C4×D3—68no—
184C4×D3—68no—
185C4×D3—128no—
186C4×D3—128no—
187C2×C32—41no—
188C2×C32C2×#11711yescharacteristic
189C2×C32#56812yes—
190C3⋊D3—22no—
191C3⋊D3—41no—
192C24—91no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—91no—
198C22×C4—92no—
199C22×C4—92no—
200C22×C4—182no—
201C22×C4—182no—
202C22×C4C2×#15711yescharacteristic
203M16—184no—
204M16—184no—
205C2×C8—94no—
206C2×C8—94no—
207C4⋊C4—92no—
208C4⋊C4—92no—
209C4⋊C4—92no—
210C4⋊C4C2×#15712yes—
211C22⋊C4—92no—
212C22⋊C4—92no—
213C22⋊C4—92no—
214C22⋊C4C2×#15712yes—
215C42—92no—
216C42—92no—
217C42—91no—
218C42—91no—
219C42C2×#15711yescharacteristic
220C42C2×#15711yescharacteristic
221C22×C3—24no—
222C22×C3—22no—
223C22×C3—44no—
224C2×D3—64no—
225C2×D3—68no—
226C2×D3—64no—
227C2×D3—124no—
228C2×D3—1216no—
229C3×C4—24no—
230C3×C4—24no—
231C3×C4—44no—
232C3×C4—44no—
233Dic3—62no—
234Dic3—62no—
235Dic3—64no—
236Dic3—124no—
237Dic3—124no—
238C32#292111yescharacteristic, complemented, Sylow
239C23—91no—
240C23—91no—
241C23—182no—
242C23—362no—
243C23C22×#15711yescharacteristic
244C2×C4—22no—
245C2×C4—91no—
246C2×C4—92no—
247C2×C4—92no—
248C2×C4—92no—
249C2×C4—92no—
250C2×C4—91no—
251C2×C4—181no—
252C2×C4—181no—
253C2×C4—182no—
254C2×C4—181no—
255C2×C4—181no—
256C2×C4—182no—
257C2×C4—362no—
258C2×C4—362no—
259C2×C4C22×#15712yes—
260C2×C4C22×#15712yes—
261C2×C4C22×#15711yescharacteristic
262C2×C4C22×#15711yescharacteristic
263C8—184no—
264C8—184no—
265C2×C3—22no—
266C2×C3—24no—
267C2×C3—44no—
268D3—68no—
269D3—124no—
270C22—21no—
271C22—22no—
272C22—92no—
273C22—182no—
274C22—181no—
275C22—182no—
276C22—364no—
277C22C23×#15711yescharacteristic
278C4—21no—
279C4—22no—
280C4—22no—
281C4—91no—
282C4—91no—
283C4—181no—
284C4—182no—
285C4—182no—
286C4#6428612yes—
287C3—22no—
288C2—41no—
289C2—182no—
290C2—361no—
291C2C2×#6428611yescharacteristic
292C2#1059664812yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#117C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C3⋊Dic3C24
hypercenter#117#157
hypocenterC32#2921
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #10593753C2semidirect
4. #10593744C2semidirect
5. #10593729C2semidirect
6. #10593728C2semidirect
7. C4×#3788C2semidirect
22. #63779C22semidirect
24. #63777C22semidirect
25. C4⋊#622C22semidirect
26. C4×#622C22semidirect
238. C32#2921semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
#105938032
#105937532
#105937442
#105937292
#105937282
C4×#37882
#29219