Finite Group Databasebeta

← #11775913

Subgroups — #11775913

Order 1152.

479 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 479 conjugacy classes of subgroups — too many to draw. Only its 86 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#10593854C211yesmaximal, characteristic
2#10592404C211yesmaximal, characteristic
3#10590322C211yesmaximal, characteristic
4C3×#4465C212yesmaximal, complemented
5#10589088C212yesmaximal, complemented
6#68365—32nomaximal
7C42×C3⋊D3C2211yescharacteristic
8C3×#870C2212yes—
9#63919C411yescharacteristic
10#63919C411yescharacteristic
11#63865—21no—
12#63865—21no—
13#63849C412yes—
14#63838—21no—
15#63838—21no—
16C2×#3710—21no—
17C32×#97C2211yescharacteristic
18#63647—21no—
19#63641—21no—
20#63630C2211yescharacteristic
21C3×#803C2212yes—
22#63555—21no—
23#5688—32no—
24#4705—32no—
25#4705—61no—
26D3×#97—32no—
27C3×#330—32no—
28#4543—32no—
29#4465—32no—
30#4465D312yescomplemented
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×#627—21no—
35C2×#627—21no—
36C2×C32×C8—21no—
37C32×C42C2311yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C2×C3⋊(C3⋊C8)—21no—
42C3×C4⋊Dic3C2×C412yes—
43C3×C4⋊Dic3C2×C412yes—
44C3×Dic3⋊C4—22no—
45C3×Dic3⋊C4—22no—
46C2×C3×C3⋊C8—22no—
47#3724—21no—
48#3724—21no—
49#3722—22no—
50Dic32—22no—
51#3710—24no—
52#1531—91noSylow
53C3×#125—32no—
54C2×D3×C8—62no—
55#896—62no—
56#896—62no—
57#892—32no—
58#892—32no—
59#888—32no—
60#888—32no—
61#887—62no—
62#887—62no—
63C42×D3—32no—
64C42×D3—61no—
65#870C2×D312yes—
66C3×#97—21no—
67C3×#97—32no—
68C3×#97C2×D312yes—
69(C2×D3)⋊C8—62no—
70(C2×D3)⋊C8—62no—
71#815—62no—
72Dic3⋊C8—62no—
73Dic3⋊C8—62no—
74#803—32no—
75#803—61no—
76#803C2×D312yes—
77C22×C3⋊D3C22⋊C411yescharacteristic
78C2×C32×C4C22×C411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C4×C3⋊D3—22no—
85C4×C3⋊D3—22no—
86C4×C3⋊D3—41no—
87C2×C3×Dic3—22no—
88C2×C3×Dic3—22no—
89#627—42no—
90#627—42no—
91C32×C8—41no—
92C3⋊(C3⋊C8)—41no—
93C3×C3⋊C8—24no—
94#533—91no—
95#432—91no—
96C2×#97—91no—
97#330—32no—
98#330—92no—
99C2×C4×D3—32no—
100C2×C4×D3—32no—
101C2×C4×D3—32no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×Dic6—62no—
106C2×Dic6—62no—
107C2×C3×C8—22no—
108C2×C3×C8—22no—
109C2×C3×C8—62no—
110C3×C4⋊C4—32no—
111C3×C4⋊C4—32no—
112C3×C4⋊C4—62no—
113C3×C4⋊C4—62no—
114C3×C42—21no—
115C3×C42C22×D312yes—
116(C2×D3)⋊C4—62no—
117(C2×D3)⋊C4—62no—
118C4⋊Dic3C4×D312yes—
119C4⋊Dic3C4×D312yes—
120Dic3⋊C4—22no—
121Dic3⋊C4—22no—
122Dic3⋊C4—62no—
123Dic3⋊C4—62no—
124C4×Dic3—32no—
125C4×Dic3—32no—
126C4×Dic3—32no—
127C4×Dic3—61no—
128C4×Dic3—61no—
129C4×Dic3—61no—
130C4×Dic3—62no—
131C4×Dic3—62no—
132C2×C3⋊C8—22no—
133C2×C3⋊C8—62no—
134C2×C3⋊C8—62no—
135D3×C8—68no—
136C22×C32C2×C22⋊C411yescharacteristic
137C2×C3⋊D3—21no—
138C2×C3⋊D3—21no—
139C2×C3⋊D3#10112yes—
140C32×C4—21no—
141C32×C4—21no—
142C32×C4—21no—
143C3⋊Dic3—21no—
144C3⋊Dic3—21no—
145C3⋊Dic3#10412yes—
146C3×Dic3—42no—
147C3×Dic3—42no—
148C22×C8—181no—
149C4⋊Q8—91no—
150C4⋊Q8—91no—
151#125—32no—
152C22⋊Q8—181no—
153C22⋊Q8—181no—
154C4×Q8—181no—
155C4×Q8—181no—
156#117—92no—
157C2×C42—91no—
158C4⋊C8—181no—
159C22⋊C8—181no—
160#97—32no—
161#97—91no—
162#97—181no—
163#97D3211yescharacteristic
164C22×D3—32no—
165C22×D3—61no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—62no—
170C2×C3×C4—62no—
171C2×C3×C4C2×C4×D312yes—
172C2×C3×C4D3×D412yes—
173C2×C3×C4D3×D412yes—
174C2×Dic3—22no—
175C2×Dic3—22no—
176C2×Dic3—32no—
177C2×Dic3—32no—
178C2×Dic3—32no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C4×D3—64no—
183C4×D3—64no—
184C4×D3—122no—
185C4×D3—122no—
186C4×D3—122no—
187C4×D3—122no—
188Dic6—124no—
189Dic6—124no—
190C3×C8—42no—
191C3×C8—42no—
192C3×C8—64no—
193C3⋊C8—24no—
194C3⋊C8—122no—
195C3⋊C8—122no—
196C2×C32C2×#10111yescharacteristic
197C2×C32C2×#10411yescharacteristic
198C2×C32#42111yescharacteristic
199C3⋊D3—22no—
200C2×Q8—181no—
201C2×Q8—181no—
202C22×C4—91no—
203C22×C4—91no—
204C22×C4—91no—
205C2×C8—21no—
206C2×C8—62no—
207C2×C8—184no—
208C2×C8—181no—
209C4⋊C4—32no—
210C4⋊C4—32no—
211C4⋊C4—62no—
212C4⋊C4—62no—
213C4⋊C4—181no—
214C4⋊C4—181no—
215C22⋊C4—182no—
216C42—91no—
217C42—91no—
218C42—91no—
219C42—182no—
220C42C2×D3211yescharacteristic
221C22×C3—21no—
222C22×C3D3×C22⋊C412yes—
223C2×D3—34no—
224C2×D3—62no—
225C2×D3—62no—
226C2×D3—62no—
227C2×D3—121no—
228C2×D3—121no—
229C3×C4—22no—
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—22no—
233C3×C4—41no—
234C3×C4—41no—
235C3×C4—122no—
236C3×C4—122no—
237Dic3—34no—
238Dic3—42no—
239Dic3—42no—
240Dic3—62no—
241Dic3—62no—
242Dic3—62no—
243Dic3—121no—
244Dic3—121no—
245C32#153111yescharacteristic, complemented, Sylow
246C23—91no—
247Q8—362no—
248Q8—362no—
249C2×C4—62no—
250C2×C4—62no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—182no—
255C2×C4—182no—
256C2×C4—361no—
257C2×C4C4×D3211yescharacteristic
258C2×C4#380211yescharacteristic
259C2×C4#381111yescharacteristic
260C8—41no—
261C8—64no—
262C8—361no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3D3×#10112yes—
267C2×C3D3×#10412yes—
268C2×C3#482112yes—
269D3—64no—
270D3—122no—
271C22—92no—
272C22—181no—
273C22—181no—
274C22#6392111yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—92no—
279C4—122no—
280C4—122no—
281C4—181no—
282C4—181no—
283C3—21no—
284C3#6836512yescomplemented
285C2—182no—
286C2#1059039411yescharacteristic
287C2#1059100311yescharacteristic
288C2#1059100811yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenter#97D32
hypocenterC32#1531
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
4. C3×#4465C2semidirect
5. #10589088C2semidirect
30. #4465D3semidirect
245. C32#1531semidirect
284. C3#68365semidirect

Maximal subgroups

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

subgroupindex
#105938542
#105924042
#105903222
C3×#44652
#105890882
#683653