Finite Group Databasebeta

← #11796538

Subgroups — #11796538

Order 1152.

595 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 595 conjugacy classes of subgroups — too many to draw. Only its 78 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#10596195C211yesmaximal, characteristic
2#10591639C212yesmaximal, complemented
3C3×#4548C212yesmaximal, complemented
4#10589183C212yesmaximal, complemented
5#69171—32nomaximal
6C2×#3832C411yescharacteristic
7C2×Q8×C3⋊D3C2211yescharacteristic
8C32×C4⋊Q8C2211yescharacteristic
9#64156C2211yescharacteristic
10#64153C411yescharacteristic
11#64105—22no—
12#64103—22no—
13#64084C411yescharacteristic
14#64081C411yescharacteristic
15#63818—22no—
16C3×#836C2214yes—
17#63561—22no—
18#5724—32no—
19#5724—61no—
20D3×#101—34no—
21C3×#356—32no—
22#4548D312yescomplemented
23#4477—34no—
24C2×C32×Q8C2×C411yescharacteristic
25C2×C32×Q8C2311yescharacteristic
26#3832—42no—
27Q8×C3⋊D3—42no—
28C2×C4⋊(C3⋊D3)—21no—
29C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D412yes—
33C2×#634C2×C411yescharacteristic
34C2×#634D412yes—
35C32×C4⋊C4—22no—
36C32×C42C2×C411yescharacteristic
37#3752—21no—
38#3752—22no—
39#3752—22no—
40#3750—21no—
41#3750—22no—
42C4×C3⋊Dic3C2×C411yescharacteristic
43C3×#208—24no—
44#3712—42no—
45#3710—42no—
46#2133—91noSylow
47C2×#239—32no—
48C2×#239—61no—
49C2×D3×Q8—32no—
50C2×D3×Q8—61no—
51C3×C4⋊Q8—21no—
52C3×C4⋊Q8C2×D312yes—
53#947—32no—
54#947—61no—
55#944—32no—
56#944—61no—
57D3×M16—64no—
58#896—64no—
59#896—64no—
60#894—64no—
61#894—64no—
62#875—32no—
63#875—61no—
64#872—32no—
65#872—61no—
66C3×#101—34no—
67#836C2×D314yes—
68#824—64no—
69C22×C3⋊D3—21no—
70C22×C3⋊D3C22⋊C411yescharacteristic
71C32×Q8—41no—
72C32×Q8—41no—
73C2×C32×C4—21no—
74C2×C32×C4—21no—
75C2×C32×C4C22×C411yescharacteristic
76C2×C32×C4C2×D412yes—
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3C22⋊C412yes—
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C4⋊(C3⋊D3)—41no—
81C4⋊(C3⋊D3)—42no—
82C4×C3⋊D3—22no—
83C4×C3⋊D3—22no—
84C4×C3⋊D3—22no—
85C4×C3⋊D3—42no—
86#634—41no—
87#634—42no—
88C3×C3⋊C8—44no—
89#536—91no—
90C2×#101—92no—
91#356—32no—
92#355—92no—
93C2×C3×Q8—21no—
94C2×C3×Q8—21no—
95C2×C3×Q8C4×D312yes—
96C2×C3×Q8C22×D312yes—
97#239—124no—
98#239—124no—
99D3×Q8—124no—
100D3×Q8—124no—
101C2×D12—32no—
102C2×D12—61no—
103C2×D12—62no—
104C2×D12—62no—
105C2×C4×D3—32no—
106C2×C4×D3—34no—
107C2×C4×D3—61no—
108C2×C4×D3—62no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×Dic6—32no—
112C2×Dic6—34no—
113C2×Dic6—61no—
114C2×Dic6—62no—
115C3×M16—64no—
116C3×C4⋊C4—24no—
117C3×C4⋊C4—24no—
118C3×C42—21no—
119C3×C42C4×D312yes—
120(C2×D3)⋊C4—64no—
121(C2×D3)⋊C4—62no—
122(C2×D3)⋊C4—62no—
123(C2×D3)⋊C4—64no—
124(C2×D3)⋊C4—64no—
125(C2×D3)⋊C4—64no—
126Dic3⋊C4—62no—
127Dic3⋊C4—64no—
128Dic3⋊C4—62no—
129Dic3⋊C4—64no—
130C4×Dic3—32no—
131C4×Dic3—61no—
132#208—24no—
133ΓL(1,𝔽25)—124no—
134D3×C8—124no—
135C22×C32C2×C22⋊C411yescharacteristic
136C2×C3⋊D3—41no—
137C2×C3⋊D3—42no—
138C2×C3⋊D3—41no—
139C2×C3⋊D3#9912yes—
140C32×C4—21no—
141C32×C4—22no—
142C32×C4—41no—
143C32×C4—41no—
144C3⋊Dic3—21no—
145C3⋊Dic3—22no—
146C3⋊Dic3—41no—
147C2×#41—91no—
148C22×Q8—91no—
149C2×M16—182no—
150C4⋊Q8—91no—
151C4⋊Q8D3211yescharacteristic
152#124—91no—
153#124—91no—
154#123—182no—
155C22⋊Q8—182no—
156#117—91no—
157#101—34no—
158#101—182no—
159C22×D3—32no—
160C22×D3—61no—
161C22×D3—62no—
162C22×D3—62no—
163C3×Q8—42no—
164C3×Q8—42no—
165C3×Q8—42no—
166C3×Q8—42no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—21no—
172C2×C3×C4—22no—
173C2×C3×C4C2×C4×D312yes—
174C2×C3×C4D3×D414yes—
175C2×Dic3—34no—
176C2×Dic3—32no—
177C2×Dic3—61no—
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—62no—
181D12—122no—
182D12—122no—
183D12—124no—
184D12—124no—
185C4×D3—64no—
186C4×D3—64no—
187C4×D3—64no—
188C4×D3—64no—
189C4×D3—122no—
190C4×D3—122no—
191C4×D3—124no—
192C4×D3—124no—
193Dic6—124no—
194Dic6—122no—
195Dic6—124no—
196Dic6—122no—
197C3×C8—124no—
198C3⋊C8—44no—
199C2×C32—21no—
200C2×C32C2×#9911yescharacteristic
201C3⋊D3—22no—
202C3⋊D3—81no—
203#41—362no—
204C2×Q8—91no—
205C2×Q8—92no—
206C2×Q8—362no—
207C2×Q8#62411yescharacteristic
208C2×Q8C2×D3211yescharacteristic
209C2×D4—91no—
210C2×D4—181no—
211C22×C4—91no—
212C22×C4—92no—
213C22×C4—181no—
214M16—64no—
215M16—362no—
216C2×C8—362no—
217C4⋊C4—22no—
218C4⋊C4—181no—
219C4⋊C4—182no—
220C22⋊C4—182no—
221C22⋊C4—181no—
222C22⋊C4—182no—
223C42—91no—
224C42#62411yescharacteristic
225C22×C3—21no—
226C22×C3D3×C22⋊C412yes—
227C2×D3—34no—
228C2×D3—62no—
229C2×D3—122no—
230C2×D3—122no—
231C2×D3—122no—
232C2×D3—124no—
233C2×D3—124no—
234C2×D3—122no—
235C3×C4—22no—
236C3×C4—24no—
237C3×C4—22no—
238C3×C4—42no—
239C3×C4—42no—
240C3×C4—42no—
241C3×C4—42no—
242C3×C4—42no—
243Dic3—62no—
244Dic3—62no—
245Dic3—64no—
246Dic3—122no—
247Dic3—122no—
248Dic3—122no—
249C32#213311yescharacteristic, complemented, Sylow
250C23—91no—
251C23—181no—
252Q8—41no—
253Q8—41no—
254Q8—362no—
255Q8—361no—
256D4—361no—
257D4—362no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—92no—
261C2×C4—91no—
262C2×C4—182no—
263C2×C4—182no—
264C2×C4—182no—
265C2×C4—181no—
266C2×C4—362no—
267C2×C4C2×#62411yescharacteristic
268C2×C4#381112yes—
269C8—124no—
270C2×C3—22no—
271C2×C3—22no—
272C2×C3—21no—
273C2×C3D3×#9912yes—
274D3—64no—
275D3—122no—
276D3—242no—
277D3—242no—
278C22—92no—
279C22—361no—
280C22—362no—
281C22—361no—
282C22#6397411yescharacteristic
283C4—22no—
284C4—21no—
285C4—41no—
286C4—41no—
287C4—181no—
288C4—182no—
289C4—361no—
290C3—21no—
291C3#6917112yescomplemented
292C2—21no—
293C2—182no—
294C2—721no—
295C2#1059152711yescharacteristic
subgroupG/H
centerC2#10591527
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C2×D32
FittingC32×C4⋊Q8C22
socleC2×C32C2×#99
prime radicalC2×#3832C4
cosocleC2×C32×Q8C23
hypercenterC4⋊Q8D32
hypocenterC32#2133
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10591639C2semidirect
3. C3×#4548C2semidirect
4. #10589183C2semidirect
22. #4548D3semidirect
249. C32#2133semidirect
291. C3#69171semidirect

Maximal subgroups

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

subgroupindex
#105961952
#105916392
C3×#45482
#105891832
#691713