Finite Group Databasebeta

← #11775885

Subgroups — #11775885

Order 1152.

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

normal subgroups only

This group has 567 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#10593971C211yesmaximal, characteristic
2#10592404C211yesmaximal, characteristic, complemented
3#10590322C211yesmaximal, characteristic, complemented
4C3×#4464C212yesmaximal, complemented
5#10589086C212yesmaximal, complemented
6#68345—32nomaximal
7C2×#3796C412yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×#875C2212yes—
10#63914C411yescharacteristic
11#63912—21no—
12#63912—21no—
13#63902—21no—
14#63902—21no—
15#63873C411yescharacteristic
16C2×#3710—21no—
17C32×#97C2211yescharacteristic
18#63647—21no—
19#63641—21no—
20#63630C2211yescharacteristic
21C3×#803C2212yes—
22#63555—21no—
23#5668—32no—
24#4705—32no—
25#4705—61no—
26D3×#97—32no—
27C3×#329—32no—
28#4540—32no—
29#4464—32no—
30#4464D312yescomplemented
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C3×D12C2×C412yes—
35C2×C3×Dic6C2×C412yes—
36C2×#626—22no—
37C2×#625—21no—
38C2×#625—21no—
39C2×D3×Dic3—22no—
40#3796—44no—
41C2×C32×C8—21no—
42C32×C42C2311yescharacteristic
43C4×C3⋊Dic3C2×C411yescharacteristic
44C4×C3⋊Dic3D411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C3×(C2×D3)⋊C4—22no—
48C3×(C2×D3)⋊C4—22no—
49C2×C3×C3⋊C8—22no—
50#3724—21no—
51#3724—21no—
52#3710—24no—
53#1530—91noSylow
54C2×#239—32no—
55C2×#237—32no—
56C3×#124—32no—
57#944—32no—
58#940—32no—
59C2×D3×C8—62no—
60#884—62no—
61#884—62no—
62#67⋊C4—62no—
63#67⋊C4—62no—
64#875C2×D312yes—
65C42×D3—32no—
66C42×D3—61no—
67C3×#97—21no—
68C3×#97—32no—
69C3×#97C2×D312yes—
70(C2×D3)⋊C8—62no—
71(C2×D3)⋊C8—62no—
72#815—62no—
73Dic3⋊C8—62no—
74Dic3⋊C8—62no—
75#803—32no—
76#803—61no—
77#803C2×D312yes—
78C22×C3⋊D3C22⋊C411yescharacteristic
79C22×C3×D3—22no—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C4×C3⋊D3—22no—
87C4×C3⋊D3—22no—
88C4×C3⋊D3—41no—
89C2×C3×Dic3—22no—
90C3×D12—42no—
91C3×Dic6—42no—
92#626—44no—
93#625—42no—
94#625—42no—
95D3×Dic3—44no—
96C32×C8—41no—
97C3⋊(C3⋊C8)—41no—
98C3×C3⋊C8—24no—
99#532—91no—
100#432—91no—
101C2×#97—91no—
102#329—32no—
103#329—92no—
104C2×C3×Q8—32no—
105C2×C3×D4—32no—
106C2×#67—62no—
107C2×#67—62no—
108C2×#67—62no—
109C22×Dic3—62no—
110#239—124no—
111#237—124no—
112C2×D12—62no—
113C2×D12C4×D312yes—
114C2×C4×D3—32no—
115C2×C4×D3—32no—
116C2×C4×D3—32no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—62no—
121C2×Dic6C4×D312yes—
122C2×C3×C8—22no—
123C2×C3×C8—22no—
124C2×C3×C8—62no—
125C3×C22⋊C4—62no—
126C3×C22⋊C4—62no—
127C3×C42—21no—
128C3×C42C22×D312yes—
129(C2×D3)⋊C4—22no—
130(C2×D3)⋊C4—22no—
131Dic3⋊C4—62no—
132Dic3⋊C4—62no—
133C4×Dic3—32no—
134C4×Dic3—32no—
135C4×Dic3—32no—
136C4×Dic3—61no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C2×C3⋊C8—22no—
140C2×C3⋊C8—62no—
141C2×C3⋊C8—62no—
142D3×C8—68no—
143C22×C32C2×C22⋊C411yescharacteristic
144C2×C3⋊D3—21no—
145C2×C3⋊D3—21no—
146C2×C3⋊D3#10012yes—
147C2×C3×D3—42no—
148C2×C3×D3—42no—
149C2×C3×D3—42no—
150C32×C4—21no—
151C32×C4—21no—
152C32×C4—21no—
153C3⋊Dic3—21no—
154C3⋊Dic3—21no—
155C3⋊Dic3#10412yes—
156C3×Dic3—42no—
157C2×#41—92no—
158C22×C8—181no—
159C4⋊Q8—91no—
160#127—91no—
161#124—32no—
162#121—181no—
163#121—181no—
164C4×D4—181no—
165C4×D4—181no—
166C2×C42—91no—
167C4⋊C8—181no—
168C22⋊C8—181no—
169#97—32no—
170#97—91no—
171#97—181no—
172#97D3211yescharacteristic
173C23×C3—62no—
174C22×D3—22no—
175C22×D3—32no—
176C22×D3—61no—
177C3×Q8—122no—
178C3×D4—122no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—62no—
183C2×C3×C4C2×C4×D312yes—
184C2×C3×C4D3×D412yes—
185C2×C3×C4D3×D412yes—
186#67—124no—
187#67—124no—
188#67—124no—
189C2×Dic3—22no—
190C2×Dic3—32no—
191C2×Dic3—32no—
192C2×Dic3—32no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—124no—
197D12—42no—
198D12—124no—
199C4×D3—64no—
200C4×D3—64no—
201C4×D3—122no—
202C4×D3—122no—
203C4×D3—122no—
204C4×D3—124no—
205C4×D3—122no—
206Dic6—42no—
207C3×C8—42no—
208C3×C8—42no—
209C3×C8—64no—
210C3⋊C8—24no—
211C3⋊C8—122no—
212C3⋊C8—122no—
213C2×C32C2×#10011yescharacteristic
214C2×C32C2×#10411yescharacteristic
215C2×C32#42111yescharacteristic
216C3⋊D3—22no—
217C3×D3—82no—
218#41—364no—
219C2×Q8—32no—
220C2×D4—32no—
221C2×D4—182no—
222C2×D4—181no—
223C2×D4—181no—
224C22×C4—91no—
225C22×C4—91no—
226C22×C4—91no—
227C22×C4—182no—
228C2×C8—21no—
229C2×C8—62no—
230C2×C8—184no—
231C2×C8—181no—
232C4⋊C4—181no—
233C4⋊C4—181no—
234C22⋊C4—62no—
235C22⋊C4—62no—
236C42—91no—
237C42—91no—
238C42—91no—
239C42C2×D3211yescharacteristic
240C22×C3—21no—
241C22×C3—122no—
242C22×C3—122no—
243C22×C3—122no—
244C22×C3D3×C22⋊C412yes—
245C2×D3—34no—
246C2×D3—42no—
247C2×D3—42no—
248C2×D3—42no—
249C2×D3—62no—
250C2×D3—62no—
251C2×D3—62no—
252C2×D3—121no—
253C2×D3—121no—
254C3×C4—22no—
255C3×C4—22no—
256C3×C4—22no—
257C3×C4—22no—
258C3×C4—41no—
259C3×C4—41no—
260C3×C4—122no—
261Dic3—34no—
262Dic3—42no—
263Dic3—62no—
264Dic3—62no—
265Dic3—62no—
266Dic3—121no—
267Dic3—121no—
268C32#153011yescharacteristic, complemented, Sylow
269C23—62no—
270C23—91no—
271Q8—122no—
272D4—122no—
273D4—362no—
274D4—364no—
275D4—362no—
276C2×C4—62no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—182no—
281C2×C4—182no—
282C2×C4—361no—
283C2×C4—364no—
284C2×C4C4×D3211yescharacteristic
285C2×C4#380211yescharacteristic
286C2×C4#381111yescharacteristic
287C8—41no—
288C8—64no—
289C8—361no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—242no—
294C2×C3D3×#10012yes—
295C2×C3D3×#10412yes—
296C2×C3#482112yes—
297D3—64no—
298D3—82no—
299D3—122no—
300C22—92no—
301C22—122no—
302C22—122no—
303C22—122no—
304C22—181no—
305C22—181no—
306C22#6392111yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—92no—
311C4—122no—
312C4—181no—
313C4—181no—
314C3—21no—
315C3#6834512yescomplemented
316C2—182no—
317C2—242no—
318C2#1059039411yescharacteristic
319C2#1059100111yescharacteristic
320C2#1059100811yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32C2×C22⋊C4
prime radical#10593971C2
cosocleC32×C42C23
hypercenter#97D32
hypocenterC32#1530
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
2. #10592404C2semidirect
3. #10590322C2semidirect
4. C3×#4464C2semidirect
5. #10589086C2semidirect
30. #4464D3semidirect
268. C32#1530semidirect
315. C3#68345semidirect

Maximal subgroups

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

subgroupindex
#105939712
#105924042
#105903222
C3×#44642
#105890862
#683453