Finite Group Databasebeta

← #11775744

Subgroups — #11775744

Order 1152.

611 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 611 conjugacy classes of subgroups — too many to draw. Only its 88 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#10592406C211yesmaximal, characteristic, complemented
3#10590247C211yesmaximal, characteristic, complemented
4C3×#4464C212yesmaximal, complemented
5#10589086C212yesmaximal, complemented
6#68342—32nomaximal
7C2×#3796C412yes—
8C2×#3743—21no—
9C42×C3⋊D3C2211yescharacteristic
10C3×#875C2212yes—
11#63914C411yescharacteristic
12#63912—21no—
13#63912—21no—
14#63902—21no—
15#63902—21no—
16#63873C411yescharacteristic
17C2×#3712—21no—
18C32×#97C2211yescharacteristic
19C8×C3⋊Dic3—21no—
20#63630C2211yescharacteristic
21C3×#803C2212yes—
22#63553—21no—
23#5668—32no—
24#4707—32no—
25#4707—32no—
26#4707—61no—
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—
47#3743—24no—
48C3×(C2×D3)⋊C4—22no—
49C3×(C2×D3)⋊C4—22no—
50C2×C3×C3⋊C8—22no—
51#3724—21no—
52#3724—21no—
53#3712—24no—
54#1525—91noSylow
55C2×#239—32no—
56C2×#237—32no—
57C3×#124—32no—
58#944—32no—
59#940—32no—
60C2×ΓL(1,𝔽25)—62no—
61C2×ΓL(1,𝔽25)—62no—
62C2×ΓL(1,𝔽25)—62no—
63#884—62no—
64#884—62no—
65#67⋊C4—62no—
66#67⋊C4—62no—
67#875C2×D312yes—
68C42×D3—32no—
69C42×D3—61no—
70C3×#97—21no—
71C3×#97—32no—
72C3×#97C2×D312yes—
73C8×Dic3—62no—
74C8×Dic3—62no—
75C8×Dic3—62no—
76#803—32no—
77#803—61no—
78#803C2×D312yes—
79C22×C3⋊D3C22⋊C411yescharacteristic
80C22×C3×D3—22no—
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C4×C3⋊D3—22no—
88C4×C3⋊D3—22no—
89C4×C3⋊D3—22no—
90C2×C3×Dic3—22no—
91C3×D12—42no—
92C3×Dic6—42no—
93#626—44no—
94#625—42no—
95#625—42no—
96D3×Dic3—44no—
97C32×C8—22no—
98C3⋊(C3⋊C8)—22no—
99C3×C3⋊C8—24no—
100#532—91no—
101C4×M16—91no—
102C4×M16—91no—
103#329—32no—
104#329—92no—
105C2×C3×Q8—32no—
106C2×C3×D4—32no—
107C2×#67—62no—
108C2×#67—62no—
109C2×#67—62no—
110C22×Dic3—62no—
111#239—124no—
112#237—124no—
113C2×D12—62no—
114C2×D12C4×D312yes—
115C2×C4×D3—32no—
116C2×C4×D3—32no—
117C2×C4×D3—32no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—62no—
122C2×Dic6C4×D312yes—
123C2×C3×C8—22no—
124C2×C3×C8—22no—
125C2×C3×C8—62no—
126C3×C22⋊C4—62no—
127C3×C22⋊C4—62no—
128C3×C42—21no—
129C3×C42C22×D312yes—
130(C2×D3)⋊C4—22no—
131(C2×D3)⋊C4—22no—
132Dic3⋊C4—62no—
133Dic3⋊C4—62no—
134C4×Dic3—32no—
135C4×Dic3—32no—
136C4×Dic3—32no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C2×C3⋊C8—22no—
141C2×C3⋊C8—62no—
142C2×C3⋊C8—62no—
143ΓL(1,𝔽25)—68no—
144ΓL(1,𝔽25)—68no—
145ΓL(1,𝔽25)—68no—
146C22×C32C2×C22⋊C411yescharacteristic
147C2×C3⋊D3—21no—
148C2×C3⋊D3—21no—
149C2×C3⋊D3—21no—
150C2×C3×D3—42no—
151C2×C3×D3—42no—
152C2×C3×D3—42no—
153C32×C4—21no—
154C32×C4—21no—
155C32×C4—21no—
156C3⋊Dic3#10012yes—
157C3⋊Dic3#10412yes—
158C3⋊Dic3#10412yes—
159C3×Dic3—42no—
160C2×#41—92no—
161C2×M16—181no—
162C2×M16—181no—
163C4⋊Q8—91no—
164#127—91no—
165#124—32no—
166#121—181no—
167#121—181no—
168C4×D4—181no—
169C4×D4—181no—
170C2×C42—91no—
171#97—32no—
172#97—91no—
173#97D3211yescharacteristic
174C4×C8—181no—
175C4×C8—181no—
176C23×C3—62no—
177C22×D3—22no—
178C22×D3—32no—
179C22×D3—61no—
180C3×Q8—122no—
181C3×D4—122no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—62no—
186C2×C3×C4C2×C4×D312yes—
187C2×C3×C4D3×D412yes—
188C2×C3×C4D3×D412yes—
189#67—124no—
190#67—124no—
191#67—124no—
192C2×Dic3—22no—
193C2×Dic3—32no—
194C2×Dic3—32no—
195C2×Dic3—32no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—124no—
200D12—42no—
201D12—124no—
202C4×D3—64no—
203C4×D3—64no—
204C4×D3—64no—
205C4×D3—64no—
206C4×D3—122no—
207C4×D3—122no—
208C4×D3—124no—
209Dic6—42no—
210C3×C8—24no—
211C3×C8—24no—
212C3×C8—64no—
213C3⋊C8—24no—
214C3⋊C8—64no—
215C3⋊C8—64no—
216C2×C32C2×#10011yescharacteristic
217C2×C32C2×#10411yescharacteristic
218C2×C32C2×#10411yescharacteristic
219C3⋊D3—41no—
220C3×D3—82no—
221#41—364no—
222C2×Q8—32no—
223C2×D4—32no—
224C2×D4—182no—
225C2×D4—181no—
226C2×D4—181no—
227C22×C4—91no—
228C22×C4—91no—
229C22×C4—91no—
230C22×C4—182no—
231M16—184no—
232M16—184no—
233C2×C8—21no—
234C2×C8—62no—
235C2×C8—181no—
236C4⋊C4—181no—
237C4⋊C4—181no—
238C22⋊C4—62no—
239C22⋊C4—62no—
240C42—91no—
241C42—91no—
242C42—91no—
243C42C2×D3211yescharacteristic
244C22×C3—21no—
245C22×C3—122no—
246C22×C3—122no—
247C22×C3—122no—
248C22×C3D3×C22⋊C412yes—
249C2×D3—42no—
250C2×D3—42no—
251C2×D3—42no—
252C2×D3—62no—
253C2×D3—62no—
254C2×D3—62no—
255C2×D3—62no—
256C2×D3—121no—
257C2×D3—121no—
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—22no—
261C3×C4—22no—
262C3×C4—41no—
263C3×C4—41no—
264C3×C4—122no—
265Dic3—34no—
266Dic3—34no—
267Dic3—34no—
268Dic3—42no—
269Dic3—62no—
270Dic3—62no—
271Dic3—62no—
272C32#152511yescharacteristic, complemented, Sylow
273C23—62no—
274C23—91no—
275Q8—122no—
276D4—122no—
277D4—362no—
278D4—362no—
279D4—364no—
280C2×C4—62no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—182no—
285C2×C4—182no—
286C2×C4—182no—
287C2×C4—364no—
288C2×C4C4×D3211yescharacteristic
289C2×C4#380211yescharacteristic
290C2×C4#381111yescharacteristic
291C8—22no—
292C8—64no—
293C8—182no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—242no—
298C2×C3D3×#10012yes—
299C2×C3D3×#10412yes—
300C2×C3D3×#10412yes—
301D3—82no—
302D3—122no—
303D3—122no—
304C22—122no—
305C22—122no—
306C22—122no—
307C22—181no—
308C22—181no—
309C22—181no—
310C22#6392111yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—92no—
315C4—92no—
316C4—92no—
317C4—122no—
318C3—21no—
319C3#6834212yescomplemented
320C2—242no—
321C2—361no—
322C2#1059039311yescharacteristic
323C2#1059100111yescharacteristic
324C2#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#1525
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. #10592406C2semidirect
3. #10590247C2semidirect
4. C3×#4464C2semidirect
5. #10589086C2semidirect
30. #4464D3semidirect
272. C32#1525semidirect
319. C3#68342semidirect

Maximal subgroups

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

subgroupindex
#105939712
#105924062
#105902472
C3×#44642
#105890862
#683423