Finite Group Databasebeta

← #11791468

Subgroups — #11791468

Order 1152.

630 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×#64231C211yesmaximal, characteristic
2C4⋊C4×#157C211yesmaximal, characteristic, complemented
3C2×#63732C211yesmaximal, characteristic, complemented
4C2×#63729C212yesmaximal, complemented
5#10590593C212yesmaximal, complemented
6C22×GO+(4,𝔽2)—21no—
7C22×GO+(4,𝔽2)—21no—
8C2×#3802C2212yes—
9C2×C4⋊#157C2211yescharacteristic
10C2×C4×#157—21no—
11C2×C4×#157C2211yescharacteristic
12#64231—22no—
13#64231C414yescomplemented
14C4⋊C4×C3⋊D3C2211yescharacteristic
15C2×#3710C2212yes—
16#63781—21no—
17#63732—22no—
18#63729—24no—
19C3×#809—22no—
20#63563—22no—
21D3×#102—62no—
22C22×D32—22no—
23C22×#157—21no—
24C22×#157D411yescharacteristic
25C22×#157D411yescharacteristic
26C2×GO+(4,𝔽2)—24no—
27C2×GO+(4,𝔽2)—24no—
28C2×GO+(4,𝔽2)—42no—
29C2×GO+(4,𝔽2)—42no—
30C2×GO+(4,𝔽2)—42no—
31C2×GO+(4,𝔽2)—42no—
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3C2311yescharacteristic
34C2×C3×D12—22no—
35C2×#625—22no—
36#3802—22no—
37#3802—22no—
38#3802—22no—
39#3802C2×C414yes—
40C4⋊#157—21no—
41C4⋊#157D412yescomplemented
42C4×#157—42no—
43C4×#157C2×C412yes—
44C4×#157D412yes—
45C32×C4⋊C4D411yescharacteristic, complemented
46C4⋊(C3⋊Dic3)D411yescharacteristic, complemented
47#3750—21no—
48C2×C3×C3⋊C8—22no—
49#3710—22no—
50#3710—22no—
51#1982—91nomaximal, Sylow
52C2×D3×D4—62no—
53C2×D3×C8—62no—
54D3×C4⋊C4—62no—
55C3×#102—62no—
56#832—62no—
57#821—62no—
58#809—22no—
59C22×C3⋊D3C2×D411yescharacteristic
60C22×C3×D3—42no—
61C2×D32—24no—
62C2×D32—42no—
63C2×D32—42no—
64C2×D32—42no—
65C2×D32—42no—
66C2×D32—42no—
67C2×#157—21no—
68C2×#157—21no—
69C2×#157—22no—
70C2×#157—41no—
71C2×#157—41no—
72C2×#157C22⋊C412yes—
73C2×#157C22⋊C412yes—
74C2×#157D812yes—
75C2×#157SD1612yes—
76GO+(4,𝔽2)—48no—
77GO+(4,𝔽2)—48no—
78C2×C32×C4—21no—
79C2×C32×C4C2×D411yescharacteristic
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3#4111yescharacteristic
82C4×C3⋊D3—41no—
83C4×C3⋊D3—41no—
84C4×C3⋊D3C22×C411yescharacteristic
85C4×C3⋊D3C2×D411yescharacteristic
86C4×C3⋊D3C2×D411yescharacteristic
87C4×C3⋊D3#4111yescharacteristic
88C3×D12—24no—
89C3×D12—42no—
90#625—24no—
91#625—42no—
92C3×C3⋊C8—42no—
93C2×#127—91no—
94C2×C4⋊C8—91no—
95C2×#102—92no—
96C2×#102—92no—
97C4×C4⋊C4—91no—
98C23×D3—122no—
99C2×C3×D4—62no—
100C2×#67—122no—
101D3×D4—64no—
102D3×D4—64no—
103D3×D4—122no—
104D3×D4—122no—
105C2×D12—22no—
106C2×C4×D3—62no—
107C2×C4×D3—122no—
108C2×C3×C8—62no—
109C3×C4⋊C4—22no—
110C4⋊Dic3—62no—
111Dic3⋊C4—122no—
112C2×C3⋊C8—22no—
113D3×C8—122no—
114D3×C8—122no—
115C22×C32#12111yescharacteristic
116C2×C3⋊D3C2×C22⋊C411yescharacteristic
117C2×C3⋊D3#12111yescharacteristic
118C2×C3⋊D3C2×D811yescharacteristic
119C2×C3⋊D3C2×SD1611yescharacteristic
120C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
121C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
122C2×C3×D3—44no—
123C2×C3×D3—82no—
124C2×C3×D3—82no—
125D32—44no—
126D32—44no—
127D32—82no—
128D32—82no—
129#157—22no—
130#157—42no—
131#157#10214yescomplemented
132C32×C4—41no—
133C32×C4C4×D411yescharacteristic
134C32×C4#12711yescharacteristic
135C3⋊Dic3—41no—
136C3⋊Dic3C4×D411yescharacteristic
137C3⋊Dic3#12411yescharacteristic
138C22×D4—92no—
139C22×D4—181no—
140C22×D4—181no—
141C22×C8—92no—
142#127—94no—
143#127—182no—
144C2×C4⋊C4—91no—
145C2×C4⋊C4—91no—
146C2×C42—91no—
147C2×C42—181no—
148C4⋊C8—182no—
149#102—62no—
150#102—182no—
151#102—184no—
152#95—181no—
153C23×C3—122no—
154C22×D3—42no—
155C22×D3—62no—
156C22×D3—124no—
157C22×D3—124no—
158C22×D3—242no—
159C22×D3—242no—
160C22×D3—242no—
161C22×D3—242no—
162C3×D4—64no—
163C3×D4—122no—
164C2×C3×C4—22no—
165C2×C3×C4—42no—
166#67—124no—
167#67—124no—
168C2×Dic3—62no—
169C2×Dic3—122no—
170D12—24no—
171D12—42no—
172C4×D3—62no—
173C4×D3—62no—
174C4×D3—62no—
175C4×D3—62no—
176C4×D3—242no—
177C4×D3—242no—
178C3×C8—122no—
179C3⋊C8—42no—
180C2×C32#39011yescharacteristic
181C2×C32#45911yescharacteristic
182C2×C32#46011yescharacteristic
183C3⋊D3C2×#10211yescharacteristic
184C3⋊D3#41811yescharacteristic
185C3⋊D3#45911yescharacteristic
186C3⋊D3#46011yescharacteristic
187C3×D3—84no—
188C24—182no—
189C2×D4—62no—
190C2×D4—94no—
191C2×D4—182no—
192C2×D4—182no—
193C2×D4—182no—
194C2×D4—182no—
195C2×D4—184no—
196C2×D4—184no—
197C2×D4—362no—
198C2×D4—362no—
199C2×D4—362no—
200C2×D4—362no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4—91no—
204C22×C4—181no—
205C22×C4—181no—
206C2×C8—62no—
207C2×C8—182no—
208C2×C8—182no—
209C4⋊C4—92no—
210C4⋊C4—91no—
211C4⋊C4—181no—
212C4⋊C4—181no—
213C4⋊C4GO+(4,𝔽2)11yescharacteristic, complemented
214C42—92no—
215C42—92no—
216C42—362no—
217C22×C3—22no—
218C22×C3—124no—
219C22×C3—242no—
220C22×C3—242no—
221C2×D3—44no—
222C2×D3—62no—
223C2×D3—62no—
224C2×D3—62no—
225C2×D3—62no—
226C2×D3—62no—
227C2×D3—62no—
228C2×D3—82no—
229C2×D3—82no—
230C2×D3—244no—
231C2×D3—244no—
232C2×D3—244no—
233C2×D3—244no—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—82no—
237Dic3—62no—
238Dic3—62no—
239Dic3—242no—
240C32#198211yescharacteristic, complemented, Sylow
241C23—91no—
242C23—122no—
243C23—184no—
244C23—362no—
245C23—362no—
246C23—362no—
247C23—362no—
248C23—362no—
249D4—64no—
250D4—122no—
251D4—184no—
252D4—362no—
253D4—368no—
254D4—368no—
255C2×C4—21no—
256C2×C4—92no—
257C2×C4—92no—
258C2×C4—92no—
259C2×C4—91no—
260C2×C4—91no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4—92no—
265C2×C4—181no—
266C2×C4—181no—
267C2×C4—182no—
268C2×C4—181no—
269C2×C4—361no—
270C2×C4—361no—
271C2×C4—361no—
272C2×C4—361no—
273C2×C4C2×GO+(4,𝔽2)11yescharacteristic
274C8—122no—
275C2×C3—22no—
276C2×C3—22no—
277C2×C3—22no—
278C2×C3—244no—
279D3—62no—
280D3—62no—
281D3—62no—
282D3—62no—
283D3—84no—
284C22—91no—
285C22—91no—
286C22—91no—
287C22—91no—
288C22—91no—
289C22—91no—
290C22—124no—
291C22—242no—
292C22—242no—
293C22—364no—
294C22—364no—
295C22—722no—
296C22—722no—
297C22#6424211yescharacteristic
298C4—41no—
299C4—94no—
300C4—91no—
301C4—91no—
302C4—182no—
303C4—362no—
304C4—361no—
305C4C4×GO+(4,𝔽2)11yescharacteristic
306C4#6423111yescharacteristic
307C3—22no—
308C2—91no—
309C2—91no—
310C2—91no—
311C2—91no—
312C2—244no—
313C2#1059345411yescharacteristic
314C2#1059346411yescharacteristic
315C2#1059347611yescharacteristic
subgroupG/H
centerC22#64242
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC2×#64231C2
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1982
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×#157C2semidirect
3. C2×#63732C2semidirect
4. C2×#63729C2semidirect
5. #10590593C2semidirect
13. #64231C4semidirect
41. C4⋊#157D4semidirect
45. C32×C4⋊C4D4semidirect
46. C4⋊(C3⋊Dic3)D4semidirect
131. #157#102semidirect
213. C4⋊C4GO+(4,𝔽2)semidirect
240. C32#1982semidirect

Maximal subgroups

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

subgroupindex
C2×#642312
C4⋊C4×#1572
C2×#637322
C2×#637292
#105905932
#19829