Finite Group Databasebeta

← #11775436

Subgroups — #11775436

Order 1152.

476 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 55 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#10595032C211yesmaximal, characteristic
2#10593804C211yesmaximal, characteristic, complemented
3#10591229C211yesmaximal, characteristic, complemented
4#10590071C214yesmaximal, complemented
5C2×C3×#235—21no—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7#63980—21no—
8#63980C2212yes—
9#63914C411yescharacteristic, complemented
10C4×#625—21no—
11C4×#625C412yescomplemented
12#63873C411yescharacteristic, complemented
13#63863—21no—
14C22⋊#622C2212yes—
15#63779—21no—
16#63777—21no—
17C3×C3⋊#95—21no—
18#63579—21no—
19#63579C2212yes—
20#5832—61no—
21#4651—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C2×C3×#67—22no—
26C22×C3×Dic3—22no—
27C3×#235—44no—
28C2×C3×D12—21no—
29C2×C3×C4×D3—22no—
30C2×C3×Dic6—21no—
31C2×#625—21no—
32C2×#625C2×C412yes—
33C2×#622—22no—
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38#3724—21no—
39#3724C2×C412yes—
40(C2×D3)⋊Dic3—22no—
41(C2×D3)⋊Dic3—22no—
42#1514—91nomaximal, Sylow
43C2×C3×#41—61no—
44C2×#235—21no—
45#947—61no—
46#944—61no—
47#940—61no—
48#939—62no—
49#939—62no—
50#936—61no—
51C4×#67—62no—
52C4×#67—62no—
53C2×C4×Dic3—61no—
54C2×C4×Dic3—61no—
55C3×#95—61no—
56C3⋊#95—21no—
57C3⋊#95—62no—
58C3⋊#95—62no—
59C23×C32C2×D411yescharacteristic
60C22×C3×D3—22no—
61C2×C32×C4—22no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—41no—
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22×C411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C3×#67—44no—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—42no—
73C2×C3×Dic3—42no—
74C2×C3×Dic3—42no—
75C3×D12—42no—
76C3×C4×D3—44no—
77C3×Dic6—42no—
78#625—42no—
79#625—42no—
80#622—42no—
81#532—91no—
82#432—91no—
83#383—91no—
84#327—94no—
85C3×#41—124no—
86C2×C3×Q8—61no—
87C2×C3×D4—61no—
88C2×C3×D4—62no—
89C22×C3×C4—21no—
90C22×C3×C4—21no—
91C22×C3×C4—62no—
92C22×C3×C4—62no—
93C2×#67—22no—
94C2×#67—62no—
95C2×#67—62no—
96C22×Dic3—22no—
97C22×Dic3—61no—
98C22×Dic3—61no—
99C22×Dic3—61no—
100C22×Dic3—61no—
101#235—44no—
102C2×D12—21no—
103C2×C4×D3—22no—
104C2×Dic6—21no—
105#217—62no—
106#217—62no—
107(C2×D3)⋊C4—62no—
108(C2×D3)⋊C4—62no—
109Dic3⋊C4—62no—
110Dic3⋊C4—62no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C22×C32—21no—
120C22×C32—21no—
121C22×C32C2×C22⋊C411yescharacteristic
122C22×C32AGL(1,ℤ/8)12yes—
123C2×C3×D3—42no—
124C2×C3×D3—42no—
125C2×C3×D3—42no—
126C32×C4—21no—
127C32×C4—21no—
128C3⋊Dic3—21no—
129C3⋊Dic3—21no—
130C3⋊Dic3—21no—
131C3⋊Dic3—21no—
132C3×Dic3—42no—
133C3×Dic3—82no—
134C2×#41—61no—
135C4⋊Q8—91no—
136#127—91no—
137#124—181no—
138#121—92no—
139#121—181no—
140C4×D4—92no—
141C4×D4—181no—
142C2×C42—91no—
143C4⋊C8—181no—
144C22⋊C8—92no—
145#97—181no—
146#95—61no—
147#95—92no—
148#95—181no—
149C23×C3—21no—
150C23×C3—21no—
151C23×C3—62no—
152C22×D3—22no—
153C3×Q8—122no—
154C3×D4—122no—
155C3×D4—124no—
156C2×C3×C4—24no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—42no—
162C2×C3×C4—62no—
163C2×C3×C4—124no—
164C2×C3×C4—122no—
165C2×C3×C4—122no—
166C2×C3×C4—122no—
167#67—44no—
168#67—124no—
169#67—124no—
170C2×Dic3—22no—
171C2×Dic3—42no—
172C2×Dic3—42no—
173C2×Dic3—42no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—122no—
183C2×Dic3—122no—
184C2×Dic3—121no—
185C2×Dic3—122no—
186C2×Dic3—121no—
187D12—42no—
188C4×D3—44no—
189Dic6—42no—
190C2×C32—22no—
191C2×C32#41011yescharacteristic
192C2×C32#41811yescharacteristic
193C2×C32#42111yescharacteristic
194C3×D3—82no—
195#41—124no—
196C2×Q8—61no—
197C2×D4—62no—
198C2×D4—61no—
199C2×D4—92no—
200C2×D4—181no—
201C22×C4—62no—
202C22×C4—62no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4GO+(4,𝔽2)11yescharacteristic
206C2×C8—182no—
207C4⋊C4—92no—
208C4⋊C4—181no—
209C22⋊C4—182no—
210C22⋊C4—182no—
211C42—91no—
212C42—91no—
213C42—91no—
214C42—91no—
215C22×C3—21no—
216C22×C3—22no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—22no—
221C22×C3—22no—
222C22×C3—41no—
223C22×C3—41no—
224C22×C3—122no—
225C22×C3—122no—
226C22×C3—122no—
227C2×D3—42no—
228C2×D3—42no—
229C2×D3—42no—
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—41no—
233C3×C4—41no—
234C3×C4—122no—
235C3×C4—242no—
236Dic3—42no—
237Dic3—62no—
238Dic3—62no—
239Dic3—82no—
240Dic3—121no—
241Dic3—121no—
242Dic3—121no—
243Dic3—121no—
244Dic3—121no—
245Dic3—121no—
246C32#151411yescharacteristic, complemented, Sylow
247C23—62no—
248C23C2×GO+(4,𝔽2)11yescharacteristic
249Q8—122no—
250D4—122no—
251D4—124no—
252D4—362no—
253D4—362no—
254C2×C4—22no—
255C2×C4—62no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—91no—
259C2×C4—91no—
260C2×C4—124no—
261C2×C4—122no—
262C2×C4—122no—
263C2×C4—122no—
264C2×C4—361no—
265C2×C4—361no—
266C2×C4D32⋊C411yescharacteristic
267C2×C4D32⋊C411yescharacteristic
268C8—362no—
269C2×C3—22no—
270C2×C3—22no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—42no—
278C2×C3—242no—
279D3—82no—
280C22—21no—
281C22—21no—
282C22—122no—
283C22—122no—
284C22—122no—
285C22C2×D32⋊C411yescharacteristic
286C22#6423612yes—
287C4—21no—
288C4—21no—
289C4—122no—
290C4—181no—
291C4—181no—
292C4—181no—
293C4—181no—
294C4—242no—
295C3—21no—
296C3—21no—
297C2—22no—
298C2—242no—
299C2#1059334511yescharacteristic
300C2#1059338111yescharacteristic
301C2#1059349311yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10595032C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1514
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593804C2semidirect
3. #10591229C2semidirect
4. #10590071C2semidirect
9. #63914C4semidirect
11. C4×#625C4semidirect
12. #63873C4semidirect
246. C32#1514semidirect

Maximal subgroups

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

subgroupindex
#105950322
#105938042
#105912292
#105900712
#15149