Finite Group Databasebeta

← #11775424

Subgroups — #11775424

Order 1152.

562 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 56 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#10596019C211yesmaximal, characteristic
2#10593737C211yesmaximal, characteristic, complemented
3#10593730C211yesmaximal, characteristic, complemented
4#10590209C212yesmaximal, complemented
5#10590157C212yesmaximal, complemented
6C2×#3828—21no—
7C32×C4×D4C411yescharacteristic, complemented
8#64149C411yescharacteristic, complemented
9#64147C2211yescharacteristic
10C4×#638—21no—
11#64104C2211yescharacteristic
12#64097C411yescharacteristic, complemented
13#64094—21no—
14#64093—21no—
15C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
16C42×C3⋊D3C2211yescharacteristic
17#63781—21no—
18#63781—21no—
19#63781C2212yes—
20#63778C2212yes—
21#63777—21no—
22C4⋊#622—21no—
23#5548—62no—
24C22×#157—22no—
25C2×C32×D4C2×C411yescharacteristic
26C22×C32×C4—21no—
27C2×#638—21no—
28C2×#638—21no—
29C2×#638—21no—
30#3828—44no—
31C2×C4⋊(C3⋊D3)—21no—
32C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×#634—21no—
38C2×#622—22no—
39C32×C4⋊C4C2×C411yescharacteristic
40C32×C22⋊C4—21no—
41C32×C42C2×C411yescharacteristic
42#3757—21no—
43#3752—21no—
44#3752—21no—
45C4⋊(C3⋊Dic3)C2×C411yescharacteristic
46#3750—21no—
47C4×C3⋊Dic3C2×C411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50#1514—91nomaximal, Sylow
51C2×#235—64no—
52C3×C4×D4—22no—
53#940—62no—
54#938—62no—
55C4×#67—64no—
56#895—62no—
57#888—62no—
58#885—64no—
59#884—64no—
60C4×D12—62no—
61C42×D3—62no—
62C23×C32—21no—
63C22×C3⋊D3—21no—
64C22×C3⋊D3C2×D411yescharacteristic
65C2×#157—42no—
66C2×#157—42no—
67C2×#157—42no—
68C32×D4—41no—
69C2×C32×C4—21no—
70C2×C32×C4—42no—
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C22×C411yescharacteristic
74#638—42no—
75#638—42no—
76#638—42no—
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C2×D411yescharacteristic
81C4⋊(C3⋊D3)—41no—
82C4⋊(C3⋊D3)—42no—
83C4×C3⋊D3—22no—
84C4×C3⋊D3—41no—
85C4×C3⋊D3—41no—
86C4×C3⋊D3—42no—
87#634—42no—
88#622—42no—
89#532—91no—
90#432—91no—
91#383—91no—
92#327—92no—
93#327—92no—
94C2×C3×D4—22no—
95C22×C3×C4—24no—
96C2×#67—64no—
97C2×#67—64no—
98C2×#67—64no—
99#235—1216no—
100C2×D12—62no—
101C2×D12—64no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—64no—
106C2×Dic6—64no—
107C3×C4⋊C4—22no—
108C3×C22⋊C4—24no—
109C3×C42—22no—
110#217—64no—
111(C2×D3)⋊C4—64no—
112(C2×D3)⋊C4—64no—
113C4⋊Dic3—62no—
114Dic3⋊C4—64no—
115C4×Dic3—62no—
116C4×Dic3—62no—
117C4×Dic3—62no—
118C22×C32—41no—
119C22×C32—41no—
120C22×C32—41no—
121C22×C32C2×C22⋊C411yescharacteristic
122C2×C3⋊D3—21no—
123C2×C3⋊D3—21no—
124C2×C3⋊D3—41no—
125C2×C3⋊D3—41no—
126C2×C3⋊D3—41no—
127C2×C3⋊D3AGL(1,ℤ/8)12yes—
128#157—82no—
129C32×C4—21no—
130C32×C4—21no—
131C32×C4—21no—
132C32×C4—41no—
133C3⋊Dic3—21no—
134C3⋊Dic3—21no—
135C3⋊Dic3—21no—
136C3⋊Dic3—41no—
137C2×#41—181no—
138C4⋊Q8—91no—
139#127—91no—
140#124—181no—
141#121—91no—
142#121—91no—
143#121—181no—
144C4×D4—91no—
145C4×D4—181no—
146C4×D4#15711yescharacteristic, complemented
147C2×C42—91no—
148C4⋊C8—181no—
149C22⋊C8—92no—
150#97—181no—
151#95—92no—
152#95—181no—
153#95—181no—
154C23×C3—24no—
155C22×D3—62no—
156C22×D3—64no—
157C3×D4—44no—
158C2×C3×C4—24no—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×C3×C4—22no—
162C2×C3×C4—48no—
163#67—128no—
164#67—128no—
165#67—128no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—62no—
169C2×Dic3—64no—
170D12—124no—
171D12—128no—
172C4×D3—68no—
173C4×D3—124no—
174C4×D3—124no—
175C4×D3—128no—
176Dic6—128no—
177C2×C32—81no—
178C2×C32#41011yescharacteristic
179C2×C32#41811yescharacteristic
180C2×C32#42111yescharacteristic
181C3⋊D3—22no—
182C3⋊D3—81no—
183#41—364no—
184C2×Q8—181no—
185C2×D4—91no—
186C2×D4—181no—
187C2×D4—181no—
188C2×D4—181no—
189C2×D4—181no—
190C2×D4C2×#15711yescharacteristic
191C22×C4—21no—
192C22×C4—91no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—181no—
196C22×C4—182no—
197C2×C8—182no—
198C4⋊C4—91no—
199C4⋊C4—181no—
200C4⋊C4C2×#15711yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—181no—
203C22⋊C4—181no—
204C22⋊C4—181no—
205C42—91no—
206C42—91no—
207C42—91no—
208C42C2×#15711yescharacteristic
209C22×C3—22no—
210C22×C3—44no—
211C22×C3—44no—
212C22×C3—44no—
213C2×D3—64no—
214C2×D3—122no—
215C2×D3—122no—
216C2×D3—124no—
217C2×D3—124no—
218C2×D3—124no—
219C3×C4—24no—
220C3×C4—24no—
221C3×C4—42no—
222C3×C4—44no—
223Dic3—64no—
224Dic3—64no—
225Dic3—122no—
226Dic3—124no—
227C32#151411yescharacteristic, complemented, Sylow
228C23—21no—
229C23—91no—
230C23—181no—
231Q8—362no—
232D4—41no—
233D4—361no—
234D4—362no—
235D4—362no—
236D4—362no—
237D4—362no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—91no—
241C2×C4—91no—
242C2×C4—91no—
243C2×C4—182no—
244C2×C4—181no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C4—362no—
248C2×C4—362no—
249C2×C4—362no—
250C2×C4—362no—
251C2×C4C22⋊#15711yescharacteristic
252C2×C4C22⋊#15711yescharacteristic
253C2×C4C22×#15711yescharacteristic
254C8—362no—
255C2×C3—22no—
256C2×C3—22no—
257C2×C3—22no—
258C2×C3—84no—
259D3—124no—
260D3—244no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—92no—
265C22—181no—
266C22—181no—
267C22—361no—
268C22—361no—
269C22—361no—
270C22C2×C22⋊#15711yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—41no—
275C4—181no—
276C4—181no—
277C4—181no—
278C4—361no—
279C4—722no—
280C3—22no—
281C2—81no—
282C2—182no—
283C2—721no—
284C2#1059379211yescharacteristic
285C2#1059381411yescharacteristic
286C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×D4C4
socleC22×C32C2×C22⋊C4
prime radical#10596019C2
cosocleC2×C4×C3⋊D3C23
hypercenterC4×D4#157
hypocenterC32#1514
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593737C2semidirect
3. #10593730C2semidirect
4. #10590209C2semidirect
5. #10590157C2semidirect
7. C32×C4×D4C4semidirect
8. #64149C4semidirect
12. #64097C4semidirect
15. C4×C4⋊(C3⋊D3)C4semidirect
146. C4×D4#157semidirect
227. C32#1514semidirect

Maximal subgroups

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

subgroupindex
#105960192
#105937372
#105937302
#105902092
#105901572
#15149