Finite Group Databasebeta

← #11775150

Subgroups — #11775150

Order 1152.

582 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 58 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#10593733C211yesmaximal, characteristic, complemented
3#10593731C211yesmaximal, characteristic, complemented
4#10590209C212yesmaximal, complemented
5#10590157C212yesmaximal, complemented
6C2×#3828—21no—
7C2×C4×#157—21no—
8C32×C4×D4C411yescharacteristic, complemented
9#64149C411yescharacteristic, complemented
10#64147C2211yescharacteristic
11C4×#638—21no—
12#64104C2211yescharacteristic
13#64097C411yescharacteristic, complemented
14#64094—21no—
15#64093—21no—
16C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
17C42×C3⋊D3C2211yescharacteristic
18#63781—21no—
19#63781C2212yes—
20#63779—21no—
21#63778C2212yes—
22#63777—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—
39C4×#157—24no—
40C32×C4⋊C4C2×C411yescharacteristic
41C32×C22⋊C4—21no—
42C32×C42C2×C411yescharacteristic
43#3757—21no—
44#3752—21no—
45#3752—21no—
46C4⋊(C3⋊Dic3)C2×C411yescharacteristic
47#3750—21no—
48C4×C3⋊Dic3C2×C411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3D411yescharacteristic
51#1505—91nomaximal, Sylow
52C2×#235—64no—
53C3×C4×D4—22no—
54#940—62no—
55#938—62no—
56C4×#67—64no—
57#895—62no—
58#888—62no—
59#885—64no—
60#884—64no—
61C4×D12—62no—
62C42×D3—62no—
63C23×C32—21no—
64C22×C3⋊D3—21no—
65C22×C3⋊D3C2×D411yescharacteristic
66C2×#157—24no—
67C2×#157—42no—
68C2×#157—42no—
69C32×D4—41no—
70C2×C32×C4—21no—
71C2×C32×C4—42no—
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C22⋊C411yescharacteristic
74C2×C32×C4C22×C411yescharacteristic
75#638—42no—
76#638—42no—
77#638—42no—
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C2×D411yescharacteristic
82C4⋊(C3⋊D3)—41no—
83C4⋊(C3⋊D3)—42no—
84C4×C3⋊D3—22no—
85C4×C3⋊D3—22no—
86C4×C3⋊D3—41no—
87C4×C3⋊D3—42no—
88#634—42no—
89#622—42no—
90#532—91no—
91#432—91no—
92#376—91no—
93#327—92no—
94#327—92no—
95C2×C3×D4—22no—
96C22×C3×C4—24no—
97C2×#67—64no—
98C2×#67—64no—
99C2×#67—64no—
100#235—1216no—
101C2×D12—62no—
102C2×D12—64no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—62no—
106C2×C4×D3—64no—
107C2×Dic6—64no—
108C3×C4⋊C4—22no—
109C3×C22⋊C4—24no—
110C3×C42—22no—
111#217—64no—
112(C2×D3)⋊C4—64no—
113(C2×D3)⋊C4—64no—
114C4⋊Dic3—62no—
115Dic3⋊C4—64no—
116C4×Dic3—62no—
117C4×Dic3—62no—
118C4×Dic3—62no—
119C22×C32—41no—
120C22×C32—41no—
121C22×C32—41no—
122C22×C32C2×C22⋊C411yescharacteristic
123C2×C3⋊D3—21no—
124C2×C3⋊D3—21no—
125C2×C3⋊D3—41no—
126C2×C3⋊D3—41no—
127C2×C3⋊D3—41no—
128C2×C3⋊D3AGL(1,ℤ/8)12yes—
129#157—44no—
130C32×C4—21no—
131C32×C4—21no—
132C32×C4—21no—
133C32×C4—41no—
134C3⋊Dic3—21no—
135C3⋊Dic3—21no—
136C3⋊Dic3—41no—
137C3⋊Dic3#10412yes—
138C2×#41—181no—
139C4⋊Q8—91no—
140#127—91no—
141#124—181no—
142#121—91no—
143#121—91no—
144#121—181no—
145C4×D4—91no—
146C4×D4—181no—
147C4×D4#15711yescharacteristic, complemented
148C2×C42—91no—
149C2×C42—181no—
150C4⋊C8—181no—
151C22⋊C8—92no—
152#97—181no—
153#95—92no—
154#95—181no—
155C23×C3—24no—
156C22×D3—62no—
157C22×D3—64no—
158C3×D4—44no—
159C2×C3×C4—24no—
160C2×C3×C4—22no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—48no—
164#67—128no—
165#67—128no—
166#67—128no—
167C2×Dic3—62no—
168C2×Dic3—62no—
169C2×Dic3—62no—
170C2×Dic3—64no—
171D12—124no—
172D12—128no—
173C4×D3—68no—
174C4×D3—124no—
175C4×D3—124no—
176C4×D3—128no—
177Dic6—128no—
178C2×C32—81no—
179C2×C32#41011yescharacteristic
180C2×C32#41811yescharacteristic
181C2×C32C2×#10411yescharacteristic
182C3⋊D3—22no—
183C3⋊D3—81no—
184#41—364no—
185C2×Q8—181no—
186C2×D4—91no—
187C2×D4—181no—
188C2×D4—181no—
189C2×D4—181no—
190C2×D4—181no—
191C2×D4C2×#15711yescharacteristic
192C22×C4—21no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—91no—
196C22×C4—182no—
197C22×C4—181no—
198C2×C8—182no—
199C4⋊C4—91no—
200C4⋊C4—181no—
201C4⋊C4C2×#15711yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—181no—
204C22⋊C4—181no—
205C22⋊C4—181no—
206C42—91no—
207C42—91no—
208C42—91no—
209C42—184no—
210C42C2×#15711yescharacteristic
211C22×C3—22no—
212C22×C3—44no—
213C22×C3—44no—
214C22×C3—44no—
215C2×D3—64no—
216C2×D3—122no—
217C2×D3—122no—
218C2×D3—124no—
219C2×D3—124no—
220C2×D3—124no—
221C3×C4—24no—
222C3×C4—24no—
223C3×C4—42no—
224C3×C4—44no—
225Dic3—64no—
226Dic3—64no—
227Dic3—122no—
228Dic3—124no—
229C32#150511yescharacteristic, complemented, Sylow
230C23—21no—
231C23—91no—
232C23—181no—
233Q8—362no—
234D4—41no—
235D4—361no—
236D4—362no—
237D4—362no—
238D4—362no—
239D4—362no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—91no—
243C2×C4—91no—
244C2×C4—91no—
245C2×C4—182no—
246C2×C4—182no—
247C2×C4—184no—
248C2×C4—181no—
249C2×C4—361no—
250C2×C4—362no—
251C2×C4—362no—
252C2×C4—362no—
253C2×C4C22⋊#15711yescharacteristic
254C2×C4C22⋊#15711yescharacteristic
255C2×C4C22×#15711yescharacteristic
256C8—362no—
257C2×C3—22no—
258C2×C3—22no—
259C2×C3—22no—
260C2×C3—84no—
261D3—124no—
262D3—244no—
263C22—41no—
264C22—41no—
265C22—41no—
266C22—92no—
267C22—181no—
268C22—181no—
269C22—361no—
270C22—361no—
271C22—361no—
272C22C2×C22⋊#15711yescharacteristic
273C4—21no—
274C4—21no—
275C4—21no—
276C4—41no—
277C4—92no—
278C4—181no—
279C4—181no—
280C4—364no—
281C4—361no—
282C3—22no—
283C2—81no—
284C2—182no—
285C2—721no—
286C2#1059379211yescharacteristic
287C2#1059381411yescharacteristic
288C2#1059383911yescharacteristic
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#1505
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. #10593733C2semidirect
3. #10593731C2semidirect
4. #10590209C2semidirect
5. #10590157C2semidirect
8. C32×C4×D4C4semidirect
9. #64149C4semidirect
13. #64097C4semidirect
16. C4×C4⋊(C3⋊D3)C4semidirect
147. C4×D4#157semidirect
229. C32#1505semidirect

Maximal subgroups

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

subgroupindex
#105960192
#105937332
#105937312
#105902092
#105901572
#15059