Finite Group Databasebeta

← #11775054

Subgroups — #11775054

Order 1152.

594 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 68 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
2C4×C4⋊#157C211yesmaximal, characteristic, complemented
3#10593725C211yesmaximal, characteristic, complemented
4#10590209C212yesmaximal, complemented
5#10590157C212yesmaximal, complemented
6C2×#3828—21no—
7C2×C4⋊#157—21no—
8C2×C4×#157—21no—
9C32×C4×D4C411yescharacteristic, complemented
10#64149C411yescharacteristic, complemented
11#64147C2211yescharacteristic
12C4×#638—21no—
13#64104C2211yescharacteristic
14#64097C411yescharacteristic, complemented
15#64094—21no—
16#64093—21no—
17C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
18C42×C3⋊D3C2211yescharacteristic
19#63781C2212yes—
20#63779—21no—
21#63778C2212yes—
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—42no—
31#3828—42no—
32C2×C4⋊(C3⋊D3)—21no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3C2311yescharacteristic
38C2×#634—21no—
39C2×#622—22no—
40C4⋊#157—24no—
41C4×#157—42no—
42C32×C4⋊C4C2×C411yescharacteristic
43C32×C22⋊C4—21no—
44C32×C42C2×C411yescharacteristic
45#3757—21no—
46#3752—21no—
47#3752—21no—
48C4⋊(C3⋊Dic3)C2×C411yescharacteristic
49#3750—21no—
50C4×C3⋊Dic3C2×C411yescharacteristic
51C4×C3⋊Dic3D411yescharacteristic
52C4×C3⋊Dic3D411yescharacteristic
53#1502—91nomaximal, Sylow
54C2×#235—64no—
55C3×C4×D4—22no—
56#940—62no—
57#938—62no—
58C4×#67—64no—
59#895—62no—
60#888—62no—
61#885—64no—
62#884—64no—
63C4×D12—62no—
64C42×D3—62no—
65C23×C32—21no—
66C22×C3⋊D3—21no—
67C22×C3⋊D3C2×D411yescharacteristic
68C2×#157—24no—
69C2×#157—42no—
70C2×#157—42no—
71C32×D4—41no—
72C2×C32×C4—21no—
73C2×C32×C4—42no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C22×C411yescharacteristic
77#638—41no—
78#638—41no—
79#638—42no—
80#638—42no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C4⋊(C3⋊D3)—41no—
86C4⋊(C3⋊D3)—41no—
87C4⋊(C3⋊D3)—41no—
88C4×C3⋊D3—22no—
89C4×C3⋊D3—41no—
90C4×C3⋊D3—42no—
91C4×C3⋊D3D812yes—
92C4×C3⋊D3SD1612yes—
93#634—42no—
94#622—42no—
95#532—91no—
96#431—91no—
97C4×C4⋊C4—91no—
98#327—92no—
99#327—92no—
100C2×C3×D4—22no—
101C22×C3×C4—24no—
102C2×#67—64no—
103C2×#67—64no—
104C2×#67—64no—
105#235—128no—
106#235—128no—
107C2×D12—62no—
108C2×D12—64no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—62no—
112C2×C4×D3—64no—
113C2×Dic6—64no—
114C3×C4⋊C4—22no—
115C3×C22⋊C4—24no—
116C3×C42—22no—
117#217—64no—
118(C2×D3)⋊C4—64no—
119(C2×D3)⋊C4—64no—
120C4⋊Dic3—62no—
121Dic3⋊C4—64no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C22×C32—41no—
126C22×C32—41no—
127C22×C32—41no—
128C22×C32C2×C22⋊C411yescharacteristic
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3—41no—
132C2×C3⋊D3—41no—
133C2×C3⋊D3—41no—
134C2×C3⋊D3C2×D811yescharacteristic
135C2×C3⋊D3C2×SD1611yescharacteristic
136#157—44no—
137C32×C4—21no—
138C32×C4—21no—
139C32×C4—41no—
140C32×C4#10212yes—
141C3⋊Dic3—21no—
142C3⋊Dic3—41no—
143C3⋊Dic3#10212yes—
144C3⋊Dic3#10412yes—
145C2×#41—181no—
146C4⋊Q8—91no—
147#127—91no—
148#124—181no—
149#121—91no—
150#121—91no—
151#121—181no—
152C4×D4—91no—
153C4×D4—181no—
154C4×D4#15711yescharacteristic, complemented
155C2×C4⋊C4—181no—
156C2×C42—91no—
157C2×C42—181no—
158C4⋊C8—181no—
159C22⋊C8—92no—
160C4×C8—181no—
161#95—92no—
162C23×C3—24no—
163C22×D3—62no—
164C22×D3—64no—
165C3×D4—44no—
166C2×C3×C4—24no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—48no—
171#67—128no—
172#67—128no—
173#67—124no—
174#67—124no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—64no—
179D12—124no—
180D12—124no—
181D12—124no—
182C4×D3—64no—
183C4×D3—64no—
184C4×D3—124no—
185C4×D3—124no—
186C4×D3—128no—
187Dic6—128no—
188C2×C32—81no—
189C2×C32#41011yescharacteristic
190C2×C32C2×#10211yescharacteristic
191C2×C32C2×#10411yescharacteristic
192C3⋊D3—21no—
193C3⋊D3—21no—
194C3⋊D3—81no—
195#41—362no—
196#41—362no—
197C2×Q8—181no—
198C2×D4—91no—
199C2×D4—181no—
200C2×D4—181no—
201C2×D4—181no—
202C2×D4—181no—
203C2×D4C2×#15711yescharacteristic
204C22×C4—21no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—182no—
209C22×C4—181no—
210C2×C8—182no—
211C4⋊C4—91no—
212C4⋊C4—181no—
213C4⋊C4—184no—
214C4⋊C4C2×#15711yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—181no—
217C22⋊C4—181no—
218C22⋊C4—181no—
219C42—91no—
220C42—91no—
221C42—91no—
222C42—362no—
223C42C2×#15711yescharacteristic
224C22×C3—22no—
225C22×C3—44no—
226C22×C3—44no—
227C22×C3—44no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—122no—
231C2×D3—122no—
232C2×D3—124no—
233C2×D3—124no—
234C2×D3—124no—
235C3×C4—24no—
236C3×C4—24no—
237C3×C4—42no—
238C3×C4—44no—
239Dic3—64no—
240Dic3—64no—
241Dic3—122no—
242Dic3—124no—
243C32#150211yescharacteristic, complemented, Sylow
244C23—21no—
245C23—91no—
246C23—181no—
247Q8—362no—
248D4—41no—
249D4—361no—
250D4—361no—
251D4—361no—
252D4—362no—
253D4—362no—
254D4—361no—
255D4—361no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—91no—
259C2×C4—91no—
260C2×C4—92no—
261C2×C4—92no—
262C2×C4—91no—
263C2×C4—182no—
264C2×C4—184no—
265C2×C4—181no—
266C2×C4—361no—
267C2×C4—362no—
268C2×C4—362no—
269C2×C4—362no—
270C2×C4C22⋊#15711yescharacteristic
271C2×C4C22⋊#15711yescharacteristic
272C2×C4C22×#15711yescharacteristic
273C8—362no—
274C2×C3—22no—
275C2×C3—22no—
276C2×C3—22no—
277C2×C3—84no—
278D3—122no—
279D3—122no—
280D3—244no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—91no—
285C22—91no—
286C22—181no—
287C22—181no—
288C22—361no—
289C22—361no—
290C22—361no—
291C22C2×C22⋊#15711yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—92no—
296C4—92no—
297C4—181no—
298C4—364no—
299C4—361no—
300C4#6378212yes—
301C3—22no—
302C2—81no—
303C2—181no—
304C2—181no—
305C2—721no—
306C2#1059379211yescharacteristic
307C2C2×#6378211yescharacteristic
308C2#1059383911yescharacteristic
subgroupG/H
centerC2×C4C22⋊#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#1502
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#157C2semidirect
3. #10593725C2semidirect
4. #10590209C2semidirect
5. #10590157C2semidirect
9. C32×C4×D4C4semidirect
10. #64149C4semidirect
14. #64097C4semidirect
17. C4×C4⋊(C3⋊D3)C4semidirect
154. C4×D4#157semidirect
243. C32#1502semidirect

Maximal subgroups

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

subgroupindex
#105960192
C4×C4⋊#1572
#105937252
#105902092
#105901572
#15029