Finite Group Databasebeta

← #11774429

Subgroups — #11774429

Order 1152.

446 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 60 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#10596151C211yesmaximal, characteristic
2#10593727C211yesmaximal, characteristic, complemented
3#10593727C211yesmaximal, characteristic, complemented
4Q8⋊#622C212yesmaximal, complemented
5D4⋊#622C212yesmaximal, complemented
6C32×#124C411yescharacteristic
7#64155C411yescharacteristic
8Q8×C3⋊Dic3C2211yescharacteristic
9#64147C411yescharacteristic
10D4×C3⋊Dic3C2211yescharacteristic
11#64092—21no—
12#64090—21no—
13#64088—21no—
14#64086—21no—
15C42×C3⋊D3C2211yescharacteristic
16#64079C411yescharacteristic
17#63778—21no—
18#63778—21no—
19C4⋊#622—21no—
20C4⋊#622C2212yes—
21C4×#622—21no—
22C4×#622C2212yes—
23#5680—62no—
24C2×C32×Q8C2×C411yescharacteristic
25C2×C32×D4C2×C411yescharacteristic
26C2×#638—21no—
27C22×C3⋊Dic3—21no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×#622—22no—
32C2×#622—22no—
33C32×C22⋊C4—21no—
34C32×C22⋊C4—21no—
35C32×C42C2×C411yescharacteristic
36#3757—21no—
37#3757—21no—
38#3752—21no—
39C4⋊(C3⋊Dic3)—21no—
40C4⋊(C3⋊Dic3)C2×C411yescharacteristic
41C4⋊(C3⋊Dic3)C2×C411yescharacteristic
42#3750—21no—
43#3750—21no—
44#3750—21no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3D411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C4×C3⋊Dic3C2311yescharacteristic
49#1482—91nomaximal, Sylow
50C3×#124—22no—
51#946—62no—
52Q8×Dic3—62no—
53#938—62no—
54D4×Dic3—62no—
55#883—64no—
56#67⋊C4—64no—
57#879—64no—
58#877—64no—
59C42×D3—62no—
60#870—62no—
61C23×C32—21no—
62C22×C3⋊D3C22⋊C411yescharacteristic
63C32×Q8—22no—
64C32×D4—22no—
65C2×C32×C4—21no—
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C22×C411yescharacteristic
69#638—42no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—42no—
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C4×C3⋊D3—22no—
77C4×C3⋊D3—22no—
78C4×C3⋊D3—41no—
79#622—42no—
80#622—42no—
81#529—91no—
82#431—91no—
83#431—91no—
84Q8⋊C8—92no—
85D4⋊C8—92no—
86C2×C3×Q8—22no—
87C2×C3×D4—22no—
88C2×#67—64no—
89C22×Dic3—64no—
90C2×C4×D3—62no—
91C2×C4×D3—62no—
92C2×C4×D3—62no—
93C3×C22⋊C4—24no—
94C3×C22⋊C4—24no—
95C3×C42—22no—
96#217—64no—
97#217—64no—
98(C2×D3)⋊C4—64no—
99C4⋊Dic3—62no—
100C4⋊Dic3—62no—
101C4⋊Dic3—64no—
102Dic3⋊C4—64no—
103Dic3⋊C4—64no—
104Dic3⋊C4—64no—
105C4×Dic3—62no—
106C4×Dic3—62no—
107C4×Dic3—62no—
108C4×Dic3—64no—
109C22×C32—41no—
110C22×C32—41no—
111C22×C32—41no—
112C22×C32C2×C22⋊C411yescharacteristic
113C2×C3⋊D3—21no—
114C2×C3⋊D3—21no—
115C2×C3⋊D3—21no—
116C32×C4—21no—
117C32×C4—21no—
118C32×C4—41no—
119C32×C4#13112yes—
120C3⋊Dic3—21no—
121C3⋊Dic3—21no—
122C3⋊Dic3—41no—
123C3⋊Dic3—41no—
124C3⋊Dic3#13512yes—
125#126—181no—
126#125—91no—
127#124#15711yescharacteristic
128#123—181no—
129C22⋊Q8—91no—
130#121—91no—
131C4×Q8—91no—
132C4×D4—91no—
133C4×D4—181no—
134#117—181no—
135C2×C42—91no—
136C4⋊C8—92no—
137C4⋊C8—181no—
138C22⋊C8—181no—
139C22⋊C8—181no—
140C4×C8—92no—
141C4×C8—181no—
142C23×C3—24no—
143C22×D3—62no—
144C3×Q8—44no—
145C3×D4—44no—
146C2×C3×C4—24no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150#67—128no—
151C2×Dic3—62no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—64no—
155C2×Dic3—64no—
156C2×Dic3—128no—
157C4×D3—124no—
158C4×D3—124no—
159C4×D3—124no—
160C2×C32—81no—
161C2×C32#40811yescharacteristic
162C2×C32#41611yescharacteristic
163C2×C32#42111yescharacteristic
164C3⋊D3—41no—
165C2×Q8C2×#15711yescharacteristic
166C2×D4—181no—
167C2×D4C2×#15711yescharacteristic
168C22×C4—91no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—181no—
172C2×C8—182no—
173C2×C8—182no—
174C4⋊C4—91no—
175C4⋊C4—91no—
176C4⋊C4—181no—
177C4⋊C4—181no—
178C4⋊C4—181no—
179C4⋊C4—181no—
180C22⋊C4—21no—
181C22⋊C4—21no—
182C22⋊C4—181no—
183C22⋊C4—181no—
184C22⋊C4—181no—
185C42—91no—
186C42—91no—
187C42—91no—
188C42—181no—
189C42C2×#15711yescharacteristic
190C22×C3—22no—
191C22×C3—44no—
192C22×C3—44no—
193C22×C3—44no—
194C2×D3—64no—
195C2×D3—122no—
196C2×D3—122no—
197C3×C4—24no—
198C3×C4—42no—
199C3×C4—42no—
200C3×C4—44no—
201Dic3—64no—
202Dic3—122no—
203Dic3—122no—
204Dic3—124no—
205Dic3—124no—
206C32#148211yescharacteristic, complemented, Sylow
207C23—21no—
208C23—91no—
209Q8—22no—
210D4—22no—
211D4—362no—
212C2×C4—21no—
213C2×C4—91no—
214C2×C4—91no—
215C2×C4—91no—
216C2×C4—182no—
217C2×C4—182no—
218C2×C4—181no—
219C2×C4—181no—
220C2×C4—361no—
221C2×C4—362no—
222C2×C4C22⋊#15711yescharacteristic
223C2×C4C22⋊#15711yescharacteristic
224C2×C4C22×#15711yescharacteristic
225C8—362no—
226C8—362no—
227C2×C3—22no—
228C2×C3—22no—
229C2×C3—22no—
230C2×C3—84no—
231D3—124no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—181no—
236C22—181no—
237C22—181no—
238C22C2×C22⋊#15711yescharacteristic
239C4—21no—
240C4—21no—
241C4—41no—
242C4—92no—
243C4—181no—
244C4—181no—
245C4—361no—
246C4—361no—
247C4#6428712yes—
248C3—22no—
249C2—81no—
250C2—361no—
251C2#1059382311yescharacteristic
252C2#1059384111yescharacteristic
253C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#124C4
socleC22×C32C2×C22⋊C4
prime radical#64147C4
cosocleC4×C3⋊Dic3C23
hypercenter#124#157
hypocenterC32#1482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10593727C2semidirect
3. #10593727C2semidirect
4. Q8⋊#622C2semidirect
5. D4⋊#622C2semidirect
206. C32#1482semidirect

Maximal subgroups

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

subgroupindex
#105961512
#105937272
Q8⋊#6222
D4⋊#6222
#14829