Finite Group Databasebeta

← #11774837

Subgroups — #11774837

Order 1152.

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

normal subgroups only

This group has 450 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#10593728C211yesmaximal, characteristic, complemented
3#10593725C211yesmaximal, characteristic, complemented
4Q8⋊#622C212yesmaximal, complemented
5D4⋊#622C212yesmaximal, complemented
6C2×#3788—21no—
7C32×#124C411yescharacteristic
8#64155C411yescharacteristic
9Q8×C3⋊Dic3C2211yescharacteristic
10#64147C411yescharacteristic
11D4×C3⋊Dic3C2211yescharacteristic
12#64092—21no—
13#64090—21no—
14#64088—21no—
15#64086—21no—
16C42×C3⋊D3C2211yescharacteristic
17#64079C411yescharacteristic
18#63779—21no—
19#63778—21no—
20C4⋊#622—21no—
21C4⋊#622C2212yes—
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—
33#3788—42no—
34C32×C22⋊C4—21no—
35C32×C22⋊C4—21no—
36C32×C42C2×C411yescharacteristic
37#3757—21no—
38#3757—21no—
39#3752—21no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)C2×C411yescharacteristic
42C4⋊(C3⋊Dic3)C2×C411yescharacteristic
43#3750—21no—
44#3750—21no—
45#3750—21no—
46C4×C3⋊Dic3—21no—
47C4×C3⋊Dic3D411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3C2311yescharacteristic
50#1495—91nomaximal, Sylow
51C3×#124—22no—
52#946—62no—
53Q8×Dic3—62no—
54#938—62no—
55D4×Dic3—62no—
56#883—64no—
57#67⋊C4—64no—
58#879—64no—
59#877—64no—
60C42×D3—62no—
61#870—62no—
62C23×C32—21no—
63C22×C3⋊D3C22⋊C411yescharacteristic
64C32×Q8—22no—
65C32×D4—22no—
66C2×C32×C4—21no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4C22×C411yescharacteristic
70#638—42no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77C2×C3⋊Dic3C2×D411yescharacteristic
78C4×C3⋊D3—22no—
79C4×C3⋊D3—21no—
80C4×C3⋊D3—21no—
81C4×C3⋊D3—41no—
82#622—42no—
83#622—42no—
84#529—91no—
85#431—91no—
86#423—91no—
87Q8⋊C8—92no—
88D4⋊C8—92no—
89C2×C3×Q8—22no—
90C2×C3×D4—22no—
91C2×#67—64no—
92C22×Dic3—64no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C3×C22⋊C4—24no—
97C3×C22⋊C4—24no—
98C3×C42—22no—
99#217—64no—
100#217—64no—
101(C2×D3)⋊C4—64no—
102C4⋊Dic3—62no—
103C4⋊Dic3—62no—
104C4⋊Dic3—64no—
105Dic3⋊C4—64no—
106Dic3⋊C4—64no—
107Dic3⋊C4—64no—
108C4×Dic3—62no—
109C4×Dic3—62no—
110C4×Dic3—62no—
111C4×Dic3—64no—
112C22×C32—41no—
113C22×C32—41no—
114C22×C32—41no—
115C22×C32C2×C22⋊C411yescharacteristic
116C2×C3⋊D3—21no—
117C2×C3⋊D3—21no—
118C2×C3⋊D3—21no—
119C32×C4—21no—
120C32×C4—21no—
121C32×C4—41no—
122C32×C4#13112yes—
123C3⋊Dic3—21no—
124C3⋊Dic3—21no—
125C3⋊Dic3—41no—
126C3⋊Dic3—41no—
127C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
128C3⋊Dic3#13711yescharacteristic
129C2×M16—181no—
130#126—181no—
131#125—91no—
132#124#15711yescharacteristic
133#123—181no—
134C22⋊Q8—91no—
135#121—91no—
136C4×Q8—91no—
137C4×D4—91no—
138C4×D4—181no—
139#117—181no—
140C2×C42—91no—
141C4⋊C8—92no—
142C4⋊C8—181no—
143C4⋊C8—181no—
144C22⋊C8—181no—
145C4×C8—92no—
146C23×C3—24no—
147C22×D3—62no—
148C3×Q8—44no—
149C3×D4—44no—
150C2×C3×C4—24no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—22no—
154#67—128no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—62no—
158C2×Dic3—64no—
159C2×Dic3—64no—
160C2×Dic3—124no—
161C2×Dic3—124no—
162C4×D3—122no—
163C4×D3—122no—
164C4×D3—124no—
165C4×D3—124no—
166C2×C32—81no—
167C2×C32#40811yescharacteristic
168C2×C32#41711yescharacteristic
169C2×C32#42111yescharacteristic
170C3⋊D3—41no—
171C2×Q8C2×#15711yescharacteristic
172C2×D4—181no—
173C2×D4C2×#15711yescharacteristic
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—181no—
178M16—362no—
179C2×C8—182no—
180C2×C8—182no—
181C4⋊C4—91no—
182C4⋊C4—91no—
183C4⋊C4—181no—
184C4⋊C4—181no—
185C4⋊C4—181no—
186C4⋊C4—181no—
187C22⋊C4—21no—
188C22⋊C4—21no—
189C22⋊C4—181no—
190C22⋊C4—181no—
191C22⋊C4—181no—
192C42—91no—
193C42—91no—
194C42—91no—
195C42—181no—
196C42C2×#15711yescharacteristic
197C22×C3—22no—
198C22×C3—44no—
199C22×C3—44no—
200C22×C3—44no—
201C2×D3—64no—
202C2×D3—122no—
203C2×D3—122no—
204C3×C4—24no—
205C3×C4—42no—
206C3×C4—42no—
207C3×C4—44no—
208Dic3—62no—
209Dic3—62no—
210Dic3—122no—
211Dic3—122no—
212Dic3—124no—
213Dic3—124no—
214C32#149511yescharacteristic, complemented, Sylow
215C23—21no—
216C23—91no—
217Q8—22no—
218D4—22no—
219D4—362no—
220C2×C4—21no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—181no—
225C2×C4—181no—
226C2×C4—182no—
227C2×C4—181no—
228C2×C4—181no—
229C2×C4—361no—
230C2×C4—361no—
231C2×C4—361no—
232C2×C4C22⋊#15711yescharacteristic
233C2×C4C22⋊#15711yescharacteristic
234C2×C4C22×#15711yescharacteristic
235C8—362no—
236C8—362no—
237C2×C3—22no—
238C2×C3—22no—
239C2×C3—22no—
240C2×C3—84no—
241D3—124no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—181no—
246C22—181no—
247C22—181no—
248C22C2×C22⋊#15711yescharacteristic
249C4—21no—
250C4—21no—
251C4—41no—
252C4—91no—
253C4—91no—
254C4—181no—
255C4—181no—
256C4—361no—
257C4—361no—
258C4#6428712yes—
259C3—22no—
260C2—81no—
261C2—361no—
262C2#1059382311yescharacteristic
263C2#1059384011yescharacteristic
264C2#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#1495
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. #10593728C2semidirect
3. #10593725C2semidirect
4. Q8⋊#622C2semidirect
5. D4⋊#622C2semidirect
214. C32#1495semidirect

Maximal subgroups

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

subgroupindex
#105961512
#105937282
#105937252
Q8⋊#6222
D4⋊#6222
#14959