Finite Group Databasebeta

← #11774366

Subgroups — #11774366

Order 1152.

570 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 70 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#10596067C211yesmaximal, characteristic
2#10593801C211yesmaximal, characteristic, complemented
3C2×C4⋊#622C211yesmaximal, characteristic, complemented
4D4⋊#622C212yesmaximal, complemented
5#10590160C212yesmaximal, complemented
6C2×#3830—21no—
7C22×#622—21no—
8C32×#121C411yescharacteristic
9#64149C411yescharacteristic
10#64148—21no—
11D4×C3⋊Dic3C2211yescharacteristic
12#64139C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64102C2211yescharacteristic
15#64097C411yescharacteristic
16#64094—21no—
17#64090—21no—
18C22⋊#622—21no—
19#63779—21no—
20C4⋊#622—21no—
21C4⋊#622C2212yes—
22C4×#622C2212yes—
23#5596—62no—
24C2×C32×D4—21no—
25C2×C32×D4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C2×#638—21no—
28C2×#638—21no—
29C2×#638—21no—
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33#3830—42no—
34#3830—42no—
35C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
36C2×C4×C3⋊D3—21no—
37C2×#634—21no—
38C2×#622—22no—
39C2×#622—22no—
40C2×#622—42no—
41C32×C4⋊C4C2×C411yescharacteristic
42C32×C22⋊C4—21no—
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
51C4×C3⋊Dic3C2311yescharacteristic
52#1480—91nomaximal, Sylow
53C2×#237—64no—
54C3×#121—22no—
55#940—62no—
56#939—64no—
57D4×Dic3—62no—
58#930—62no—
59C2×C4×Dic3—62no—
60#893—62no—
61#888—62no—
62#885—64no—
63#67⋊C4—64no—
64C23×C32—21no—
65C23×C32C22⋊C411yescharacteristic
66C22×C3⋊D3—21no—
67C32×D4—22no—
68C32×D4—42no—
69C2×C32×C4—21no—
70C2×C32×C4—22no—
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22×C411yescharacteristic
73#638—42no—
74#638—42no—
75#638—42no—
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3D812yes—
83C2×C3⋊Dic3SD1612yes—
84C2×C3⋊Dic3C2×D411yescharacteristic
85C2×C3⋊Dic3C2×D411yescharacteristic
86C4⋊(C3⋊D3)—22no—
87C4×C3⋊D3—41no—
88C4×C3⋊D3—41no—
89#634—42no—
90#622—42no—
91#622—42no—
92#532—91no—
93#431—91no—
94C2×C4⋊C8—91no—
95D4⋊C8—92no—
96D4⋊C8—92no—
97C2×C3×D4—24no—
98C2×C3×D4—22no—
99C22×C3×C4—22no—
100C2×#67—64no—
101C2×#67—64no—
102C2×#67—64no—
103C22×Dic3—62no—
104C22×Dic3—62no—
105C22×Dic3—64no—
106#237—128no—
107#237—128no—
108C2×D12—62no—
109C2×C4×D3—64no—
110C2×Dic6—64no—
111C3×C4⋊C4—22no—
112C3×C22⋊C4—24no—
113#217—64no—
114(C2×D3)⋊C4—64no—
115(C2×D3)⋊C4—64no—
116C4⋊Dic3—62no—
117Dic3⋊C4—64no—
118C4×Dic3—62no—
119C4×Dic3—62no—
120C4×Dic3—62no—
121C4×Dic3—62no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—41no—
125C22×C32—41no—
126C22×C32—41no—
127C22×C32#10212yes—
128C22×C32C2×C22⋊C411yescharacteristic
129C2×C3⋊D3—41no—
130C2×C3⋊D3—41no—
131C2×C3⋊D3—41no—
132C32×C4—21no—
133C32×C4—41no—
134C32×C4#13112yes—
135C3⋊Dic3—21no—
136C3⋊Dic3—21no—
137C3⋊Dic3—41no—
138C3⋊Dic3#10212yes—
139C3⋊Dic3C2×D811yescharacteristic
140C3⋊Dic3C2×SD1611yescharacteristic
141C2×#41—181no—
142C22×C8—181no—
143C4⋊Q8—91no—
144#127—91no—
145#124—181no—
146#121—91no—
147#121—181no—
148#121#15711yescharacteristic
149C4×D4—91no—
150C4×D4—91no—
151C4×D4—181no—
152C2×C42—91no—
153C4⋊C8—92no—
154C4⋊C8—181no—
155C4⋊C8—181no—
156C22⋊C8—181no—
157C4×C8—92no—
158C23×C3—24no—
159C23×C3—22no—
160C22×D3—64no—
161C3×D4—44no—
162C3×D4—48no—
163C2×C3×C4—24no—
164C2×C3×C4—22no—
165C2×C3×C4—22no—
166C2×C3×C4—44no—
167#67—128no—
168#67—128no—
169#67—128no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—64no—
173C2×Dic3—64no—
174C2×Dic3—62no—
175C2×Dic3—62no—
176C2×Dic3—64no—
177C2×Dic3—124no—
178C2×Dic3—124no—
179C2×Dic3—124no—
180D12—124no—
181C4×D3—124no—
182C4×D3—124no—
183Dic6—128no—
184C2×C32—22no—
185C2×C32—81no—
186C2×C32#40811yescharacteristic
187C2×C32C2×#10211yescharacteristic
188C2×C32#42111yescharacteristic
189C3⋊D3—81no—
190#41—362no—
191#41—362no—
192C2×Q8—181no—
193C2×D4—21no—
194C2×D4—91no—
195C2×D4—181no—
196C2×D4—181no—
197C2×D4—181no—
198C2×D4C2×#15711yescharacteristic
199C22×C4—91no—
200C22×C4—91no—
201C22×C4—181no—
202C22×C4—181no—
203C22×C4C2×#15711yescharacteristic
204C2×C8—182no—
205C2×C8—182no—
206C2×C8—362no—
207C4⋊C4—91no—
208C4⋊C4—181no—
209C4⋊C4C2×#15711yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—181no—
212C22⋊C4—181no—
213C22⋊C4—181no—
214C42—91no—
215C42—91no—
216C42—91no—
217C42—91no—
218C22×C3—22no—
219C22×C3—24no—
220C22×C3—42no—
221C22×C3—42no—
222C22×C3—44no—
223C22×C3—44no—
224C22×C3—44no—
225C2×D3—124no—
226C2×D3—124no—
227C2×D3—124no—
228C3×C4—24no—
229C3×C4—42no—
230C3×C4—44no—
231Dic3—64no—
232Dic3—62no—
233Dic3—62no—
234Dic3—64no—
235Dic3—122no—
236Dic3—124no—
237C32#148011yescharacteristic, complemented, Sylow
238C23—21no—
239C23—181no—
240C23C22⋊#15711yescharacteristic
241Q8—362no—
242D4—22no—
243D4—42no—
244D4—182no—
245D4—362no—
246D4—362no—
247D4—362no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—92no—
253C2×C4—92no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—181no—
257C2×C4—361no—
258C2×C4—361no—
259C2×C4—361no—
260C2×C4—361no—
261C2×C4—361no—
262C2×C4C22⋊#15711yescharacteristic
263C2×C4C22×#15711yescharacteristic
264C8—362no—
265C8—362no—
266C2×C3—22no—
267C2×C3—22no—
268C2×C3—22no—
269C2×C3—44no—
270C2×C3—84no—
271D3—244no—
272C22—21no—
273C22—21no—
274C22—41no—
275C22—41no—
276C22—41no—
277C22—361no—
278C22—361no—
279C22—361no—
280C22#6378212yes—
281C22C2×C22⋊#15711yescharacteristic
282C4—21no—
283C4—41no—
284C4—91no—
285C4—91no—
286C4—92no—
287C4—181no—
288C4—181no—
289C4—361no—
290C4#6428712yes—
291C3—22no—
292C2—22no—
293C2—81no—
294C2—721no—
295C2C2×#6378211yescharacteristic
296C2#1059382211yescharacteristic
297C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#121C4
socleC22×C32C2×C22⋊C4
prime radical#10596067C2
cosocleC4×C3⋊Dic3C23
hypercenter#121#157
hypocenterC32#1480
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10593801C2semidirect
3. C2×C4⋊#622C2semidirect
4. D4⋊#622C2semidirect
5. #10590160C2semidirect
237. C32#1480semidirect

Maximal subgroups

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

subgroupindex
#105960672
#105938012
C2×C4⋊#6222
D4⋊#6222
#105901602
#14809