Finite Group Databasebeta

← #11775068

Subgroups — #11775068

Order 1152.

498 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 67 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#10593972C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic, complemented
3#10590297C211yesmaximal, characteristic, complemented
4#10590033C214yesmaximal, complemented
5C2×#3798—21no—
6C2×C4⋊#157—21no—
7C2×C4×#157—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×D12—21no—
10#63919C411yescharacteristic, complemented
11#63916—21no—
12#63915—21no—
13#63914C411yescharacteristic, complemented
14#63912C2212yes—
15C4×#625C412yescomplemented
16#63781C2212yes—
17C3×C4×C3⋊C8—21no—
18#63572—21no—
19#63557C2212yes—
20#5548—61no—
21#4685—61no—
22C22×#157—22no—
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×C3×D12—21no—
27C2×C3×C4×D3—22no—
28C2×#627—21no—
29C2×#626—22no—
30C2×#625—21no—
31C2×#625C2×C412yes—
32#3798—42no—
33#3798—42no—
34C4⋊#157—24no—
35C4×#157—42no—
36C32×C42D411yescharacteristic
37C4×C3⋊Dic3C2×C411yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C3×(C2×D3)⋊C4—22no—
41C3×C4⋊Dic3—21no—
42C2×C3×C3⋊C8—22no—
43#3724C2×C412yes—
44(C2×D3)⋊Dic3—22no—
45#1502—91nomaximal, Sylow
46C2×#235—62no—
47C3×C4×D4—61no—
48#940—61no—
49#938—61no—
50C4×#67—62no—
51#895—61no—
52#888—61no—
53#885—62no—
54#884—62no—
55C4×D12—21no—
56C42×D3—61no—
57C42×D3—61no—
58C3×C4×C8—61no—
59(C2×D3)⋊C8—62no—
60Dic3⋊C8—62no—
61C4×C3⋊C8—21no—
62C22×C3⋊D3C2×D411yescharacteristic
63C22×C3×D3—22no—
64C2×#157—24no—
65C2×#157—42no—
66C2×#157—42no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4C2×D411yescharacteristic
70C2×C3⋊Dic3C22⋊C411yescharacteristic
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C22×C411yescharacteristic
73C4×C3⋊D3—22no—
74C4×C3⋊D3—41no—
75C4×C3⋊D3D812yes—
76C4×C3⋊D3SD1612yes—
77C2×C3×Dic3—22no—
78C3×D12—42no—
79C3×C4×D3—44no—
80#627—42no—
81#626—42no—
82#626—42no—
83#625—42no—
84#625—42no—
85C3×C3⋊C8—42no—
86#532—91no—
87#431—91no—
88C4×C4⋊C4—91no—
89#327—94no—
90C2×C3×D4—61no—
91C22×C3×C4—62no—
92C2×#67—62no—
93C2×#67—62no—
94C2×#67—62no—
95#235—124no—
96#235—124no—
97C2×D12—21no—
98C2×D12—62no—
99C2×C4×D3—22no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×Dic6—62no—
107C2×C3×C8—62no—
108C3×C4⋊C4—61no—
109C3×C22⋊C4—62no—
110C3×C42—21no—
111C3×C42—21no—
112#217—62no—
113(C2×D3)⋊C4—22no—
114(C2×D3)⋊C4—62no—
115C4⋊Dic3—21no—
116Dic3⋊C4—62no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C2×C3⋊C8—22no—
124C22×C32C2×C22⋊C411yescharacteristic
125C2×C3⋊D3—21no—
126C2×C3⋊D3—21no—
127C2×C3⋊D3C2×D811yescharacteristic
128C2×C3⋊D3C2×SD1611yescharacteristic
129C2×C3×D3—42no—
130C2×C3×D3—42no—
131C2×C3×D3—42no—
132#157—44no—
133C32×C4—21no—
134C32×C4#10212yes—
135C32×C4#10412yes—
136C3⋊Dic3—21no—
137C3⋊Dic3—21no—
138C3⋊Dic3#10212yes—
139C3×Dic3—42no—
140C2×#41—181no—
141C4⋊Q8—91no—
142#127—91no—
143#124—181no—
144#121—92no—
145#121—181no—
146C4×D4—61no—
147C4×D4—92no—
148C2×C4⋊C4—181no—
149C2×C42—91no—
150C2×C42—181no—
151C4⋊C8—181no—
152C22⋊C8—92no—
153C4×C8—61no—
154#95—92no—
155C23×C3—62no—
156C22×D3—22no—
157C22×D3—61no—
158C22×D3—61no—
159C3×D4—122no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—62no—
167C2×C3×C4—124no—
168#67—122no—
169#67—122no—
170#67—124no—
171#67—124no—
172C2×Dic3—22no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179D12—42no—
180D12—122no—
181D12—122no—
182C4×D3—44no—
183C4×D3—62no—
184C4×D3—62no—
185C4×D3—62no—
186C4×D3—62no—
187C4×D3—122no—
188C4×D3—122no—
189C4×D3—122no—
190C4×D3—122no—
191Dic6—124no—
192C3×C8—122no—
193C3⋊C8—42no—
194C2×C32#41011yescharacteristic
195C2×C32C2×#10211yescharacteristic
196C2×C32C2×#10411yescharacteristic
197C3⋊D3—21no—
198C3⋊D3—21no—
199C3×D3—82no—
200#41—362no—
201#41—362no—
202C2×Q8—181no—
203C2×D4—61no—
204C2×D4—92no—
205C2×D4—182no—
206C2×D4—181no—
207C22×C4—62no—
208C22×C4—91no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4—182no—
212C2×C8—62no—
213C4⋊C4—61no—
214C4⋊C4—92no—
215C4⋊C4—184no—
216C22⋊C4—62no—
217C22⋊C4—182no—
218C42—91no—
219C42—91no—
220C42—91no—
221C42—362no—
222C42GO+(4,𝔽2)11yescharacteristic
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—122no—
226C22×C3—122no—
227C22×C3—122no—
228C2×D3—42no—
229C2×D3—42no—
230C2×D3—42no—
231C2×D3—61no—
232C2×D3—61no—
233C2×D3—61no—
234C2×D3—61no—
235C2×D3—121no—
236C2×D3—121no—
237C2×D3—121no—
238C2×D3—121no—
239C3×C4—22no—
240C3×C4—22no—
241C3×C4—22no—
242C3×C4—22no—
243C3×C4—22no—
244C3×C4—41no—
245C3×C4—122no—
246Dic3—42no—
247Dic3—62no—
248Dic3—62no—
249Dic3—62no—
250Dic3—121no—
251Dic3—121no—
252Dic3—121no—
253C32#150211yescharacteristic, complemented, Sylow
254C23—62no—
255C23—91no—
256Q8—362no—
257D4—122no—
258D4—362no—
259D4—362no—
260D4—362no—
261D4—362no—
262C2×C4—62no—
263C2×C4—91no—
264C2×C4—92no—
265C2×C4—92no—
266C2×C4—91no—
267C2×C4—91no—
268C2×C4—124no—
269C2×C4—182no—
270C2×C4—184no—
271C2×C4—361no—
272C2×C4—362no—
273C2×C4—362no—
274C2×C4D32⋊C411yescharacteristic
275C2×C4D32⋊C411yescharacteristic
276C2×C4C2×GO+(4,𝔽2)11yescharacteristic
277C8—122no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—242no—
285D3—82no—
286D3—121no—
287D3—121no—
288D3—121no—
289D3—121no—
290C22—91no—
291C22—91no—
292C22—122no—
293C22—122no—
294C22—122no—
295C22—181no—
296C22—181no—
297C22C2×D32⋊C411yescharacteristic
298C4—21no—
299C4—92no—
300C4—122no—
301C4—181no—
302C4—181no—
303C4—364no—
304C4#6372912yes—
305C4#6373112yes—
306C3—21no—
307C3—21no—
308C2—181no—
309C2—181no—
310C2—242no—
311C2C2×#6372911yescharacteristic
312C2C2×#6373111yescharacteristic
313C2#1059334511yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593972C2
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1502
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#157C2semidirect
3. #10590297C2semidirect
4. #10590033C2semidirect
10. #63919C4semidirect
13. #63914C4semidirect
15. C4×#625C4semidirect
253. C32#1502semidirect

Maximal subgroups

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

subgroupindex
#105939722
C4×C4⋊#1572
#105902972
#105900332
#15029