Finite Group Databasebeta

← #11776147

Subgroups — #11776147

Order 1152.

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

normal subgroups only

This group has 470 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
2#10593726C211yesmaximal, characteristic, complemented
3#10590297C211yesmaximal, characteristic, complemented
4#10590039C212yesmaximal, complemented
5#10590037C212yesmaximal, complemented
6C2×#3798—21no—
7C2×#3787—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×D12—21no—
10#63919C2211yescharacteristic
11#63916—21no—
12#63915—21no—
13#63914C2211yescharacteristic
14#63912C412yes—
15C4×#625C412yes—
16#63779—21no—
17C4⋊#622C2212yes—
18C3×C4×C3⋊C8—21no—
19#63572C2212yes—
20#63557—21no—
21#5548—61no—
22#4685—61no—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
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—
34C2×#622—22no—
35#3787—42no—
36C32×C42D411yescharacteristic
37C4×C3⋊Dic3C2×C411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C4×C3⋊Dic3C2311yescharacteristic
40C3×(C2×D3)⋊C4—22no—
41C3×C4⋊Dic3—21no—
42C2×C3×C3⋊C8—22no—
43#3724C2×C412yes—
44(C2×D3)⋊Dic3—22no—
45#1540—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⋊D3C22⋊C411yescharacteristic
63C22×C3×D3—22no—
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22×C411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C4×C3⋊D3—22no—
71C4×C3⋊D3—41no—
72C4×C3⋊D3D812yes—
73C4×C3⋊D3SD1612yes—
74C2×C3×Dic3—22no—
75C3×D12—42no—
76C3×C4×D3—44no—
77#627—41no—
78#627—41no—
79#626—44no—
80#625—42no—
81#625—41no—
82#625—41no—
83#622—42no—
84C3×C3⋊C8—42no—
85#532—91no—
86#431—91no—
87C2×C4⋊C8—91no—
88#332—92no—
89#331—92no—
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⋊D3#10212yes—
128C2×C3×D3—42no—
129C2×C3×D3—42no—
130C2×C3×D3—42no—
131C32×C4—21no—
132C32×C4#10212yes—
133C32×C4#13512yes—
134C3⋊Dic3—21no—
135C3⋊Dic3—21no—
136C3⋊Dic3C2×D811yescharacteristic
137C3⋊Dic3C2×SD1611yescharacteristic
138C3×Dic3—42no—
139C2×#41—181no—
140C22×C8—181no—
141C4⋊Q8—91no—
142#127—91no—
143#124—181no—
144#121—92no—
145#121—181no—
146C4×D4—61no—
147C4×D4—92no—
148C2×C42—91no—
149C4⋊C8—92no—
150C4⋊C8—92no—
151C4⋊C8—181no—
152C22⋊C8—181no—
153C4×C8—61no—
154C23×C3—62no—
155C22×D3—22no—
156C22×D3—61no—
157C22×D3—61no—
158C3×D4—122no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—62no—
166C2×C3×C4—124no—
167#67—124no—
168#67—122no—
169#67—122no—
170#67—124no—
171C2×Dic3—22no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178D12—42no—
179D12—124no—
180C4×D3—44no—
181C4×D3—62no—
182C4×D3—62no—
183C4×D3—62no—
184C4×D3—62no—
185C4×D3—122no—
186C4×D3—122no—
187C4×D3—122no—
188C4×D3—122no—
189Dic6—122no—
190Dic6—122no—
191C3×C8—122no—
192C3⋊C8—42no—
193C2×C32#41311yescharacteristic
194C2×C32C2×#10211yescharacteristic
195C2×C32#41611yescharacteristic
196C3⋊D3—22no—
197C3×D3—82no—
198#41—362no—
199#41—362no—
200C2×Q8—181no—
201C2×D4—61no—
202C2×D4—92no—
203C2×D4—182no—
204C2×D4—181no—
205C22×C4—62no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C2×C8—62no—
210C2×C8—182no—
211C2×C8—362no—
212C4⋊C4—61no—
213C4⋊C4—92no—
214C22⋊C4—62no—
215C22⋊C4—182no—
216C42—91no—
217C42—91no—
218C42—91no—
219C42GO+(4,𝔽2)11yescharacteristic
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—122no—
223C22×C3—122no—
224C22×C3—122no—
225C2×D3—42no—
226C2×D3—42no—
227C2×D3—42no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—121no—
231C2×D3—121no—
232C2×D3—121no—
233C2×D3—121no—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—22no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—41no—
240C3×C4—122no—
241Dic3—42no—
242Dic3—61no—
243Dic3—61no—
244Dic3—61no—
245Dic3—61no—
246Dic3—62no—
247Dic3—121no—
248Dic3—121no—
249Dic3—121no—
250C32#154011yescharacteristic, complemented, Sylow
251C23—62no—
252C23—91no—
253Q8—361no—
254Q8—361no—
255D4—122no—
256D4—361no—
257D4—361no—
258D4—364no—
259D4—362no—
260C2×C4—62no—
261C2×C4—91no—
262C2×C4—92no—
263C2×C4—92no—
264C2×C4—91no—
265C2×C4—91no—
266C2×C4—124no—
267C2×C4—182no—
268C2×C4—361no—
269C2×C4D32⋊C411yescharacteristic
270C2×C4D32⋊C411yescharacteristic
271C2×C4C2×GO+(4,𝔽2)11yescharacteristic
272C8—122no—
273C8—362no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—242no—
281D3—82no—
282D3—122no—
283D3—122no—
284C22—92no—
285C22—122no—
286C22—122no—
287C22—122no—
288C22—181no—
289C22—181no—
290C22C2×D32⋊C411yescharacteristic
291C4—21no—
292C4—91no—
293C4—91no—
294C4—122no—
295C4—181no—
296C4—181no—
297C4#6372912yes—
298C4#6422312yes—
299C3—21no—
300C3—21no—
301C2—182no—
302C2—242no—
303C2#1059331111yescharacteristic
304C2C2×#6372911yescharacteristic
305C2#1059334911yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593972C2
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1540
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. #10593726C2semidirect
3. #10590297C2semidirect
4. #10590039C2semidirect
5. #10590037C2semidirect
250. C32#1540semidirect

Maximal subgroups

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

subgroupindex
#105939722
#105937262
#105902972
#105900392
#105900372
#15409