Finite Group Databasebeta

← #11774508

Subgroups — #11774508

Order 1152.

476 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 61 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×#3788C211yesmaximal, characteristic, complemented
3#10590297C211yesmaximal, characteristic, complemented
4#10590029C214yesmaximal, complemented
5C2×#3798—21no—
6C2×#3788—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×C4×D12—21no—
9#63919C411yescharacteristic
10#63916—21no—
11#63915—21no—
12#63914C411yescharacteristic
13#63912C412yes—
14C4×#625C2212yes—
15#63777—21no—
16C4×#622C2212yes—
17C3×C4×C3⋊C8—21no—
18#63572C2212yes—
19#63557—21no—
20#5548—61no—
21#4685—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×D12—21no—
26C2×C3×C4×D3—22no—
27C2×#627—21no—
28C2×#626—22no—
29C2×#625—21no—
30C2×#625C2×C412yes—
31#3798—44no—
32C2×#622—22no—
33#3788—24no—
34C32×C42D411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3C2311yescharacteristic
38C3×(C2×D3)⋊C4—22no—
39C3×C4⋊Dic3—21no—
40C2×C3×C3⋊C8—22no—
41#3724C2×C412yes—
42(C2×D3)⋊Dic3—22no—
43#1484—91nomaximal, Sylow
44C2×#235—62no—
45C3×C4×D4—61no—
46#940—61no—
47#938—61no—
48C4×#67—62no—
49#895—61no—
50#888—61no—
51#885—62no—
52#884—62no—
53C4×D12—21no—
54C42×D3—61no—
55C42×D3—61no—
56C3×C4×C8—61no—
57(C2×D3)⋊C8—62no—
58Dic3⋊C8—62no—
59C4×C3⋊C8—21no—
60C22×C3⋊D3C22⋊C411yescharacteristic
61C22×C3×D3—22no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22×C411yescharacteristic
67C2×C3⋊Dic3C2×D411yescharacteristic
68C4×C3⋊D3—22no—
69C4×C3⋊D3—22no—
70C4×C3⋊D3—22no—
71C2×C3×Dic3—22no—
72C3×D12—42no—
73C3×C4×D3—44no—
74#627—42no—
75#626—44no—
76#625—24no—
77#625—42no—
78#622—24no—
79C3×C3⋊C8—42no—
80#532—91no—
81#431—91no—
82C4×M16—91no—
83D4⋊C8—94no—
84C2×C3×D4—61no—
85C22×C3×C4—62no—
86C2×#67—62no—
87C2×#67—62no—
88C2×#67—62no—
89#235—128no—
90C2×D12—21no—
91C2×D12—62no—
92C2×C4×D3—22no—
93C2×C4×D3—61no—
94C2×C4×D3—61no—
95C2×C4×D3—61no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×Dic6—62no—
100C2×C3×C8—62no—
101C3×C4⋊C4—61no—
102C3×C22⋊C4—62no—
103C3×C42—21no—
104C3×C42—21no—
105#217—62no—
106(C2×D3)⋊C4—22no—
107(C2×D3)⋊C4—62no—
108C4⋊Dic3—21no—
109Dic3⋊C4—62no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C2×C3⋊C8—22no—
117C22×C32C2×C22⋊C411yescharacteristic
118C2×C3⋊D3—21no—
119C2×C3⋊D3—21no—
120C2×C3⋊D3—21no—
121C2×C3×D3—42no—
122C2×C3×D3—42no—
123C2×C3×D3—42no—
124C32×C4—21no—
125C32×C4#10412yes—
126C32×C4AGL(1,ℤ/8)12yes—
127C3⋊Dic3—21no—
128C3⋊Dic3—21no—
129C3⋊Dic3#13112yes—
130C3×Dic3—42no—
131C2×#41—181no—
132C2×M16—181no—
133C4⋊Q8—91no—
134#127—91no—
135#124—181no—
136#121—92no—
137#121—181no—
138C4×D4—61no—
139C4×D4—92no—
140C2×C42—91no—
141C4⋊C8—92no—
142C22⋊C8—181no—
143#97—181no—
144C4×C8—61no—
145C4×C8—92no—
146C23×C3—62no—
147C22×D3—22no—
148C22×D3—61no—
149C22×D3—61no—
150C3×D4—122no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—62no—
158C2×C3×C4—124no—
159#67—124no—
160#67—124no—
161#67—124no—
162C2×Dic3—22no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169D12—42no—
170D12—124no—
171C4×D3—44no—
172C4×D3—64no—
173C4×D3—64no—
174C4×D3—122no—
175C4×D3—122no—
176C4×D3—122no—
177C4×D3—122no—
178Dic6—124no—
179C3×C8—122no—
180C3⋊C8—42no—
181C2×C32#40811yescharacteristic
182C2×C32#41811yescharacteristic
183C2×C32C2×#10411yescharacteristic
184C3⋊D3—41no—
185C3×D3—82no—
186#41—364no—
187C2×Q8—181no—
188C2×D4—61no—
189C2×D4—92no—
190C2×D4—182no—
191C2×D4—181no—
192C22×C4—62no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—91no—
196M16—184no—
197C2×C8—62no—
198C2×C8—182no—
199C4⋊C4—61no—
200C4⋊C4—92no—
201C22⋊C4—62no—
202C22⋊C4—182no—
203C42—91no—
204C42—91no—
205C42—91no—
206C42GO+(4,𝔽2)11yescharacteristic
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—122no—
210C22×C3—122no—
211C22×C3—122no—
212C2×D3—42no—
213C2×D3—42no—
214C2×D3—42no—
215C2×D3—62no—
216C2×D3—62no—
217C2×D3—121no—
218C2×D3—121no—
219C2×D3—121no—
220C2×D3—121no—
221C3×C4—22no—
222C3×C4—22no—
223C3×C4—22no—
224C3×C4—22no—
225C3×C4—22no—
226C3×C4—41no—
227C3×C4—122no—
228Dic3—42no—
229Dic3—62no—
230Dic3—62no—
231Dic3—62no—
232Dic3—121no—
233Dic3—121no—
234Dic3—121no—
235C32#148411yescharacteristic, complemented, Sylow
236C23—62no—
237C23—91no—
238Q8—362no—
239D4—122no—
240D4—184no—
241D4—364no—
242D4—362no—
243C2×C4—62no—
244C2×C4—91no—
245C2×C4—91no—
246C2×C4—91no—
247C2×C4—124no—
248C2×C4—182no—
249C2×C4—182no—
250C2×C4—182no—
251C2×C4D32⋊C411yescharacteristic
252C2×C4D32⋊C411yescharacteristic
253C2×C4C2×GO+(4,𝔽2)11yescharacteristic
254C8—122no—
255C8—184no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—242no—
263D3—82no—
264D3—122no—
265D3—122no—
266C22—122no—
267C22—122no—
268C22—122no—
269C22—181no—
270C22—181no—
271C22—181no—
272C22C2×D32⋊C411yescharacteristic
273C4—21no—
274C4—92no—
275C4—122no—
276C4—181no—
277C4—181no—
278C4#6373112yes—
279C4#6422412yes—
280C3—21no—
281C3—21no—
282C2—242no—
283C2—361no—
284C2#1059330811yescharacteristic
285C2C2×#6373111yescharacteristic
286C2#1059336311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593972C2
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1484
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×#3788C2semidirect
3. #10590297C2semidirect
4. #10590029C2semidirect
235. C32#1484semidirect

Maximal subgroups

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

subgroupindex
#105939722
C4×#37882
#105902972
#105900292
#14849