Finite Group Databasebeta

← #11775749

Subgroups — #11775749

Order 1152.

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

normal subgroups only

This group has 496 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
3C4×#3712C211yesmaximal, characteristic, complemented
4#10590035C214yesmaximal, complemented
5C2×#3798C412yes—
6C2×#3788—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×C4×D12—21no—
9#63919C411yescharacteristic
10#63916—21no—
11#63915C2212yes—
12#63914C411yescharacteristic
13#63912—21no—
14C4×#625—21no—
15C2×#3712—21no—
16#63777C2212yes—
17C4×#622—21no—
18C3×C4×C3⋊C8—21no—
19#63555C2212yes—
20#5548—61no—
21C4×ΓL(1,𝔽25)—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×D12—21no—
26C2×C3×C4×D3—22no—
27C2×#627C2×C412yes—
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#3724—21no—
42(C2×D3)⋊Dic3—22no—
43#3712—24no—
44#1525—91nomaximal, Sylow
45C2×#235—62no—
46C3×C4×D4—61no—
47#940—61no—
48#938—61no—
49C4×#67—62no—
50C2×ΓL(1,𝔽25)—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#815—62no—
60C4×C3⋊C8—21no—
61C22×C3⋊D3C22⋊C411yescharacteristic
62C22×C3×D3—22no—
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22×C411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C4×C3⋊D3—22no—
70C4×C3⋊D3—22no—
71C4×C3⋊D3—22no—
72C2×C3×Dic3—22no—
73C3×D12—42no—
74C3×C4×D3—44no—
75#627—42no—
76#626—44no—
77#625—42no—
78#625—42no—
79#622—24no—
80C3×C3⋊C8—24no—
81#532—91no—
82C4×M16—91no—
83C4×M16—91no—
84#329—94no—
85C2×C3×D4—61no—
86C22×C3×C4—62no—
87C2×#67—62no—
88C2×#67—62no—
89C2×#67—62no—
90#235—128no—
91C2×D12—21no—
92C2×D12—62no—
93C2×C4×D3—22no—
94C2×C4×D3—61no—
95C2×C4×D3—61no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×Dic6—62no—
101C2×C3×C8—62no—
102C3×C4⋊C4—61no—
103C3×C22⋊C4—62no—
104C3×C42—21no—
105C3×C42—21no—
106#217—62no—
107(C2×D3)⋊C4—22no—
108(C2×D3)⋊C4—62no—
109C4⋊Dic3—21no—
110Dic3⋊C4—62no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C2×C3⋊C8—22no—
118ΓL(1,𝔽25)—68no—
119C22×C32C2×C22⋊C411yescharacteristic
120C2×C3⋊D3—21no—
121C2×C3⋊D3—21no—
122C2×C3⋊D3—21no—
123C2×C3×D3—42no—
124C2×C3×D3—42no—
125C2×C3×D3—42no—
126C32×C4—21no—
127C32×C4#10012yes—
128C32×C4#10412yes—
129C3⋊Dic3—21no—
130C3⋊Dic3—21no—
131C3⋊Dic3#10412yes—
132C3×Dic3—42no—
133C2×#41—92no—
134C2×M16—181no—
135C2×M16—181no—
136C4⋊Q8—91no—
137#127—91no—
138#124—92no—
139#121—181no—
140#121—181no—
141C4×D4—61no—
142C4×D4—181no—
143C2×C42—91no—
144#97—92no—
145#97—92no—
146C4×C8—61no—
147C4×C8—181no—
148C23×C3—62no—
149C22×D3—22no—
150C22×D3—61no—
151C22×D3—61no—
152C3×D4—122no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—62no—
160C2×C3×C4—124no—
161#67—124no—
162#67—124no—
163#67—124no—
164C2×Dic3—22no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171D12—42no—
172D12—124no—
173C4×D3—44no—
174C4×D3—64no—
175C4×D3—64no—
176C4×D3—122no—
177C4×D3—122no—
178C4×D3—122no—
179C4×D3—122no—
180Dic6—124no—
181C3×C8—64no—
182C3⋊C8—24no—
183C2×C32C2×#10011yescharacteristic
184C2×C32C2×#10411yescharacteristic
185C2×C32C2×#10411yescharacteristic
186C3⋊D3—41no—
187C3×D3—82no—
188#41—364no—
189C2×Q8—92no—
190C2×D4—61no—
191C2×D4—92no—
192C2×D4—182no—
193C2×D4—181no—
194C22×C4—62no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—91no—
198M16—184no—
199M16—184no—
200C2×C8—62no—
201C2×C8—182no—
202C4⋊C4—61no—
203C4⋊C4—181no—
204C22⋊C4—62no—
205C22⋊C4—182no—
206C42—91no—
207C42—91no—
208C42—91no—
209C42GO+(4,𝔽2)11yescharacteristic
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—122no—
213C22×C3—122no—
214C22×C3—122no—
215C2×D3—42no—
216C2×D3—42no—
217C2×D3—42no—
218C2×D3—62no—
219C2×D3—62no—
220C2×D3—121no—
221C2×D3—121no—
222C2×D3—121no—
223C2×D3—121no—
224C3×C4—22no—
225C3×C4—22no—
226C3×C4—22no—
227C3×C4—22no—
228C3×C4—22no—
229C3×C4—41no—
230C3×C4—122no—
231Dic3—42no—
232Dic3—62no—
233Dic3—62no—
234Dic3—62no—
235Dic3—121no—
236Dic3—121no—
237Dic3—121no—
238C32#152511yescharacteristic, complemented, Sylow
239C23—62no—
240C23—91no—
241Q8—362no—
242D4—122no—
243D4—362no—
244D4—364no—
245D4—362no—
246C2×C4—62no—
247C2×C4—91no—
248C2×C4—91no—
249C2×C4—91no—
250C2×C4—124no—
251C2×C4—182no—
252C2×C4—182no—
253C2×C4—182no—
254C2×C4D32⋊C411yescharacteristic
255C2×C4D32⋊C411yescharacteristic
256C2×C4C2×GO+(4,𝔽2)11yescharacteristic
257C8—64no—
258C8—184no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—242no—
266D3—82no—
267D3—122no—
268D3—122no—
269C22—122no—
270C22—122no—
271C22—122no—
272C22—181no—
273C22—181no—
274C22—181no—
275C22C2×D32⋊C411yescharacteristic
276C4—21no—
277C4—92no—
278C4—122no—
279C4—181no—
280C4—181no—
281C4#6372712yes—
282C4#6373112yes—
283C3—21no—
284C3—21no—
285C2—242no—
286C2—361no—
287C2C2×#6372711yescharacteristic
288C2C2×#6373111yescharacteristic
289C2#1059338011yescharacteristic
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#1525
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×#3788C2semidirect
3. C4×#3712C2semidirect
4. #10590035C2semidirect
238. C32#1525semidirect

Maximal subgroups

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

subgroupindex
#105939722
C4×#37882
C4×#37122
#105900352
#15259