Finite Group Databasebeta

← #11777362

Subgroups — #11777362

Order 1152.

326 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C4×#3774C211yesmaximal, characteristic
2#10590718C211yesmaximal, characteristic, complemented
3C8×#625C211yesmaximal, characteristic, complemented
4#10590169C211yesmaximal, characteristic, complemented
5#10590041C211yesmaximal, characteristic, complemented
6#10590029C211yesmaximal, characteristic, complemented
7#10590029C211yesmaximal, characteristic, complemented
8C2×#3774C411yescharacteristic
9C2×C3×D3×C8—21no—
10C4×#625C2211yescharacteristic
11C4×#625C2211yescharacteristic
12C2×D3×C3⋊C8—21no—
13C4×#622C2211yescharacteristic
14C4×#622C2211yescharacteristic
15#63743C411yescharacteristic
16#63739C411yescharacteristic
17#63739C411yescharacteristic
18C8×C3⋊Dic3C2211yescharacteristic
19C3×(C2×D3)⋊C8—21no—
20#63572C2211yescharacteristic
21#63572C2211yescharacteristic
22(C2×D3)⋊(C3⋊C8)—21no—
23C8×#67—61no—
24#67⋊C8—61no—
25C2×C3×C4×D3—21no—
26C2×C3×C4×D3—21no—
27C2×#625C2×C411yescharacteristic
28C2×#625C2×C411yescharacteristic
29C2×#622—21no—
30C2×#622C2×C411yescharacteristic
31C2×#622C2×C411yescharacteristic
32#3774C814yescomplemented
33C2×C32×C8D411yescharacteristic
34C4×C3⋊Dic3C2311yescharacteristic
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36C2×C3×C3⋊C8—21no—
37C2×C3×C3⋊C8—21no—
38C3×D3×C8—42no—
39#3724C2×C411yescharacteristic
40#3724C2×C411yescharacteristic
41(C2×D3)⋊Dic3—21no—
42(C2×D3)⋊Dic3—21no—
43D3×C3⋊C8—42no—
44#1580—91nomaximal, Sylow
45C22×C3×C8—61no—
46C4×#67—61no—
47C4×#67—61no—
48C22×C3⋊C8—61no—
49C2×D3×C8—21no—
50C2×D3×C8—61no—
51C3×C22⋊C8—61no—
52#830—61no—
53(C2×D3)⋊C8—21no—
54(C2×D3)⋊C8—61no—
55Dic3⋊C8—61no—
56Dic3⋊C8—61no—
57C8×Dic3—61no—
58C8×Dic3—61no—
59C22×C3×D3—21no—
60C22×C3×D3—21no—
61C2×C32×C4C2×D411yescharacteristic
62C2×C3⋊Dic3C22×C411yescharacteristic
63C2×C3⋊Dic3#4111yescharacteristic
64C2×C3×Dic3—21no—
65C2×C3×Dic3—21no—
66C3×C4×D3—41no—
67C3×C4×D3—41no—
68C3×C4×D3—41no—
69C3×C4×D3—41no—
70#625—21no—
71#625—21no—
72#625C2×C812yescomplemented
73#625C2×C812yescomplemented
74#622—21no—
75#622—41no—
76#622C2×C812yescomplemented
77C32×C8—21no—
78C3⋊(C3⋊C8)—21no—
79C3×C3⋊C8—41no—
80C3×C3⋊C8—41no—
81C4×D8—91no—
82C8×D4—91no—
83C8×D4—91no—
84#334—91no—
85D4⋊C8—91no—
86D4⋊C8—91no—
87#322—91no—
88C22×C3×C4—61no—
89C22×C3×C4—61no—
90C2×#67—61no—
91C2×#67—61no—
92C2×C4×D3—21no—
93C2×C4×D3—21no—
94C2×C3×C8—21no—
95C2×C3×C8—21no—
96C2×C3×C8—61no—
97C2×C3×C8—61no—
98C2×C3×C8—122no—
99#217—61no—
100#217—61no—
101(C2×D3)⋊C4—61no—
102(C2×D3)⋊C4—61no—
103Dic3⋊C4—61no—
104Dic3⋊C4—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C2×C3⋊C8—21no—
108C2×C3⋊C8—21no—
109C2×C3⋊C8—61no—
110C2×C3⋊C8—61no—
111C2×C3⋊C8—122no—
112D3×C8—42no—
113D3×C8—122no—
114C22×C32C4×D411yescharacteristic
115C2×C3×D3—22no—
116C2×C3×D3—22no—
117C2×C3×D3—41no—
118C2×C3×D3—41no—
119C2×C3×D3—41no—
120C2×C3×D3—41no—
121C32×C4AGL(1,ℤ/8)11yescharacteristic
122C32×C4AGL(1,ℤ/8)11yescharacteristic
123C3⋊Dic3—21no—
124C3⋊Dic3C22×C811yescharacteristic
125C3⋊Dic3#13111yescharacteristic
126C3×Dic3—41no—
127C3×Dic3—41no—
128C2×D8—91no—
129C22×C8—61no—
130C22×C8—181no—
131C4×D4—91no—
132C4×D4—91no—
133#107—91no—
134C4⋊C8—91no—
135C4⋊C8—91no—
136#102—91no—
137#102—91no—
138C22⋊C8—61no—
139C22⋊C8—181no—
140C4×C8—91no—
141C4×C8—91no—
142C4×C8—91no—
143C23×C3—61no—
144C23×C3—61no—
145C22×D3—21no—
146C22×D3—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—61no—
150C2×C3×C4—61no—
151C2×C3×C4—121no—
152C2×C3×C4—121no—
153C2×C3×C4—121no—
154C2×C3×C4—121no—
155#67—62no—
156#67—62no—
157#67—62no—
158#67—62no—
159C2×Dic3—21no—
160C2×Dic3—21no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C4×D3—41no—
166C4×D3—41no—
167C4×D3—41no—
168C4×D3—41no—
169C3×C8—22no—
170C3×C8—41no—
171C3×C8—121no—
172C3×C8—121no—
173C3⋊C8—41no—
174C3⋊C8—41no—
175C3⋊C8—62no—
176C3⋊C8—121no—
177C2×C32C8×D411yescharacteristic
178C2×C32#44211yescharacteristic
179C2×C32#44411yescharacteristic
180C3×D3—42no—
181C3×D3—42no—
182C2×D4—91no—
183C2×D4—91no—
184C22×C4—61no—
185C22×C4—61no—
186D8—94no—
187C2×C8—61no—
188C2×C8—61no—
189C2×C8—91no—
190C2×C8—91no—
191C2×C8—91no—
192C2×C8—122no—
193C2×C8—181no—
194C2×C8—362no—
195C2×C8GO+(4,𝔽2)11yescharacteristic
196C4⋊C4—91no—
197C4⋊C4—91no—
198C22⋊C4—181no—
199C22⋊C4—181no—
200C42—91no—
201C22×C3—21no—
202C22×C3—21no—
203C22×C3—62no—
204C22×C3—62no—
205C22×C3—121no—
206C22×C3—121no—
207C22×C3—121no—
208C22×C3—121no—
209C2×D3—22no—
210C2×D3—22no—
211C2×D3—41no—
212C2×D3—41no—
213C2×D3—41no—
214C2×D3—41no—
215C3×C4—21no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—121no—
220C3×C4—121no—
221Dic3—41no—
222Dic3—41no—
223Dic3—61no—
224Dic3—61no—
225Dic3—61no—
226Dic3—61no—
227Dic3—121no—
228Dic3—121no—
229C32#158011yescharacteristic, complemented, Sylow
230C23—61no—
231C23—61no—
232D4—92no—
233D4—92no—
234D4—181no—
235D4—181no—
236C2×C4—61no—
237C2×C4—61no—
238C2×C4—91no—
239C2×C4—91no—
240C2×C4—121no—
241C2×C4—121no—
242C2×C4—121no—
243C2×C4—121no—
244C2×C4C2×GO+(4,𝔽2)11yescharacteristic
245C8—21no—
246C8—92no—
247C8—121no—
248C8—121no—
249C8—181no—
250C8—181no—
251C8—361no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—122no—
259C2×C3—122no—
260D3—42no—
261D3—42no—
262C22—62no—
263C22—62no—
264C22—121no—
265C22—121no—
266C22—121no—
267C22—121no—
268C22C4×GO+(4,𝔽2)11yescharacteristic
269C4—91no—
270C4—91no—
271C4—121no—
272C4—121no—
273C4—181no—
274C4#6422411yescharacteristic
275C4#6423611yescharacteristic
276C3—21no—
277C3—21no—
278C2—122no—
279C2—122no—
280C2C8×GO+(4,𝔽2)11yescharacteristic
281C2#1059329811yescharacteristic
282C2#1059341911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C22×C8
FittingC2×C32×C8D4
socleC22×C32C4×D4
prime radicalC2×#3774C4
cosocleC4×C3⋊Dic3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1580
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10590718C2semidirect
3. C8×#625C2semidirect
4. #10590169C2semidirect
5. #10590041C2semidirect
6. #10590029C2semidirect
7. #10590029C2semidirect
32. #3774C8semidirect
72. #625C2×C8semidirect
73. #625C2×C8semidirect
76. #622C2×C8semidirect
229. C32#1580semidirect

Maximal subgroups

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

subgroupindex
C4×#37742
#105907182
C8×#6252
#105901692
#105900412
#105900292
#15809