Finite Group Databasebeta

← #11776048

Subgroups — #11776048

Order 1152.

448 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 53 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#10594929C211yesmaximal, characteristic
2#10593804C211yesmaximal, characteristic, complemented
3#10591066C211yesmaximal, characteristic, complemented
4#10590035C214yesmaximal, complemented
5C2×#3805C412yes—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×#930—21no—
8#63980—21no—
9#63919C411yescharacteristic
10#63915C2212yes—
11#63914C411yescharacteristic
12#63902—21no—
13#63898—21no—
14C22⋊#622—21no—
15#63779—21no—
16#63777C2212yes—
17C3×#830—21no—
18#63572—21no—
19#63555C2212yes—
20#5596—61no—
21#4719—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C3×#67—22no—
26C2×C3×D12—21no—
27C2×#627C2×C412yes—
28C2×#625—21no—
29C2×#625C2×C412yes—
30#3805—44no—
31C2×D3×Dic3—22no—
32C2×#622—22no—
33C4×C3⋊Dic3C2×C411yescharacteristic
34C4×C3⋊Dic3D411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C3×(C2×D3)⋊C4—22no—
38C3×C4⋊Dic3—21no—
39C2×C3×C3⋊C8—22no—
40#3724—21no—
41(C2×D3)⋊Dic3—22no—
42#1536—91nomaximal, Sylow
43C2×#237—62no—
44C3×#121—61no—
45#940—61no—
46#939—62no—
47D4×Dic3—61no—
48#930—21no—
49C2×C4×Dic3—61no—
50C2×C4×Dic3—61no—
51#893—61no—
52#888—61no—
53#885—62no—
54#67⋊C4—62no—
55C3×C22⋊C8—61no—
56#830—21no—
57#815—62no—
58Dic3⋊C8—62no—
59C23×C32C22⋊C411yescharacteristic
60C22×C3×D3—22no—
61C2×C32×C4—41no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3—41no—
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22×C411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C3×#67—44no—
71C2×C3×Dic3—22no—
72C3×D12—42no—
73#627—42no—
74#625—42no—
75#625—42no—
76D3×Dic3—44no—
77#622—42no—
78C3×C3⋊C8—42no—
79#532—91no—
80#432—91no—
81#432—91no—
82#329—94no—
83C2×C3×D4—61no—
84C2×C3×D4—62no—
85C22×C3×C4—21no—
86C22×C3×C4—21no—
87C2×#67—22no—
88C2×#67—62no—
89C2×#67—62no—
90C22×Dic3—61no—
91C22×Dic3—61no—
92C22×Dic3—61no—
93C22×Dic3—61no—
94C22×Dic3—62no—
95#237—128no—
96C2×D12—21no—
97C2×C4×D3—62no—
98C2×Dic6—62no—
99C2×C3×C8—62no—
100C3×C4⋊C4—61no—
101C3×C22⋊C4—62no—
102#217—62no—
103(C2×D3)⋊C4—22no—
104(C2×D3)⋊C4—62no—
105C4⋊Dic3—21no—
106Dic3⋊C4—62no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C2×C3⋊C8—22no—
116C22×C32—21no—
117C22×C32—21no—
118C22×C32—21no—
119C22×C32C2×C22⋊C411yescharacteristic
120C2×C3×D3—42no—
121C2×C3×D3—42no—
122C2×C3×D3—42no—
123C32×C4—21no—
124C32×C4—21no—
125C3⋊Dic3—21no—
126C3⋊Dic3—21no—
127C3⋊Dic3—21no—
128C3⋊Dic3#10012yes—
129C3×Dic3—42no—
130C2×#41—92no—
131C4⋊Q8—91no—
132#127—91no—
133#124—92no—
134#121—61no—
135#121—181no—
136C4×D4—181no—
137C4×D4—181no—
138C2×C42—91no—
139C4⋊C8—181no—
140C4⋊C8—181no—
141C22⋊C8—61no—
142C22⋊C8—181no—
143#97—92no—
144#97—92no—
145C23×C3—21no—
146C23×C3—21no—
147C23×C3—62no—
148C22×D3—22no—
149C3×D4—122no—
150C3×D4—124no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—42no—
156C2×C3×C4—42no—
157C2×C3×C4—62no—
158#67—44no—
159#67—124no—
160#67—124no—
161C2×Dic3—22no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—64no—
171C2×Dic3—122no—
172C2×Dic3—124no—
173C2×Dic3—122no—
174C2×Dic3—122no—
175D12—42no—
176C4×D3—124no—
177Dic6—124no—
178C3×C8—122no—
179C3⋊C8—42no—
180C2×C32—41no—
181C2×C32C2×#10011yescharacteristic
182C2×C32#42111yescharacteristic
183C2×C32#42111yescharacteristic
184C3×D3—82no—
185#41—364no—
186C2×Q8—92no—
187C2×D4—62no—
188C2×D4—61no—
189C2×D4—92no—
190C2×D4—181no—
191C22×C4—91no—
192C22×C4—91no—
193C22×C4—182no—
194C22×C4GO+(4,𝔽2)11yescharacteristic
195C2×C8—62no—
196C2×C8—182no—
197C4⋊C4—61no—
198C4⋊C4—181no—
199C22⋊C4—62no—
200C22⋊C4—182no—
201C42—91no—
202C42—91no—
203C42—91no—
204C42—91no—
205C22×C3—22no—
206C22×C3—22no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—41no—
210C22×C3—41no—
211C22×C3—41no—
212C22×C3—41no—
213C22×C3—122no—
214C22×C3—122no—
215C22×C3—122no—
216C2×D3—42no—
217C2×D3—42no—
218C2×D3—42no—
219C3×C4—22no—
220C3×C4—22no—
221C3×C4—41no—
222C3×C4—41no—
223C3×C4—122no—
224Dic3—42no—
225Dic3—62no—
226Dic3—62no—
227Dic3—62no—
228Dic3—62no—
229Dic3—121no—
230Dic3—121no—
231Dic3—121no—
232Dic3—121no—
233C32#153611yescharacteristic, complemented, Sylow
234C23—62no—
235C23D32⋊C411yescharacteristic
236Q8—362no—
237D4—122no—
238D4—124no—
239D4—362no—
240D4—362no—
241C2×C4—41no—
242C2×C4—62no—
243C2×C4—91no—
244C2×C4—91no—
245C2×C4—91no—
246C2×C4—91no—
247C2×C4—182no—
248C2×C4—364no—
249C2×C4—361no—
250C2×C4D32⋊C411yescharacteristic
251C2×C4C2×GO+(4,𝔽2)11yescharacteristic
252C8—122no—
253C8—362no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—42no—
261C2×C3—42no—
262C2×C3—242no—
263D3—82no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—122no—
268C22—122no—
269C22—122no—
270C22C2×D32⋊C411yescharacteristic
271C4—21no—
272C4—21no—
273C4—92no—
274C4—122no—
275C4—181no—
276C4—181no—
277C4—181no—
278C3—21no—
279C3—21no—
280C2—41no—
281C2—242no—
282C2#1059331211yescharacteristic
283C2#1059332411yescharacteristic
284C2#1059350611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1536
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593804C2semidirect
3. #10591066C2semidirect
4. #10590035C2semidirect
233. C32#1536semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105938042
#105910662
#105900352
#15369