Finite Group Databasebeta

← #11774041

Subgroups — #11774041

Order 1152.

476 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 57 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#10594009C211yesmaximal, characteristic
2#10593727C211yesmaximal, characteristic, complemented
3#10590260C211yesmaximal, characteristic, complemented
4#10590027C214yesmaximal, complemented
5C2×#3802C411yescharacteristic
6C2×#3797C411yescharacteristic
7C42×C3⋊D3C2211yescharacteristic
8C3×#875—21no—
9#63921C412yes—
10#63921C2212yes—
11#63915—21no—
12#63915—21no—
13#63863—21no—
14#63778C2212yes—
15C4⋊#622—21no—
16C4×#622—21no—
17C3×C4⋊(C3⋊C8)—21no—
18#63557C2212yes—
19#63555—21no—
20D3×#124—61no—
21#4835—61no—
22C22×D32C2×C412yes—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×C3×D12—21no—
27C2×C3×Dic6—21no—
28C2×#627—21no—
29C2×#625—21no—
30C2×#624C2×C412yes—
31#3802—42no—
32#3797—42no—
33C2×#622—22no—
34C32×C42D411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C3×(C2×D3)⋊C4—22no—
39C3×(C2×D3)⋊C4—22no—
40C2×C3×C3⋊C8—22no—
41(C2×D3)⋊Dic3—22no—
42(C2×D3)⋊Dic3—22no—
43#1469—91nomaximal, Sylow
44C2×D3×Q8—61no—
45C2×D3×D4—61no—
46C3×#124—61no—
47#947—61no—
48#936—61no—
49#885—62no—
50#885—62no—
51D3×C22⋊C4—62no—
52D3×C22⋊C4—62no—
53#875—21no—
54C42×D3—61no—
55C42×D3—61no—
56C3×C4⋊C8—61no—
57(C2×D3)⋊C8—62no—
58#815—62no—
59C4⋊(C3⋊C8)—21no—
60C22×C3⋊D3C22×C411yescharacteristic
61C22×C3×D3—22no—
62C2×D32—24no—
63C2×D32—42no—
64C2×D32—42no—
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C32×C4C2×D411yescharacteristic
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C22⋊C411yescharacteristic
70C2×C3⋊Dic3C2×D411yescharacteristic
71C4×C3⋊D3—22no—
72C4×C3⋊D3—22no—
73C4×C3⋊D3—41no—
74C2×C3×Dic3—22no—
75C3×D12—42no—
76C3×Dic6—42no—
77#627—42no—
78#625—42no—
79#624—42no—
80#622—42no—
81C3×C3⋊C8—42no—
82C2×#124—91no—
83#432—91no—
84#431—91no—
85#323—94no—
86C23×D3—62no—
87C2×C3×Q8—61no—
88C2×C3×D4—61no—
89C2×#67—62no—
90D3×Q8—124no—
91D3×D4—124no—
92C2×D12—21no—
93C2×C4×D3—61no—
94C2×C4×D3—62no—
95C2×C4×D3—61no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×Dic6—21no—
101C2×Dic6—62no—
102C2×C3×C8—62no—
103C3×C22⋊C4—62no—
104C3×C22⋊C4—62no—
105C3×C42—21no—
106C3×C42—21no—
107#217—62no—
108#217—62no—
109(C2×D3)⋊C4—22no—
110(C2×D3)⋊C4—22no—
111(C2×D3)⋊C4—62no—
112(C2×D3)⋊C4—62no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C2×C3⋊C8—22no—
120C22×C32C2×C22⋊C411yescharacteristic
121C2×C3⋊D3—21no—
122C2×C3⋊D3—21no—
123C2×C3⋊D3#13112yes—
124C2×C3×D3—42no—
125C2×C3×D3—42no—
126C2×C3×D3—42no—
127D32—84no—
128C32×C4—21no—
129C32×C4—21no—
130C32×C4#10012yes—
131C3⋊Dic3—21no—
132C3⋊Dic3—21no—
133C3⋊Dic3—21no—
134C3×Dic3—42no—
135C22×Q8—91no—
136C22×D4—91no—
137#124—61no—
138#124—181no—
139#124—181no—
140#124—181no—
141C2×C22⋊C4—92no—
142C2×C22⋊C4—92no—
143C2×C42—91no—
144C4⋊C8—61no—
145C4⋊C8—181no—
146C22⋊C8—92no—
147C22⋊C8—92no—
148#97—181no—
149C4×C8—181no—
150C23×C3—62no—
151C22×D3—22no—
152C22×D3—61no—
153C22×D3—61no—
154C22×D3—124no—
155C22×D3—124no—
156C22×D3—124no—
157C3×Q8—122no—
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—
166#67—124no—
167C2×Dic3—22no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174D12—42no—
175C4×D3—64no—
176C4×D3—122no—
177C4×D3—122no—
178C4×D3—122no—
179C4×D3—124no—
180C4×D3—121no—
181C4×D3—121no—
182C4×D3—122no—
183Dic6—42no—
184Dic6—124no—
185C3×C8—122no—
186C3⋊C8—42no—
187C2×C32#40811yescharacteristic
188C2×C32#41011yescharacteristic
189C2×C32C2×#10011yescharacteristic
190C3⋊D3—22no—
191C3×D3—82no—
192C24—92no—
193C2×Q8—61no—
194C2×Q8—181no—
195C2×Q8—362no—
196C2×D4—61no—
197C2×D4—181no—
198C2×D4—362no—
199C22×C4—92no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4—91no—
203C2×C8—62no—
204C2×C8—182no—
205C22⋊C4—62no—
206C22⋊C4—62no—
207C22⋊C4—182no—
208C22⋊C4—182no—
209C42—91no—
210C42—91no—
211C42—91no—
212C42GO+(4,𝔽2)11yescharacteristic
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—122no—
216C22×C3—122no—
217C22×C3—122no—
218C2×D3—42no—
219C2×D3—42no—
220C2×D3—42no—
221C2×D3—62no—
222C2×D3—62no—
223C2×D3—62no—
224C2×D3—62no—
225C2×D3—121no—
226C2×D3—121no—
227C2×D3—248no—
228C3×C4—21no—
229C3×C4—21no—
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—41no—
233C3×C4—41no—
234C3×C4—41no—
235C3×C4—122no—
236Dic3—42no—
237Dic3—62no—
238Dic3—121no—
239Dic3—121no—
240Dic3—121no—
241Dic3—121no—
242Dic3—121no—
243C32#146911yescharacteristic, complemented, Sylow
244C23—62no—
245C23—91no—
246C23—184no—
247C23—362no—
248C23—362no—
249Q8—122no—
250Q8—362no—
251D4—122no—
252D4—362no—
253C2×C4—62no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—182no—
258C2×C4—182no—
259C2×C4—361no—
260C2×C4—362no—
261C2×C4D32⋊C411yescharacteristic
262C2×C4D32⋊C411yescharacteristic
263C2×C4C2×GO+(4,𝔽2)11yescharacteristic
264C8—122no—
265C8—362no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—242no—
273D3—64no—
274D3—82no—
275D3—122no—
276C22—92no—
277C22—122no—
278C22—122no—
279C22—122no—
280C22—181no—
281C22—181no—
282C22—724no—
283C22C2×D32⋊C411yescharacteristic
284C4—21no—
285C4—21no—
286C4—122no—
287C4—181no—
288C4—181no—
289C4—181no—
290C4#6372712yes—
291C3—21no—
292C3—21no—
293C2—182no—
294C2—242no—
295C2#1059330911yescharacteristic
296C2C2×#6372711yescharacteristic
297C2#1059334611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC22×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3802C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1469
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593727C2semidirect
3. #10590260C2semidirect
4. #10590027C2semidirect
243. C32#1469semidirect

Maximal subgroups

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

subgroupindex
#105940092
#105937272
#105902602
#105900272
#14699