Finite Group Databasebeta

← #11785730

Subgroups — #11785730

Order 1152.

620 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#63900C211yesmaximal, characteristic
2#10593803C211yesmaximal, characteristic
3#10591159C211yesmaximal, characteristic
4#10590052C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#624C412yes—
7C2×#3788C2212yes—
8C2×C3×C4⋊Dic3—21no—
9C2×#3724—21no—
10#63900—21no—
11#63900—21no—
12#63900C412yes—
13#63900C2212yes—
14C2×#3712C2212yes—
15C22⋊#622—21no—
16#63778—21no—
17C3×#830—21no—
18#63557—21no—
19C2×D3×C4⋊C4—61no—
20#4726—61no—
21C23×C3⋊D3C2×C411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C2×C4×C3⋊D3—24no—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3C2311yescharacteristic
29C22×C3×Dic3—22no—
30C2×#624—22no—
31C2×#624—44no—
32C2×#624C2×C414yes—
33C2×#622—22no—
34#3788—24no—
35C3×C4⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C2×C3×C3⋊C8—22no—
38#3724—22no—
39#3724—22no—
40#3712—24no—
41#1821—91nomaximal, Sylow
42C22×C4×D3—61no—
43C22×C4×D3—62no—
44C22×C4×D3—61no—
45C2×C3×C4⋊C4—61no—
46C2×C4⋊Dic3—21no—
47C2×Dic3⋊C4—62no—
48C2×ΓL(1,𝔽25)—62no—
49D3×C4⋊C4—62no—
50D3×C4⋊C4—62no—
51D3×C4⋊C4—62no—
52D3×C4⋊C4—62no—
53C3×C22⋊C8—61no—
54#830—21no—
55(C2×D3)⋊C8—62no—
56C23×C32C22⋊C411yescharacteristic
57C22×C3⋊D3—22no—
58C22×C3⋊D3—22no—
59C22×C3⋊D3—22no—
60C22×C3⋊D3C22⋊C411yescharacteristic
61C22×C3⋊D3C22×C411yescharacteristic
62C2×C32×C4—22no—
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C2×D411yescharacteristic
68C4×C3⋊D3—22no—
69C4×C3⋊D3—22no—
70C4×C3⋊D3—22no—
71C4×C3⋊D3#4114yes—
72C2×C3×Dic3—24no—
73C2×C3×Dic3—44no—
74#624—44no—
75#624—44no—
76#622—42no—
77C3×C3⋊C8—42no—
78C22×C4⋊C4—91no—
79#407—91no—
80#407—91no—
81#343—94no—
82C23×D3—61no—
83C23×D3—61no—
84C22×C3×C4—21no—
85C22×C3×C4—21no—
86C22×C3×C4—62no—
87C22×Dic3—22no—
88C22×Dic3—61no—
89C22×Dic3—61no—
90C2×C4×D3—61no—
91C2×C4×D3—61no—
92C2×C4×D3—61no—
93C2×C4×D3—61no—
94C2×C4×D3—61no—
95C2×C4×D3—64no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×C4×D3—68no—
100C2×C4×D3—64no—
101C2×C4×D3—124no—
102C2×C4×D3—128no—
103C2×C3×C8—62no—
104C3×C4⋊C4—62no—
105C3×C4⋊C4—62no—
106C4⋊Dic3—22no—
107C4⋊Dic3—22no—
108Dic3⋊C4—64no—
109Dic3⋊C4—64no—
110C2×C3⋊C8—22no—
111ΓL(1,𝔽25)—124no—
112C22×C32—21no—
113C22×C32—21no—
114C22×C32#10012yes—
115C22×C32C2×C22⋊C411yescharacteristic
116C2×C3⋊D3—28no—
117C2×C3⋊D3—21no—
118C2×C3⋊D3—21no—
119C2×C3⋊D3—21no—
120C2×C3⋊D3—21no—
121C2×C3⋊D3#10112yes—
122C2×C3⋊D3#11712yes—
123C32×C4—21no—
124C32×C4#12312yes—
125C3⋊Dic3—21no—
126C3⋊Dic3#12312yes—
127C3×Dic3—44no—
128C23×C4—92no—
129C23×C4—91no—
130C2×M16—92no—
131C2×M16—92no—
132C2×C4⋊C4—61no—
133C2×C4⋊C4—92no—
134C2×C4⋊C4—92no—
135C2×C4⋊C4—181no—
136C2×C4⋊C4—181no—
137C2×C4⋊C4—181no—
138C22⋊C8—61no—
139C22⋊C8—181no—
140C22⋊C8—181no—
141C22⋊C8—181no—
142C23×C3—21no—
143C23×C3—21no—
144C22×D3—61no—
145C22×D3—61no—
146C22×D3—61no—
147C22×D3—61no—
148C22×D3—64no—
149C22×D3—64no—
150C22×D3—64no—
151C22×D3—122no—
152C22×D3—122no—
153C22×D3—122no—
154C2×C3×C4—24no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—42no—
160C2×C3×C4—64no—
161C2×C3×C4—124no—
162C2×Dic3—24no—
163C2×Dic3—44no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—64no—
169C2×Dic3—122no—
170C4×D3—64no—
171C4×D3—64no—
172C4×D3—64no—
173C4×D3—64no—
174C4×D3—64no—
175C4×D3—122no—
176C4×D3—122no—
177C4×D3—122no—
178C4×D3—128no—
179C4×D3—128no—
180C3×C8—122no—
181C3⋊C8—42no—
182C2×C32—22no—
183C2×C32#38111yescharacteristic
184C2×C32C2×#10011yescharacteristic
185C2×C32C2×#10111yescharacteristic
186C3⋊D3—22no—
187C3⋊D3—22no—
188C24—91no—
189C22×C4—62no—
190C22×C4—94no—
191C22×C4—91no—
192C22×C4—91no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—91no—
196C22×C4—184no—
197C22×C4—182no—
198C22×C4—364no—
199C22×C4GO+(4,𝔽2)11yescharacteristic
200M16—184no—
201M16—184no—
202C2×C8—62no—
203C2×C8—182no—
204C4⋊C4—62no—
205C4⋊C4—62no—
206C4⋊C4—182no—
207C4⋊C4—182no—
208C22×C3—22no—
209C22×C3—22no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—22no—
213C22×C3—22no—
214C22×C3—41no—
215C22×C3—41no—
216C2×D3—62no—
217C2×D3—62no—
218C2×D3—62no—
219C2×D3—62no—
220C2×D3—62no—
221C2×D3—62no—
222C2×D3—62no—
223C2×D3—616no—
224C2×D3—62no—
225C2×D3—121no—
226C2×D3—121no—
227C2×D3—121no—
228C2×D3—121no—
229C2×D3—128no—
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—22no—
233C3×C4—41no—
234C3×C4—124no—
235Dic3—44no—
236Dic3—62no—
237Dic3—62no—
238Dic3—62no—
239Dic3—121no—
240C32#182111yescharacteristic, complemented, Sylow
241C23—91no—
242C23—91no—
243C23—182no—
244C23—182no—
245C23—182no—
246C23D32⋊C411yescharacteristic
247C2×C4—22no—
248C2×C4—64no—
249C2×C4—91no—
250C2×C4—94no—
251C2×C4—91no—
252C2×C4—124no—
253C2×C4—182no—
254C2×C4—182no—
255C2×C4—182no—
256C2×C4—182no—
257C2×C4—364no—
258C2×C4—364no—
259C2×C4D32⋊C411yescharacteristic
260C2×C4C2×GO+(4,𝔽2)11yescharacteristic
261C8—122no—
262C8—362no—
263C2×C3—24no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—42no—
271D3—64no—
272D3—64no—
273D3—122no—
274D3—122no—
275C22—21no—
276C22—21no—
277C22—92no—
278C22—92no—
279C22—188no—
280C22—181no—
281C22—181no—
282C22—181no—
283C22—181no—
284C22#6372712yes—
285C22C2×D32⋊C411yescharacteristic
286C4—21no—
287C4—92no—
288C4—124no—
289C4—181no—
290C4#6423312yes—
291C3—21no—
292C3—21no—
293C2—22no—
294C2—182no—
295C2—182no—
296C2C2×#6372711yescharacteristic
297C2#1059331511yescharacteristic
298C2#1059348811yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC22×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1821
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590052C2semidirect
240. C32#1821semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
#105938032
#105911592
#105900522
#18219