Finite Group Databasebeta

← #11794668

Subgroups — #11794668

Order 1152.

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

normal subgroups only

This group has 476 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
1#10593827C211yesmaximal, characteristic
2#10593413C211yesmaximal, characteristic, complemented
3#10591416C212yesmaximal
4#10590049C212yesmaximal, complemented
5#10590044C211yesmaximal, characteristic, complemented
6C2×D4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157—21no—
8C2×C22⋊#157—21no—
9C2×C4⋊#157C2211yescharacteristic
10C2×C4×#157C2211yescharacteristic
11C2×#3773—21no—
12C2×#3773—21no—
13#63900C2212yes—
14C2×#3710C2212yes—
15C3×#832—22no—
16#63564—22no—
17D3×#102—62no—
18C23×C3⋊D3—21no—
19C22×#157—21no—
20C22×#157D411yescharacteristic
21C22×#157D411yescharacteristic
22C2×C32×D4D411yescharacteristic
23C2×#638—21no—
24D4×C3⋊D3—22no—
25D4×C3⋊D3—22no—
26C2×C4⋊(C3⋊D3)D411yescharacteristic
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×#624—22no—
29C22⋊#157—42no—
30C22⋊#157—42no—
31C4⋊#157—22no—
32C4×#157—22no—
33#3773—42no—
34#3773—42no—
35C3×C4⋊Dic3—22no—
36C2×C3×C3⋊C8—22no—
37#3724—22no—
38#3710—22no—
39#3710—22no—
40#2071—91nomaximal, Sylow
41C2×D3×D4—62no—
42C2×D3×C8—62no—
43D3×C4⋊C4—62no—
44C3×#102—62no—
45#832—22no—
46#821—62no—
47#809—62no—
48C23×C32—21no—
49C22×C3⋊D3—21no—
50C22×C3⋊D3—41no—
51C22×C3⋊D3—41no—
52C22×C3⋊D3—41no—
53C22×C3⋊D3—41no—
54C22×C3⋊D3—41no—
55C22×C3⋊D3—41no—
56C22×C3⋊D3C2×D411yescharacteristic
57C2×#157—21no—
58C2×#157—21no—
59C2×#157—21no—
60C2×#157—21no—
61C2×#157—41no—
62C2×#157—41no—
63C2×#157—41no—
64C2×#157D812yes—
65C2×#157SD1612yes—
66C32×D4—22no—
67C2×C32×C4C2×D411yescharacteristic
68#638—42no—
69C2×C3⋊Dic3#4111yescharacteristic
70C4⋊(C3⋊D3)—22no—
71C4×C3⋊D3#4112yes—
72C4×C3⋊D3#4112yes—
73C2×C3×Dic3—42no—
74#624—42no—
75#624—42no—
76C3×C3⋊C8—42no—
77C2×#102—92no—
78#390—91no—
79#384—91no—
80#340—92no—
81#336—91no—
82C23×D3—122no—
83C2×C3×D4—22no—
84C2×#67—122no—
85D3×D4—64no—
86D3×D4—64no—
87D3×D4—122no—
88D3×D4—122no—
89C2×D12—62no—
90C2×C4×D3—62no—
91C2×C4×D3—122no—
92C2×C3×C8—62no—
93C3×C4⋊C4—62no—
94C4⋊Dic3—22no—
95Dic3⋊C4—122no—
96C2×C3⋊C8—22no—
97D3×C8—122no—
98D3×C8—122no—
99C22×C32—41no—
100C22×C32—41no—
101C22×C32—41no—
102C22×C32#12111yescharacteristic
103C2×C3⋊D3—41no—
104C2×C3⋊D3—41no—
105C2×C3⋊D3—41no—
106C2×C3⋊D3—81no—
107C2×C3⋊D3—81no—
108C2×C3⋊D3—81no—
109C2×C3⋊D3—81no—
110C2×C3⋊D3#12311yescharacteristic
111C2×C3⋊D3#12411yescharacteristic
112C2×C3⋊D3C2×D811yescharacteristic
113C2×C3⋊D3C2×SD1611yescharacteristic
114C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
115C2×C3⋊D3#13711yescharacteristic
116#157—22no—
117#157—22no—
118#157—81no—
119C32×C4#12312yes—
120C3⋊Dic3#12612yes—
121C3×Dic3—82no—
122C22×D4—91no—
123C22×C8—92no—
124C2×C4⋊C4—92no—
125C2×C4⋊C4—91no—
126C2×C4⋊C4—181no—
127C2×C4⋊C4—181no—
128C2×C22⋊C4—181no—
129C2×C22⋊C4—181no—
130C2×C42—91no—
131#102—62no—
132#102—182no—
133C23×C3—42no—
134C22×D3—62no—
135C22×D3—122no—
136C22×D3—124no—
137C22×D3—124no—
138C22×D3—242no—
139C22×D3—242no—
140C22×D3—242no—
141C22×D3—242no—
142C3×D4—24no—
143C3×D4—42no—
144C2×C3×C4—22no—
145C2×C3×C4—122no—
146#67—124no—
147#67—124no—
148C2×Dic3—42no—
149C2×Dic3—62no—
150D12—64no—
151D12—122no—
152C4×D3—62no—
153C4×D3—62no—
154C4×D3—62no—
155C4×D3—62no—
156C4×D3—242no—
157C4×D3—242no—
158C3×C8—122no—
159C3⋊C8—42no—
160C2×C32—81no—
161C2×C32#39711yescharacteristic
162C2×C32#45911yescharacteristic
163C2×C32#46111yescharacteristic
164C3⋊D3—81no—
165C3⋊D3#48011yescharacteristic
166C3⋊D3#48111yescharacteristic
167C3⋊D3#48611yescharacteristic
168C3⋊D3#48911yescharacteristic
169C24—181no—
170C2×D4—91no—
171C2×D4—182no—
172C2×D4—182no—
173C2×D4—181no—
174C2×D4GO+(4,𝔽2)11yescharacteristic
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4—182no—
179C22×C4—181no—
180C2×C8—62no—
181C2×C8—182no—
182C2×C8—182no—
183C4⋊C4—62no—
184C4⋊C4—182no—
185C4⋊C4—182no—
186C4⋊C4—362no—
187C4⋊C4—362no—
188C22⋊C4—362no—
189C22⋊C4—362no—
190C42—182no—
191C22×C3—22no—
192C22×C3—44no—
193C22×C3—82no—
194C22×C3—82no—
195C2×D3—62no—
196C2×D3—62no—
197C2×D3—62no—
198C2×D3—62no—
199C2×D3—62no—
200C2×D3—62no—
201C2×D3—124no—
202C2×D3—242no—
203C2×D3—242no—
204C2×D3—244no—
205C2×D3—244no—
206C2×D3—244no—
207C2×D3—244no—
208C3×C4—22no—
209C3×C4—22no—
210C3×C4—242no—
211Dic3—62no—
212Dic3—62no—
213Dic3—82no—
214C32#207111yescharacteristic, complemented, Sylow
215C23—21no—
216C23—91no—
217C23—181no—
218C23—361no—
219C23—361no—
220C23—361no—
221C23—361no—
222C23—361no—
223C23—361no—
224D4—22no—
225D4—182no—
226D4—362no—
227C2×C4—91no—
228C2×C4—92no—
229C2×C4—92no—
230C2×C4—92no—
231C2×C4—92no—
232C2×C4—122no—
233C2×C4—181no—
234C2×C4—181no—
235C2×C4—181no—
236C2×C4—181no—
237C2×C4—362no—
238C2×C4—362no—
239C2×C4—361no—
240C2×C4—361no—
241C2×C4—361no—
242C2×C4C2×GO+(4,𝔽2)11yescharacteristic
243C8—122no—
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—22no—
247C2×C3—84no—
248D3—62no—
249D3—62no—
250D3—62no—
251D3—62no—
252D3—244no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—91no—
257C22—91no—
258C22—91no—
259C22—91no—
260C22—91no—
261C22—91no—
262C22—361no—
263C22—361no—
264C22—361no—
265C22—721no—
266C22—721no—
267C22—721no—
268C22—721no—
269C22#6424211yescharacteristic
270C4—92no—
271C4—182no—
272C4—182no—
273C4—242no—
274C4—721no—
275C4#6423312yes—
276C3—22no—
277C2—81no—
278C2—91no—
279C2—91no—
280C2—91no—
281C2—91no—
282C2—721no—
283C2#1059346411yescharacteristic
284C2#1059346511yescharacteristic
285C2#1059348611yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×D4D4
socleC22×C32#121
prime radicalC2×D4×C3⋊D3C22
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#2071
LCSG ▷ C2×C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10593413C2semidirect
4. #10590049C2semidirect
5. #10590044C2semidirect
214. C32#2071semidirect

Maximal subgroups

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

subgroupindex
#105938272
#105934132
#105914162
#105900492
#105900442
#20719