Finite Group Databasebeta

← #11790073

Subgroups — #11790073

Order 1152.

569 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63642C211yesmaximal, characteristic
2C2×C3×Dic3⋊C8C212yesmaximal
3C4×#3724C211yesmaximal, characteristic
4C2×#63572C211yesmaximal, characteristic
5#10589155C212yesmaximal
6#70452—32nomaximal
7C22×C32×C8C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4×Dic3C2212yes—
11C22×C3×C3⋊C8C2212yes—
12C2×#3724C412yes—
13#63642—22no—
14C3×Dic3⋊C8—24no—
15#63579C411yescharacteristic
16#63579C411yescharacteristic
17#63572—22no—
18C2×C3×C4⋊C8—32no—
19C2×#815—32no—
20C2×#815—61no—
21C2×Dic3⋊C8—32no—
22C2×Dic3⋊C8D312yes—
23C4×Dic3⋊C4—32no—
24#4550—32no—
25#4524—32no—
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3×Dic3C2×C412yes—
30C22×C3×Dic3C2×C412yes—
31C2×C32×C8—21no—
32C2×C32×C8—21no—
33C2×C32×C8D412yes—
34C4×C3⋊Dic3D412yes—
35C4×C3⋊Dic3Q812yes—
36C2×C3⋊(C3⋊C8)—21no—
37C2×C3⋊(C3⋊C8)—21no—
38C2×C3⋊(C3⋊C8)Q812yes—
39C3×C4×Dic3—22no—
40C3×C4×Dic3—22no—
41C2×C3×C3⋊C8—22no—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8—22no—
44#3724—24no—
45#1940—91noSylow
46C22×C3×C8—21no—
47C22×C3×C8—32no—
48C22×C3×C8C2×D312yes—
49C2×C3×C42—32no—
50C2×Dic3⋊C4—32no—
51C2×Dic3⋊C4—32no—
52C2×C4×Dic3—32no—
53C2×C4×Dic3—61no—
54C2×C4×Dic3C2×D312yes—
55C22×C3⋊C8—32no—
56C22×C3⋊C8—61no—
57C22×C3⋊C8C2×D312yes—
58C3×C4⋊C8—64no—
59C3⋊#95—32no—
60C3⋊#95—32no—
61#815—64no—
62#815—64no—
63Dic3⋊C8—24no—
64Dic3⋊C8—64no—
65C23×C32C22×C411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4C2×Q811yescharacteristic
69C2×C32×C4C2×Q811yescharacteristic
70C2×C32×C4#4111yescharacteristic
71C2×C32×C4#4111yescharacteristic
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3C4⋊C412yes—
75C2×C3⋊Dic3C4⋊C412yes—
76C2×C3×Dic3—22no—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—22no—
80C2×C3×Dic3—22no—
81C2×C3×Dic3M1614yes—
82C32×C8—22no—
83C3⋊(C3⋊C8)—22no—
84C3×C3⋊C8—42no—
85C2×C4⋊C8—32no—
86C2×C4⋊C8—91no—
87C2×#97—91no—
88C4×C4⋊C4—91no—
89#336—92no—
90C22×C3×C4—21no—
91C22×C3×C4—32no—
92C22×C3×C4—32no—
93C22×C3×C4C22×D312yes—
94C22×Dic3—32no—
95C22×Dic3—32no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C22×Dic3C4×D312yes—
99C22×Dic3C4×D312yes—
100C2×C3×C8—22no—
101C2×C3×C8—22no—
102C2×C3×C8—22no—
103C2×C3×C8—22no—
104C2×C3×C8—22no—
105C2×C3×C8—62no—
106C2×C3×C8—62no—
107C2×C3×C8—62no—
108C2×C3×C8#6714yes—
109C3×C42—62no—
110C3×C42—62no—
111Dic3⋊C4—64no—
112Dic3⋊C4—64no—
113C4×Dic3—22no—
114C4×Dic3—22no—
115C4×Dic3—34no—
116C4×Dic3—34no—
117C4×Dic3—62no—
118C4×Dic3—62no—
119C2×C3⋊C8—22no—
120C2×C3⋊C8—22no—
121C2×C3⋊C8—22no—
122C2×C3⋊C8—34no—
123C2×C3⋊C8—62no—
124C2×C3⋊C8—62no—
125C2×C3⋊C8—62no—
126C2×C3⋊C8—62no—
127C2×C3⋊C8—62no—
128C22×C32C2×C4⋊C411yescharacteristic
129C22×C32C4×D411yescharacteristic
130C22×C32C4×Q811yescharacteristic
131C22×C32C2×M1612yes—
132C22×C32#13112yes—
133C32×C4#12111yescharacteristic
134C32×C4C22⋊Q811yescharacteristic
135C32×C4#12511yescharacteristic
136C32×C4C4⋊Q811yescharacteristic
137C3⋊Dic3—22no—
138C3⋊Dic3—22no—
139C3×Dic3—24no—
140C3×Dic3—42no—
141C22×C8—32no—
142C22×C8—91no—
143C22×C8D3211yescharacteristic
144C2×C4⋊C4—92no—
145C2×C42—32no—
146C2×C42—91no—
147C4⋊C8—64no—
148C4⋊C8—182no—
149#97—182no—
150#95—91no—
151#95—91no—
152C23×C3—21no—
153C23×C3C2×C4×D312yes—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—34no—
161C2×C3×C4—62no—
162C2×C3×C4—62no—
163C2×C3×C4—62no—
164C2×C3×C4—62no—
165C2×C3×C4—62no—
166C2×C3×C4#23512yes—
167C2×C3×C4D3×D412yes—
168C2×C3×C4#23712yes—
169C2×C3×C4D3×Q812yes—
170C2×C3×C4D3×Q812yes—
171C2×C3×C4C2×#6712yes—
172C2×Dic3—22no—
173C2×Dic3—22no—
174C2×Dic3—22no—
175C2×Dic3—22no—
176C2×Dic3—22no—
177C2×Dic3—34no—
178C2×Dic3—34no—
179C2×Dic3—62no—
180C2×Dic3—62no—
181C2×Dic3—62no—
182C2×Dic3—62no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187C2×Dic3ΓL(1,𝔽25)14yes—
188C3×C8—24no—
189C3×C8—24no—
190C3×C8—122no—
191C3⋊C8—42no—
192C3⋊C8—64no—
193C3⋊C8—64no—
194C2×C32#38911yescharacteristic
195C2×C32#42311yescharacteristic
196C2×C32#42411yescharacteristic
197C2×C32#43512yes—
198C2×C32#44612yes—
199C22×C4—32no—
200C22×C4—32no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4C2×D3211yescharacteristic
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—62no—
207C2×C8—62no—
208C2×C8—62no—
209C2×C8—92no—
210C2×C8—181no—
211C2×C8—181no—
212C2×C8#62512yes—
213C4⋊C4—184no—
214C42—62no—
215C42—62no—
216C42—92no—
217C42—92no—
218C22×C3—22no—
219C22×C3—22no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3#88712yes—
224C22×C3D3×C4⋊C412yes—
225C22×C3C2×ΓL(1,𝔽25)12yes—
226C22×C3#90112yes—
227C22×C3D3×M1612yes—
228C22×C3#90712yes—
229C22×C3C4×#6712yes—
230C3×C4—21no—
231C3×C4—21no—
232C3×C4—21no—
233C3×C4—21no—
234C3×C4—64no—
235C3×C4—122no—
236C3×C4#88912yes—
237C3×C4#89612yes—
238C3×C4#93912yes—
239C3×C4#94412yes—
240Dic3—24no—
241Dic3—42no—
242Dic3—64no—
243Dic3—64no—
244Dic3—122no—
245Dic3—122no—
246C32#194011yescharacteristic, complemented, Sylow
247C23C4×D3211yescharacteristic
248C2×C4—34no—
249C2×C4—62no—
250C2×C4—62no—
251C2×C4—62no—
252C2×C4—62no—
253C2×C4—62no—
254C2×C4—92no—
255C2×C4—92no—
256C2×C4—182no—
257C2×C4—182no—
258C2×C4#379711yescharacteristic
259C2×C4#379711yescharacteristic
260C2×C4#379811yescharacteristic
261C2×C4#380511yescharacteristic
262C2×C4C2×#62511yescharacteristic
263C2×C4#381111yescharacteristic
264C8—22no—
265C8—122no—
266C8—182no—
267C2×C3—22no—
268C2×C3—21no—
269C2×C3—22no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3#482812yes—
273C2×C3#483112yes—
274C2×C3#483712yes—
275C2×C3#483912yes—
276C2×C3#497612yes—
277C2×C3#511112yes—
278C2×C3#512712yes—
279C22D3×ΓL(1,𝔽25)12yes—
280C22#6380412yes—
281C22#6383811yescharacteristic
282C22#6388311yescharacteristic
283C22C4×#62511yescharacteristic
284C4—64no—
285C4—122no—
286C4—182no—
287C4—182no—
288C4#6386511yescharacteristic
289C4#6387011yescharacteristic
290C4#6387311yescharacteristic
291C4#6398011yescharacteristic
292C3—21no—
293C3#7045212yescomplemented
294C2#1059064612yes—
295C2#1059066611yescharacteristic
296C2#1059070211yescharacteristic
297C2#1059072212yes—
298C2#1059133711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutator, socle, prime radicalC23×C32C22×C4
FittingC22×C32×C8C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1940
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
246. C32#1940semidirect
293. C3#70452semidirect

Maximal subgroups

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

subgroupindex
C2×#636422
C2×C3×Dic3⋊C82
C4×#37242
C2×#635722
#105891552
#704523