Finite Group Databasebeta

← #11776302

Subgroups — #11776302

Order 1152.

543 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 543 conjugacy classes of subgroups — too many to draw. Only its 108 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#10593909C211yesmaximal, characteristic
2#10592536C211yesmaximal, characteristic
3#10590256C211yesmaximal, characteristic
4C3×#4482C212yesmaximal, complemented
5#10589092C212yesmaximal, complemented
6#68420—32nomaximal
7C2×#3797—21no—
8C2×#3743—21no—
9C42×C3⋊D3C2211yescharacteristic
10C3×#869C2212yes—
11#63919—21no—
12#63919C412yes—
13#63900—21no—
14#63900C412yes—
15#63873—21no—
16C32×C4⋊C8C2211yescharacteristic
17#63641—21no—
18C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2212yes—
20#63557—21no—
21#63553—21no—
22D3×C4⋊Q8—32no—
23#4837—32no—
24#4837—61no—
25#4833—32no—
26C3×#332—32no—
27#4547—32no—
28#4486—32no—
29#4482D312yescomplemented
30C2×C4×C3⋊D3C2×C411yescharacteristic
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C3×Dic6—22no—
34C2×#627—22no—
35C2×#624—22no—
36#3797—42no—
37#3797—42no—
38C2×C32×C8—21no—
39C32×C42C2311yescharacteristic
40C4×C3⋊Dic3C2×C411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C2×C3⋊(C3⋊C8)—21no—
44#3743—42no—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3C2×C414yes—
47C2×C3×C3⋊C8—22no—
48#3724—22no—
49#3724—22no—
50#1546—91noSylow
51C2×D3×Q8—62no—
52C3×C4⋊Q8—32no—
53#944—62no—
54C2×ΓL(1,𝔽25)—62no—
55C2×ΓL(1,𝔽25)—62no—
56D3×C4⋊C4—34no—
57D3×C4⋊C4—62no—
58#888—34no—
59#888—62no—
60C42×D3—32no—
61C42×D3—61no—
62#869C2×D312yes—
63C3×C4⋊C8—21no—
64C3×C4⋊C8—32no—
65C3×C4⋊C8C2×D312yes—
66(C2×D3)⋊C8—62no—
67Dic3⋊C8—62no—
68Dic3⋊C8—62no—
69C8×Dic3—62no—
70C4⋊(C3⋊C8)—32no—
71C4⋊(C3⋊C8)—61no—
72C4⋊(C3⋊C8)C2×D312yes—
73C22×C3⋊D3C22⋊C411yescharacteristic
74C2×C32×C4C22×C411yescharacteristic
75C2×C32×C4C2×D411yescharacteristic
76C2×C32×C4C2×D411yescharacteristic
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C4×C3⋊D3—22no—
81C4×C3⋊D3—22no—
82C4×C3⋊D3D812yes—
83C4×C3⋊D3SD1612yes—
84C2×C3×Dic3—24no—
85C3×Dic6—42no—
86C3×Dic6—42no—
87#627—44no—
88#624—44no—
89C32×C8—41no—
90C3⋊(C3⋊C8)—41no—
91C3×C3⋊C8—42no—
92C2×C4⋊Q8—91no—
93#431—91no—
94#423—91no—
95#332—32no—
96#332—92no—
97C2×C3×Q8—62no—
98D3×Q8—124no—
99D3×Q8—124no—
100C2×C4×D3—32no—
101C2×C4×D3—32no—
102C2×C4×D3—32no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—64no—
107C2×Dic6—22no—
108C2×Dic6—64no—
109C2×C3×C8—22no—
110C2×C3×C8—22no—
111C2×C3×C8—62no—
112C3×C4⋊C4—34no—
113C3×C4⋊C4—62no—
114C3×C42—21no—
115C3×C42C22×D312yes—
116C4⋊Dic3—22no—
117C4⋊Dic3C4×D314yes—
118Dic3⋊C4—64no—
119Dic3⋊C4—64no—
120C4×Dic3—32no—
121C4×Dic3—32no—
122C4×Dic3—32no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C2×C3⋊C8—22no—
127C2×C3⋊C8—62no—
128C2×C3⋊C8—62no—
129ΓL(1,𝔽25)—124no—
130ΓL(1,𝔽25)—124no—
131C22×C32C2×C22⋊C411yescharacteristic
132C2×C3⋊D3—21no—
133C2×C3⋊D3—21no—
134C2×C3⋊D3#10212yes—
135C32×C4—21no—
136C32×C4C2×D811yescharacteristic
137C32×C4C2×SD1611yescharacteristic
138C32×C4#13712yes—
139C3⋊Dic3—21no—
140C3⋊Dic3#10112yes—
141C3⋊Dic3#10212yes—
142C3×Dic3—44no—
143C22×Q8—181no—
144C2×M16—181no—
145C4⋊Q8—32no—
146C4⋊Q8—92no—
147C4⋊Q8—181no—
148C4⋊Q8—181no—
149C2×C4⋊C4—92no—
150C2×C4⋊C4—181no—
151C2×C42—91no—
152C4⋊C8—32no—
153C4⋊C8—91no—
154C4⋊C8—181no—
155C4⋊C8D3211yescharacteristic
156C22⋊C8—181no—
157C4×C8—181no—
158C22×D3—32no—
159C22×D3—61no—
160C3×Q8—122no—
161C3×Q8—122no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—64no—
166C2×C3×C4C2×C4×D312yes—
167C2×C3×C4D3×D412yes—
168C2×C3×C4D3×D412yes—
169C2×Dic3—24no—
170C2×Dic3—32no—
171C2×Dic3—32no—
172C2×Dic3—32no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C4×D3—34no—
177C4×D3—34no—
178C4×D3—62no—
179C4×D3—62no—
180C4×D3—64no—
181C4×D3—62no—
182C4×D3—62no—
183C4×D3—122no—
184C4×D3—122no—
185C4×D3—128no—
186Dic6—42no—
187Dic6—42no—
188Dic6—128no—
189C3×C8—42no—
190C3×C8—42no—
191C3×C8—122no—
192C3⋊C8—42no—
193C3⋊C8—122no—
194C3⋊C8—122no—
195C2×C32C2×#10111yescharacteristic
196C2×C32C2×#10211yescharacteristic
197C2×C32#41911yescharacteristic
198C3⋊D3—22no—
199C2×Q8—62no—
200C2×Q8—182no—
201C2×Q8—362no—
202C2×Q8—362no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—182no—
207M16—362no—
208C2×C8—21no—
209C2×C8—62no—
210C2×C8—181no—
211C4⋊C4—34no—
212C4⋊C4—62no—
213C4⋊C4—182no—
214C4⋊C4—182no—
215C42—91no—
216C42—91no—
217C42—91no—
218C42C2×D3211yescharacteristic
219C22×C3—21no—
220C22×C3D3×C22⋊C412yes—
221C2×D3—34no—
222C2×D3—62no—
223C2×D3—62no—
224C2×D3—62no—
225C2×D3—121no—
226C2×D3—121no—
227C3×C4—22no—
228C3×C4—22no—
229C3×C4—21no—
230C3×C4—21no—
231C3×C4—41no—
232C3×C4—124no—
233C3×C4D3×D812yes—
234C3×C4D3×SD1612yes—
235C3×C4#91512yes—
236C3×C4#91812yes—
237Dic3—34no—
238Dic3—34no—
239Dic3—44no—
240Dic3—62no—
241Dic3—62no—
242Dic3—62no—
243Dic3—121no—
244C32#154611yescharacteristic, complemented, Sylow
245C23—91no—
246Q8—122no—
247Q8—122no—
248Q8—364no—
249C2×C4—64no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—92no—
253C2×C4—92no—
254C2×C4—91no—
255C2×C4—182no—
256C2×C4—182no—
257C2×C4—364no—
258C2×C4C4×D3211yescharacteristic
259C2×C4#380211yescharacteristic
260C2×C4#381111yescharacteristic
261C8—41no—
262C8—122no—
263C8—361no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3D3×#10112yes—
268C2×C3D3×#10212yes—
269C2×C3#480212yes—
270D3—64no—
271D3—122no—
272C22—92no—
273C22—181no—
274C22—181no—
275C22#6392111yescharacteristic
276C4—21no—
277C4—92no—
278C4—92no—
279C4—124no—
280C4—181no—
281C4#6381112yes—
282C4#6392611yescharacteristic
283C4#6394011yescharacteristic
284C3—21no—
285C3#6842012yescomplemented
286C2—182no—
287C2#1059059311yescharacteristic
288C2#1059069111yescharacteristic
289C2#1059100311yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1546
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4482C2semidirect
5. #10589092C2semidirect
29. #4482D3semidirect
244. C32#1546semidirect
285. C3#68420semidirect

Maximal subgroups

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

subgroupindex
#105939092
#105925362
#105902562
C3×#44822
#105890922
#684203