Finite Group Databasebeta

← #11776295

Subgroups — #11776295

Order 1152.

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

normal subgroups only

This group has 539 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#10592532C211yesmaximal, characteristic
3#10590340C211yesmaximal, characteristic
4C3×#4486C212yesmaximal, complemented
5#10589093C212yesmaximal, complemented
6#68420—32nomaximal
7C2×#3797—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×#869C2212yes—
10#63919—21no—
11#63919C412yes—
12#63900—21no—
13#63900C412yes—
14#63873—21no—
15C2×#3712—21no—
16C32×C4⋊C8C2211yescharacteristic
17#63647—21no—
18C8×C3⋊Dic3—21no—
19C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2212yes—
21#63572—21no—
22D3×C4⋊Q8—32no—
23#4837—32no—
24#4833—32no—
25#4833—61no—
26C3×#332—32no—
27#4547—32no—
28#4486D312yescomplemented
29#4482—32no—
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—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3C2×C414yes—
46C2×C3×C3⋊C8—22no—
47#3724—22no—
48#3724—22no—
49#3712—42no—
50#1546—91noSylow
51C2×D3×Q8—62no—
52C3×C4⋊Q8—32no—
53#944—62no—
54C2×ΓL(1,𝔽25)—62no—
55D3×C4⋊C4—34no—
56D3×C4⋊C4—62no—
57#888—34no—
58#888—62no—
59C42×D3—32no—
60C42×D3—61no—
61#869C2×D312yes—
62C3×C4⋊C8—21no—
63C3×C4⋊C8—32no—
64C3×C4⋊C8C2×D312yes—
65(C2×D3)⋊C8—62no—
66(C2×D3)⋊C8—62no—
67Dic3⋊C8—62no—
68C8×Dic3—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—21no—
81C4×C3⋊D3—21no—
82C4×C3⋊D3—22no—
83C4×C3⋊D3D812yes—
84C4×C3⋊D3SD1612yes—
85C2×C3×Dic3—24no—
86C3×Dic6—42no—
87C3×Dic6—42no—
88#627—44no—
89#624—44no—
90C32×C8—41no—
91C3⋊(C3⋊C8)—41no—
92C3×C3⋊C8—42no—
93C2×C4⋊Q8—91no—
94#431—91no—
95#423—91no—
96#332—32no—
97#332—92no—
98C2×C3×Q8—62no—
99D3×Q8—124no—
100D3×Q8—124no—
101C2×C4×D3—32no—
102C2×C4×D3—32no—
103C2×C4×D3—32no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—64no—
108C2×Dic6—22no—
109C2×Dic6—64no—
110C2×C3×C8—22no—
111C2×C3×C8—22no—
112C2×C3×C8—62no—
113C3×C4⋊C4—34no—
114C3×C4⋊C4—62no—
115C3×C42—21no—
116C3×C42C22×D312yes—
117C4⋊Dic3—22no—
118C4⋊Dic3C4×D314yes—
119Dic3⋊C4—64no—
120Dic3⋊C4—64no—
121C4×Dic3—32no—
122C4×Dic3—32no—
123C4×Dic3—32no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C2×C3⋊C8—22no—
128C2×C3⋊C8—62no—
129C2×C3⋊C8—62no—
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#13711yescharacteristic
139C32×C4#13711yescharacteristic
140C3⋊Dic3—21no—
141C3⋊Dic3#10112yes—
142C3⋊Dic3#10212yes—
143C3×Dic3—44no—
144C22×Q8—181no—
145C2×M16—181no—
146C4⋊Q8—32no—
147C4⋊Q8—92no—
148C4⋊Q8—181no—
149C4⋊Q8—181no—
150C2×C4⋊C4—92no—
151C2×C4⋊C4—181no—
152C2×C42—91no—
153C4⋊C8—32no—
154C4⋊C8—91no—
155C4⋊C8—181no—
156C4⋊C8D3211yescharacteristic
157C22⋊C8—181no—
158C4×C8—181no—
159C22×D3—32no—
160C22×D3—61no—
161C3×Q8—122no—
162C3×Q8—122no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—64no—
167C2×C3×C4C2×C4×D312yes—
168C2×C3×C4D3×D412yes—
169C2×C3×C4D3×D412yes—
170C2×Dic3—24no—
171C2×Dic3—32no—
172C2×Dic3—32no—
173C2×Dic3—32no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C4×D3—34no—
178C4×D3—34no—
179C4×D3—62no—
180C4×D3—62no—
181C4×D3—64no—
182C4×D3—62no—
183C4×D3—62no—
184C4×D3—122no—
185C4×D3—121no—
186C4×D3—121no—
187C4×D3—128no—
188Dic6—42no—
189Dic6—42no—
190Dic6—128no—
191C3×C8—42no—
192C3×C8—42no—
193C3×C8—122no—
194C3⋊C8—42no—
195C3⋊C8—122no—
196C3⋊C8—122no—
197C2×C32C2×#10111yescharacteristic
198C2×C32C2×#10211yescharacteristic
199C2×C32#41911yescharacteristic
200C3⋊D3—22no—
201C2×Q8—62no—
202C2×Q8—182no—
203C2×Q8—362no—
204C2×Q8—362no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—182no—
209M16—362no—
210C2×C8—21no—
211C2×C8—62no—
212C2×C8—181no—
213C4⋊C4—34no—
214C4⋊C4—62no—
215C4⋊C4—182no—
216C4⋊C4—182no—
217C42—91no—
218C42—91no—
219C42—91no—
220C42C2×D3211yescharacteristic
221C22×C3—21no—
222C22×C3D3×C22⋊C412yes—
223C2×D3—34no—
224C2×D3—62no—
225C2×D3—62no—
226C2×D3—62no—
227C2×D3—121no—
228C2×D3—121no—
229C3×C4—22no—
230C3×C4—21no—
231C3×C4—21no—
232C3×C4—21no—
233C3×C4—21no—
234C3×C4—41no—
235C3×C4—124no—
236C3×C4D3×D812yes—
237C3×C4D3×SD1612yes—
238C3×C4#91512yes—
239C3×C4#91812yes—
240Dic3—34no—
241Dic3—34no—
242Dic3—44no—
243Dic3—62no—
244Dic3—62no—
245Dic3—62no—
246Dic3—121no—
247C32#154611yescharacteristic, complemented, Sylow
248C23—91no—
249Q8—122no—
250Q8—122no—
251Q8—364no—
252C2×C4—64no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—92no—
256C2×C4—92no—
257C2×C4—91no—
258C2×C4—182no—
259C2×C4—181no—
260C2×C4—181no—
261C2×C4—364no—
262C2×C4C4×D3211yescharacteristic
263C2×C4#380211yescharacteristic
264C2×C4#381111yescharacteristic
265C8—41no—
266C8—122no—
267C8—361no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3D3×#10112yes—
272C2×C3D3×#10212yes—
273C2×C3#480212yes—
274D3—64no—
275D3—122no—
276C22—92no—
277C22—181no—
278C22—181no—
279C22#6392111yescharacteristic
280C4—21no—
281C4—92no—
282C4—92no—
283C4—124no—
284C4—181no—
285C4#6379611yescharacteristic
286C4#6379711yescharacteristic
287C4#6393111yescharacteristic
288C4#6394511yescharacteristic
289C3—21no—
290C3#6842012yescomplemented
291C2—182no—
292C2#1059060211yescharacteristic
293C2#1059094011yescharacteristic
294C2#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×#4486C2semidirect
5. #10589093C2semidirect
28. #4486D3semidirect
247. C32#1546semidirect
290. C3#68420semidirect

Maximal subgroups

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

subgroupindex
#105939092
#105925322
#105903402
C3×#44862
#105890932
#684203