Finite Group Databasebeta

← #11776247

Subgroups — #11776247

Order 1152.

515 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 515 conjugacy classes of subgroups — too many to draw. Only its 102 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#10596199C211yesmaximal, characteristic
2#10590256C211yesmaximal, characteristic
3#10590256C211yesmaximal, characteristic
4C3×#4547C212yesmaximal, complemented
5#10589094C212yesmaximal, complemented
6#68419—32nomaximal
7C32×C4⋊Q8C2211yescharacteristic
8#64155—21no—
9Q8×C3⋊Dic3—21no—
10#64106—21no—
11#64101C412yes—
12#64099C412yes—
13#64096—21no—
14C42×C3⋊D3C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×C4⋊(C3⋊C8)C2212yes—
17C3×C4⋊(C3⋊C8)C2212yes—
18#63557—21no—
19#63557—21no—
20#63553—21no—
21#63553—21no—
22#5728—32no—
23#5728—61no—
24#4833—32no—
25#4833—32no—
26C3×#332—32no—
27#4547D312yescomplemented
28#4486—32no—
29#4482—32no—
30C2×C32×Q8—21no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×#634—21no—
35C32×C4⋊C4—21no—
36C32×C4⋊C4C2×C412yes—
37C32×C42C2311yescharacteristic
38#3752—22no—
39C4⋊(C3⋊Dic3)—21no—
40C4⋊(C3⋊Dic3)—22no—
41C4⋊(C3⋊Dic3)C2×C412yes—
42#3750—22no—
43C4×C3⋊Dic3—22no—
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C2×C3×C3⋊C8—22no—
48C2×C3×C3⋊C8—22no—
49#1544—91noSylow
50C3×C4⋊Q8—21no—
51C3×C4⋊Q8C2×D312yes—
52#946—62no—
53#946—62no—
54Q8×Dic3—62no—
55Q8×Dic3—62no—
56#897—62no—
57#897—62no—
58#892—34no—
59#892—62no—
60#890—34no—
61#890—62no—
62#887—62no—
63#887—62no—
64C42×D3—32no—
65C42×D3—61no—
66#869—32no—
67#869—61no—
68C3×C4⋊C8—32no—
69C3×C4⋊C8—32no—
70(C2×D3)⋊C8—62no—
71(C2×D3)⋊C8—62no—
72C8×Dic3—62no—
73C8×Dic3—62no—
74C4⋊(C3⋊C8)C2×D312yes—
75C4⋊(C3⋊C8)C2×D312yes—
76C22×C3⋊D3C22⋊C411yescharacteristic
77C32×Q8—42no—
78C2×C32×C4—22no—
79C2×C32×C4C22×C411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C4×C3⋊D3—22no—
87C4×C3⋊D3—22no—
88C4×C3⋊D3—22no—
89#634—42no—
90C3×C3⋊C8—42no—
91C3×C3⋊C8—42no—
92#533—91no—
93#431—91no—
94#431—91no—
95#332—32no—
96#332—92no—
97C2×C3×Q8—22no—
98C2×C3×Q8—22no—
99C2×C4×D3—32no—
100C2×C4×D3—32no—
101C2×C4×D3—32no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×Dic6—62no—
106C2×Dic6—62no—
107C2×C3×C8—62no—
108C2×C3×C8—62no—
109C3×C4⋊C4—22no—
110C3×C4⋊C4—22no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4C4×D314yes—
113C3×C42—21no—
114C3×C42C22×D312yes—
115(C2×D3)⋊C4—64no—
116(C2×D3)⋊C4—64no—
117C4⋊Dic3—34no—
118C4⋊Dic3—62no—
119C4⋊Dic3—64no—
120C4⋊Dic3—62no—
121C4⋊Dic3—64no—
122C4⋊Dic3—62no—
123Dic3⋊C4—64no—
124Dic3⋊C4—64no—
125C4×Dic3—32no—
126C4×Dic3—32no—
127C4×Dic3—32no—
128C4×Dic3—61no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131C4×Dic3—64no—
132C4×Dic3—64no—
133C2×C3⋊C8—22no—
134C2×C3⋊C8—22no—
135C22×C32C2×C22⋊C411yescharacteristic
136C2×C3⋊D3—21no—
137C2×C3⋊D3—21no—
138C2×C3⋊D3—21no—
139C32×C4—21no—
140C32×C4—42no—
141C32×C4#13512yes—
142C32×C4#13512yes—
143C3⋊Dic3—21no—
144C3⋊Dic3—21no—
145C3⋊Dic3—42no—
146C3⋊Dic3#10112yes—
147C4⋊Q8—91no—
148C4⋊Q8D3211yescharacteristic
149#125—92no—
150C22⋊Q8—181no—
151C22⋊Q8—181no—
152C4×Q8—181no—
153C4×Q8—181no—
154#117—92no—
155C2×C42—91no—
156C4⋊C8—32no—
157C4⋊C8—32no—
158C22⋊C8—181no—
159C22⋊C8—181no—
160C4×C8—181no—
161C4×C8—181no—
162C22×D3—32no—
163C22×D3—61no—
164C3×Q8—44no—
165C3×Q8—42no—
166C3×Q8—42no—
167C2×C3×C4—24no—
168C2×C3×C4—24no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4C2×C4×D312yes—
173C2×C3×C4D3×D412yes—
174C2×C3×C4D3×D412yes—
175C2×Dic3—32no—
176C2×Dic3—32no—
177C2×Dic3—32no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—64no—
182C2×Dic3—64no—
183C4×D3—64no—
184C4×D3—64no—
185C4×D3—62no—
186C4×D3—62no—
187C4×D3—62no—
188C4×D3—62no—
189C4×D3—122no—
190C4×D3—122no—
191Dic6—124no—
192Dic6—122no—
193Dic6—122no—
194C3×C8—122no—
195C3×C8—122no—
196C3⋊C8—42no—
197C3⋊C8—42no—
198C2×C32C2×#10111yescharacteristic
199C2×C32#41611yescharacteristic
200C2×C32#41611yescharacteristic
201C3⋊D3—41no—
202C2×Q8—21no—
203C2×Q8—181no—
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—91no—
207C2×C8—62no—
208C2×C8—62no—
209C4⋊C4—21no—
210C4⋊C4—92no—
211C4⋊C4—182no—
212C4⋊C4—182no—
213C4⋊C4—181no—
214C4⋊C4#62412yes—
215C22⋊C4—182no—
216C42—91no—
217C42—91no—
218C42—91no—
219C42—182no—
220C42C2×D3211yescharacteristic
221C22×C3—21no—
222C22×C3D3×C22⋊C412yes—
223C2×D3—62no—
224C2×D3—62no—
225C2×D3—62no—
226C2×D3—62no—
227C2×D3—121no—
228C2×D3—121no—
229C3×C4—22no—
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—22no—
233C3×C4—44no—
234C3×C4—44no—
235C3×C4#91212yes—
236C3×C4#91612yes—
237C3×C4#91612yes—
238C3×C4#91912yes—
239Dic3—34no—
240Dic3—62no—
241Dic3—62no—
242Dic3—62no—
243Dic3—121no—
244Dic3—121no—
245Dic3—124no—
246Dic3—124no—
247C32#154411yescharacteristic, complemented, Sylow
248C23—91no—
249Q8—42no—
250Q8—362no—
251C2×C4—22no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—182no—
256C2×C4—182no—
257C2×C4—182no—
258C2×C4—182no—
259C2×C4C2×#62411yescharacteristic
260C2×C4#381111yescharacteristic
261C2×C4#381111yescharacteristic
262C8—122no—
263C8—122no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3D3×#10112yes—
268C2×C3#477212yes—
269C2×C3#480412yes—
270D3—122no—
271D3—122no—
272C22—181no—
273C22—181no—
274C22—181no—
275C22#6397411yescharacteristic
276C4—21no—
277C4—42no—
278C4—92no—
279C4—181no—
280C4—181no—
281C4—362no—
282C4#6393612yes—
283C4#6395012yes—
284C3—21no—
285C3#6841912yescomplemented
286C2—361no—
287C2#1059142411yescharacteristic
288C2#1059156011yescharacteristic
289C2#1059163911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊Q8D32
hypocenterC32#1544
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. C3×#4547C2semidirect
5. #10589094C2semidirect
27. #4547D3semidirect
247. C32#1544semidirect
285. C3#68419semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105902562
C3×#45472
#105890942
#684193