Finite Group Databasebeta

← #11791875

Subgroups — #11791875

Order 1152.

583 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 583 conjugacy classes of subgroups — too many to draw. Only its 134 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
1C2×#63919C211yesmaximal, characteristic
2#10592817C211yesmaximal, characteristic
3#10591060C211yesmaximal, characteristic
4C3×#4554C212yesmaximal
5#10589167C212yesmaximal
6#68974—32nomaximal
7C22×#627C412yes—
8C2×C32×M16C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×#3748C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×#208C2212yes—
13C2×#3724C412yes—
14#63919—21no—
15#63919—21no—
16#63919—21no—
17#63919—21no—
18#63641—21no—
19#63641—21no—
20#63555—21no—
21#63553—21no—
22C2×#888—32no—
23#5118—32no—
24#5118—61no—
25Dic3×M16—32no—
26C3×#343—32no—
27#4554—32no—
28#4554D312yes—
29#4530—32no—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3×Dic3C2×C414yes—
34C2×#627—22no—
35C2×#627—22no—
36C2×#627—44no—
37C32×M16—22no—
38C2×C32×C8—21no—
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43#3748—22no—
44C2×C3⋊(C3⋊C8)—21no—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3—22no—
47C3×#208—22no—
48C3×#208Q814yescomplemented
49C2×C3×C3⋊C8—22no—
50#3724—22no—
51#3724—22no—
52#1997—91noSylow
53C22×Dic6—34no—
54C2×C3×M16—21no—
55C2×C3×M16—32no—
56C2×C3×M16C2×D312yes—
57C2×C3×C4⋊C4—32no—
58C2×C4⋊Dic3C2×D312yes—
59C2×Dic3⋊C4—34no—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—61no—
62C2×#208—32no—
63C2×#208—61no—
64C2×#208C2×D312yes—
65#888—62no—
66#888—62no—
67#888—62no—
68#888—62no—
69#815—62no—
70Dic3⋊C8—62no—
71Dic3⋊C8—62no—
72Dic3⋊C8—62no—
73Dic3⋊C8—62no—
74C8×Dic3—62no—
75C23×C32C22×C411yescharacteristic
76C2×C32×C4C2×D411yescharacteristic
77C2×C32×C4C2×D411yescharacteristic
78C2×C32×C4C2×Q812yes—
79C2×C32×C4#4112yes—
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3—22no—
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3×Dic3—24no—
87C2×C3×Dic3—44no—
88#627—44no—
89#627—44no—
90C32×C8—41no—
91C3⋊(C3⋊C8)—41no—
92C3×C3⋊C8—24no—
93C2×C4⋊Q8—91no—
94#423—91no—
95C4×M16—91no—
96#343—32no—
97#343—92no—
98C22×C3×C4—21no—
99C22×C3×C4—34no—
100C22×C3×C4C22×D312yes—
101C22×Dic3—32no—
102C22×Dic3—32no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3C4×D314yes—
106C2×Dic6—64no—
107C2×Dic6—64no—
108C2×Dic6—128no—
109C3×M16—22no—
110C3×M16—22no—
111C3×M16—34no—
112C3×M16—42no—
113C3×M16—62no—
114C2×C3×C8—22no—
115C2×C3×C8—22no—
116C2×C3×C8—62no—
117C3×C4⋊C4—62no—
118C3×C4⋊C4—62no—
119C4⋊Dic3—22no—
120C4⋊Dic3—22no—
121Dic3⋊C4—64no—
122Dic3⋊C4—64no—
123C4×Dic3—32no—
124C4×Dic3—32no—
125C4×Dic3—32no—
126C4×Dic3—32no—
127C4×Dic3—61no—
128C4×Dic3—61no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131#208—22no—
132#208—62no—
133#208—62no—
134#208—122no—
135#208Dic614yescomplemented
136C2×C3⋊C8—22no—
137C2×C3⋊C8—62no—
138C2×C3⋊C8—62no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32C2×C22⋊C411yescharacteristic
142C22×C32C4×Q812yes—
143C32×C4C22⋊Q812yes—
144C32×C4#12411yescharacteristic
145C32×C4C4⋊Q811yescharacteristic
146C3⋊Dic3—21no—
147C3⋊Dic3—21no—
148C3⋊Dic3#10012yes—
149C3⋊Dic3#10112yes—
150C3×Dic3—44no—
151C22×Q8—92no—
152C2×M16—32no—
153C2×M16—91no—
154C2×M16D3211yescharacteristic
155C4⋊Q8—181no—
156C4⋊Q8—181no—
157C4⋊Q8—181no—
158C4⋊Q8—181no—
159C2×C4⋊C4—32no—
160C2×C4⋊C4—92no—
161C2×C42—91no—
162C4⋊C8—181no—
163C4⋊C8—181no—
164#97—181no—
165C4×C8—181no—
166C23×C3—21no—
167C23×C3C2×C4×D312yes—
168C2×C3×C4—22no—
169C2×C3×C4—21no—
170C2×C3×C4—22no—
171C2×C3×C4—21no—
172C2×C3×C4—64no—
173C2×C3×C4—124no—
174C2×C3×C4C2×Dic612yes—
175C2×C3×C4#23512yes—
176C2×C3×C4D3×D412yes—
177C2×C3×C4D3×D412yes—
178C2×C3×C4#23712yes—
179C2×C3×C4D3×Q812yes—
180C2×Dic3—24no—
181C2×Dic3—32no—
182C2×Dic3—32no—
183C2×Dic3—32no—
184C2×Dic3—32no—
185C2×Dic3—44no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—64no—
191C2×Dic3—64no—
192C2×Dic3—122no—
193C2×Dic3—122no—
194Dic6—128no—
195Dic6—128no—
196C3×C8—42no—
197C3×C8—42no—
198C3×C8—64no—
199C3⋊C8—24no—
200C3⋊C8—122no—
201C3⋊C8—122no—
202C2×C32—22no—
203C2×C32#39111yescharacteristic
204C2×C32C2×#10011yescharacteristic
205C2×C32C2×#10111yescharacteristic
206C2×Q8—182no—
207C2×Q8—182no—
208C2×Q8—364no—
209C22×C4—34no—
210C22×C4—91no—
211C22×C4—91no—
212C22×C4C2×D3211yescharacteristic
213M16—22no—
214M16—34no—
215M16—62no—
216M16—182no—
217C2×C8—21no—
218C2×C8—62no—
219C2×C8—181no—
220C4⋊C4—62no—
221C4⋊C4—62no—
222C4⋊C4—182no—
223C4⋊C4—182no—
224C42—91no—
225C42—91no—
226C42—91no—
227C42—91no—
228C22×C3—22no—
229C22×C3—22no—
230C22×C3—22no—
231C22×C3—21no—
232C22×C3—41no—
233C22×C3—41no—
234C22×C3C4×Dic612yes—
235C22×C3D3×C22⋊C412yes—
236C22×C3#88712yes—
237C3×C4—21no—
238C3×C4—22no—
239C3×C4—21no—
240C3×C4—124no—
241C3×C4#87812yes—
242C3×C4#88512yes—
243C3×C4#88812yes—
244C3×C4#89612yes—
245Dic3—34no—
246Dic3—34no—
247Dic3—44no—
248Dic3—62no—
249Dic3—62no—
250Dic3—62no—
251Dic3—62no—
252Dic3—121no—
253Dic3—121no—
254C32#199711yescharacteristic, complemented, Sylow
255C23C4×D3211yescharacteristic
256Q8—364no—
257Q8—364no—
258C2×C4—64no—
259C2×C4—91no—
260C2×C4—91no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—124no—
264C2×C4—182no—
265C2×C4—182no—
266C2×C4D3×Dic612yes—
267C2×C4#380211yescharacteristic
268C2×C4#380412yes—
269C2×C4#381111yescharacteristic
270C8—41no—
271C8—64no—
272C8—361no—
273C2×C3—22no—
274C2×C3—22no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—42no—
279C2×C3#464612yes—
280C2×C3D3×#10012yes—
281C2×C3D3×#10112yes—
282C22—21no—
283C22—21no—
284C22#6383712yes—
285C22#6392111yescharacteristic
286C4—92no—
287C4—92no—
288C4—124no—
289C4—181no—
290C4—181no—
291C4#6384011yescharacteristic
292C4#6389912yes—
293C4#6395311yescharacteristic
294C3—21no—
295C3#6897412yescomplemented
296C2—22no—
297C2#1059100111yescharacteristic
298C2#1059100311yescharacteristic
299C2#1059123611yescharacteristic
subgroupG/H
centerC22#63921
commutator, prime radicalC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1997
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
48. C3×#208Q8semidirect
135. #208Dic6semidirect
254. C32#1997semidirect
295. C3#68974semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
#105928172
#105910602
C3×#45542
#105891672
#689743