Finite Group Databasebeta

← #11784056

Subgroups — #11784056

Order 1152.

570 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 103 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×#63838C211yesmaximal, characteristic
2C2×#63777C211yesmaximal, characteristic
3C2×#63740C212yesmaximal
4C4×#3724C211yesmaximal, characteristic
5#10590075C212yesmaximal
6C22×#627C2211yescharacteristic
7C22×#622C2212yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×C3×Dic3⋊C4—21no—
10C2×C3×C4×Dic3—21no—
11C2×#3724C2212yes—
12C2×#3724C2211yescharacteristic
13C2×Dic32—21no—
14#63838—22no—
15#63838C414yescomplemented
16#63777—22no—
17#63740C418yescomplemented
18#63579—21no—
19C2×#887—61no—
20C4×Dic3⋊C4—61no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3C2311yescharacteristic
24C22×C3×Dic3—21no—
25C22×C3×Dic3—22no—
26C22×C3×Dic3—21no—
27C2×#627—21no—
28C2×#627—22no—
29C2×#627C2×C412yes—
30C2×#627C2×C414yes—
31C2×#622—22no—
32C2×#622—22no—
33C2×#622C2×C414yes—
34C4×C3⋊Dic3C2×C412yes—
35C4×C3⋊Dic3D412yes—
36C3×Dic3⋊C4—24no—
37C3×C4×Dic3—42no—
38#3724—21no—
39#3724—22no—
40#3724C2×C412yes—
41#3724C2×C414yes—
42Dic32—24no—
43#1763—91nomaximal, Sylow
44C22×Dic6—61no—
45C2×C3×C4⋊C4—61no—
46C2×C3×C42—61no—
47C2×Dic3⋊C4—21no—
48C2×Dic3⋊C4—62no—
49C2×Dic3⋊C4—61no—
50C2×C4×Dic3—21no—
51C2×C4×Dic3—61no—
52C2×C4×Dic3—61no—
53C2×C4×Dic3—61no—
54C2×C4×Dic3—61no—
55#887—64no—
56#887—64no—
57C3⋊#95—62no—
58C23×C32C2×D411yescharacteristic
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4C22⋊C412yes—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3C22⋊C412yes—
64C2×C3⋊Dic3C22×C411yescharacteristic
65C2×C3⋊Dic3C22×C412yes—
66C2×C3⋊Dic3C2×D411yescharacteristic
67C2×C3⋊Dic3#4112yes—
68C2×C3×Dic3—22no—
69C2×C3×Dic3—24no—
70C2×C3×Dic3—22no—
71C2×C3×Dic3—24no—
72C2×C3×Dic3—42no—
73C2×C3×Dic3—41no—
74C2×C3×Dic3—41no—
75C2×C3×Dic3—42no—
76#627—22no—
77#627—24no—
78#627C4214yescomplemented
79#622—24no—
80C2×C4×Q8—91no—
81C2×#103—92no—
82C2×#97—91no—
83C4×C4⋊C4—91no—
84#340—92no—
85C22×C3×C4—21no—
86C22×C3×C4—21no—
87C22×C3×C4—61no—
88C22×C3×C4—62no—
89C22×C3×C4—61no—
90C22×Dic3—21no—
91C22×Dic3—22no—
92C22×Dic3—21no—
93C22×Dic3—61no—
94C22×Dic3—61no—
95C22×Dic3—61no—
96C22×Dic3—61no—
97C2×Dic6—62no—
98C2×Dic6—64no—
99C2×Dic6—62no—
100C2×Dic6—64no—
101C3×C4⋊C4—64no—
102C3×C42—122no—
103Dic3⋊C4—24no—
104Dic3⋊C4—62no—
105Dic3⋊C4—64no—
106Dic3⋊C4—62no—
107Dic3⋊C4—64no—
108C4×Dic3—42no—
109C4×Dic3—62no—
110C4×Dic3—62no—
111C4×Dic3—62no—
112C4×Dic3—62no—
113C4×Dic3—64no—
114C4×Dic3—64no—
115C22×C32C2×C22⋊C411yescharacteristic
116C22×C32C4×D412yes—
117C22×C32AGL(1,ℤ/8)11yescharacteristic
118C22×C32#13711yescharacteristic
119C22×C32#13712yes—
120C32×C4—22no—
121C3⋊Dic3—22no—
122C3⋊Dic3C2×C4211yescharacteristic
123C3⋊Dic3#11711yescharacteristic
124C3⋊Dic3C4×D412yes—
125C3×Dic3—24no—
126C3×Dic3—42no—
127C3×Dic3—44no—
128C22×Q8—91no—
129C22×C8—92no—
130C4×Q8—94no—
131C4×Q8—182no—
132C2×C4⋊C4—61no—
133C2×C4⋊C4—91no—
134C2×C4⋊C4—92no—
135C2×C42—61no—
136C2×C42—91no—
137C2×C42—181no—
138#103—98no—
139#97—182no—
140#95—181no—
141C23×C3—21no—
142C23×C3—21no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—22no—
147C2×C3×C4—41no—
148C2×C3×C4—41no—
149C2×C3×C4—62no—
150C2×C3×C4—64no—
151C2×C3×C4—62no—
152C2×C3×C4—64no—
153C2×C3×C4—122no—
154C2×C3×C4—122no—
155C2×C3×C4—121no—
156C2×C3×C4—121no—
157C2×Dic3—22no—
158C2×Dic3—24no—
159C2×Dic3—22no—
160C2×Dic3—24no—
161C2×Dic3—42no—
162C2×Dic3—42no—
163C2×Dic3—41no—
164C2×Dic3—41no—
165C2×Dic3—62no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—62no—
169C2×Dic3—62no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—64no—
176C2×Dic3—122no—
177Dic6—64no—
178Dic6—64no—
179Dic6—68no—
180C2×C32C4×C22⋊C411yescharacteristic
181C2×C32#41711yescharacteristic
182C2×C32#41911yescharacteristic
183C2×C32#44012yes—
184C2×C32#44112yes—
185C2×Q8—94no—
186C2×Q8—92no—
187C2×Q8—181no—
188C2×Q8—182no—
189C22×C4—61no—
190C22×C4—62no—
191C22×C4—61no—
192C22×C4—91no—
193C22×C4—91no—
194C22×C4GO+(4,𝔽2)11yescharacteristic
195C2×C8—94no—
196C2×C8—182no—
197C2×C8—182no—
198C4⋊C4—64no—
199C4⋊C4—94no—
200C4⋊C4—92no—
201C4⋊C4—181no—
202C4⋊C4—182no—
203C42—92no—
204C42—92no—
205C42—122no—
206C42—184no—
207C22×C3—22no—
208C22×C3—22no—
209C22×C3—22no—
210C22×C3—22no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—21no—
217C3×C4—24no—
218C3×C4—42no—
219C3×C4—64no—
220C3×C4—124no—
221C3×C4—122no—
222Dic3—24no—
223Dic3—44no—
224Dic3—42no—
225Dic3—61no—
226Dic3—61no—
227Dic3—62no—
228Dic3—61no—
229Dic3—61no—
230Dic3—62no—
231Dic3—64no—
232Dic3—122no—
233C32#176311yescharacteristic, complemented, Sylow
234C23C2×GO+(4,𝔽2)11yescharacteristic
235Q8—94no—
236Q8—184no—
237Q8—182no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—64no—
241C2×C4—62no—
242C2×C4—64no—
243C2×C4—62no—
244C2×C4—92no—
245C2×C4—92no—
246C2×C4—91no—
247C2×C4—91no—
248C2×C4—92no—
249C2×C4—122no—
250C2×C4—122no—
251C2×C4—121no—
252C2×C4—121no—
253C2×C4—182no—
254C2×C4D32⋊C412yes—
255C8—184no—
256C2×C3—22no—
257C2×C3—22no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—22no—
263C2×C3—22no—
264C2×C3—21no—
265C2×C3—21no—
266C22#6422612yes—
267C22C4×GO+(4,𝔽2)12yes—
268C22C2×D32⋊C411yescharacteristic
269C22#6423611yescharacteristic
270C22#6423911yescharacteristic
271C4—22no—
272C4—64no—
273C4—92no—
274C4—91no—
275C4—91no—
276C4—124no—
277C4—122no—
278C4—182no—
279C3—21no—
280C3—21no—
281C2#1059336912yes—
282C2#1059337411yescharacteristic
283C2C4×D32⋊C411yescharacteristic
284C2#1059343112yes—
285C2#1059349611yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C2×C42
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1763
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
15. #63838C4semidirect
17. #63740C4semidirect
78. #627C42semidirect
233. C32#1763semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
C2×#637772
C2×#637402
C4×#37242
#105900752
#17639