Finite Group Databasebeta

← #11786083

Subgroups — #11786083

Order 1152.

394 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 79 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×#63777C211yesmaximal, characteristic
2#10591360C211yesmaximal, characteristic
3#10591359C211yesmaximal, characteristic
4#10590075C212yesmaximal
5#10590075C212yesmaximal
6C22×#622C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×C4⋊Dic3—21no—
9C2×#3724—21no—
10C2×#3724C2212yes—
11C2×#3724C2211yescharacteristic
12C2×#3724C2211yescharacteristic
13#63777C414yescomplemented
14C3×C3⋊#95—21no—
15#63579—21no—
16#4975—61no—
17#4650—61no—
18C22×C32×C4D411yescharacteristic
19C22×C3⋊Dic3D411yescharacteristic
20C22×C3⋊Dic3C2311yescharacteristic
21C22×C3×Dic3—22no—
22C22×C3×Dic3—21no—
23C22×C3×Dic3—21no—
24C2×#622—22no—
25C2×#622—22no—
26C2×#622C2×C414yes—
27C4×C3⋊Dic3C2×C412yes—
28C4×C3⋊Dic3Q812yes—
29C3×C4⋊Dic3—42no—
30#3724—24no—
31#3724—22no—
32#3724—22no—
33#3724—42no—
34#1836—91nomaximal, Sylow
35C2×C3×C4⋊C4—61no—
36C2×C4⋊Dic3—21no—
37C2×Dic3⋊C4—61no—
38C2×Dic3⋊C4—61no—
39C2×Dic3⋊C4—62no—
40C2×Dic3⋊C4—62no—
41C2×C4×Dic3—61no—
42C2×C4×Dic3—61no—
43C3×#95—61no—
44C3⋊#95—21no—
45C3⋊#95—61no—
46C3⋊#95—61no—
47C23×C32C2×D411yescharacteristic
48C2×C32×C4—21no—
49C2×C32×C4—21no—
50C2×C32×C4C4⋊C412yes—
51C2×C3⋊Dic3—21no—
52C2×C3⋊Dic3—21no—
53C2×C3⋊Dic3C4⋊C412yes—
54C2×C3⋊Dic3C22×C411yescharacteristic
55C2×C3⋊Dic3C2×Q811yescharacteristic
56C2×C3⋊Dic3#4112yes—
57C2×C3⋊Dic3#4112yes—
58C2×C3×Dic3—41no—
59C2×C3×Dic3—41no—
60C2×C3×Dic3—42no—
61C2×C3×Dic3—42no—
62C2×C3×Dic3—42no—
63C2×C3×Dic3—41no—
64C2×C3×Dic3—41no—
65C2×C3×Dic3—41no—
66C2×C3×Dic3—41no—
67#622—24no—
68C2×#97—91no—
69#384—91no—
70#382—91no—
71#340—92no—
72#340—92no—
73C22×C3×C4—21no—
74C22×C3×C4—21no—
75C22×C3×C4—61no—
76C22×C3×C4—61no—
77C22×C3×C4—62no—
78C22×Dic3—21no—
79C22×Dic3—21no—
80C22×Dic3—22no—
81C22×Dic3—61no—
82C22×Dic3—61no—
83C22×Dic3—61no—
84C22×Dic3—61no—
85C3×C4⋊C4—122no—
86C4⋊Dic3—42no—
87Dic3⋊C4—122no—
88Dic3⋊C4—122no—
89Dic3⋊C4—124no—
90Dic3⋊C4—124no—
91C4×Dic3—62no—
92C4×Dic3—62no—
93C4×Dic3—62no—
94C4×Dic3—62no—
95C22×C32C2×C4⋊C411yescharacteristic
96C22×C32#12411yescharacteristic
97C22×C32#12411yescharacteristic
98C22×C32AGL(1,ℤ/8)11yescharacteristic
99C22×C32AGL(1,ℤ/8)11yescharacteristic
100C22×C32#13711yescharacteristic
101C22×C32#13711yescharacteristic
102C32×C4—22no—
103C3⋊Dic3—22no—
104C3⋊Dic3#11712yes—
105C3⋊Dic3#12512yes—
106C3×Dic3—81no—
107C3×Dic3—81no—
108C3×Dic3—82no—
109C22×C8—92no—
110C2×C4⋊C4—61no—
111C2×C4⋊C4—91no—
112C2×C4⋊C4—91no—
113C2×C4⋊C4—92no—
114C2×C4⋊C4—181no—
115C2×C42—91no—
116#97—94no—
117#95—61no—
118#95—181no—
119C23×C3—21no—
120C23×C3—21no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×C3×C4—41no—
126C2×C3×C4—41no—
127C2×C3×C4—121no—
128C2×C3×C4—121no—
129C2×C3×C4—122no—
130C2×C3×C4—122no—
131C2×C3×C4—122no—
132C2×C3×C4—121no—
133C2×C3×C4—121no—
134C2×C3×C4—121no—
135C2×C3×C4—121no—
136C2×Dic3—41no—
137C2×Dic3—41no—
138C2×Dic3—42no—
139C2×Dic3—42no—
140C2×Dic3—42no—
141C2×Dic3—41no—
142C2×Dic3—41no—
143C2×Dic3—41no—
144C2×Dic3—41no—
145C2×Dic3—62no—
146C2×Dic3—61no—
147C2×Dic3—61no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150C2×Dic3—62no—
151C2×Dic3—62no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—121no—
158C2×Dic3—121no—
159C2×C32#38211yescharacteristic
160C2×C32#42811yescharacteristic
161C2×C32#42811yescharacteristic
162C2×C32#48911yescharacteristic
163C2×C32#48911yescharacteristic
164C2×C32#49011yescharacteristic
165C2×C32#49111yescharacteristic
166C22×C4—61no—
167C22×C4—61no—
168C22×C4—62no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4GO+(4,𝔽2)11yescharacteristic
172C2×C8—94no—
173C2×C8—182no—
174C2×C8—182no—
175C4⋊C4—122no—
176C4⋊C4—182no—
177C4⋊C4—182no—
178C4⋊C4—184no—
179C4⋊C4—362no—
180C42—92no—
181C42—92no—
182C22×C3—21no—
183C22×C3—21no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—21no—
192C22×C3—21no—
193C22×C3—21no—
194C22×C3—21no—
195C22×C3—21no—
196C3×C4—24no—
197C3×C4—42no—
198C3×C4—242no—
199C3×C4—241no—
200C3×C4—241no—
201Dic3—62no—
202Dic3—62no—
203Dic3—62no—
204Dic3—62no—
205Dic3—64no—
206Dic3—82no—
207Dic3—81no—
208Dic3—81no—
209Dic3—122no—
210C32#183611yescharacteristic, complemented, Sylow
211C23C2×GO+(4,𝔽2)11yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—92no—
215C2×C4—92no—
216C2×C4—91no—
217C2×C4—91no—
218C2×C4—92no—
219C2×C4—122no—
220C2×C4—121no—
221C2×C4—121no—
222C2×C4—122no—
223C2×C4—121no—
224C2×C4—121no—
225C2×C4—122no—
226C2×C4—121no—
227C2×C4—121no—
228C2×C4—181no—
229C2×C4—181no—
230C2×C4#377312yes—
231C8—184no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C22#6422111yescharacteristic
247C22#6422111yescharacteristic
248C22#6422411yescharacteristic
249C22#6422611yescharacteristic
250C22C2×#377311yescharacteristic
251C22#6423611yescharacteristic
252C22#6423911yescharacteristic
253C4—22no—
254C4—92no—
255C4—92no—
256C4—182no—
257C4—242no—
258C4—241no—
259C4—241no—
260C3—21no—
261C3—21no—
262C2#1059334411yescharacteristic
263C2#1059335611yescharacteristic
264C2#1059335811yescharacteristic
265C2#1059336211yescharacteristic
266C2#1059337811yescharacteristic
267C2#1059339411yescharacteristic
268C2#1059350711yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1836
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
13. #63777C4semidirect
210. C32#1836semidirect

Maximal subgroups

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

subgroupindex
C2×#637772
#105913602
#105913592
#105900752
#18369