Finite Group Databasebeta

← #11795094

Subgroups — #11795094

Order 1152.

408 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 73 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×#63743C212yesmaximal
2#10591359C211yesmaximal, characteristic
3#10591337C211yesmaximal, characteristic
4#10590207C211yesmaximal, characteristic
5#10590075C212yesmaximal
6C22×#622C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×C4⋊Dic3—21no—
9C2×C3×Dic3⋊C4—21no—
10C2×#3724—21no—
11C2×#3724C2211yescharacteristic
12C2×#3724C2212yes—
13C2×#3724C2211yescharacteristic
14#63743—24no—
15#63579—21no—
16#4976—61no—
17#4975—61no—
18C22×C32×C4D411yescharacteristic
19C22×C3⋊Dic3D411yescharacteristic
20C22×C3⋊Dic3C2311yescharacteristic
21C22×C3×Dic3—21no—
22C22×C3×Dic3—21no—
23C22×C3×Dic3—22no—
24C2×#622—22no—
25C2×#622—22no—
26C2×#622Q814yes—
27C4×C3⋊Dic3—22no—
28C3×C4⋊Dic3—42no—
29C3×Dic3⋊C4—42no—
30#3724—21no—
31#3724—22no—
32#3724—22no—
33#3724—22no—
34#3724—42no—
35#3724D412yes—
36#2083—91nomaximal, Sylow
37C2×C3×C4⋊C4—61no—
38C2×C3×C4⋊C4—61no—
39C2×C4⋊Dic3—21no—
40C2×Dic3⋊C4—21no—
41C2×Dic3⋊C4—61no—
42C2×Dic3⋊C4—62no—
43C2×Dic3⋊C4—61no—
44C2×Dic3⋊C4—62no—
45C2×C4×Dic3—61no—
46C2×C4×Dic3—61no—
47C3⋊#95—61no—
48C3⋊#95—61no—
49C23×C32C2×D411yescharacteristic
50C2×C32×C4—21no—
51C2×C32×C4—21no—
52C2×C32×C4D812yes—
53C2×C3⋊Dic3—21no—
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3Q1612yes—
56C2×C3⋊Dic3C2×D411yescharacteristic
57C2×C3⋊Dic3C2×Q812yes—
58C2×C3⋊Dic3#4112yes—
59C2×C3⋊Dic3#4111yescharacteristic
60C2×C3×Dic3—22no—
61C2×C3×Dic3—41no—
62C2×C3×Dic3—41no—
63C2×C3×Dic3—42no—
64C2×C3×Dic3—41no—
65C2×C3×Dic3—41no—
66C2×C3×Dic3—42no—
67C2×C3×Dic3—42no—
68C2×C3×Dic3—41no—
69#622—24no—
70C2×#107—92no—
71#389—91no—
72#384—91no—
73#340—92no—
74#336—91no—
75C22×C3×C4—21no—
76C22×C3×C4—21no—
77C22×C3×C4—61no—
78C22×C3×C4—61no—
79C22×C3×C4—62no—
80C22×Dic3—21no—
81C22×Dic3—21no—
82C22×Dic3—22no—
83C22×Dic3—61no—
84C22×Dic3—61no—
85C22×Dic3—61no—
86C22×Dic3—61no—
87C3×C4⋊C4—122no—
88C3×C4⋊C4—122no—
89C4⋊Dic3—42no—
90Dic3⋊C4—42no—
91Dic3⋊C4—62no—
92Dic3⋊C4—62no—
93Dic3⋊C4—122no—
94Dic3⋊C4—122no—
95Dic3⋊C4—122no—
96Dic3⋊C4—124no—
97C4×Dic3—64no—
98C4×Dic3—122no—
99C22×C32#12111yescharacteristic
100C22×C32#12311yescharacteristic
101C22×C32C4⋊Q811yescharacteristic
102C22×C32C2×D811yescharacteristic
103C22×C32C2×Q1611yescharacteristic
104C22×C32AGL(1,ℤ/8)11yescharacteristic
105C22×C32#13711yescharacteristic
106C32×C4—22no—
107C3⋊Dic3—22no—
108C3⋊Dic3C22⋊Q812yes—
109C3⋊Dic3#12512yes—
110C3×Dic3—42no—
111C3×Dic3—82no—
112C3×Dic3—81no—
113C22×C8—92no—
114C2×C4⋊C4—61no—
115C2×C4⋊C4—61no—
116C2×C4⋊C4—91no—
117C2×C4⋊C4—91no—
118C2×C4⋊C4—92no—
119C2×C4⋊C4—181no—
120C2×C42—91no—
121#107—184no—
122#95—181no—
123C23×C3—21no—
124C23×C3—21no—
125C2×C3×C4—22no—
126C2×C3×C4—22no—
127C2×C3×C4—22no—
128C2×C3×C4—22no—
129C2×C3×C4—41no—
130C2×C3×C4—41no—
131C2×C3×C4—62no—
132C2×C3×C4—121no—
133C2×C3×C4—121no—
134C2×C3×C4—122no—
135C2×C3×C4—122no—
136C2×C3×C4—121no—
137C2×C3×C4—121no—
138C2×C3×C4—122no—
139C2×C3×C4—121no—
140C2×Dic3—22no—
141C2×Dic3—41no—
142C2×Dic3—41no—
143C2×Dic3—41no—
144C2×Dic3—42no—
145C2×Dic3—42no—
146C2×Dic3—41no—
147C2×Dic3—42no—
148C2×Dic3—41no—
149C2×Dic3—62no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—62no—
159C2×Dic3—62no—
160C2×Dic3—62no—
161C2×Dic3—121no—
162C2×Dic3—121no—
163C2×C32#39811yescharacteristic
164C2×C32#45911yescharacteristic
165C2×C32#46211yescharacteristic
166C2×C32#48011yescharacteristic
167C2×C32#48411yescharacteristic
168C2×C32#50011yescharacteristic
169C2×C32#50111yescharacteristic
170C22×C4—61no—
171C22×C4—61no—
172C22×C4—62no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4GO+(4,𝔽2)11yescharacteristic
176C2×C8—94no—
177C2×C8—182no—
178C2×C8—182no—
179C4⋊C4—92no—
180C4⋊C4—122no—
181C4⋊C4—122no—
182C4⋊C4—181no—
183C4⋊C4—182no—
184C4⋊C4—182no—
185C4⋊C4—182no—
186C4⋊C4—362no—
187C42—182no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—21no—
192C22×C3—21no—
193C22×C3—21no—
194C22×C3—21no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3—21no—
201C22×C3—21no—
202C3×C4—24no—
203C3×C4—42no—
204C3×C4—122no—
205C3×C4—242no—
206C3×C4—241no—
207Dic3—42no—
208Dic3—62no—
209Dic3—62no—
210Dic3—62no—
211Dic3—62no—
212Dic3—64no—
213Dic3—82no—
214Dic3—81no—
215Dic3—122no—
216C32#208311yescharacteristic, complemented, Sylow
217C23C2×GO+(4,𝔽2)11yescharacteristic
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—62no—
221C2×C4—92no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—92no—
225C2×C4—92no—
226C2×C4—121no—
227C2×C4—121no—
228C2×C4—122no—
229C2×C4—122no—
230C2×C4—121no—
231C2×C4—122no—
232C2×C4—121no—
233C2×C4—121no—
234C2×C4—181no—
235C2×C4—181no—
236C2×C4#377412yes—
237C8—184no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C22#6422211yescharacteristic
253C22#6422411yescharacteristic
254C22#6422811yescharacteristic
255C22#6423011yescharacteristic
256C22#6423311yescharacteristic
257C22C2×#377411yescharacteristic
258C22#6423911yescharacteristic
259C4—22no—
260C4—92no—
261C4—92no—
262C4—122no—
263C4—182no—
264C4—242no—
265C4—241no—
266C3—21no—
267C3—21no—
268C2#1059333911yescharacteristic
269C2#1059337211yescharacteristic
270C2#1059338311yescharacteristic
271C2#1059338811yescharacteristic
272C2#1059341711yescharacteristic
273C2#1059344811yescharacteristic
274C2#1059349211yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊Dic3C23
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2083
LCSG ▷ C22×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
216. C32#2083semidirect

Maximal subgroups

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

subgroupindex
C2×#637432
#105913592
#105913372
#105902072
#105900752
#20839