Finite Group Databasebeta

← #11875051

Subgroups — #11875051

Order 1152.

642 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 127 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#10593948C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic
3#10593723C211yesmaximal, characteristic
4#10593396C212yesmaximal
5#10593392C214yesmaximal, complemented
6#10593387C212yesmaximal
7#10593383C214yesmaximal, complemented
8C2×#3797—21no—
9C2×#3787C2212yes—
10C42×C3⋊D3C2211yescharacteristic
11C3×#870—21no—
12C3×#869—21no—
13#63919—21no—
14#63919C2212yes—
15#63900—21no—
16#63900C2211yescharacteristic
17#63900C2212yes—
18#63900C2211yescharacteristic
19#63883—21no—
20#63883—21no—
21#63873C2212yes—
22#63872—21no—
23#63870C2212yes—
24#63870C2212yes—
25#63777C2212yes—
26#63777C2212yes—
27#63743C2218yes—
28#63742C2218yes—
29D3×C4⋊Q8—61no—
30D3×#125—61no—
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3C2311yescharacteristic
34C2×C3×Dic6—22no—
35C2×#627—22no—
36C2×#624—22no—
37C2×#624—21no—
38C2×#624—21no—
39#3797—44no—
40C2×#622C2314yes—
41#3787Q818yescomplemented
42C32×C42D411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C4×C3⋊Dic3C2311yescharacteristic
45C4×C3⋊Dic3C2311yescharacteristic
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3—21no—
48C3×C4⋊Dic3—22no—
49C3×C4⋊Dic3—22no—
50C3×Dic3⋊C4—22no—
51C3×Dic3⋊C4—22no—
52#3724—22no—
53#3724C2312yes—
54#3724C2312yes—
55#3724C2314yes—
56Dic3⋊Dic3—22no—
57Dic3⋊Dic3—22no—
58C2×#501—91nomaximal, Sylow
59C2×D3×Q8—62no—
60C3×C4⋊Q8—61no—
61C3×#125—61no—
62#944—62no—
63D3×C4⋊C4—61no—
64D3×C4⋊C4—61no—
65D3×C4⋊C4—62no—
66D3×C4⋊C4—62no—
67D3×C4⋊C4—62no—
68D3×C4⋊C4—62no—
69#890—61no—
70#890—61no—
71#889—62no—
72#889—62no—
73#888—62no—
74#888—62no—
75C42×D3—61no—
76C42×D3—61no—
77#870—21no—
78#869—21no—
79C22×C3⋊D3C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3C2×D411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C2×C3⋊Dic3C2411yescharacteristic
86C4×C3⋊D3—22no—
87C4×C3⋊D3—22no—
88C4×C3⋊D3C2×Q814yes—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—24no—
92C3×Dic6—44no—
93#627—44no—
94#624—44no—
95#624—42no—
96#624—42no—
97#622C2×Q818yescomplemented
98C2×C4⋊Q8—91no—
99C2×#125—91no—
100#501—94no—
101#501—94no—
102C2×#107—92no—
103C2×#106—92no—
104C2×#97—91no—
105C2×C3×Q8—62no—
106D3×Q8—128no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×C4×D3—62no—
114C2×C4×D3—62no—
115C2×C4×D3—64no—
116C2×Dic6—22no—
117C2×Dic6—64no—
118C3×C4⋊C4—62no—
119C3×C4⋊C4—62no—
120C3×C4⋊C4—62no—
121C3×C4⋊C4—62no—
122C3×C4⋊C4—61no—
123C3×C4⋊C4—61no—
124C3×C42—21no—
125C3×C42—21no—
126C4⋊Dic3—22no—
127C4⋊Dic3—22no—
128C4⋊Dic3—21no—
129C4⋊Dic3—21no—
130C4⋊Dic3—62no—
131C4⋊Dic3—62no—
132Dic3⋊C4—22no—
133Dic3⋊C4—22no—
134Dic3⋊C4—64no—
135Dic3⋊C4—62no—
136Dic3⋊C4—62no—
137Dic3⋊C4—64no—
138Dic3⋊C4—62no—
139Dic3⋊C4—62no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C22×C32C22×D411yescharacteristic
147C2×C3⋊D3C4⋊Q812yes—
148C2×C3⋊D3AGL(1,ℤ/8)12yes—
149C2×C3⋊D3#13712yes—
150C32×C4—21no—
151C32×C4—21no—
152C32×C4C4⋊Q812yes—
153C3⋊Dic3—21no—
154C3⋊Dic3—21no—
155C3⋊Dic3C22×Q812yes—
156C3×Dic3—44no—
157C3×Dic3—42no—
158C3×Dic3—42no—
159C22×Q8—181no—
160C22×C8—92no—
161C4⋊Q8—61no—
162C4⋊Q8—92no—
163C4⋊Q8—92no—
164C4⋊Q8—181no—
165#125—61no—
166#125—92no—
167#125—92no—
168#125—181no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4—91no—
171C2×C4⋊C4—92no—
172C2×C4⋊C4—181no—
173C2×C4⋊C4—181no—
174C2×C4⋊C4—181no—
175C2×C42—91no—
176#107—98no—
177#106—98no—
178#97—92no—
179#97—92no—
180C22×D3—61no—
181C22×D3—61no—
182C3×Q8—124no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—62no—
190C2×C3×C4—62no—
191C2×C3×C4—64no—
192C2×Dic3—22no—
193C2×Dic3—22no—
194C2×Dic3—24no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C4×D3—64no—
202C4×D3—64no—
203C4×D3—64no—
204C4×D3—64no—
205C4×D3—122no—
206C4×D3—122no—
207C4×D3—124no—
208C4×D3—124no—
209C4×D3—128no—
210Dic6—44no—
211Dic6—128no—
212C2×C32C2×C4⋊Q811yescharacteristic
213C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C32C2×#13711yescharacteristic
215C3⋊D3#50114yescomplemented
216C2×Q8—62no—
217C2×Q8—182no—
218C2×Q8—364no—
219C22×C4—91no—
220C22×C4—91no—
221C22×C4—91no—
222C22×C4—181no—
223C22×C4—181no—
224C22×C4—182no—
225C2×C8—94no—
226C2×C8—98no—
227C4⋊C4—61no—
228C4⋊C4—61no—
229C4⋊C4—62no—
230C4⋊C4—62no—
231C4⋊C4—62no—
232C4⋊C4—62no—
233C4⋊C4—92no—
234C4⋊C4—94no—
235C4⋊C4—92no—
236C4⋊C4—182no—
237C4⋊C4—182no—
238C4⋊C4—182no—
239C42—91no—
240C42—91no—
241C42—91no—
242C42GO+(4,𝔽2)11yescharacteristic
243C22×C3—21no—
244C22×C3—21no—
245C2×D3—62no—
246C2×D3—62no—
247C2×D3—62no—
248C2×D3—62no—
249C2×D3—62no—
250C2×D3—62no—
251C3×C4—22no—
252C3×C4—22no—
253C3×C4—22no—
254C3×C4—22no—
255C3×C4—41no—
256C3×C4—41no—
257C3×C4—124no—
258C3×C4—122no—
259C3×C4—122no—
260Dic3—44no—
261Dic3—42no—
262Dic3—42no—
263Dic3—62no—
264Dic3—62no—
265Dic3—62no—
266Dic3—62no—
267Dic3—121no—
268Dic3—121no—
269C32C2×#50111yescharacteristic, complemented, Sylow
270C23—91no—
271Q8—124no—
272Q8—364no—
273C2×C4—62no—
274C2×C4—62no—
275C2×C4—64no—
276C2×C4—91no—
277C2×C4—94no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—182no—
281C2×C4—182no—
282C2×C4—364no—
283C2×C4—362no—
284C2×C4—362no—
285C2×C4C2×GO+(4,𝔽2)11yescharacteristic
286C2×C4C2×GO+(4,𝔽2)11yescharacteristic
287C2×C4C2×GO+(4,𝔽2)11yescharacteristic
288C8—98no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295D3—64no—
296D3—64no—
297C22—92no—
298C22—92no—
299C22—92no—
300C22C22×GO+(4,𝔽2)11yescharacteristic
301C4—21no—
302C4—21no—
303C4—92no—
304C4—124no—
305C4—122no—
306C4—122no—
307C4—181no—
308C4—181no—
309C4#6422212yes—
310C3—21no—
311C3—21no—
312C2—94no—
313C2C2×#6422211yescharacteristic
314C2#1059650111yescharacteristic
315C2#1059650511yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#501
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
5. #10593392C2semidirect
7. #10593383C2semidirect
41. #3787Q8semidirect
97. #622C2×Q8semidirect
215. C3⋊D3#501semidirect
269. C32C2×#501semidirect

Maximal subgroups

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

subgroupindex
#105939482
#105939092
#105937232
#105933962
#105933922
#105933872
#105933832
C2×#5019