Finite Group Databasebeta

← #11793090

Subgroups — #11793090

Order 1152.

732 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 155 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#10595941C211yesmaximal, characteristic, complemented
2#10592838C211yesmaximal, characteristic
3#10592705C211yesmaximal, characteristic
4C2×#63632C211yesmaximal, characteristic
5C32×#339C211yesmaximal, characteristic, complemented
6#10589422C211yesmaximal, characteristic, complemented
7#10589397C211yesmaximal, characteristic, complemented
8#68779—34nomaximal
9C2×#3828C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13#64135C2211yescharacteristic
14#64135C2211yescharacteristic
15#64133—22no—
16C2×#3748C2211yescharacteristic
17#64079—21no—
18#64078—21no—
19C4×#634—22no—
20#63652—22no—
21#63633—22no—
22#63632—21no—
23#63632—21no—
24#5470—34no—
25#5139—34no—
26#5006—34no—
27C2×#805—34no—
28C3×#339D314yescomplemented
29#4556—34no—
30#4531—34no—
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C2×#638—21no—
34#3828—21no—
35#3828—21no—
36#3828—21no—
37#3828—21no—
38C2×C4⋊(C3⋊D3)Q811yescharacteristic, complemented
39C2×C4×C3⋊D3—21no—
40C2×#634—22no—
41C2×#634Q811yescharacteristic, complemented
42C32×M16—21no—
43C32×M16—21no—
44C2×C32×C8—21no—
45C32×C4⋊C4—21no—
46C32×C22⋊C4—21no—
47C32×C42—21no—
48C32×C42—21no—
49C32×C42D411yescharacteristic
50C32×C42D411yescharacteristic
51#3757—21no—
52#3757D412yes—
53C4⋊(C3⋊Dic3)—22no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56#3750—24no—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3D412yes—
59#3748—21no—
60#3748—21no—
61C2×C3⋊(C3⋊C8)—21no—
62#2031—91noSylow
63C2×#235—34no—
64C2×C3×M16C2×D314yes—
65C3×#117C2×D314yes—
66C2×C3×C42C2×D314yes—
67#926—34no—
68#926—34no—
69#924—68no—
70C2×#208—34no—
71#870—64no—
72#869—64no—
73C4×Dic6—68no—
74#825—68no—
75#806—68no—
76#805—64no—
77#805—64no—
78C23×C32C2×D411yescharacteristic
79C22×C3⋊D3—21no—
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4—42no—
83C2×C32×C4—41no—
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×Q811yescharacteristic
87C2×C32×C4#4111yescharacteristic
88C2×C32×C4#4111yescharacteristic
89C2×C32×C4#4111yescharacteristic
90#638—41no—
91#638—41no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—21no—
95C4⋊(C3⋊D3)—21no—
96C4⋊(C3⋊D3)—21no—
97C4×C3⋊D3—41no—
98C4×C3⋊D3—41no—
99#634—21no—
100#634—21no—
101#634—44no—
102C32×C8—41no—
103C3⋊(C3⋊C8)—41no—
104#533—91no—
105#421—91no—
106C2×#104—91no—
107#410—91no—
108#344—91no—
109#339C3⋊D311yescharacteristic, complemented
110H(3,ℤ/4)—91no—
111C22×C3×C4—24no—
112C22×C3×C4C22×D314yes—
113C2×#67—64no—
114#235—64no—
115#235—64no—
116#235—64no—
117#235—64no—
118C2×D12—34no—
119C2×C4×D3—64no—
120C2×Dic6—34no—
121C2×Dic6—68no—
122C3×M16—24no—
123C3×M16—24no—
124C2×C3×C8—24no—
125C3×C4⋊C4—24no—
126C3×C22⋊C4—24no—
127C3×C42—24no—
128C3×C42—24no—
129C3×C42D1214yes—
130C3×C42D1214yes—
131#217—38no—
132#217—64no—
133C4⋊Dic3—68no—
134C4⋊Dic3—64no—
135C4⋊Dic3—64no—
136Dic3⋊C4—616no—
137C4×Dic3—38no—
138C4×Dic3—64no—
139#208—64no—
140#208—64no—
141C2×C3⋊C8—64no—
142C22×C32—41no—
143C22×C32#12011yescharacteristic
144C22×C32C22⋊Q811yescharacteristic
145C22×C32#12411yescharacteristic
146C2×C3⋊D3—41no—
147C2×C3⋊D3—81no—
148C32×C4—22no—
149C32×C4—41no—
150C32×C4—81no—
151C32×C4C22⋊Q811yescharacteristic
152C32×C4C22⋊Q811yescharacteristic
153C32×C4#12411yescharacteristic
154C32×C4#12411yescharacteristic
155C3⋊Dic3—42no—
156C3⋊Dic3—42no—
157C3⋊Dic3—41no—
158C2×#41—91no—
159C2×M16—91no—
160C2×M16C2×C3⋊D311yescharacteristic
161C4⋊Q8—181no—
162#125—181no—
163C22⋊Q8—182no—
164C4×Q8—182no—
165#117—91no—
166#117—91no—
167#117C2×C3⋊D311yescharacteristic
168C2×C42C2×C3⋊D311yescharacteristic
169#104—182no—
170#104—181no—
171#104—181no—
172#99—182no—
173C23×C3D3×D414yes—
174C22×D3—64no—
175C2×C3×C4—24no—
176C2×C3×C4—24no—
177C2×C3×C4—48no—
178C2×C3×C4—44no—
179C2×C3×C4C2×D1214yes—
180C2×C3×C4#23514yes—
181C2×C3×C4#23514yes—
182C2×C3×C4D3×D414yes—
183C2×C3×C4#23714yes—
184C2×C3×C4D3×Q814yes—
185#67—124no—
186#67—124no—
187C2×Dic3—68no—
188C2×Dic3—68no—
189C2×Dic3—64no—
190D12—64no—
191D12—64no—
192C4×D3—124no—
193C4×D3—124no—
194Dic6—64no—
195Dic6—64no—
196Dic6—1216no—
197C3×C8—44no—
198C3⋊C8—124no—
199C2×C32—21no—
200C2×C32—21no—
201C2×C32—21no—
202C2×C32#39311yescharacteristic
203C3⋊D3—81no—
204#41—181no—
205#41—181no—
206#41—181no—
207#41—181no—
208C2×Q8—91no—
209C2×Q8—182no—
210C2×D4—91no—
211C2×D4—181no—
212C22×C4—21no—
213C22×C4—181no—
214C22×C4C22×C3⋊D311yescharacteristic
215M16—21no—
216M16—21no—
217M16—181no—
218M16—181no—
219C2×C8—21no—
220C2×C8—181no—
221C4⋊C4—21no—
222C4⋊C4—184no—
223C4⋊C4—182no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C22⋊C4—21no—
227C22⋊C4—92no—
228C22⋊C4—181no—
229C42—21no—
230C42—21no—
231C42—92no—
232C42—181no—
233C42C4⋊(C3⋊D3)11yescharacteristic
234C42C4⋊(C3⋊D3)11yescharacteristic
235C22×C3—44no—
236C22×C3#88214yes—
237C22×C3#88514yes—
238C22×C3#89614yes—
239C2×D3—124no—
240C2×D3—244no—
241C3×C4—28no—
242C3×C4—44no—
243C3×C4—84no—
244C3×C4#87514yes—
245C3×C4#88514yes—
246C3×C4#89614yes—
247C3×C4#89714yes—
248Dic3—128no—
249Dic3—128no—
250Dic3—124no—
251C32#203111yescharacteristic, complemented, Sylow
252C23—181no—
253C23D4×C3⋊D311yescharacteristic
254Q8—181no—
255Q8—181no—
256Q8—364no—
257D4—181no—
258D4—181no—
259D4—361no—
260D4—361no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—182no—
266C2×C4—182no—
267C2×C4—181no—
268C2×C4—361no—
269C2×C4—361no—
270C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
271C2×C4#382811yescharacteristic
272C2×C4#382811yescharacteristic
273C2×C4D4×C3⋊D311yescharacteristic
274C2×C4#383011yescharacteristic
275C2×C4Q8×C3⋊D311yescharacteristic
276C8—41no—
277C8—361no—
278C2×C3—24no—
279C2×C3—24no—
280C2×C3—24no—
281C2×C3#467314yes—
282D3—244no—
283C22—41no—
284C22—361no—
285C22—721no—
286C22#6409111yescharacteristic
287C22#6409411yescharacteristic
288C22#6410511yescharacteristic
289C4—22no—
290C4—41no—
291C4—81no—
292C4—362no—
293C4—362no—
294C4—361no—
295C4#6408411yescharacteristic
296C4#6409411yescharacteristic
297C4#6410511yescharacteristic
298C4#6410611yescharacteristic
299C3#6877914yescomplemented
300C2—21no—
301C2—21no—
302C2—21no—
303C2—721no—
304C2#1059237211yescharacteristic
subgroupG/H
centerC4#64094
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#339C2
socleC2×C32#393
prime radicalC2×#3828C22
hypercenter#339C3⋊D3
hypocenterC32#2031
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #10595941C2semidirect
5. C32×#339C2semidirect
6. #10589422C2semidirect
7. #10589397C2semidirect
28. C3×#339D3semidirect
38. C2×C4⋊(C3⋊D3)Q8semidirect
41. C2×#634Q8semidirect
109. #339C3⋊D3semidirect
251. C32#2031semidirect
299. C3#68779semidirect

Maximal subgroups

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

subgroupindex
#105959412
#105928382
#105927052
C2×#636322
C32×#3392
#105894222
#105893972
#687793