Finite Group Databasebeta

← #11874999

Subgroups — #11874999

Order 1152.

823 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 823 conjugacy classes of subgroups — too many to draw. Only its 184 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#10596159C211yesmaximal, characteristic
2#10593854C211yesmaximal, characteristic
3C3×#5065C212yesmaximal, complemented
4#10590574C214yesmaximal
5#10590416C212yesmaximal, complemented
6#10590415C212yesmaximal, complemented
7C4×#3710C211yesmaximal, characteristic
8#10590304C212yesmaximal, complemented
9#81916—32nomaximal
10C32×#125C2211yescharacteristic
11#64105—22no—
12#64101C2212yes—
13#64097C2212yes—
14#64096—22no—
15C42×C3⋊D3C2211yescharacteristic
16#64079C2211yescharacteristic
17C3×#870C2212yes—
18#63919C2212yes—
19#63865—22no—
20#63849C2212yes—
21#63838—22no—
22C2×#3710C2212yes—
23C3×#808C2214yes—
24C3×#807C2214yes—
25C3×C4×C3⋊C8C2212yes—
26#63575C2214yes—
27#63573C2214yes—
28#63553C2211yescharacteristic
29#63553C2211yescharacteristic
30#5688—32no—
31#5688—32no—
32#5688—61no—
33C3×#499—32no—
34#5065—32no—
35#5065D312yescomplemented
36#4880—34no—
37#4874—34no—
38#4860—34no—
39#4855—34no—
40C4×D3×C8—32no—
41#4683—32no—
42C2×C4×C3⋊D3D412yes—
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×#634—22no—
45C2×#627—22no—
46C32×C4⋊C4—22no—
47C32×C4⋊C4C2312yes—
48C32×C42C2311yescharacteristic
49#3752—22no—
50C4⋊(C3⋊Dic3)C2312yes—
51#3750—22no—
52#3750—22no—
53C4×C3⋊Dic3—22no—
54C4×C3⋊Dic3D412yes—
55C4×C3⋊Dic3C2311yescharacteristic
56C3×C4⋊Dic3C2314yes—
57C3×Dic3⋊C4—24no—
58C2×C3×C3⋊C8C2312yes—
59C2×C3×C3⋊C8C2312yes—
60#3724—22no—
61#3722—22no—
62Dic32—22no—
63#3710Q818yescomplemented
64#3160—91noSylow
65C3×#125—21no—
66C3×#125—32no—
67C3×#125C2×D312yes—
68C2×D3×C8—32no—
69C2×D3×C8—32no—
70#896—64no—
71#896—64no—
72#896—64no—
73#892—34no—
74#892—34no—
75#892—62no—
76#888—34no—
77#888—34no—
78#888—62no—
79#887—64no—
80#887—64no—
81#887—64no—
82C42×D3—32no—
83C42×D3—61no—
84#870—32no—
85#870—61no—
86#870C2×D312yes—
87C3×#107—34no—
88C3×#106—34no—
89C3×C4×C8—32no—
90#818—34no—
91#817—34no—
92C8×Dic3—32no—
93C8×Dic3—32no—
94#808—34no—
95#808C2×D314yes—
96#807—34no—
97#807C2×D314yes—
98C4×C3⋊C8C2×D312yes—
99C22×C3⋊D3C2×D411yescharacteristic
100C2×C32×C4—22no—
101C2×C32×C4C2×D412yes—
102C2×C32×C4C2411yescharacteristic
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3C2×D411yescharacteristic
105C2×C3⋊Dic3C2×D412yes—
106C4×C3⋊D3—24no—
107C4×C3⋊D3C2×Q814yes—
108#634—44no—
109C2×C3×Dic3—24no—
110#627—44no—
111C3×C3⋊C8C2×Q814yes—
112C3×C3⋊C8C2×Q814yes—
113#533—91no—
114#533—91no—
115#500—92no—
116#499—32no—
117#499—92no—
118#498—92no—
119#427—94no—
120C2×C4×C8—91no—
121C2×C4×D3—32no—
122C2×C4×D3—34no—
123C2×C4×D3—61no—
124C2×C4×D3—62no—
125C2×Dic6—64no—
126C2×Dic6—64no—
127C2×Dic6—64no—
128C2×C3×C8—32no—
129C2×C3×C8—32no—
130C3×C4⋊C4—24no—
131C3×C4⋊C4—24no—
132C3×C4⋊C4—22no—
133C3×C4⋊C4—34no—
134C3×C4⋊C4—64no—
135C3×C4⋊C4C22×D314yes—
136C3×C42—21no—
137C3×C42C22×D312yes—
138(C2×D3)⋊C4—64no—
139(C2×D3)⋊C4—64no—
140(C2×D3)⋊C4—64no—
141C4⋊Dic3—34no—
142C4⋊Dic3—62no—
143C4⋊Dic3C22×D314yes—
144Dic3⋊C4—24no—
145Dic3⋊C4—64no—
146Dic3⋊C4—64no—
147Dic3⋊C4—64no—
148Dic3⋊C4—64no—
149Dic3⋊C4—64no—
150C4×Dic3—34no—
151C4×Dic3—32no—
152C4×Dic3—62no—
153C4×Dic3—61no—
154C4×Dic3—64no—
155C4×Dic3—64no—
156C4×Dic3—64no—
157C2×C3⋊C8C22×D312yes—
158C2×C3⋊C8C22×D312yes—
159D3×C8—38no—
160D3×C8—38no—
161C22×C32C22×D411yescharacteristic
162C2×C3⋊D3—22no—
163C2×C3⋊D3C4⋊Q812yes—
164C32×C4—22no—
165C32×C4—42no—
166C32×C4C22×Q812yes—
167C3⋊Dic3—42no—
168C3⋊Dic3C4⋊Q812yes—
169C3⋊Dic3#13514yes—
170C3×Dic3—44no—
171C22×C8—92no—
172C4⋊Q8—92no—
173C4⋊Q8—92no—
174#125—32no—
175#125—91no—
176#125D3211yescharacteristic
177C22⋊Q8—182no—
178C22⋊Q8—182no—
179C4×Q8—182no—
180C4×Q8—182no—
181#117—92no—
182#117—92no—
183C2×C42—91no—
184#107—34no—
185#107—94no—
186#106—34no—
187#106—94no—
188C4×C8—32no—
189C4×C8—91no—
190C4×C8—91no—
191C22×D3—32no—
192C22×D3—61no—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—21no—
196C2×C3×C4—22no—
197C2×C3×C4—64no—
198C2×C3×C4D3×D414yes—
199C2×C3×C4C23×D312yes—
200C2×Dic3—24no—
201C2×Dic3—32no—
202C2×Dic3—34no—
203C2×Dic3—61no—
204C2×Dic3—62no—
205C2×Dic3—64no—
206C2×Dic3—64no—
207C4×D3—34no—
208C4×D3—34no—
209C4×D3—64no—
210C4×D3—68no—
211C4×D3—124no—
212Dic6—128no—
213Dic6—128no—
214Dic6—128no—
215C3×C8—34no—
216C3×C8—34no—
217C3⋊C8D3×Q814yes—
218C3⋊C8D3×Q814yes—
219C2×C32C2×C4⋊Q811yescharacteristic
220C2×C32C2×#13512yes—
221C3⋊D3—22no—
222C2×Q8—182no—
223C2×Q8—182no—
224C22×C4—91no—
225C22×C4—92no—
226C2×C8—32no—
227C2×C8—32no—
228C2×C8—98no—
229C4⋊C4—22no—
230C4⋊C4—34no—
231C4⋊C4—64no—
232C4⋊C4—92no—
233C4⋊C4—182no—
234C4⋊C4—182no—
235C4⋊C4—182no—
236C4⋊C4C2×D3212yes—
237C22⋊C4—182no—
238C22⋊C4—182no—
239C42—91no—
240C42—92no—
241C42—182no—
242C42—182no—
243C42C2×D3211yescharacteristic
244C22×C3—21no—
245C22×C3C2×D3×D412yes—
246C2×D3—34no—
247C2×D3—62no—
248C2×D3—64no—
249C2×D3—122no—
250C3×C4—24no—
251C3×C4—22no—
252C3×C4—42no—
253C3×C4—44no—
254C3×C4—44no—
255C3×C4—124no—
256C3×C4C2×D3×Q812yes—
257C3×C4C2×D3×Q812yes—
258Dic3—34no—
259Dic3—38no—
260Dic3—44no—
261Dic3—64no—
262Dic3—62no—
263Dic3—124no—
264Dic3—124no—
265C32#316011yescharacteristic, complemented, Sylow
266C23—91no—
267Q8—364no—
268Q8—364no—
269C2×C4—22no—
270C2×C4—64no—
271C2×C4—91no—
272C2×C4—92no—
273C2×C4—94no—
274C2×C4—184no—
275C2×C4—182no—
276C2×C4#381112yes—
277C2×C4C22×D3211yescharacteristic
278C8—34no—
279C8—34no—
280C2×C3—21no—
281C2×C3—22no—
282C2×C3D3×C4⋊Q812yes—
283C2×C3D3×#13514yes—
284D3—64no—
285D3—122no—
286C22—92no—
287C22—182no—
288C22C2×#381111yescharacteristic
289C4—22no—
290C4—42no—
291C4—92no—
292C4—94no—
293C4—124no—
294C4—362no—
295C4D32×Q812yes—
296C3—21no—
297C3#8191612yescomplemented
298C2—182no—
299C2#1059536511yescharacteristic
300C2#1059545912yes—
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#125D32
hypocenterC32#3160
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. C3×#5065C2semidirect
5. #10590416C2semidirect
6. #10590415C2semidirect
8. #10590304C2semidirect
35. #5065D3semidirect
63. #3710Q8semidirect
265. C32#3160semidirect
297. C3#81916semidirect

Maximal subgroups

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

subgroupindex
#105961592
#105938542
C3×#50652
#105905742
#105904162
#105904152
C4×#37102
#105903042
#819163