Finite Group Databasebeta

← #11874992

Subgroups — #11874992

Order 1152.

823 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 823 conjugacy classes of subgroups — too many to draw. Only its 216 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#10595988C211yesmaximal, characteristic
2#10595050C211yesmaximal, characteristic
3C3×#4998C212yesmaximal
4#10591122C212yesmaximal
5C2×#63553C211yesmaximal, characteristic
6#10590417C214yesmaximal, complemented
7#10590416C212yesmaximal, complemented
8#10590415C212yesmaximal, complemented
9#79170—32nomaximal
10C32×#117C2211yescharacteristic
11#64135C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#64099C2212yes—
14#64097C2212yes—
15#64087—22no—
16C4×#634—22no—
17C3×#926C2212yes—
18C22×C3×C3⋊C8C2212yes—
19#63982—22no—
20#63919C2212yes—
21C4×#627—22no—
22#63872C2212yes—
23C3×#808C2214yes—
24C3×#807C2214yes—
25#63575C2214yes—
26#63573C2214yes—
27#63553C2211yescharacteristic
28#63553C2211yescharacteristic
29#63553C2212yes—
30#5517—32no—
31#5517—32no—
32#5517—61no—
33C3×#427—32no—
34#5106—32no—
35C2×C8×Dic3—32no—
36#4998—32no—
37#4998D312yes—
38#4878—34no—
39#4874—34no—
40#4858—34no—
41#4855—34no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D412yes—
44C2×#634—22no—
45C2×#627—22no—
46C32×C4⋊C4C2312yes—
47C32×C22⋊C4—21no—
48C32×C42—21no—
49#3757—21no—
50C4⋊(C3⋊Dic3)—22no—
51C4⋊(C3⋊Dic3)C2312yes—
52#3750—22no—
53#3750—22no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3D412yes—
56C4×C3⋊Dic3C2311yescharacteristic
57C4×C3⋊Dic3C2311yescharacteristic
58C3×#217—22no—
59C3×C4⋊Dic3C2314yes—
60C3×C4×Dic3—22no—
61C2×C3×C3⋊C8Q818yescomplemented
62C2×C3×C3⋊C8C2312yes—
63C2×C3×C3⋊C8C2312yes—
64#3724—22no—
65Dic3⋊Dic3—24no—
66#3160—91noSylow
67C22×C3×C8—32no—
68C3×#117—21no—
69C3×#117—32no—
70C3×#117C2×D312yes—
71#926—32no—
72#926—61no—
73#926C2×D312yes—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—61no—
76C22×C3⋊C8C2×D312yes—
77#890—34no—
78#890—34no—
79#890—62no—
80#888—34no—
81#888—34no—
82#888—62no—
83#878—64no—
84#878—64no—
85#878—64no—
86C4×Dic6—64no—
87C4×Dic6—64no—
88C4×Dic6—64no—
89C3×#107—34no—
90C3×#106—34no—
91#818—34no—
92#817—34no—
93C8×Dic3—32no—
94C8×Dic3—32no—
95C8×Dic3—32no—
96C8×Dic3—32no—
97#808—34no—
98#808C2×D314yes—
99#807—34no—
100#807C2×D314yes—
101C23×C32C2×D411yescharacteristic
102C2×C32×C4—22no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×Q814yes—
105C2×C32×C4C2411yescharacteristic
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—24no—
108C2×C3⋊Dic3C2×D412yes—
109C2×C3⋊Dic3C2×D412yes—
110#634—44no—
111C2×C3×Dic3—24no—
112#627—44no—
113C3×C3⋊C8C2×Q814yes—
114C3×C3⋊C8C2×Q814yes—
115#533—91no—
116#533—91no—
117#500—92no—
118#499—94no—
119#498—92no—
120#427—32no—
121#427—92no—
122C2×C4×C8—91no—
123C22×C3×C4—21no—
124C22×C3×C4C22×D312yes—
125C22×Dic3—34no—
126C22×Dic3—62no—
127C2×Dic6—64no—
128C2×Dic6—64no—
129C2×Dic6—64no—
130C2×C3×C8—38no—
131C2×C3×C8—32no—
132C2×C3×C8—32no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—34no—
135C3×C4⋊C4C22×D314yes—
136C3×C22⋊C4—22no—
137C3×C22⋊C4—22no—
138C3×C22⋊C4—62no—
139C3×C42—22no—
140C3×C42—22no—
141C3×C42—62no—
142#217—22no—
143#217—62no—
144#217—62no—
145C4⋊Dic3—34no—
146C4⋊Dic3—62no—
147C4⋊Dic3—64no—
148C4⋊Dic3—64no—
149C4⋊Dic3—64no—
150C4⋊Dic3C22×D314yes—
151Dic3⋊C4—64no—
152Dic3⋊C4—64no—
153Dic3⋊C4—64no—
154Dic3⋊C4—64no—
155Dic3⋊C4—64no—
156Dic3⋊C4—64no—
157C4×Dic3—22no—
158C4×Dic3—34no—
159C4×Dic3—32no—
160C4×Dic3—32no—
161C4×Dic3—62no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C4×Dic3—62no—
165C4×Dic3—62no—
166C2×C3⋊C8Dic618yescomplemented
167C2×C3⋊C8C22×D312yes—
168C2×C3⋊C8C22×D312yes—
169C22×C32—22no—
170C22×C32C4⋊Q812yes—
171C22×C32C22×D411yescharacteristic
172C32×C4—42no—
173C32×C4C4⋊Q812yes—
174C32×C4C22×Q812yes—
175C3⋊Dic3—22no—
176C3⋊Dic3—42no—
177C3⋊Dic3#13514yes—
178C3×Dic3—44no—
179C22×C8—32no—
180C4⋊Q8—92no—
181C4⋊Q8—92no—
182#125—92no—
183#125—92no—
184C22⋊Q8—182no—
185C22⋊Q8—182no—
186C4×Q8—182no—
187C4×Q8—182no—
188#117—32no—
189#117—91no—
190#117D3211yescharacteristic
191C2×C42—91no—
192#107—34no—
193#107—94no—
194#106—34no—
195#106—94no—
196C4×C8—91no—
197C4×C8—92no—
198C4×C8—91no—
199C23×C3—21no—
200C23×C3D3×D412yes—
201C2×C3×C4—24no—
202C2×C3×C4—24no—
203C2×C3×C4—21no—
204C2×C3×C4—24no—
205C2×C3×C4—21no—
206C2×C3×C4—64no—
207C2×C3×C4C2×Dic614yes—
208C2×C3×C4D3×D412yes—
209C2×C3×C4D3×Q814yes—
210C2×C3×C4C23×D312yes—
211C2×Dic3—24no—
212C2×Dic3—34no—
213C2×Dic3—34no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—68no—
217C2×Dic3—64no—
218C2×Dic3—64no—
219C2×Dic3—124no—
220Dic6—128no—
221Dic6—128no—
222Dic6—128no—
223C3×C8—34no—
224C3×C8—34no—
225C3⋊C8C2×Dic614yes—
226C3⋊C8C2×Dic614yes—
227C2×C32—22no—
228C2×C32C2×C4⋊Q811yescharacteristic
229C2×C32C2×#13512yes—
230C2×Q8—182no—
231C2×Q8—182no—
232C22×C4—92no—
233C22×C4C2×D3211yescharacteristic
234C2×C8—32no—
235C2×C8—32no—
236C2×C8—38no—
237C4⋊C4—34no—
238C4⋊C4—92no—
239C4⋊C4—182no—
240C4⋊C4—182no—
241C4⋊C4—182no—
242C4⋊C4—184no—
243C4⋊C4—182no—
244C4⋊C4C2×D3212yes—
245C22⋊C4—21no—
246C22⋊C4—62no—
247C22⋊C4—181no—
248C42—21no—
249C42—62no—
250C42—91no—
251C42—91no—
252C42—92no—
253C42—181no—
254C22×C3—24no—
255C22×C3—21no—
256C22×C3—22no—
257C22×C3—42no—
258C22×C3#88814yes—
259C22×C3C2×D3×D412yes—
260C3×C4—22no—
261C3×C4—22no—
262C3×C4—44no—
263C3×C4—44no—
264C3×C4—124no—
265C3×C4#88814yes—
266C3×C4C22×Dic612yes—
267C3×C4C2×D3×Q812yes—
268Dic3—38no—
269Dic3—44no—
270Dic3—64no—
271Dic3—64no—
272Dic3—122no—
273Dic3—124no—
274Dic3—124no—
275C32#316011yescharacteristic, complemented, Sylow
276C23#381111yescharacteristic
277Q8—364no—
278Q8—364no—
279C2×C4—22no—
280C2×C4—64no—
281C2×C4—92no—
282C2×C4—92no—
283C2×C4—184no—
284C2×C4—182no—
285C2×C4D3×Dic614yes—
286C2×C4#381111yescharacteristic
287C2×C4C22×D3211yescharacteristic
288C8—34no—
289C8—34no—
290C2×C3—24no—
291C2×C3—22no—
292C2×C3—21no—
293C2×C3—42no—
294C2×C3C2×#88812yes—
295C2×C3D3×#13514yes—
296C22—22no—
297C22#6384012yes—
298C22C2×#381111yescharacteristic
299C4—42no—
300C4—94no—
301C4—124no—
302C4—182no—
303C4—362no—
304C4#6384012yes—
305C4C2×D3×Dic612yes—
306C3—21no—
307C3#7917012yescomplemented
308C2—22no—
309C2C2×#6384011yescharacteristic
310C2#1059545912yes—
subgroupG/H
centerC2×C4#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenter#117D32
hypocenterC32#3160
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
6. #10590417C2semidirect
7. #10590416C2semidirect
8. #10590415C2semidirect
61. C2×C3×C3⋊C8Q8semidirect
166. C2×C3⋊C8Dic6semidirect
275. C32#3160semidirect
307. C3#79170semidirect

Maximal subgroups

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

subgroupindex
#105959882
#105950502
C3×#49982
#105911222
C2×#635532
#105904172
#105904162
#105904152
#791703