Finite Group Databasebeta

← #11898397

Subgroups — #11898397

Order 1152.

787 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 787 conjugacy classes of subgroups — too many to draw. Only its 156 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#10595119C212yesmaximal, complemented
2D8×C3⋊Dic3C211yesmaximal, characteristic
3C3×#5155C212yesmaximal
4#10591497C212yesmaximal, complemented
5#10591442C214yesmaximal, complemented
6#10590905C211yesmaximal, characteristic, complemented
7Dic3×Dic12C212yesmaximal, complemented
8C8×#627C211yesmaximal, characteristic, complemented
9#81813—32nomaximal
10C2×C32×D8C2211yescharacteristic
11D4×C3⋊Dic3C2212yes—
12C3×#936C2214yes—
13C2×C3×#214C2214yes—
14C2×C3×Dic12C2212yes—
15#63982—22no—
16#63957—22no—
17#63956—24no—
18C4×#627C2211yescharacteristic
19#63873C2212yes—
20Dic3×Dic6C2214yes—
21C2×#3718C2212yes—
22#63659C2212yes—
23#63645C2211yescharacteristic
24C8×C3⋊Dic3C2211yescharacteristic
25C3×C8×Dic3C2212yes—
26#63572C2211yescharacteristic
27Dic3⋊(C3⋊C8)C2212yes—
28#63566C2214yes—
29#5671—34no—
30C3×#495—32no—
31#5183—32no—
32Dic3×Q16—32no—
33#5166—34no—
34#5162—34no—
35#5155D312yes—
36Dic3×D8—32no—
37Dic3×D8—61no—
38#5054—34no—
39C4×Dic12—32no—
40C8×Dic6—32no—
41C2×C32×D4C2312yes—
42C22×C3⋊Dic3—22no—
43C2×C3×Dic6C2314yes—
44C2×#627D411yescharacteristic
45C32×D8—22no—
46C2×C32×C8C2311yescharacteristic
47#3757—22no—
48C4⋊(C3⋊Dic3)C2312yes—
49C4×C3⋊Dic3C2311yescharacteristic
50C2×C3⋊(C3⋊C8)C2311yescharacteristic
51C3×#217—24no—
52C3×#217—24no—
53C3×#214—44no—
54C3×C4×Dic3C2312yes—
55C2×C3×C3⋊C8C2312yes—
56C3×Dic12—24no—
57#3724—22no—
58#3724—22no—
59#3724D411yescharacteristic
60Dic3⋊Dic3—24no—
61Dic3⋊Dic3D412yes—
62Dic32—24no—
63#3718—42no—
64#3393—91noSylow
65C2×C3×Q16—32no—
66C2×C3×SD16—34no—
67C2×C3×D8—21no—
68C2×C3×D8C2×D312yes—
69C3×#124—34no—
70Q8×Dic3—34no—
71#944—34no—
72C2×#216—34no—
73#936C2×D314yes—
74D4×Dic3—34no—
75D4×Dic3—62no—
76C2×#214C2×D314yes—
77C2×Dic12C2×D312yes—
78#879—64no—
79#879—64no—
80#878—64no—
81#877—64no—
82C4×Dic6—32no—
83C4×Dic6—34no—
84C3×C4×C8—32no—
85#835—34no—
86#832—34no—
87#832—62no—
88#818—32no—
89#818—61no—
90#816—34no—
91Dic3⋊C8—32no—
92Dic3⋊C8—32no—
93C8×Dic3—32no—
94C8×Dic3—61no—
95C8×Dic3C2×D312yes—
96C4⋊(C3⋊C8)—32no—
97C23×C32—22no—
98C32×D4—22no—
99C32×D4—22no—
100C2×C32×C4C2411yescharacteristic
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—44no—
103C2×C3⋊Dic3C2×D411yescharacteristic
104C2×C3⋊Dic3C2×D411yescharacteristic
105C2×C3×Dic3—24no—
106C2×C3×Dic3C2×D412yes—
107C2×C3×Dic3C2×D412yes—
108C3×Dic6—24no—
109C3×Dic6—24no—
110#627—22no—
111C32×C8#4112yes—
112C3⋊(C3⋊C8)—21no—
113C3×C3⋊C8—22no—
114#556—92no—
115#495—32no—
116#494—91no—
117#464—94no—
118#461—92no—
119C8×Q8—91no—
120C4×Q16—92no—
121C4×D8—91no—
122C2×C3×Q8—34no—
123C2×C3×D4—22no—
124C2×C3×D4C22×D314yes—
125C22×Dic3—64no—
126C22×Dic3—122no—
127C2×Dic6—32no—
128C2×Dic6C22×D314yes—
129C3×Q16—64no—
130C3×SD16—124no—
131C3×D8—24no—
132C3×D8—24no—
133C2×C3×C8—21no—
134C2×C3×C8—32no—
135C2×C3×C8C22×D312yes—
136C3×C22⋊C4—64no—
137C3×C22⋊C4—64no—
138C3×C42—32no—
139#217—24no—
140#217—24no—
141#217—64no—
142#217—122no—
143#216—124no—
144#214—44no—
145C4⋊Dic3—32no—
146C4⋊Dic3—34no—
147C4⋊Dic3—62no—
148C4⋊Dic3—64no—
149Dic3⋊C4—32no—
150Dic3⋊C4—32no—
151Dic3⋊C4—64no—
152Dic3⋊C4—64no—
153Dic3⋊C4—64no—
154C4×Dic3—32no—
155C4×Dic3—61no—
156C4×Dic3—64no—
157C4×Dic3—64no—
158C4×Dic3C22×D312yes—
159C2×C3⋊C8—32no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8C22×D312yes—
162Dic12—24no—
163C22×C32—42no—
164C22×C32—42no—
165C22×C32—42no—
166C22×C32C22×D411yescharacteristic
167C32×C4C2×#4111yescharacteristic
168C32×C4H(5,𝔽2)11yescharacteristic
169C3⋊Dic3—21no—
170C3⋊Dic3—42no—
171C3⋊Dic3#13512yes—
172C3×Dic3—22no—
173C3×Dic3—22no—
174C3×Dic3—44no—
175C2×Q16—32no—
176C2×Q16—92no—
177C2×SD16—34no—
178C2×D8D3211yescharacteristic
179C4⋊Q8—92no—
180#126—184no—
181#124—34no—
182C22⋊Q8—182no—
183C4×Q8—91no—
184C4×Q8—94no—
185C4×D4—92no—
186#117—182no—
187#107—91no—
188C4⋊C8—92no—
189C4⋊C8—91no—
190#103—94no—
191#102—92no—
192C4×C8—32no—
193C4×C8—91no—
194C23×C3—24no—
195C23×C3—42no—
196C3×Q8—64no—
197C3×Q8—64no—
198C3×D4—24no—
199C3×D4—24no—
200C3×D4—24no—
201C3×D4—42no—
202C2×C3×C4—21no—
203C2×C3×C4—32no—
204C2×C3×C4—32no—
205C2×C3×C4—64no—
206C2×C3×C4C23×D312yes—
207C2×Dic3—24no—
208C2×Dic3—32no—
209C2×Dic3—32no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—64no—
213C2×Dic3—122no—
214C2×Dic3—128no—
215C2×Dic3—244no—
216C2×Dic3D3×D412yes—
217C2×Dic3D3×D412yes—
218Dic6—24no—
219Dic6—24no—
220Dic6—64no—
221C3×C8—22no—
222C3×C8—62no—
223C3×C8#23714yes—
224C3⋊C8—22no—
225C3⋊C8—62no—
226C3⋊C8—121no—
227C2×C32—82no—
228C2×C32#55011yescharacteristic
229C2×C32C2×#13511yescharacteristic
230C2×C32#57811yescharacteristic
231C2×Q8—34no—
232C2×Q8—91no—
233C2×D4C2×D3212yes—
234C22×C4—182no—
235Q16—64no—
236Q16—362no—
237SD16—124no—
238D8—22no—
239C2×C8—32no—
240C2×C8—91no—
241C2×C8C2×D3211yescharacteristic
242C4⋊C4—91no—
243C4⋊C4—92no—
244C4⋊C4—92no—
245C4⋊C4—184no—
246C4⋊C4—182no—
247C4⋊C4—182no—
248C22⋊C4—64no—
249C22⋊C4—64no—
250C22⋊C4—182no—
251C42—32no—
252C42—91no—
253C42—184no—
254C22×C3—21no—
255C22×C3—44no—
256C22×C3—44no—
257C22×C3—44no—
258C22×C3—44no—
259C22×C3—82no—
260C22×C3—82no—
261C22×C3C2×D3×D412yes—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—62no—
265C3×C4—62no—
266C3×C4—124no—
267C3×C4C2×#23712yes—
268C3×C4#100412yes—
269Dic3—22no—
270Dic3—22no—
271Dic3—34no—
272Dic3—44no—
273Dic3—62no—
274Dic3—62no—
275Dic3—121no—
276Dic3—124no—
277Dic3—242no—
278C32#339311yescharacteristic, complemented, Sylow
279C23—22no—
280Q8—64no—
281Q8—64no—
282Q8—182no—
283D4—22no—
284D4—22no—
285C2×C4—32no—
286C2×C4—32no—
287C2×C4—64no—
288C2×C4—91no—
289C2×C4—91no—
290C2×C4—182no—
291C2×C4—364no—
292C2×C4C22×D3211yescharacteristic
293C8—62no—
294C8—181no—
295C8#380512yes—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—84no—
300C2×C3—84no—
301C2×C3#571812yes—
302C2×C3D3×#13512yes—
303C2×C3#577112yes—
304C22—42no—
305C22—42no—
306C22—42no—
307C22D32×D411yescharacteristic
308C4—62no—
309C4—62no—
310C4—92no—
311C4—124no—
312C4—181no—
313C4—362no—
314C4#6431311yescharacteristic
315C4C2×#380511yescharacteristic
316C3—21no—
317C3#8181312yescomplemented
318C2—82no—
319C2#1059473011yescharacteristic
320C2#1059473711yescharacteristic
321C2#1059514411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595119C2semidirect
4. #10591497C2semidirect
5. #10591442C2semidirect
6. #10590905C2semidirect
7. Dic3×Dic12C2semidirect
8. C8×#627C2semidirect
278. C32#3393semidirect
317. C3#81813semidirect

Maximal subgroups

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

subgroupindex
#105951192
D8×C3⋊Dic32
C3×#51552
#105914972
#105914422
#105909052
Dic3×Dic122
C8×#6272
#818133