Finite Group Databasebeta

← #11791877

Subgroups — #11791877

Order 1152.

591 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 591 conjugacy classes of subgroups — too many to draw. Only its 136 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
1C2×#63919C211yesmaximal, characteristic
2M16×C3⋊Dic3C211yesmaximal, characteristic
3#10591120C211yesmaximal, characteristic
4C3×#4554C212yesmaximal
5#10589167C212yesmaximal
6#68974—32nomaximal
7C22×#627C412yes—
8C2×C32×M16C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×#3748C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×#208C2212yes—
13C2×#3724C412yes—
14#63919—21no—
15#63919—21no—
16#63919—21no—
17#63919—21no—
18#63642—21no—
19C8×C3⋊Dic3—21no—
20#63572—21no—
21#63572—21no—
22C2×#888—32no—
23#5118—32no—
24Dic3×M16—32no—
25Dic3×M16—61no—
26C3×#343—32no—
27#4554—32no—
28#4554D312yes—
29#4530—32no—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3×Dic3C2×C414yes—
34C2×#627—22no—
35C2×#627—22no—
36C2×#627—44no—
37C32×M16—21no—
38C32×M16Q812yescomplemented
39C2×C32×C8—21no—
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44#3748—21no—
45#3748Q812yescomplemented
46C2×C3⋊(C3⋊C8)—21no—
47C3×C4⋊Dic3—22no—
48C3×C4⋊Dic3—22no—
49C3×#208—22no—
50C3×#208—22no—
51C2×C3×C3⋊C8—22no—
52#3724—22no—
53#3724—22no—
54#1997—91noSylow
55C22×Dic6—34no—
56C2×C3×M16—21no—
57C2×C3×M16—32no—
58C2×C3×M16C2×D312yes—
59C2×C3×C4⋊C4—32no—
60C2×C4⋊Dic3C2×D312yes—
61C2×Dic3⋊C4—34no—
62C2×C4×Dic3—32no—
63C2×C4×Dic3—61no—
64C2×#208—32no—
65C2×#208—61no—
66C2×#208C2×D312yes—
67#888—62no—
68#888—62no—
69#888—62no—
70#888—62no—
71#815—62no—
72#815—62no—
73Dic3⋊C8—62no—
74Dic3⋊C8—62no—
75C8×Dic3—62no—
76C8×Dic3—62no—
77C23×C32C22×C411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×Q811yescharacteristic
81C2×C32×C4C2×Q811yescharacteristic
82C2×C32×C4#4111yescharacteristic
83C2×C32×C4#4111yescharacteristic
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C22⋊C411yescharacteristic
88C2×C3⋊Dic3C22⋊C411yescharacteristic
89C2×C3⋊Dic3C22⋊C411yescharacteristic
90C2×C3×Dic3—24no—
91C2×C3×Dic3—44no—
92#627—44no—
93#627—44no—
94C32×C8—22no—
95C3⋊(C3⋊C8)—22no—
96C3×C3⋊C8—42no—
97C2×C4⋊Q8—91no—
98#423—91no—
99C4×M16—91no—
100#343—32no—
101#343—92no—
102C22×C3×C4—21no—
103C22×C3×C4—34no—
104C22×C3×C4C22×D312yes—
105C22×Dic3—32no—
106C22×Dic3—32no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C22×Dic3C4×D314yes—
110C2×Dic6—64no—
111C2×Dic6—64no—
112C2×Dic6—128no—
113C3×M16—22no—
114C3×M16—22no—
115C3×M16—22no—
116C3×M16—62no—
117C3×M16—62no—
118C3×M16Dic614yescomplemented
119C2×C3×C8—22no—
120C2×C3×C8—22no—
121C2×C3×C8—62no—
122C3×C4⋊C4—62no—
123C3×C4⋊C4—62no—
124C4⋊Dic3—22no—
125C4⋊Dic3—22no—
126Dic3⋊C4—64no—
127Dic3⋊C4—64no—
128C4×Dic3—32no—
129C4×Dic3—32no—
130C4×Dic3—32no—
131C4×Dic3—32no—
132C4×Dic3—61no—
133C4×Dic3—61no—
134C4×Dic3—61no—
135C4×Dic3—61no—
136#208—22no—
137#208—22no—
138#208—34no—
139#208—62no—
140#208—62no—
141#208—62no—
142C2×C3⋊C8—22no—
143C2×C3⋊C8—62no—
144C2×C3⋊C8—62no—
145C22×C32—21no—
146C22×C32—21no—
147C22×C32C2×C22⋊C411yescharacteristic
148C22×C32C4×Q811yescharacteristic
149C22×C32C4×Q811yescharacteristic
150C32×C4C22⋊Q811yescharacteristic
151C32×C4C22⋊Q811yescharacteristic
152C32×C4#12411yescharacteristic
153C32×C4C4⋊Q811yescharacteristic
154C3⋊Dic3—21no—
155C3⋊Dic3—21no—
156C3⋊Dic3#10012yes—
157C3⋊Dic3#10112yes—
158C3×Dic3—44no—
159C22×Q8—92no—
160C2×M16—32no—
161C2×M16—91no—
162C2×M16D3211yescharacteristic
163C4⋊Q8—181no—
164C4⋊Q8—181no—
165C4⋊Q8—181no—
166C4⋊Q8—181no—
167C2×C4⋊C4—32no—
168C2×C4⋊C4—92no—
169C2×C42—91no—
170C4⋊C8—181no—
171C4⋊C8—181no—
172#97—181no—
173C4×C8—181no—
174C23×C3—21no—
175C23×C3C2×C4×D312yes—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—64no—
183C2×C3×C4—124no—
184C2×C3×C4C2×Dic612yes—
185C2×C3×C4#23512yes—
186C2×C3×C4D3×D412yes—
187C2×C3×C4D3×D412yes—
188C2×C3×C4#23712yes—
189C2×C3×C4D3×Q812yes—
190C2×Dic3—24no—
191C2×Dic3—32no—
192C2×Dic3—32no—
193C2×Dic3—32no—
194C2×Dic3—32no—
195C2×Dic3—44no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—122no—
203C2×Dic3—122no—
204Dic6—128no—
205Dic6—128no—
206C3×C8—24no—
207C3×C8—24no—
208C3×C8—122no—
209C3⋊C8—42no—
210C3⋊C8—64no—
211C3⋊C8—64no—
212C2×C32—21no—
213C2×C32—21no—
214C2×C32#39111yescharacteristic
215C2×C32C2×#10011yescharacteristic
216C2×C32C2×#10111yescharacteristic
217C2×Q8—182no—
218C2×Q8—182no—
219C2×Q8—364no—
220C22×C4—34no—
221C22×C4—91no—
222C22×C4—91no—
223C22×C4C2×D3211yescharacteristic
224M16—21no—
225M16—62no—
226M16—62no—
227M16—92no—
228M16—181no—
229M16#62712yescomplemented
230C2×C8—21no—
231C2×C8—62no—
232C2×C8—181no—
233C4⋊C4—62no—
234C4⋊C4—62no—
235C4⋊C4—182no—
236C4⋊C4—182no—
237C42—91no—
238C42—91no—
239C42—91no—
240C42—91no—
241C22×C3—22no—
242C22×C3—22no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—41no—
247C22×C3—41no—
248C22×C3C4×Dic612yes—
249C22×C3D3×C22⋊C412yes—
250C22×C3#88712yes—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—124no—
256C3×C4#87812yes—
257C3×C4#88512yes—
258C3×C4#88812yes—
259C3×C4#89612yes—
260Dic3—34no—
261Dic3—34no—
262Dic3—44no—
263Dic3—62no—
264Dic3—62no—
265Dic3—62no—
266Dic3—62no—
267Dic3—121no—
268Dic3—121no—
269C32#199711yescharacteristic, complemented, Sylow
270C23C4×D3211yescharacteristic
271Q8—364no—
272Q8—364no—
273C2×C4—64no—
274C2×C4—91no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—124no—
279C2×C4—182no—
280C2×C4—182no—
281C2×C4#379711yescharacteristic
282C2×C4#379811yescharacteristic
283C2×C4#380211yescharacteristic
284C2×C4#380511yescharacteristic
285C2×C4C2×#62711yescharacteristic
286C2×C4#381111yescharacteristic
287C8—22no—
288C8—122no—
289C8—182no—
290C2×C3—22no—
291C2×C3—22no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—41no—
296C2×C3—41no—
297C2×C3#464612yes—
298C2×C3D3×#10012yes—
299C2×C3D3×#10112yes—
300C22—21no—
301C22—21no—
302C22#6383811yescharacteristic
303C22C4×#62711yescharacteristic
304C22#6392111yescharacteristic
305C4—92no—
306C4—92no—
307C4—124no—
308C4—181no—
309C4—181no—
310C4#6386511yescharacteristic
311C4#6391511yescharacteristic
312C4#6391911yescharacteristic
313C4#6398211yescharacteristic
314C3—21no—
315C3#6897412yescomplemented
316C2—21no—
317C2—21no—
318C2#1059100111yescharacteristic
319C2#1059100311yescharacteristic
320C2#1059139611yescharacteristic
subgroupG/H
centerC22#63921
commutator, prime radicalC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1997
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
38. C32×M16Q8semidirect
45. #3748Q8semidirect
118. C3×M16Dic6semidirect
229. M16#627semidirect
269. C32#1997semidirect
315. C3#68974semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
M16×C3⋊Dic32
#105911202
C3×#45542
#105891672
#689743