Finite Group Databasebeta

← #11786615

Subgroups — #11786615

Order 1152.

637 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 637 conjugacy classes of subgroups — too many to draw. Only its 130 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#10594828C211yesmaximal, characteristic
2#10592672C211yesmaximal, characteristic
3C3×#4964C212yesmaximal
4C2×#63561C211yesmaximal, characteristic
5#10589160C212yesmaximal
6#70677—32nomaximal
7C22×#634C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C3×#926C2212yes—
11C2×C3×#208C2212yes—
12#63957—22no—
13#63844—22no—
14#63844—22no—
15#63658—22no—
16C3×#808—22no—
17C3×#807—22no—
18#63561C414yescomplemented
19#5516—32no—
20C3×#428—32no—
21C2×#824—32no—
22#4973—32no—
23#4973—61no—
24#4964D312yes—
25#4555—32no—
26#4532—32no—
27C22×C32×C4—21no—
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3D412yes—
31C2×#634—22no—
32C2×#634—22no—
33C2×#634C2×C412yes—
34C2×#634Q812yes—
35C32×C4⋊C4—22no—
36C4×C3⋊Dic3—22no—
37C3×#217—22no—
38C3×C4⋊Dic3D412yes—
39C3×C4⋊Dic3D412yes—
40C3×C4×Dic3—22no—
41C3×#208—22no—
42C3×#208C2×C414yes—
43C2×C3×C3⋊C8—22no—
44#3724—22no—
45#3724—22no—
46Dic32—24no—
47#1857—91noSylow
48C22×Dic6—32no—
49C22×Dic6—61no—
50C2×C3×M16—32no—
51C3×#117—32no—
52C2×C3×C4⋊C4—21no—
53C2×C3×C4⋊C4C2×D312yes—
54#926C2×D312yes—
55C2×C4×Dic3—32no—
56C2×C4×Dic3—61no—
57C2×#208C2×D312yes—
58#887—62no—
59#887—62no—
60#877—64no—
61C4×Dic6—62no—
62C4×Dic6—62no—
63C3×#107—62no—
64C3×#106—62no—
65C3⋊#95—64no—
66C3⋊#95—64no—
67#824—38no—
68#808—22no—
69#807—22no—
70C23×C32C2×D411yescharacteristic
71C2×C32×C4—42no—
72C2×C32×C4—41no—
73C2×C32×C4C22×C411yescharacteristic
74C2×C32×C4C2×D412yes—
75C2×C32×C4C2×Q811yescharacteristic
76C2×C32×C4#4112yes—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3C4⋊C414yes—
83#634—24no—
84#634—24no—
85C2×C3×Dic3—22no—
86C2×C3×Dic3—22no—
87C3×C3⋊C8—24no—
88#519—91no—
89#428—32no—
90C2×#101—91no—
91#391—91no—
92#339—92no—
93C22×C3×C4—22no—
94C22×C3×C4—22no—
95C22×C3×C4—21no—
96C22×C3×C4C22×D312yes—
97C22×Dic3—34no—
98C22×Dic3—62no—
99C22×Dic3—62no—
100C22×Dic3—62no—
101C2×Dic6—34no—
102C2×Dic6—34no—
103C2×Dic6—62no—
104C2×Dic6—62no—
105C2×Dic6—62no—
106C2×Dic6—62no—
107C2×Dic6—62no—
108C2×Dic6—62no—
109C2×Dic6—122no—
110C2×Dic6—122no—
111C3×M16—34no—
112C3×M16—62no—
113C2×C3×C8—62no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4—32no—
117C3×C4⋊C4—32no—
118C3×C4⋊C4—42no—
119C3×C22⋊C4—62no—
120C3×C42—62no—
121#217—22no—
122C4⋊Dic3#6712yes—
123C4⋊Dic3#6712yes—
124Dic3⋊C4—64no—
125Dic3⋊C4—64no—
126C4×Dic3—22no—
127C4×Dic3—64no—
128C4×Dic3—64no—
129C4×Dic3—62no—
130C4×Dic3—62no—
131C4×Dic3—122no—
132#208—22no—
133#208C4×D314yes—
134C2×C3⋊C8—22no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32C2×C4⋊C411yescharacteristic
138C22×C32#12011yescharacteristic
139C22×C32#12311yescharacteristic
140C32×C4—81no—
141C32×C4C4×D412yes—
142C32×C4C22⋊Q812yes—
143C3⋊Dic3—24no—
144C3⋊Dic3—42no—
145C3×Dic3—42no—
146C3×Dic3—42no—
147C22×Q8—91no—
148C2×M16—32no—
149C4×Q8—182no—
150C4×Q8—182no—
151#117—32no—
152#117—182no—
153C2×C4⋊C4D3211yescharacteristic
154C2×C42—91no—
155#107—62no—
156#106—62no—
157#101—94no—
158#95—182no—
159C23×C3—21no—
160C23×C3D3×D412yes—
161C2×C3×C4—21no—
162C2×C3×C4—22no—
163C2×C3×C4—21no—
164C2×C3×C4—22no—
165C2×C3×C4—42no—
166C2×C3×C4—44no—
167C2×C3×C4—44no—
168C2×C3×C4—42no—
169C2×C3×C4—62no—
170C2×C3×C4—62no—
171C2×C3×C4C2×C4×D312yes—
172C2×C3×C4#23512yes—
173C2×C3×C4D3×D412yes—
174C2×C3×C4D3×Q812yes—
175C2×C3×C4#23912yes—
176C2×C3×C4C2×#6712yes—
177C2×Dic3—22no—
178C2×Dic3—22no—
179C2×Dic3—38no—
180C2×Dic3—64no—
181C2×Dic3—64no—
182C2×Dic3—64no—
183C2×Dic3—64no—
184C2×Dic3—64no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187C2×Dic3—122no—
188C2×Dic3—122no—
189C2×Dic3—122no—
190C2×Dic3—122no—
191Dic6—64no—
192Dic6—64no—
193Dic6—64no—
194Dic6—64no—
195Dic6—124no—
196Dic6—124no—
197C3×C8—64no—
198C3⋊C8—24no—
199C2×C32—21no—
200C2×C32—21no—
201C2×C32#38511yescharacteristic
202C2×C32#45411yescharacteristic
203C2×C32#45611yescharacteristic
204C2×Q8—92no—
205C2×Q8—92no—
206C2×Q8—182no—
207C2×Q8—182no—
208C22×C4—21no—
209C22×C4—92no—
210C22×C4—181no—
211C22×C4C2×D3211yescharacteristic
212M16—34no—
213M16—62no—
214C2×C8—62no—
215C4⋊C4—22no—
216C4⋊C4—32no—
217C4⋊C4—32no—
218C4⋊C4—182no—
219C4⋊C4—182no—
220C22⋊C4—62no—
221C42—62no—
222C42—184no—
223C42—182no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3D3×C4⋊C412yes—
232C22×C3#89412yes—
233C22×C3#93712yes—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—82no—
237C3×C4—82no—
238C3×C4—122no—
239C3×C4—122no—
240C3×C4#89312yes—
241C3×C4#89612yes—
242C3×C4C4×#6712yes—
243C3×C4#94612yes—
244Dic3—42no—
245Dic3—42no—
246Dic3—68no—
247Dic3—124no—
248Dic3—124no—
249Dic3—124no—
250C32#185711yescharacteristic, complemented, Sylow
251C23#381111yescharacteristic
252Q8—184no—
253Q8—184no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—62no—
257C2×C4—62no—
258C2×C4—94no—
259C2×C4—182no—
260C2×C4—182no—
261C2×C4—182no—
262C2×C4—361no—
263C2×C4—361no—
264C2×C4#379711yescharacteristic
265C2×C4#379912yes—
266C2×C4C4×D3211yescharacteristic
267C2×C4D3×#6712yes—
268C8—64no—
269C2×C3—22no—
270C2×C3—22no—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3#498912yes—
277C2×C3#520112yes—
278C2×C3#520512yes—
279C22—21no—
280C22—21no—
281C22#6388311yescharacteristic
282C22#6389711yescharacteristic
283C22#6398311yescharacteristic
284C4—81no—
285C4—122no—
286C4—122no—
287C4—184no—
288C4—362no—
289C4#6388812yes—
290C4#6390412yes—
291C3—21no—
292C3#7067712yescomplemented
293C2—21no—
294C2—21no—
295C2#1059137411yescharacteristic
296C2#1059152411yescharacteristic
297C2#1059166011yescharacteristic
subgroupG/H
centerC22#63983
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1857
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
18. #63561C4semidirect
250. C32#1857semidirect
292. C3#70677semidirect

Maximal subgroups

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

subgroupindex
#105948282
#105926722
C3×#49642
C2×#635612
#105891602
#706773