Finite Group Databasebeta

← #11791466

Subgroups — #11791466

Order 1152.

774 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 99 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×#63914C211yesmaximal, characteristic
2C2×C4⋊#622C211yesmaximal, characteristic, complemented
3C2×#63739C214yesmaximal, complemented
4C4×#3724C211yesmaximal, characteristic, complemented
5C22×C3×D12—21no—
6C22×#625—21no—
7C22×#625C2212yes—
8C22×#622C2212yes—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×C3×C4×Dic3—21no—
11C2×#3724C2212yes—
12#63914—22no—
13#63914C414yescomplemented
14C4⋊#622—22no—
15#63739—28no—
16#63579—21no—
17C2×#940—61no—
18C4×Dic3⋊C4—61no—
19C23×C3×D3—22no—
20C22×C32×C4D411yescharacteristic
21C22×C3⋊Dic3D411yescharacteristic
22C22×C3⋊Dic3C2311yescharacteristic
23C22×C3×Dic3—22no—
24C2×C3×D12—24no—
25C2×C3×D12—42no—
26C2×C3×D12—42no—
27C2×#625—24no—
28C2×#625—24no—
29C2×#625—24no—
30C2×#625—22no—
31C2×#625—44no—
32C2×#625C2×C414yes—
33C2×#622—22no—
34C2×#622—24no—
35C4×C3⋊Dic3C2×C412yes—
36C4×C3⋊Dic3D412yes—
37C3×C4×Dic3—42no—
38#3724—22no—
39#3724D414yescomplemented
40#1982—91nomaximal, Sylow
41C22×C3×D4—61no—
42C22×#67—62no—
43C22×#67—62no—
44C22×D12—21no—
45C2×C3×C42—61no—
46#940—64no—
47#940—64no—
48C2×Dic3⋊C4—62no—
49C2×C4×Dic3—21no—
50C2×C4×Dic3—61no—
51C2×C4×Dic3—61no—
52C3⋊#95—62no—
53C23×C32C2×D411yescharacteristic
54C22×C3×D3—24no—
55C22×C3×D3—44no—
56C22×C3×D3—42no—
57C22×C3×D3—42no—
58C22×C3×D3—44no—
59C2×C32×C4C22⋊C412yes—
60C2×C32×C4D812yes—
61C2×C32×C4SD1612yes—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3C22⋊C412yes—
64C2×C3⋊Dic3C22×C411yescharacteristic
65C2×C3⋊Dic3C2×D412yes—
66C2×C3⋊Dic3C2×D411yescharacteristic
67C2×C3⋊Dic3#4112yes—
68C2×C3×Dic3—24no—
69C2×C3×Dic3—42no—
70C2×C3×Dic3—42no—
71C3×D12—48no—
72#625—28no—
73#625—48no—
74#625—42no—
75#625—42no—
76#622—42no—
77C2×#127—91no—
78C2×C4⋊C8—91no—
79C2×#102—94no—
80C4×C4⋊C4—91no—
81C24×C3—62no—
82C23×D3—22no—
83C2×C3×D4—64no—
84C2×C3×D4—122no—
85C2×C3×D4—122no—
86C22×C3×C4—21no—
87C22×C3×C4—21no—
88C22×C3×C4—62no—
89C2×#67—64no—
90C2×#67—68no—
91C2×#67—64no—
92C2×#67—124no—
93C2×#67—124no—
94C2×#67—128no—
95C22×Dic3—22no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C22×Dic3—61no—
99C22×Dic3—61no—
100C2×D12—24no—
101C2×D12—42no—
102C2×D12—42no—
103C3×C42—122no—
104Dic3⋊C4—64no—
105Dic3⋊C4—64no—
106C4×Dic3—42no—
107C4×Dic3—62no—
108C4×Dic3—62no—
109C4×Dic3—62no—
110C4×Dic3—62no—
111C22×C32C2×C22⋊C411yescharacteristic
112C22×C32#12112yes—
113C22×C32C2×D811yescharacteristic
114C22×C32C2×SD1611yescharacteristic
115C22×C32AGL(1,ℤ/8)12yes—
116C2×C3×D3—44no—
117C2×C3×D3—44no—
118C2×C3×D3—44no—
119C2×C3×D3—84no—
120C2×C3×D3—84no—
121C32×C4#10214yescomplemented
122C3⋊Dic3—22no—
123C3⋊Dic3C4×D412yes—
124C3⋊Dic3#12411yescharacteristic
125C3⋊Dic3#12711yescharacteristic
126C3×Dic3—44no—
127C22×D4—61no—
128C22×D4—92no—
129C22×D4—181no—
130C22×C8—92no—
131#127—94no—
132#127—182no—
133C2×C4⋊C4—92no—
134C2×C42—61no—
135C2×C42—91no—
136C4⋊C8—182no—
137#102—188no—
138#95—181no—
139C23×C3—21no—
140C23×C3—21no—
141C23×C3—64no—
142C23×C3—124no—
143C23×C3—124no—
144C23×C3—122no—
145C23×C3—122no—
146C22×D3—24no—
147C22×D3—42no—
148C22×D3—42no—
149C22×D3—44no—
150C22×D3—44no—
151C3×D4—128no—
152C2×C3×C4—22no—
153C2×C3×C4—22no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—22no—
158C2×C3×C4—64no—
159C2×C3×C4—122no—
160C2×C3×C4—122no—
161#67—128no—
162#67—124no—
163#67—124no—
164#67—1216no—
165C2×Dic3—24no—
166C2×Dic3—42no—
167C2×Dic3—42no—
168C2×Dic3—62no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—64no—
179C2×Dic3—122no—
180D12—48no—
181C2×C32#39011yescharacteristic
182C2×C32C2×#10211yescharacteristic
183C2×C32#41811yescharacteristic
184C2×C32#45912yes—
185C2×C32#46012yes—
186C3×D3—84no—
187C24—62no—
188C2×D4—64no—
189C2×D4—94no—
190C2×D4—122no—
191C2×D4—122no—
192C2×D4—184no—
193C2×D4—184no—
194C2×D4—184no—
195C2×D4—182no—
196C2×D4—364no—
197C22×C4—62no—
198C22×C4—91no—
199C22×C4—91no—
200C22×C4GO+(4,𝔽2)11yescharacteristic
201C2×C8—184no—
202C2×C8—182no—
203C4⋊C4—94no—
204C4⋊C4—182no—
205C42—92no—
206C42—92no—
207C42—122no—
208C22×C3—22no—
209C22×C3—22no—
210C22×C3—22no—
211C22×C3—22no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—124no—
219C22×C3—124no—
220C22×C3—124no—
221C22×C3—244no—
222C22×C3—244no—
223C2×D3—44no—
224C2×D3—44no—
225C2×D3—44no—
226C2×D3—84no—
227C2×D3—84no—
228C3×C4—24no—
229C3×C4—24no—
230C3×C4—124no—
231Dic3—44no—
232Dic3—62no—
233Dic3—61no—
234Dic3—61no—
235Dic3—62no—
236Dic3—61no—
237Dic3—61no—
238Dic3—64no—
239Dic3—122no—
240C32#198211yescharacteristic, complemented, Sylow
241C23—64no—
242C23—124no—
243C23—124no—
244C23—122no—
245C23—122no—
246C23C2×GO+(4,𝔽2)11yescharacteristic
247D4—128no—
248D4—188no—
249D4—362no—
250D4—362no—
251D4—368no—
252C2×C4—64no—
253C2×C4—92no—
254C2×C4—92no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—92no—
258C2×C4—122no—
259C2×C4—122no—
260C2×C4—182no—
261C2×C4D32⋊C412yes—
262C2×C4#377412yes—
263C2×C4#377512yes—
264C8—362no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—22no—
270C2×C3—22no—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—244no—
276D3—84no—
277C22—124no—
278C22—124no—
279C22—124no—
280C22—244no—
281C22—244no—
282C22#6422412yes—
283C22#6423012yes—
284C22C2×D32⋊C411yescharacteristic
285C22C2×#377411yescharacteristic
286C22C2×#377511yescharacteristic
287C4—91no—
288C4—92no—
289C4—91no—
290C4—124no—
291C4—182no—
292C4#6373914yescomplemented
293C3—21no—
294C3—21no—
295C2—244no—
296C2#1059336311yescharacteristic
297C2#1059340511yescharacteristic
298C2#1059341712yes—
299C2#1059343912yes—
300C2C2×#6373911yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC2×#63914C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1982
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#622C2semidirect
3. C2×#63739C2semidirect
4. C4×#3724C2semidirect
13. #63914C4semidirect
39. #3724D4semidirect
121. C32×C4#102semidirect
240. C32#1982semidirect
292. C4#63739semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
C2×C4⋊#6222
C2×#637392
C4×#37242
#19829