Finite Group Databasebeta

← #11775566

Subgroups — #11775566

Order 1152.

1020 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1020 conjugacy classes of subgroups — too many to draw. Only its 229 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×#64139C211yesmaximal, characteristic
2C32×#380C211yesmaximal, characteristic, complemented
3C2×#63657C211yesmaximal, characteristic, complemented
4#10589317C214yesmaximal, complemented
5#69509—34nomaximal
6C23×C32×C4C2211yescharacteristic
7C22×#638—21no—
8C22×C4⋊(C3⋊D3)C411yescharacteristic, complemented
9C2×C32×C4⋊C4—21no—
10C2×C32×C22⋊C4—21no—
11#64139—21no—
12#64139—21no—
13#64139C412yescomplemented
14#64139C2212yes—
15C2×#3752—21no—
16C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
17C22×C3⋊(C3⋊C8)—21no—
18C32×#95C2212yescomplemented
19#63657—21no—
20#63657C2212yescomplemented
21C2×#930—34no—
22C3×#380D314yescomplemented
23C2×#830—34no—
24#4451—316no—
25C24×C32D411yescharacteristic
26C23×C3⋊D3—21no—
27C22×C32×C4—22no—
28C22×C32×C4—42no—
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C2×#638—22no—
36C2×#638—22no—
37C2×#638—42no—
38C2×#638—42no—
39C22×C3⋊Dic3—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—42no—
42C2×C4⋊(C3⋊D3)C2×C412yes—
43C32×C4⋊C4—42no—
44C32×C22⋊C4—42no—
45#3752—22no—
46#3752—22no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)C2×C412yes—
49C2×C3⋊(C3⋊C8)—22no—
50C2×C3⋊(C3⋊C8)—42no—
51#1519—91noSylow
52C23×C3×C4C2×D314yes—
53C22×#67—64no—
54C22×D12—34no—
55C2×C3×C4⋊C4—24no—
56C2×C3×C22⋊C4—24no—
57#930—38no—
58#930—38no—
59#930—64no—
60#930—64no—
61C2×(C2×D3)⋊C4—64no—
62C2×C4⋊Dic3—34no—
63C22×C3⋊C8—64no—
64C3×#95C2×D318yescomplemented
65#830—38no—
66#830—64no—
67C23×C32—41no—
68C23×C32—41no—
69C23×C32C22⋊C411yescharacteristic
70C23×C32C22⋊C411yescharacteristic
71C23×C32D812yes—
72C23×C32SD1612yes—
73C23×C32C2×D411yescharacteristic
74C22×C3⋊D3—22no—
75C22×C3⋊D3—42no—
76C22×C3⋊D3—42no—
77C22×C3⋊D3—42no—
78C2×C32×C4—22no—
79C2×C32×C4—22no—
80C2×C32×C4—22no—
81C2×C32×C4—41no—
82C2×C32×C4—41no—
83C2×C32×C4—41no—
84C2×C32×C4—42no—
85C2×C32×C4—42no—
86C2×C32×C4—42no—
87C2×C32×C4C22⋊C411yescharacteristic
88C2×C32×C4C22⋊C411yescharacteristic
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91#638—44no—
92#638—42no—
93#638—42no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—42no—
96C4⋊(C3⋊D3)—42no—
97C4⋊(C3⋊D3)—42no—
98C3⋊(C3⋊C8)—42no—
99C2×#121—91no—
100C2×C22⋊C8—91no—
101#380C3⋊D311yescharacteristic, complemented
102#327—94no—
103C24×C3#6714yes—
104C23×D3—64no—
105C22×C3×C4—28no—
106C22×C3×C4—48no—
107C22×C3×C4C4×D314yes—
108C22×C3×C4C4×D314yes—
109C22×C3×C4D1214yes—
110C22×C3×C4D1214yes—
111C22×C3×C4#6714yes—
112C22×C3×C4C22×D314yes—
113C2×#67—68no—
114C2×#67—68no—
115C2×#67—128no—
116C2×#67—128no—
117C22×Dic3—64no—
118C2×D12—38no—
119C2×D12—64no—
120C2×D12—128no—
121C3×C4⋊C4—48no—
122C3×C22⋊C4—48no—
123(C2×D3)⋊C4—68no—
124(C2×D3)⋊C4—68no—
125C4⋊Dic3—38no—
126C4⋊Dic3—64no—
127C2×C3⋊C8—68no—
128C2×C3⋊C8—128no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—42no—
136C22×C32—42no—
137C22×C32#10212yes—
138C22×C32#10212yes—
139C22×C32C2×C22⋊C411yescharacteristic
140C22×C32C2×D811yescharacteristic
141C22×C32C2×SD1611yescharacteristic
142C2×C3⋊D3—42no—
143C2×C3⋊D3—42no—
144C2×C3⋊D3—42no—
145C2×C3⋊D3—84no—
146C32×C4—21no—
147C32×C4—21no—
148C32×C4—21no—
149C32×C4—82no—
150C32×C4#9912yes—
151C3⋊Dic3—42no—
152C22×D4—91no—
153C22×D4—181no—
154C23×C4C2×C3⋊D311yescharacteristic
155C22×C8—181no—
156#121—92no—
157#121—92no—
158#121—181no—
159#121—181no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—91no—
162C2×C22⋊C4—21no—
163C2×C22⋊C4—181no—
164C22⋊C8—92no—
165C22⋊C8—181no—
166#95C2×C3⋊D312yescomplemented
167C23×C3—44no—
168C23×C3—44no—
169C23×C3(C2×D3)⋊C414yes—
170C23×C3(C2×D3)⋊C414yes—
171C23×C3#21318yes—
172C23×C3#21518yes—
173C23×C3C2×#6714yes—
174C22×D3—68no—
175C22×D3—128no—
176C22×D3—128no—
177C22×D3—128no—
178C2×C3×C4—28no—
179C2×C3×C4—28no—
180C2×C3×C4—28no—
181C2×C3×C4—44no—
182C2×C3×C4—44no—
183C2×C3×C4—44no—
184C2×C3×C4—48no—
185C2×C3×C4—48no—
186C2×C3×C4—48no—
187C2×C3×C4(C2×D3)⋊C414yes—
188C2×C3×C4(C2×D3)⋊C414yes—
189C2×C3×C4C2×C4×D314yes—
190C2×C3×C4C2×D1214yes—
191#67—1216no—
192#67—128no—
193#67—128no—
194C2×Dic3—68no—
195C2×Dic3—128no—
196D12—128no—
197D12—128no—
198C3⋊C8—128no—
199C2×C32—21no—
200C2×C32—22no—
201C2×C32—22no—
202C2×C32—21no—
203C2×C32C2×#9911yescharacteristic
204C2×C32C2×#10211yescharacteristic
205C2×C32#42111yescharacteristic
206C3⋊D3—82no—
207C24—181no—
208C24#63811yescharacteristic
209C2×D4—92no—
210C2×D4—182no—
211C2×D4—182no—
212C2×D4—181no—
213C2×D4—362no—
214C2×D4—362no—
215C2×D4—362no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—181no—
219C22×C4C4×C3⋊D311yescharacteristic
220C22×C4C4×C3⋊D311yescharacteristic
221C22×C4C4⋊(C3⋊D3)11yescharacteristic
222C22×C4C4⋊(C3⋊D3)11yescharacteristic
223C22×C4#63811yescharacteristic
224C22×C4C22×C3⋊D311yescharacteristic
225C2×C8—182no—
226C2×C8—362no—
227C4⋊C4—42no—
228C4⋊C4—92no—
229C4⋊C4—181no—
230C22⋊C4—42no—
231C22⋊C4—182no—
232C22⋊C4—182no—
233C22×C3—24no—
234C22×C3—24no—
235C22×C3—24no—
236C22×C3—24no—
237C22×C3—24no—
238C22×C3—24no—
239C22×C3—48no—
240C22×C3—48no—
241C22×C3#80918yes—
242C22×C3#80918yes—
243C22×C3C2×(C2×D3)⋊C414yes—
244C22×C3C2×#21314yes—
245C22×C3C2×#21514yes—
246C2×D3—128no—
247C2×D3—128no—
248C2×D3—128no—
249C2×D3—2416no—
250C3×C4—24no—
251C3×C4—24no—
252C3×C4—24no—
253C3×C4—88no—
254C3×C4#80618yes—
255Dic3—128no—
256C32#151911yescharacteristic, complemented, Sylow
257C23—41no—
258C23—41no—
259C23—182no—
260C23—362no—
261C23—362no—
262C23—362no—
263C23#375211yescharacteristic
264C23#375211yescharacteristic
265C23#375312yes—
266C23#375512yes—
267C23C2×#63811yescharacteristic
268D4—362no—
269D4—362no—
270D4—364no—
271D4—362no—
272D4—362no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—182no—
283C2×C4—362no—
284C2×C4#375211yescharacteristic
285C2×C4#375211yescharacteristic
286C2×C4C2×C4×C3⋊D311yescharacteristic
287C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
288C8—362no—
289C2×C3—24no—
290C2×C3—28no—
291C2×C3—28no—
292C2×C3—24no—
293C2×C3C2×#80614yes—
294C2×C3C2×#80914yes—
295C2×C3#500514yes—
296D3—248no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—42no—
304C22—42no—
305C22—362no—
306C22—362no—
307C22—362no—
308C22—724no—
309C22#6363612yes—
310C22#6363612yes—
311C22C2×#375211yescharacteristic
312C22C2×#375311yescharacteristic
313C22C2×#375511yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—82no—
318C4—362no—
319C4#6363312yes—
320C3#6950914yescomplemented
321C2—21no—
322C2—22no—
323C2—22no—
324C2—21no—
325C2—722no—
326C2C2×#6363311yescharacteristic
327C2C2×#6363611yescharacteristic
328C2#1059270411yescharacteristic
subgroupG/H
centerC22C2×#3752
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#380C2
socleC22×C32C2×C22⋊C4
prime radicalC2×#64139C2
cosocleC22×C32×C4C23
hypercenter#380C3⋊D3
hypocenterC32#1519
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C32×#380C2semidirect
3. C2×#63657C2semidirect
4. #10589317C2semidirect
8. C22×C4⋊(C3⋊D3)C4semidirect
13. #64139C4semidirect
16. C2×C4⋊(C3⋊Dic3)C4semidirect
18. C32×#95C22semidirect
20. #63657C22semidirect
22. C3×#380D3semidirect
64. C3×#95C2×D3semidirect
101. #380C3⋊D3semidirect
166. #95C2×C3⋊D3semidirect
256. C32#1519semidirect
320. C3#69509semidirect

Maximal subgroups

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

subgroupindex
C2×#641392
C32×#3802
C2×#636572
#105893172
#695093