Finite Group Databasebeta

← #11773982

Subgroups — #11773982

Order 1152.

840 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 181 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×#64138C211yesmaximal, characteristic
2C2×C32×C22⋊C8C211yesmaximal, characteristic, complemented
3#10592906C211yesmaximal, characteristic, complemented
4#10589335C212yesmaximal, complemented
5#10589334C212yesmaximal, complemented
6#69920—34nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×#638C411yescharacteristic
9C22×C32×C8—21no—
10C2×#3757C411yescharacteristic
11#64138—21no—
12#64138—21no—
13#64138—21no—
14#64138—21no—
15C2×#3752C411yescharacteristic
16C2×#3752C2211yescharacteristic
17C2×#3750C411yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×#3748—21no—
20C32×C22⋊C8—21no—
21C32×C22⋊C8C2212yes—
22#63657—21no—
23#63657C2212yes—
24C2×#929—34no—
25C2×C3×C22⋊C8D314yescomplemented
26#5207—34no—
27#4469—38no—
28#4468—38no—
29C24×C32C2×C411yescharacteristic
30C23×C3⋊D3C2×C411yescharacteristic
31C22×C32×C4—42no—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C2×#638—21no—
39C2×#638—21no—
40C2×#638—42no—
41C22×C3⋊Dic3C2×C411yescharacteristic
42C22×C3⋊Dic3C2×C411yescharacteristic
43C22×C3⋊Dic3C2×C411yescharacteristic
44C2×C32×C8—22no—
45C2×C32×C8—42no—
46#3757—21no—
47#3757—21no—
48#3752—21no—
49#3752—21no—
50#3752—21no—
51#3752—21no—
52#3750—21no—
53#3750—21no—
54#3750—21no—
55#3750—21no—
56#3748—42no—
57C2×C3⋊(C3⋊C8)—22no—
58#1468—91noSylow
59C23×C3×C4C2×D314yes—
60C22×#67—34no—
61C22×C3×C8—24no—
62C2×#217—34no—
63#929—64no—
64#929—64no—
65#929—64no—
66#929—64no—
67C2×(C2×D3)⋊C4—34no—
68C2×(C2×D3)⋊C4—34no—
69C2×Dic3⋊C4—34no—
70C2×Dic3⋊C4—34no—
71C2×#208—64no—
72C3×C22⋊C8—24no—
73C3×C22⋊C8C2×D318yes—
74#830—38no—
75#830—64no—
76C23×C32—22no—
77C23×C32—22no—
78C23×C32—41no—
79C23×C32C22⋊C411yescharacteristic
80C23×C32C22⋊C411yescharacteristic
81C23×C32C22×C411yescharacteristic
82C22×C3⋊D3—21no—
83C22×C3⋊D3—22no—
84C22×C3⋊D3—41no—
85C22×C3⋊D3—41no—
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96#638—42no—
97#638—42no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C32×C8—42no—
105C3⋊(C3⋊C8)—42no—
106C2×#123—91no—
107#407—91no—
108C2×C22⋊C8C3⋊D311yescharacteristic, complemented
109#324—92no—
110#323—92no—
111C24×C3C4×D314yes—
112C23×D3—34no—
113C22×C3×C4—48no—
114C22×C3×C4C4×D314yes—
115C22×C3×C4D1214yes—
116C22×C3×C4D1214yes—
117C22×C3×C4#6714yes—
118C22×C3×C4#6714yes—
119C22×C3×C4C22×D314yes—
120C2×#67—64no—
121C2×#67—64no—
122C2×#67—128no—
123C22×Dic3—34no—
124C22×Dic3—34no—
125C22×Dic3—34no—
126C2×C3×C8—28no—
127C2×C3×C8—48no—
128#217—64no—
129#217—64no—
130(C2×D3)⋊C4—64no—
131(C2×D3)⋊C4—64no—
132(C2×D3)⋊C4—64no—
133(C2×D3)⋊C4—64no—
134Dic3⋊C4—64no—
135Dic3⋊C4—64no—
136Dic3⋊C4—64no—
137Dic3⋊C4—64no—
138#208—128no—
139C2×C3⋊C8—68no—
140C22×C32—21no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32—21no—
146C22×C32—21no—
147C22×C32—44no—
148C22×C32#9912yes—
149C22×C32C2×C22⋊C411yescharacteristic
150C22×C32#13112yes—
151C2×C3⋊D3—41no—
152C2×C3⋊D3—41no—
153C2×C3⋊D3—41no—
154C2×C3⋊D3—82no—
155C32×C4—21no—
156C32×C4—21no—
157C32×C4—21no—
158C32×C4—21no—
159C3⋊Dic3—41no—
160C3⋊Dic3—41no—
161C3⋊Dic3—41no—
162C22×D4—91no—
163C23×C4C2×C3⋊D311yescharacteristic
164C2×M16—181no—
165C22×C8—21no—
166#123—181no—
167#123—181no—
168#123—181no—
169#123—181no—
170C2×C4⋊C4—91no—
171C2×C4⋊C4—91no—
172C2×C22⋊C4—91no—
173C2×C22⋊C4—91no—
174C2×C22⋊C4—91no—
175C22⋊C8—21no—
176C22⋊C8—92no—
177C22⋊C8—181no—
178C22⋊C8C2×C3⋊D312yes—
179C23×C3—28no—
180C23×C3—28no—
181C23×C3—44no—
182C23×C3(C2×D3)⋊C414yes—
183C23×C3(C2×D3)⋊C414yes—
184C23×C3C2×C4×D314yes—
185C22×D3—64no—
186C22×D3—68no—
187C22×D3—124no—
188C22×D3—124no—
189C2×C3×C4—28no—
190C2×C3×C4—28no—
191C2×C3×C4—44no—
192C2×C3×C4—44no—
193C2×C3×C4—44no—
194C2×C3×C4—44no—
195C2×C3×C4(C2×D3)⋊C414yes—
196C2×C3×C4(C2×D3)⋊C414yes—
197C2×C3×C4C2×D1214yes—
198C2×C3×C4C2×#6714yes—
199#67—128no—
200#67—128no—
201C2×Dic3—68no—
202C2×Dic3—64no—
203C2×Dic3—64no—
204C2×Dic3—64no—
205C2×Dic3—124no—
206C2×Dic3—124no—
207C3×C8—48no—
208C3⋊C8—128no—
209C2×C32—22no—
210C2×C32—22no—
211C2×C32—41no—
212C2×C32#40811yescharacteristic
213C2×C32C2×#9911yescharacteristic
214C2×C32#41311yescharacteristic
215C3⋊D3—81no—
216C24—91no—
217C24C4×C3⋊D311yescharacteristic
218C2×D4—181no—
219C2×D4—181no—
220C2×D4—362no—
221C22×C4—42no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4—91no—
225C22×C4C4×C3⋊D311yescharacteristic
226C22×C4C4⋊(C3⋊D3)11yescharacteristic
227C22×C4C4⋊(C3⋊D3)11yescharacteristic
228C22×C4#63811yescharacteristic
229C22×C4#63811yescharacteristic
230C22×C4C22×C3⋊D311yescharacteristic
231M16—362no—
232C2×C8—22no—
233C2×C8—42no—
234C2×C8—182no—
235C4⋊C4—181no—
236C4⋊C4—181no—
237C4⋊C4—181no—
238C4⋊C4—181no—
239C22⋊C4—181no—
240C22⋊C4—181no—
241C22⋊C4—181no—
242C22⋊C4—181no—
243C22⋊C4—181no—
244C22⋊C4—181no—
245C22×C3—24no—
246C22×C3—24no—
247C22×C3—24no—
248C22×C3—24no—
249C22×C3—24no—
250C22×C3—24no—
251C22×C3—24no—
252C22×C3—416no—
253C22×C3#80618yes—
254C22×C3#90118yes—
255C22×C3C2×(C2×D3)⋊C414yes—
256C2×D3—124no—
257C2×D3—124no—
258C2×D3—124no—
259C2×D3—248no—
260C3×C4—24no—
261C3×C4—24no—
262C3×C4—24no—
263C3×C4—24no—
264Dic3—124no—
265Dic3—124no—
266Dic3—124no—
267C32#146811yescharacteristic, complemented, Sylow
268C23—22no—
269C23—22no—
270C23—41no—
271C23—181no—
272C23—182no—
273C23—361no—
274C23—361no—
275C23#375211yescharacteristic
276C23#375211yescharacteristic
277C23C2×C4×C3⋊D311yescharacteristic
278D4—362no—
279D4—362no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—182no—
287C2×C4—181no—
288C2×C4—181no—
289C2×C4—181no—
290C2×C4—361no—
291C2×C4—361no—
292C2×C4#375211yescharacteristic
293C2×C4#375211yescharacteristic
294C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
295C2×C4C2×#63811yescharacteristic
296C8—42no—
297C8—362no—
298C2×C3—28no—
299C2×C3—28no—
300C2×C3—44no—
301C2×C3C2×#80614yes—
302C2×C3#511014yes—
303C2×C3#513214yes—
304D3—244no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—44no—
313C22—361no—
314C22—361no—
315C22—361no—
316C22—722no—
317C22#6363312yes—
318C22#6411012yes—
319C22C2×#375211yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—361no—
325C4—361no—
326C4—361no—
327C3#6992014yescomplemented
328C2—22no—
329C2—22no—
330C2—41no—
331C2—721no—
332C2C2×#6363311yescharacteristic
333C2#1059280911yescharacteristic
334C2#1059283111yescharacteristic
subgroupG/H
centerC22C2×#3752
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×C22⋊C8C2
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C4
cosocleC22×C32×C4C23
hypercenterC2×C22⋊C8C3⋊D3
hypocenterC32#1468
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C32×C22⋊C8C2semidirect
3. #10592906C2semidirect
4. #10589335C2semidirect
5. #10589334C2semidirect
25. C2×C3×C22⋊C8D3semidirect
108. C2×C22⋊C8C3⋊D3semidirect
267. C32#1468semidirect
327. C3#69920semidirect

Maximal subgroups

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

subgroupindex
C2×#641382
C2×C32×C22⋊C82
#105929062
#105893352
#105893342
#699203