Finite Group Databasebeta

← #11773996

Subgroups — #11773996

Order 1152.

622 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 60 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×#64103C211yesmaximal, characteristic
2#10593803C211yesmaximal, characteristic, complemented
3#10593800C211yesmaximal, characteristic, complemented
4#10590204C212yesmaximal, complemented
5#10590203C212yesmaximal, complemented
6C22×C4⋊(C3⋊D3)C411yescharacteristic
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3788—21no—
9C2×#3787—21no—
10C2×C32×C4⋊C4C411yescharacteristic
11C2×#3752C411yescharacteristic
12C2×#3752C411yescharacteristic
13C2×#3752C2211yescharacteristic
14C2×#3750C2211yescharacteristic
15#64103—21no—
16#64103—21no—
17#64103—21no—
18#64103—21no—
19C22⋊#622C2212yes—
20C22⋊#622C2212yes—
21#63778—21no—
22#63778—21no—
23C2×#894—62no—
24C23×C3⋊D3C2×C411yescharacteristic
25C23×C3⋊D3C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2311yescharacteristic
31C2×C4⋊(C3⋊D3)—21no—
32C2×C4⋊(C3⋊D3)—21no—
33C2×C4⋊(C3⋊D3)—42no—
34C2×C4×C3⋊D3—42no—
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×#622—22no—
40C2×#622—22no—
41#3788—42no—
42#3787—42no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45#3752—21no—
46#3752—21no—
47#3752—21no—
48#3752—21no—
49#3752—21no—
50#3752—21no—
51#3750—21no—
52#3750—21no—
53#1468—91nomaximal, Sylow
54C22×D12—62no—
55C22×C4×D3—62no—
56C2×C3×C4⋊C4—22no—
57C2×(C2×D3)⋊C4—62no—
58C2×(C2×D3)⋊C4—62no—
59C2×(C2×D3)⋊C4—62no—
60C2×Dic3⋊C4—62no—
61#894—64no—
62#894—64no—
63#894—64no—
64#894—64no—
65C23×C32C22×C411yescharacteristic
66C22×C3⋊D3—22no—
67C22×C3⋊D3—21no—
68C22×C3⋊D3—22no—
69C22×C3⋊D3—22no—
70C22×C3⋊D3—41no—
71C22×C3⋊D3—41no—
72C22×C3⋊D3—41no—
73C22×C3⋊D3C22⋊C411yescharacteristic
74C22×C3⋊D3C22⋊C411yescharacteristic
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4—41no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3C2×D411yescharacteristic
86C2×C3⋊Dic3C2×D411yescharacteristic
87C4⋊(C3⋊D3)—42no—
88C4⋊(C3⋊D3)—42no—
89C4×C3⋊D3—22no—
90C4×C3⋊D3—22no—
91C4×C3⋊D3—41no—
92C4×C3⋊D3—41no—
93#622—42no—
94#622—42no—
95C2×#123—91no—
96#407—91no—
97C2×C22⋊C8—91no—
98#324—92no—
99#323—92no—
100C23×D3—62no—
101C23×D3—62no—
102C22×C3×C4—22no—
103C22×C3×C4—22no—
104C22×C3×C4—22no—
105C22×Dic3—62no—
106C22×Dic3—62no—
107C2×D12—64no—
108C2×D12—64no—
109C2×D12—128no—
110C2×C4×D3—62no—
111C2×C4×D3—62no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—128no—
115C3×C4⋊C4—24no—
116C3×C4⋊C4—24no—
117(C2×D3)⋊C4—64no—
118(C2×D3)⋊C4—64no—
119(C2×D3)⋊C4—64no—
120(C2×D3)⋊C4—64no—
121(C2×D3)⋊C4—64no—
122(C2×D3)⋊C4—64no—
123Dic3⋊C4—64no—
124Dic3⋊C4—64no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32C2×C22⋊C411yescharacteristic
128C22×C32#13112yes—
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3—21no—
132C2×C3⋊D3—21no—
133C2×C3⋊D3—21no—
134C2×C3⋊D3—44no—
135C2×C3⋊D3—41no—
136C2×C3⋊D3—41no—
137C2×C3⋊D3—41no—
138C2×C3⋊D3—82no—
139C2×C3⋊D3#9912yes—
140C32×C4—21no—
141C32×C4—21no—
142C32×C4—41no—
143C32×C4—41no—
144C3⋊Dic3—21no—
145C3⋊Dic3—21no—
146C3⋊Dic3—41no—
147C22×D4—91no—
148C23×C4—91no—
149C2×M16—181no—
150C22×C8—181no—
151#123—181no—
152#123—181no—
153#123—181no—
154#123—181no—
155C2×C4⋊C4—91no—
156C2×C4⋊C4#15711yescharacteristic
157C2×C22⋊C4—91no—
158C2×C22⋊C4—91no—
159C2×C22⋊C4—91no—
160C22⋊C8—92no—
161C22⋊C8—92no—
162C22⋊C8—181no—
163C22⋊C8—181no—
164C23×C3—22no—
165C22×D3—62no—
166C22×D3—62no—
167C22×D3—68no—
168C22×D3—64no—
169C22×D3—124no—
170C22×D3—124no—
171C22×D3—124no—
172C22×D3—124no—
173C22×D3—124no—
174C2×C3×C4—24no—
175C2×C3×C4—24no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—44no—
179C2×C3×C4—44no—
180C2×C3×C4—44no—
181C2×Dic3—62no—
182C2×Dic3—62no—
183C2×Dic3—64no—
184C2×Dic3—124no—
185C2×Dic3—124no—
186D12—128no—
187D12—128no—
188C4×D3—124no—
189C4×D3—124no—
190C4×D3—124no—
191C4×D3—124no—
192C2×C32—22no—
193C2×C32#40811yescharacteristic
194C2×C32C2×#9911yescharacteristic
195C2×C32#41311yescharacteristic
196C3⋊D3—22no—
197C3⋊D3—41no—
198C3⋊D3—81no—
199C24—91no—
200C24—91no—
201C2×D4—181no—
202C2×D4—181no—
203C2×D4—362no—
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—91no—
210C22×C4—362no—
211C22×C4C2×#15711yescharacteristic
212C22×C4C2×#15711yescharacteristic
213C22×C4C2×#15711yescharacteristic
214M16—362no—
215C2×C8—182no—
216C2×C8—182no—
217C2×C8—362no—
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—181no—
221C4⋊C4—181no—
222C22⋊C4—181no—
223C22⋊C4—181no—
224C22⋊C4—181no—
225C22⋊C4—181no—
226C22⋊C4—181no—
227C22⋊C4—181no—
228C22×C3—24no—
229C22×C3—24no—
230C22×C3—24no—
231C22×C3—22no—
232C2×D3—64no—
233C2×D3—64no—
234C2×D3—122no—
235C2×D3—122no—
236C2×D3—122no—
237C2×D3—122no—
238C2×D3—1216no—
239C2×D3—124no—
240C2×D3—124no—
241C2×D3—124no—
242C2×D3—248no—
243C3×C4—42no—
244C3×C4—42no—
245C3×C4—44no—
246C3×C4—44no—
247Dic3—122no—
248Dic3—122no—
249Dic3—124no—
250C32#146811yescharacteristic, complemented, Sylow
251C23—91no—
252C23—91no—
253C23—182no—
254C23—182no—
255C23—181no—
256C23—182no—
257C23—361no—
258C23—361no—
259C23—361no—
260C23C22×#15711yescharacteristic
261D4—362no—
262D4—362no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—182no—
271C2×C4—182no—
272C2×C4—182no—
273C2×C4—181no—
274C2×C4—361no—
275C2×C4—361no—
276C2×C4—361no—
277C2×C4C22⋊#15711yescharacteristic
278C2×C4C22⋊#15711yescharacteristic
279C8—362no—
280C8—362no—
281C2×C3—28no—
282C2×C3—22no—
283C2×C3—22no—
284C2×C3—22no—
285D3—124no—
286D3—124no—
287D3—244no—
288C22—21no—
289C22—21no—
290C22—92no—
291C22—181no—
292C22—181no—
293C22—181no—
294C22—181no—
295C22—181no—
296C22—364no—
297C22—361no—
298C22—361no—
299C22—361no—
300C22—722no—
301C22#6428912yes—
302C22C2×C22⋊#15711yescharacteristic
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—181no—
308C4—181no—
309C4—361no—
310C3—22no—
311C2—22no—
312C2—182no—
313C2—361no—
314C2—721no—
315C2#1059380811yescharacteristic
316C2#1059381711yescharacteristic
317C2#1059383411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1468
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10593803C2semidirect
3. #10593800C2semidirect
4. #10590204C2semidirect
5. #10590203C2semidirect
250. C32#1468semidirect

Maximal subgroups

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

subgroupindex
C2×#641032
#105938032
#105938002
#105902042
#105902032
#14689