Finite Group Databasebeta

← #11773994

Subgroups — #11773994

Order 1152.

622 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 62 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×#64095C211yesmaximal, characteristic
2#10593845C211yesmaximal, characteristic, complemented
3C2×C22⋊#622C211yesmaximal, characteristic, complemented
4#10590204C212yesmaximal, complemented
5#10590202C212yesmaximal, complemented
6C22×#638C411yescharacteristic
7C23×C3⋊Dic3C2211yescharacteristic
8C2×#3792—21no—
9C22×#622—21no—
10C2×C32×C22⋊C4C411yescharacteristic
11C2×#3752C411yescharacteristic
12C2×#3752C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C411yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15#64095—21no—
16#64095—21no—
17#64095—21no—
18#64095—21no—
19C22⋊#622—21no—
20C22⋊#622—21no—
21C22⋊#622C2212yes—
22C22⋊#622C2212yes—
23C2×#886—62no—
24C24×C32C2×C411yescharacteristic
25C23×C3⋊D3C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C2×#638—21no—
29C2×#638—21no—
30C2×#638—42no—
31C22×C3⋊Dic3—42no—
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3C2311yescharacteristic
39#3792—42no—
40C2×#622—22no—
41C2×#622—22no—
42C2×#622—42no—
43C32×C22⋊C4—21no—
44C32×C22⋊C4—21no—
45#3752—21no—
46#3752—21no—
47#3752—21no—
48#3752—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53#1468—91nomaximal, Sylow
54C22×#67—62no—
55C23×Dic3—62no—
56C2×C3×C22⋊C4—22no—
57C2×(C2×D3)⋊C4—62no—
58C2×(C2×D3)⋊C4—62no—
59C2×C4⋊Dic3—62no—
60C2×C4⋊Dic3—62no—
61#886—64no—
62#886—64no—
63#886—64no—
64#886—64no—
65C23×C32—22no—
66C23×C32—22no—
67C23×C32—41no—
68C23×C32C22⋊C411yescharacteristic
69C23×C32C22⋊C411yescharacteristic
70C23×C32C22×C411yescharacteristic
71C22×C3⋊D3—21no—
72C22×C3⋊D3—22no—
73C22×C3⋊D3—41no—
74C22×C3⋊D3—41no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4—22no—
78C2×C32×C4—41no—
79#638—42no—
80#638—42no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3C22⋊C411yescharacteristic
90C2×C3⋊Dic3C22⋊C411yescharacteristic
91C2×C3⋊Dic3C2×D411yescharacteristic
92C2×C3⋊Dic3C2×D411yescharacteristic
93#622—42no—
94#622—42no—
95C2×#123—91no—
96#407—91no—
97C2×C22⋊C8—91no—
98#324—92no—
99#323—92no—
100C24×C3—22no—
101C23×D3—62no—
102C22×C3×C4—22no—
103C22×C3×C4—22no—
104C2×#67—64no—
105C2×#67—64no—
106C2×#67—128no—
107C22×Dic3—62no—
108C22×Dic3—62no—
109C22×Dic3—62no—
110C22×Dic3—62no—
111C22×Dic3—62no—
112C22×Dic3—62no—
113C22×Dic3—62no—
114C22×Dic3—128no—
115C3×C22⋊C4—24no—
116C3×C22⋊C4—24no—
117(C2×D3)⋊C4—64no—
118(C2×D3)⋊C4—64no—
119(C2×D3)⋊C4—64no—
120(C2×D3)⋊C4—64no—
121C4⋊Dic3—64no—
122C4⋊Dic3—64no—
123C4⋊Dic3—64no—
124C4⋊Dic3—64no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32—21no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—44no—
133C22×C32#9912yes—
134C22×C32C2×C22⋊C411yescharacteristic
135C22×C32#13112yes—
136C2×C3⋊D3—41no—
137C2×C3⋊D3—41no—
138C2×C3⋊D3—41no—
139C2×C3⋊D3—82no—
140C32×C4—41no—
141C32×C4—41no—
142C3⋊Dic3—21no—
143C3⋊Dic3—21no—
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—91no—
157C2×C22⋊C4—91no—
158C2×C22⋊C4—91no—
159C2×C22⋊C4#15711yescharacteristic
160C22⋊C8—92no—
161C22⋊C8—92no—
162C22⋊C8—181no—
163C22⋊C8—181no—
164C23×C3—28no—
165C23×C3—22no—
166C23×C3—22no—
167C23×C3—22no—
168C23×C3—44no—
169C23×C3—44no—
170C22×D3—64no—
171C22×D3—124no—
172C22×D3—124no—
173C22×D3—124no—
174C2×C3×C4—24no—
175C2×C3×C4—24no—
176C2×C3×C4—44no—
177C2×C3×C4—44no—
178#67—128no—
179#67—128no—
180C2×Dic3—62no—
181C2×Dic3—62no—
182C2×Dic3—62no—
183C2×Dic3—62no—
184C2×Dic3—64no—
185C2×Dic3—124no—
186C2×Dic3—124no—
187C2×Dic3—124no—
188C2×Dic3—124no—
189C2×Dic3—124no—
190C2×Dic3—124no—
191C2×Dic3—124no—
192C2×C32—22no—
193C2×C32—22no—
194C2×C32—41no—
195C2×C32#40811yescharacteristic
196C2×C32C2×#9911yescharacteristic
197C2×C32#41311yescharacteristic
198C3⋊D3—81no—
199C24—91no—
200C24C2×#15711yescharacteristic
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—91no—
211C22×C4—362no—
212C22×C4C2×#15711yescharacteristic
213C22×C4C2×#15711yescharacteristic
214M16—362no—
215C2×C8—182no—
216C2×C8—182no—
217C2×C8—362no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C4⋊C4—181no—
222C22⋊C4—21no—
223C22⋊C4—21no—
224C22⋊C4—181no—
225C22⋊C4—181no—
226C22⋊C4—181no—
227C22⋊C4—181no—
228C22×C3—24no—
229C22×C3—24no—
230C22×C3—24no—
231C22×C3—24no—
232C22×C3—24no—
233C22×C3—22no—
234C22×C3—42no—
235C22×C3—42no—
236C22×C3—42no—
237C22×C3—42no—
238C22×C3—416no—
239C2×D3—124no—
240C2×D3—124no—
241C2×D3—124no—
242C2×D3—248no—
243C3×C4—44no—
244C3×C4—44no—
245Dic3—122no—
246Dic3—122no—
247Dic3—122no—
248Dic3—122no—
249Dic3—124no—
250C32#146811yescharacteristic, complemented, Sylow
251C23—22no—
252C23—22no—
253C23—41no—
254C23—181no—
255C23—182no—
256C23—361no—
257C23—361no—
258C23C22⋊#15711yescharacteristic
259C23C22⋊#15711yescharacteristic
260C23C22×#15711yescharacteristic
261D4—362no—
262D4—362no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—91no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—182no—
272C2×C4—182no—
273C2×C4—181no—
274C2×C4—361no—
275C2×C4—361no—
276C2×C4—361no—
277C2×C4—361no—
278C2×C4—361no—
279C8—362no—
280C8—362no—
281C2×C3—28no—
282C2×C3—22no—
283C2×C3—22no—
284C2×C3—22no—
285C2×C3—44no—
286C2×C3—44no—
287D3—244no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—44no—
296C22—361no—
297C22—361no—
298C22—361no—
299C22—722no—
300C22#6377412yes—
301C22#6428712yes—
302C22C2×C22⋊#15711yescharacteristic
303C4—41no—
304C4—41no—
305C4—181no—
306C4—181no—
307C4—181no—
308C4—181no—
309C4—361no—
310C3—22no—
311C2—22no—
312C2—22no—
313C2—41no—
314C2—721no—
315C2C2×#6377411yescharacteristic
316C2#1059382211yescharacteristic
317C2#1059382411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC2×C32×C22⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C22⋊C4#157
hypocenterC32#1468
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10593845C2semidirect
3. C2×C22⋊#622C2semidirect
4. #10590204C2semidirect
5. #10590202C2semidirect
250. C32#1468semidirect

Maximal subgroups

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

subgroupindex
C2×#640952
#105938452
C2×C22⋊#6222
#105902042
#105902022
#14689