Finite Group Databasebeta

← #11778375

Subgroups — #11778375

Order 1152.

567 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 567 conjugacy classes of subgroups — too many to draw. Only its 80 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
1#10594813C211yesmaximal, characteristic
2#10592355C211yesmaximal, characteristic
3#10591190C212yesmaximal
4C3×#4452C212yesmaximal
5#10589148C211yesmaximal, characteristic
6#68327—32nomaximal
7C22×#634C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)—21no—
9C2×#3750C2211yescharacteristic
10C3×#924C2212yes—
11#63982—21no—
12#63957—21no—
13#63847—22no—
14#63839—22no—
15C2×#3719—22no—
16C32×#95C2211yescharacteristic
17#63658—21no—
18C3×#830C2212yes—
19#63567—22no—
20#5623—32no—
21#5050—32no—
22#4739—32no—
23#4656—32no—
24#4656—61no—
25C3×#328—32no—
26#4469—32no—
27#4452D312yes—
28C22×C32×C4—21no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C2×#634—22no—
34C2×#634—42no—
35C2×C3×Dic6D412yes—
36C2×#627—21no—
37C4⋊(C3⋊Dic3)—42no—
38#3750—22no—
39C3×#217—22no—
40C3×C4⋊Dic3D412yes—
41C3×Dic3⋊C4—22no—
42C2×C3×C3⋊C8—22no—
43#3724—21no—
44#3724—21no—
45#3724—21no—
46Dic3⋊Dic3—22no—
47Dic32—22no—
48#3719—44no—
49#1605—91noSylow
50C22×Dic6—32no—
51C22×Dic6—61no—
52C3×C22⋊Q8—32no—
53#944—62no—
54C2×#216—62no—
55C2×C4⋊Dic3—62no—
56C2×C4⋊Dic3—62no—
57#924C2×D312yes—
58C2×Dic3⋊C4—32no—
59C2×Dic3⋊C4—61no—
60C2×Dic12—62no—
61#889—62no—
62#889—62no—
63#888—62no—
64#878—62no—
65#877—62no—
66C3×C22⋊C8—32no—
67C3×#95—21no—
68C3×#95C2×D312yes—
69C3⋊#95—62no—
70C3⋊#95—62no—
71#830C2×D312yes—
72#816—62no—
73#810—62no—
74C23×C32C2×D411yescharacteristic
75C2×C32×C4—22no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4C2×D412yes—
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3Q1612yescomplemented
88#634—24no—
89#634—42no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—22no—
92C3×Dic6—42no—
93#627—81no—
94C3×C3⋊C8—42no—
95#544—91no—
96#451—92no—
97#395—91no—
98#328—32no—
99#324—91no—
100C2×C3×Q8—32no—
101C22×C3×C4—22no—
102C22×C3×C4—22no—
103C22×C3×C4—21no—
104C22×C3×C4C22×D312yes—
105C22×Dic3—32no—
106C22×Dic3—32no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C22×Dic3—62no—
110C22×Dic3—62no—
111C2×Dic6—62no—
112C2×Dic6—62no—
113C2×Dic6—62no—
114C2×Dic6—122no—
115C2×Dic6—124no—
116C2×Dic6—124no—
117C2×Dic6D1212yes—
118C2×C3×C8—62no—
119C3×C4⋊C4—32no—
120C3×C4⋊C4—62no—
121C3×C22⋊C4—62no—
122#217—22no—
123#216—124no—
124C4⋊Dic3—62no—
125C4⋊Dic3—124no—
126C4⋊Dic3—124no—
127C4⋊Dic3D1212yes—
128Dic3⋊C4—22no—
129Dic3⋊C4—62no—
130Dic3⋊C4—62no—
131Dic3⋊C4—62no—
132Dic3⋊C4—62no—
133Dic3⋊C4—62no—
134Dic3⋊C4—62no—
135Dic3⋊C4—122no—
136C4×Dic3—62no—
137C4×Dic3—62no—
138C2×C3⋊C8—22no—
139Dic12—124no—
140C22×C32—21no—
141C22×C32—21no—
142C22×C32#12011yescharacteristic
143C22×C32C2×Q1611yescharacteristic
144C22×C32#13711yescharacteristic
145C32×C4—22no—
146C32×C4—42no—
147C3⋊Dic3—22no—
148C3⋊Dic3—42no—
149C3⋊Dic3—41no—
150C3×Dic3—42no—
151C3×Dic3—42no—
152C22×Q8—91no—
153C2×Q16—182no—
154C4⋊Q8—182no—
155#125—182no—
156C22⋊Q8—32no—
157C22⋊Q8—181no—
158#117—181no—
159C2×C4⋊C4—91no—
160C2×C4⋊C4—181no—
161#103—182no—
162C22⋊C8—32no—
163#95—181no—
164#95D3211yescharacteristic
165C23×C3—21no—
166C23×C3D3×D412yes—
167C3×Q8—122no—
168C2×C3×C4—24no—
169C2×C3×C4—24no—
170C2×C3×C4—22no—
171C2×C3×C4—42no—
172C2×C3×C4—42no—
173C2×C3×C4—42no—
174C2×C3×C4—42no—
175C2×C3×C4—42no—
176C2×C3×C4—42no—
177C2×C3×C4—62no—
178C2×C3×C4—62no—
179C2×C3×C4C2×D1212yes—
180C2×C3×C4D3×D412yes—
181C2×Dic3—22no—
182C2×Dic3—22no—
183C2×Dic3—34no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—62no—
187C2×Dic3—64no—
188C2×Dic3—64no—
189C2×Dic3—62no—
190C2×Dic3—121no—
191C2×Dic3—121no—
192C2×Dic3—121no—
193C2×Dic3—122no—
194C2×Dic3—122no—
195C2×Dic3—122no—
196C2×Dic3—122no—
197C2×Dic3—122no—
198C2×Dic3—122no—
199Dic6—42no—
200Dic6—64no—
201Dic6—64no—
202Dic6—124no—
203Dic6—122no—
204Dic6—122no—
205Dic6—124no—
206Dic6—242no—
207C3×C8—122no—
208C3⋊C8—42no—
209C2×C32—21no—
210C2×C32—21no—
211C2×C32#45111yescharacteristic
212C2×C32#45611yescharacteristic
213C2×C32B(4,𝔽2)11yescharacteristic
214C2×Q8—32no—
215C2×Q8—181no—
216C2×Q8—182no—
217C2×Q8—362no—
218C22×C4—21no—
219C22×C4—91no—
220C22×C4—91no—
221C22×C4—181no—
222C22×C4C2×D3211yescharacteristic
223Q16—364no—
224C2×C8—62no—
225C4⋊C4—32no—
226C4⋊C4—62no—
227C4⋊C4—181no—
228C4⋊C4—181no—
229C4⋊C4—181no—
230C4⋊C4—182no—
231C4⋊C4—182no—
232C4⋊C4—362no—
233C22⋊C4—62no—
234C42—182no—
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—22no—
238C22×C3—22no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3#88212yes—
243C22×C3#91512yes—
244C22×C3D3×Q1612yes—
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—42no—
248C3×C4—44no—
249C3×C4—44no—
250C3×C4—122no—
251C3×C4—122no—
252Dic3—42no—
253Dic3—42no—
254Dic3—64no—
255Dic3—122no—
256Dic3—124no—
257Dic3—124no—
258Dic3—122no—
259Dic3—241no—
260C32#160511yescharacteristic, complemented, Sylow
261C23#381111yescharacteristic
262Q8—122no—
263Q8—184no—
264Q8—362no—
265Q8—721no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—62no—
271C2×C4—62no—
272C2×C4—92no—
273C2×C4—181no—
274C2×C4—181no—
275C2×C4—182no—
276C2×C4—181no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4—361no—
280C2×C4D3×D1212yes—
281C8—122no—
282C2×C3—22no—
283C2×C3—22no—
284C2×C3—22no—
285C2×C3—22no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3#474112yes—
290C2×C3#480912yes—
291C2×C3#482612yes—
292C22—21no—
293C22—21no—
294C22#6392311yescharacteristic
295C22#6393111yescharacteristic
296C22#6394411yescharacteristic
297C4—22no—
298C4—42no—
299C4—122no—
300C4—122no—
301C4—182no—
302C4—362no—
303C4—361no—
304C3—21no—
305C3#6832712yescomplemented
306C2—21no—
307C2—21no—
308C2#1059040111yescharacteristic
309C2#1059041011yescharacteristic
310C2#1059060511yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenter#95D32
hypocenterC32#1605
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
87. C2×C3⋊Dic3Q16semidirect
260. C32#1605semidirect
305. C3#68327semidirect

Maximal subgroups

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

subgroupindex
#105948132
#105923552
#105911902
C3×#44522
#105891482
#683273