Finite Group Databasebeta

← #11795438

Subgroups — #11795438

Order 1152.

709 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 709 conjugacy classes of subgroups — too many to draw. Only its 148 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#10592687C211yesmaximal, characteristic
2C2×C3×#807C212yesmaximal, complemented
3#10591359C211yesmaximal, characteristic, complemented
4C2×#63564C212yesmaximal
5#10589156C211yesmaximal, characteristic, complemented
6#70641—32nomaximal
7C22×C4⋊(C3⋊D3)C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×#3752—22no—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C22×C3×C3⋊C8C2212yes—
13C2×#3724—22no—
14C3×#807—24no—
15#63564—24no—
16C2×C3×#107—32no—
17C2×#821—32no—
18#4988—32no—
19#4988—61no—
20#4975—32no—
21C2×#809—32no—
22C2×#807D312yescomplemented
23#4550—32no—
24C23×C3⋊D3—21no—
25C22×C32×C4—21no—
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3D412yes—
28C2×C4⋊(C3⋊D3)—22no—
29C2×C4⋊(C3⋊D3)—22no—
30C2×C4⋊(C3⋊D3)—21no—
31C2×C4⋊(C3⋊D3)Q812yes—
32C22×C3×Dic3—22no—
33C32×C4⋊C4—22no—
34#3752—44no—
35C4×C3⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C2×C3×C3⋊C8—22no—
39C2×C3×C3⋊C8—22no—
40C2×C3×C3⋊C8D414yes—
41#3724—44no—
42#2093—91noSylow
43C22×D12—32no—
44C22×D12—61no—
45C22×C3×C8—32no—
46C2×C3×C4⋊C4—21no—
47C2×C3×C4⋊C4—32no—
48C2×C3×C4⋊C4C2×D312yes—
49C2×(C2×D3)⋊C4—64no—
50C2×(C2×D3)⋊C4—64no—
51C2×C4⋊Dic3C2×D312yes—
52C2×Dic3⋊C4—64no—
53C2×C4×Dic3—32no—
54C2×C4×Dic3—61no—
55C22×C3⋊C8C2×D312yes—
56C3×#107—64no—
57#821—64no—
58#809—64no—
59#807—24no—
60C23×C32C2×D411yescharacteristic
61C22×C3⋊D3—22no—
62C22×C3⋊D3—41no—
63C22×C3⋊D3—41no—
64C22×C3⋊D3—42no—
65C22×C3⋊D3—42no—
66C2×C32×C4—41no—
67C2×C32×C4—42no—
68C2×C32×C4C2×D412yes—
69C2×C32×C4C2×Q811yescharacteristic
70C2×C32×C4#4111yescharacteristic
71C2×C32×C4#4112yes—
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3D814yes—
75C4⋊(C3⋊D3)—24no—
76C4⋊(C3⋊D3)—42no—
77C2×C3×Dic3—42no—
78C2×C3×Dic3—44no—
79C3×C3⋊C8—24no—
80C2×#107—32no—
81C2×#102—92no—
82#390—91no—
83#384—91no—
84#336—91no—
85C23×D3—62no—
86C23×D3—62no—
87C22×C3×C4—22no—
88C22×C3×C4—22no—
89C22×C3×C4—21no—
90C22×C3×C4—62no—
91C22×C3×C4C22×D312yes—
92C22×Dic3—22no—
93C22×Dic3—34no—
94C22×Dic3—62no—
95C2×D12—34no—
96C2×D12—62no—
97C2×D12—62no—
98C2×D12—62no—
99C2×D12—62no—
100C2×D12—62no—
101C2×D12—62no—
102C2×D12—62no—
103C2×D12—122no—
104C2×D12—122no—
105C2×C3×C8—34no—
106C2×C3×C8—62no—
107C2×C3×C8—62no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4—22no—
110C3×C4⋊C4—42no—
111C3×C4⋊C4—62no—
112C3×C4⋊C4—62no—
113(C2×D3)⋊C4—128no—
114(C2×D3)⋊C4—128no—
115C4⋊Dic3—22no—
116C4⋊Dic3—22no—
117Dic3⋊C4—128no—
118C4×Dic3—62no—
119C4×Dic3—62no—
120C4×Dic3—122no—
121C2×C3⋊C8—22no—
122C2×C3⋊C8—22no—
123C2×C3⋊C8#6714yes—
124C22×C32C22⋊Q811yescharacteristic
125C22×C32#12311yescharacteristic
126C22×C32#12711yescharacteristic
127C22×C32C2×D812yes—
128C22×C32#13712yes—
129C2×C3⋊D3—42no—
130C2×C3⋊D3—44no—
131C2×C3⋊D3—82no—
132C2×C3⋊D3—81no—
133C2×C3⋊D3—81no—
134C32×C4—81no—
135C32×C4C22⋊Q812yes—
136C32×C4#12312yes—
137C3⋊Dic3—24no—
138C3×Dic3—82no—
139C22×D4—91no—
140C22×C8—32no—
141C2×C4⋊C4—32no—
142C2×C4⋊C4—182no—
143C2×C4⋊C4D3211yescharacteristic
144C2×C22⋊C4—182no—
145C2×C42—91no—
146#107—64no—
147#102—184no—
148C23×C3—21no—
149C23×C3D3×D412yes—
150C22×D3—64no—
151C22×D3—64no—
152C22×D3—124no—
153C22×D3—122no—
154C22×D3—122no—
155C22×D3—124no—
156C22×D3—122no—
157C22×D3—124no—
158C22×D3—124no—
159C22×D3—122no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—44no—
165C2×C3×C4—42no—
166C2×C3×C4—44no—
167C2×C3×C4—42no—
168C2×C3×C4—124no—
169C2×C3×C4—122no—
170C2×C3×C4#23512yes—
171C2×C3×C4#23512yes—
172C2×C3×C4D3×D412yes—
173C2×C3×C4D3×Q812yes—
174C2×C3×C4#23912yes—
175C2×C3×C4C2×#6712yes—
176C2×Dic3—38no—
177C2×Dic3—44no—
178C2×Dic3—42no—
179C2×Dic3—64no—
180C2×Dic3—64no—
181C2×Dic3—64no—
182C2×Dic3—122no—
183C2×Dic3—122no—
184D12—64no—
185D12—64no—
186D12—124no—
187D12—124no—
188D12—122no—
189D12—122no—
190C3×C8—64no—
191C3⋊C8—24no—
192C2×C32#39911yescharacteristic
193C2×C32#47412yes—
194C2×C32#48012yes—
195C2×C32#49311yescharacteristic
196C2×C32#49711yescharacteristic
197C3⋊D3—82no—
198C24—181no—
199C2×D4—92no—
200C2×D4—181no—
201C2×D4—182no—
202C2×D4—182no—
203C22×C4—21no—
204C22×C4—62no—
205C22×C4—92no—
206C22×C4C2×D3211yescharacteristic
207C2×C8—34no—
208C2×C8—62no—
209C2×C8—62no—
210C4⋊C4—22no—
211C4⋊C4—62no—
212C4⋊C4—62no—
213C4⋊C4—364no—
214C22⋊C4—364no—
215C42—182no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—22no—
219C22×C3—22no—
220C22×C3—21no—
221C22×C3#89412yes—
222C22×C3#89612yes—
223C22×C3D3×D814yes—
224C22×C3#91814yes—
225C22×C3#94012yes—
226C2×D3—124no—
227C2×D3—128no—
228C2×D3—128no—
229C2×D3—124no—
230C2×D3—242no—
231C2×D3—244no—
232C2×D3—242no—
233C2×D3—244no—
234C2×D3—242no—
235C2×D3—242no—
236C3×C4—22no—
237C3×C4—22no—
238C3×C4—82no—
239C3×C4—82no—
240C3×C4—242no—
241C3×C4#89412yes—
242C3×C4#89612yes—
243C3×C4#92912yes—
244C3×C4#94612yes—
245Dic3—68no—
246Dic3—82no—
247Dic3—124no—
248C32#209311yescharacteristic, complemented, Sylow
249C23—182no—
250C23—361no—
251C23—362no—
252C23—362no—
253C23—361no—
254C23#381111yescharacteristic
255D4—184no—
256D4—362no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—94no—
260C2×C4—124no—
261C2×C4—122no—
262C2×C4—182no—
263C2×C4—182no—
264C2×C4#379711yescharacteristic
265C2×C4#379811yescharacteristic
266C2×C4#379912yes—
267C2×C4D3×#6712yes—
268C8—64no—
269C2×C3—21no—
270C2×C3—22no—
271C2×C3—21no—
272C2×C3—22no—
273C2×C3—21no—
274C2×C3#488214yes—
275C2×C3#489014yes—
276C2×C3#499312yes—
277C2×C3#515112yes—
278C2×C3#519012yes—
279D3—244no—
280D3—244no—
281C22—364no—
282C22—362no—
283C22—721no—
284C22—722no—
285C22—721no—
286C22#6386511yescharacteristic
287C22#6389711yescharacteristic
288C22#6392612yes—
289C22#6394512yes—
290C22#6397911yescharacteristic
291C4—81no—
292C4—184no—
293C4—242no—
294C4#6385012yes—
295C4#6388812yes—
296C3—21no—
297C3#7064112yescomplemented
298C2—722no—
299C2#1059043012yes—
300C2#1059044212yes—
301C2#1059120311yescharacteristic
302C2#1059148411yescharacteristic
303C2#1059162911yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2093
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#807C2semidirect
3. #10591359C2semidirect
5. #10589156C2semidirect
22. C2×#807D3semidirect
248. C32#2093semidirect
297. C3#70641semidirect

Maximal subgroups

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

subgroupindex
#105926872
C2×C3×#8072
#105913592
C2×#635642
#105891562
#706413