Finite Group Databasebeta

← #11774326

Subgroups — #11774326

Order 1152.

744 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 744 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2#10592532C211yesmaximal, characteristic
3#10592384C211yesmaximal, characteristic
4C32×Q8⋊C8C211yesmaximal, characteristic, complemented
5#10589401C211yesmaximal, characteristic, complemented
6#10589350C211yesmaximal, characteristic, complemented
7#10589322C211yesmaximal, characteristic, complemented
8#68231—34nomaximal
9C2×Q8×C3⋊D3C411yescharacteristic
10C32×C4×Q8C2211yescharacteristic
11Q8×C3⋊Dic3C411yescharacteristic
12C4⋊C4×C3⋊D3—21no—
13C4⋊C4×C3⋊D3C411yescharacteristic
14#64096—21no—
15#64096C411yescharacteristic
16C42×C3⋊D3—21no—
17C42×C3⋊D3C2211yescharacteristic
18C4×#634—21no—
19C4×#634C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4×C8C2211yescharacteristic
22#63647—21no—
23#63647—21no—
24#63641—21no—
25C8×C3⋊Dic3—21no—
26C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
27C4×C3⋊(C3⋊C8)C2211yescharacteristic
28C4×D3×Q8—34no—
29#4833—34no—
30#4685—34no—
31C3×Q8⋊C8D314yescomplemented
32#4535—34no—
33#4484—34no—
34#4456—34no—
35C2×C32×Q8C2×C411yescharacteristic
36Q8×C3⋊D3—22no—
37Q8×C3⋊D3C814yescomplemented
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—21no—
40C2×C4×C3⋊D3C2×C411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×#634—21no—
44C2×#634C2×C411yescharacteristic
45C2×C32×C8—21no—
46C2×C32×C8—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C42—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53#3750—21no—
54#3750—21no—
55#3750—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3C2×C411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61C4×C3⋊Dic3D411yescharacteristic
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64#1479—91noSylow
65C2×D3×Q8—34no—
66C3×C4×Q8C2×D314yes—
67Q8×Dic3—34no—
68D3×C4⋊C4—34no—
69D3×C4⋊C4—64no—
70#887—34no—
71#887—64no—
72C42×D3—34no—
73C42×D3—64no—
74C4×Dic6—34no—
75C4×Dic6—64no—
76C3×C4⋊C8C2×D314yes—
77C3×C4×C8C2×D314yes—
78(C2×D3)⋊C8—64no—
79(C2×D3)⋊C8—64no—
80Dic3⋊C8—64no—
81C8×Dic3—64no—
82C4⋊(C3⋊C8)—34no—
83C4×C3⋊C8—34no—
84C22×C3⋊D3C22⋊C411yescharacteristic
85C32×Q8—21no—
86C32×Q8C2×C812yes—
87C2×C32×C4—21no—
88C2×C32×C4—21no—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3C22⋊C411yescharacteristic
95C2×C3⋊Dic3C22⋊C411yescharacteristic
96C2×C3⋊Dic3C22⋊C411yescharacteristic
97C4×C3⋊D3—24no—
98C4×C3⋊D3—21no—
99C4×C3⋊D3—21no—
100C4×C3⋊D3—41no—
101C4×C3⋊D3—42no—
102C4×C3⋊D3C2×C812yes—
103C4×C3⋊D3M1612yes—
104#634—21no—
105#634—24no—
106#634C2×C812yes—
107C32×C8—41no—
108C32×C8—41no—
109C3⋊(C3⋊C8)—41no—
110C3⋊(C3⋊C8)—41no—
111C2×C4×Q8—91no—
112#431—91no—
113#431—91no—
114Q8⋊C8—91no—
115Q8⋊C8—91no—
116Q8⋊C8—91no—
117Q8⋊C8C3⋊D311yescharacteristic, complemented
118C2×C3×Q8C4×D314yes—
119D3×Q8—316no—
120D3×Q8—68no—
121C2×C4×D3—34no—
122C2×C4×D3—34no—
123C2×C4×D3—34no—
124C2×C4×D3—64no—
125C2×C4×D3—64no—
126C2×Dic6—34no—
127C2×Dic6—64no—
128C2×C3×C8—24no—
129C2×C3×C8—24no—
130C3×C4⋊C4—24no—
131C3×C4⋊C4C4×D314yes—
132C3×C42—24no—
133C3×C42C22×D314yes—
134C4⋊Dic3—34no—
135C4⋊Dic3—64no—
136Dic3⋊C4—64no—
137Dic3⋊C4—64no—
138Dic3⋊C4—64no—
139C4×Dic3—34no—
140C4×Dic3—34no—
141C4×Dic3—34no—
142C4×Dic3—64no—
143C4×Dic3—64no—
144C4×Dic3—64no—
145C2×C3⋊C8—64no—
146C2×C3⋊C8—64no—
147C22×C32C2×C22⋊C411yescharacteristic
148C2×C3⋊D3—21no—
149C2×C3⋊D3—21no—
150C2×C3⋊D3C22⋊C812yes—
151C32×C4—22no—
152C32×C4—21no—
153C32×C4—41no—
154C32×C4C22×C811yescharacteristic
155C32×C4C2×M1611yescharacteristic
156C32×C4#13711yescharacteristic
157C32×C4#13711yescharacteristic
158C3⋊Dic3—22no—
159C3⋊Dic3—21no—
160C3⋊Dic3—21no—
161C3⋊Dic3—41no—
162C3⋊Dic3C22⋊C812yes—
163C22×Q8—91no—
164C4×Q8—91no—
165C4×Q8—91no—
166C4×Q8—91no—
167C4×Q8—181no—
168C4×Q8—181no—
169C4×Q8C2×C3⋊D311yescharacteristic
170C2×C4⋊C4—91no—
171C2×C4⋊C4—181no—
172C2×C42—91no—
173C2×C42—181no—
174C4⋊C8—91no—
175C4⋊C8—181no—
176C4⋊C8C2×C3⋊D311yescharacteristic
177C22⋊C8—181no—
178C22⋊C8—181no—
179C4×C8—91no—
180C4×C8—181no—
181C4×C8C2×C3⋊D311yescharacteristic
182C22×D3—34no—
183C3×Q8—24no—
184C3×Q8D3×C818yes—
185C2×C3×C4—24no—
186C2×C3×C4—24no—
187C2×C3×C4C2×C4×D314yes—
188C2×C3×C4D3×D414yes—
189C2×C3×C4D3×D414yes—
190C2×Dic3—34no—
191C2×Dic3—34no—
192C2×Dic3—34no—
193C2×Dic3—64no—
194C2×Dic3—64no—
195C4×D3—38no—
196C4×D3—38no—
197C4×D3—616no—
198C4×D3—64no—
199C4×D3—64no—
200C4×D3—124no—
201C4×D3—128no—
202Dic6—38no—
203Dic6—616no—
204Dic6—64no—
205C3×C8—44no—
206C3×C8—44no—
207C3⋊C8—124no—
208C3⋊C8—124no—
209C2×C32C2×C22⋊C811yescharacteristic
210C2×C32#41911yescharacteristic
211C2×C32#42111yescharacteristic
212C3⋊D3—22no—
213C2×Q8—94no—
214C2×Q8—91no—
215C2×Q8—181no—
216C2×Q8—182no—
217C2×Q8C4×C3⋊D311yescharacteristic
218C22×C4—91no—
219C22×C4—91no—
220C22×C4—91no—
221C22×C4—181no—
222C22×C4—181no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—181no—
226C2×C8—181no—
227C4⋊C4—21no—
228C4⋊C4—91no—
229C4⋊C4—181no—
230C4⋊C4—181no—
231C4⋊C4—181no—
232C4⋊C4—181no—
233C4⋊C4C4×C3⋊D311yescharacteristic
234C42—21no—
235C42—91no—
236C42—91no—
237C42—91no—
238C42—181no—
239C42—181no—
240C42—181no—
241C42C22×C3⋊D311yescharacteristic
242C22×C3D3×C22⋊C414yes—
243C2×D3—38no—
244C2×D3—64no—
245C2×D3—64no—
246C3×C4—28no—
247C3×C4—24no—
248C3×C4—44no—
249C3×C4C2×D3×C814yes—
250C3×C4D3×M1614yes—
251C3×C4#91514yes—
252C3×C4#91814yes—
253Dic3—38no—
254Dic3—68no—
255Dic3—64no—
256Dic3—64no—
257Dic3—124no—
258C32#147911yescharacteristic, complemented, Sylow
259C23—91no—
260Q8—21no—
261Q8—92no—
262Q8—184no—
263Q8—181no—
264Q8C8×C3⋊D312yes—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—91no—
268C2×C4—92no—
269C2×C4—92no—
270C2×C4—91no—
271C2×C4—91no—
272C2×C4—184no—
273C2×C4—181no—
274C2×C4—181no—
275C2×C4—181no—
276C2×C4—181no—
277C2×C4—361no—
278C2×C4—362no—
279C2×C4C2×C4×C3⋊D311yescharacteristic
280C2×C4D4×C3⋊D311yescharacteristic
281C2×C4D4×C3⋊D311yescharacteristic
282C8—41no—
283C8—41no—
284C8—361no—
285C8—361no—
286C2×C3D3×C22⋊C814yes—
287C2×C3#480214yes—
288C2×C3#482114yes—
289D3—68no—
290C22—92no—
291C22—181no—
292C22—181no—
293C22C22⋊C4×C3⋊D311yescharacteristic
294C4—21no—
295C4—22no—
296C4—41no—
297C4—92no—
298C4—181no—
299C4—182no—
300C4—181no—
301C4—361no—
302C4C2×C8×C3⋊D311yescharacteristic
303C4M16×C3⋊D311yescharacteristic
304C4#6412411yescharacteristic
305C4#6412711yescharacteristic
306C3#6823114yescomplemented
307C2—182no—
308C2C3⋊D3×C22⋊C811yescharacteristic
309C2#1059250111yescharacteristic
310C2#1059252011yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC32×C4C22×C8
FrattiniC42C22×C3⋊D3
FittingC32×Q8⋊C8C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterQ8⋊C8C3⋊D3
hypocenterC32#1479
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C32×Q8⋊C8C2semidirect
5. #10589401C2semidirect
6. #10589350C2semidirect
7. #10589322C2semidirect
31. C3×Q8⋊C8D3semidirect
37. Q8×C3⋊D3C8semidirect
117. Q8⋊C8C3⋊D3semidirect
258. C32#1479semidirect
306. C3#68231semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
#105925322
#105923842
C32×Q8⋊C82
#105894012
#105893502
#105893222
#682313