Finite Group Databasebeta

← #11791629

Subgroups — #11791629

Order 1152.

653 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 653 conjugacy classes of subgroups — too many to draw. Only its 170 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×#63919C211yesmaximal, characteristic
2C2×#63641C211yesmaximal, characteristic
3#10591274C211yesmaximal, characteristic
4C3×#4551C212yesmaximal
5#10589163C212yesmaximal
6#68800—32nomaximal
7C22×#627—21no—
8C22×C32×C8C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×C4⋊Dic3C2212yes—
13C2×#3724—21no—
14C2×Dic32—21no—
15#63919—22no—
16#63919C414yescomplemented
17#63641—22no—
18#63579—21no—
19C2×#888—32no—
20C2×Dic3⋊C8—32no—
21C2×Dic3⋊C8—61no—
22Dic3×C4⋊C4—32no—
23C3×#340—32no—
24#4551D312yes—
25#4529—32no—
26#4529—32no—
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3D411yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C22×C3×Dic3—22no—
31C22×C3×Dic3—22no—
32C2×#627—24no—
33C2×#627—42no—
34C2×#627—42no—
35C2×C32×C8—21no—
36C2×C32×C8—22no—
37C4×C3⋊Dic3C2×C412yes—
38C4×C3⋊Dic3D412yes—
39C2×C3⋊(C3⋊C8)—21no—
40C2×C3⋊(C3⋊C8)—22no—
41C3×C4⋊Dic3—22no—
42C3×C4⋊Dic3—22no—
43C3×C4⋊Dic3C2×C414yes—
44C3×C4⋊Dic3Q814yescomplemented
45#3724—24no—
46Dic32—42no—
47#1988—91noSylow
48C22×Dic6—62no—
49C22×C3×C8—21no—
50C22×C3×C8C2×D312yes—
51C2×C3×C4⋊C4—32no—
52C2×C3×C4⋊C4—32no—
53C2×C4⋊Dic3C2×D312yes—
54C2×C4⋊Dic3C2×D312yes—
55C2×Dic3⋊C4—62no—
56C2×C4×Dic3—32no—
57C2×C4×Dic3—61no—
58C2×C4×Dic3—62no—
59C22×C3⋊C8—32no—
60C22×C3⋊C8—61no—
61#888—38no—
62#888—64no—
63C3⋊#95—62no—
64Dic3⋊C8—64no—
65Dic3⋊C8—64no—
66C23×C32C2×D411yescharacteristic
67C2×C32×C4C22×C411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4C2×Q812yes—
70C2×C32×C4#4112yes—
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3C22⋊C412yes—
73C2×C3⋊Dic3C22⋊C412yes—
74C2×C3⋊Dic3D812yes—
75C2×C3⋊Dic3SD1612yes—
76C2×C3×Dic3—24no—
77C2×C3×Dic3—24no—
78C2×C3×Dic3—42no—
79C2×C3×Dic3—42no—
80C2×C3×Dic3—42no—
81C2×C3×Dic3—42no—
82#627—48no—
83C32×C8—41no—
84C3⋊(C3⋊C8)—41no—
85C2×C4⋊Q8—91no—
86C2×C4⋊C8—91no—
87C4×C4⋊C4—91no—
88#340—32no—
89#340—92no—
90C22×C3×C4—21no—
91C22×C3×C4—62no—
92C22×C3×C4—62no—
93C22×C3×C4C22×D312yes—
94C22×Dic3—22no—
95C22×Dic3—22no—
96C22×Dic3—32no—
97C22×Dic3—32no—
98C22×Dic3—61no—
99C22×Dic3—61no—
100C2×Dic6—68no—
101C2×Dic6—124no—
102C2×Dic6—124no—
103C2×C3×C8—22no—
104C2×C3×C8—22no—
105C2×C3×C8—22no—
106C2×C3×C8—22no—
107C2×C3×C8—42no—
108C3×C4⋊C4—34no—
109C3×C4⋊C4—34no—
110C3×C4⋊C4—62no—
111C3×C4⋊C4—62no—
112C4⋊Dic3—22no—
113C4⋊Dic3—22no—
114C4⋊Dic3Dic614yescomplemented
115C4⋊Dic3C4×D314yes—
116Dic3⋊C4—68no—
117C4×Dic3—34no—
118C4×Dic3—34no—
119C4×Dic3—62no—
120C4×Dic3—62no—
121C4×Dic3—124no—
122C2×C3⋊C8—62no—
123C2×C3⋊C8—62no—
124C2×C3⋊C8—62no—
125C2×C3⋊C8—62no—
126C2×C3⋊C8—122no—
127C22×C32C2×C22⋊C411yescharacteristic
128C22×C32C22⋊Q812yes—
129C22×C32C2×D811yescharacteristic
130C22×C32C2×SD1611yescharacteristic
131C22×C32#13712yes—
132C32×C4C4×Q812yes—
133C32×C4#12411yescharacteristic
134C32×C4C4⋊Q811yescharacteristic
135C3⋊Dic3—22no—
136C3⋊Dic3#10214yes—
137C3×Dic3—44no—
138C3×Dic3—44no—
139C22×Q8—181no—
140C22×C8—91no—
141C22×C8D3211yescharacteristic
142C4⋊Q8—94no—
143C4⋊Q8—182no—
144C2×C4⋊C4—32no—
145C2×C4⋊C4—32no—
146C2×C4⋊C4—181no—
147C2×C42—91no—
148C2×C42—181no—
149C4⋊C8—182no—
150#95—181no—
151C23×C3—21no—
152C23×C3D3×D412yes—
153C2×C3×C4—22no—
154C2×C3×C4—21no—
155C2×C3×C4—22no—
156C2×C3×C4—21no—
157C2×C3×C4—64no—
158C2×C3×C4—64no—
159C2×C3×C4—122no—
160C2×C3×C4—122no—
161C2×C3×C4—122no—
162C2×C3×C4—122no—
163C2×C3×C4C2×Dic612yes—
164C2×C3×C4C2×C4×D312yes—
165C2×C3×C4#23512yes—
166C2×C3×C4D3×D412yes—
167C2×C3×C4#23712yes—
168C2×C3×C4D3×Q812yes—
169C2×Dic3—24no—
170C2×Dic3—24no—
171C2×Dic3—34no—
172C2×Dic3—34no—
173C2×Dic3—34no—
174C2×Dic3—34no—
175C2×Dic3—42no—
176C2×Dic3—42no—
177C2×Dic3—42no—
178C2×Dic3—42no—
179C2×Dic3—62no—
180C2×Dic3—62no—
181C2×Dic3—62no—
182C2×Dic3—62no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—122no—
186Dic6—1216no—
187C3×C8—42no—
188C3×C8—42no—
189C3⋊C8—122no—
190C3⋊C8—122no—
191C2×C32#39111yescharacteristic
192C2×C32C2×#10211yescharacteristic
193C2×C32#41911yescharacteristic
194C2×C32#47412yes—
195C2×C32#47512yes—
196C2×Q8—184no—
197C2×Q8—362no—
198C2×Q8—362no—
199C22×C4—62no—
200C22×C4—62no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4C2×D3211yescharacteristic
204C2×C8—22no—
205C2×C8—21no—
206C2×C8—182no—
207C2×C8—181no—
208C4⋊C4—34no—
209C4⋊C4—34no—
210C4⋊C4—62no—
211C4⋊C4—62no—
212C4⋊C4—184no—
213C42—92no—
214C42—92no—
215C42—362no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—22no—
219C22×C3—22no—
220C22×C3—21no—
221C22×C3#87812yes—
222C22×C3D3×C22⋊C412yes—
223C22×C3#89612yes—
224C22×C3D3×D812yes—
225C22×C3D3×SD1612yes—
226C22×C3#91512yes—
227C22×C3#91812yes—
228C3×C4—22no—
229C3×C4—21no—
230C3×C4—21no—
231C3×C4—124no—
232C3×C4—124no—
233C3×C4C4×Dic612yes—
234C3×C4#88512yes—
235C3×C4#88712yes—
236C3×C4#88812yes—
237Dic3—38no—
238Dic3—44no—
239Dic3—44no—
240Dic3—64no—
241Dic3—64no—
242Dic3—122no—
243C32#198811yescharacteristic, complemented, Sylow
244C23#380211yescharacteristic
245Q8—368no—
246C2×C4—64no—
247C2×C4—64no—
248C2×C4—92no—
249C2×C4—92no—
250C2×C4—92no—
251C2×C4—92no—
252C2×C4—122no—
253C2×C4—122no—
254C2×C4—122no—
255C2×C4—122no—
256C2×C4—182no—
257C2×C4D3×Dic612yes—
258C2×C4C4×D3211yescharacteristic
259C2×C4#380412yes—
260C2×C4#381111yescharacteristic
261C8—41no—
262C8—361no—
263C2×C3—21no—
264C2×C3—22no—
265C2×C3—22no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3#464612yes—
269C2×C3#475912yes—
270C2×C3D3×#10212yes—
271C2×C3#479112yes—
272C2×C3#480212yes—
273C2×C3#485412yes—
274C2×C3#489012yes—
275C22#6379611yescharacteristic
276C22#6379711yescharacteristic
277C22#6381112yes—
278C22#6389912yes—
279C22#6392111yescharacteristic
280C4—94no—
281C4—124no—
282C4—124no—
283C4—182no—
284C4#6383712yes—
285C4#6384011yescharacteristic
286C4#6395311yescharacteristic
287C3—21no—
288C3#6880012yescomplemented
289C2#1059069111yescharacteristic
290C2#1059077812yes—
291C2#1059081612yes—
292C2#1059094011yescharacteristic
293C2#1059123611yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1988
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
16. #63919C4semidirect
44. C3×C4⋊Dic3Q8semidirect
114. C4⋊Dic3Dic6semidirect
243. C32#1988semidirect
288. C3#68800semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
C2×#636412
#105912742
C3×#45512
#105891632
#688003