Finite Group Databasebeta

← #11794271

Subgroups — #11794271

Order 1152.

345 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 345 conjugacy classes of subgroups — too many to draw. Only its 104 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#10589621C211yesmaximal, characteristic
2#10588805C211yesmaximal, characteristic
3#10588679C211yesmaximal, characteristic
4#10588616C211yesmaximal, characteristic
5C9×#339C211yesmaximal, characteristic
6#10588234C211yesmaximal, characteristic
7#10588201C211yesmaximal, characteristic
8#68736—31nomaximal
9C2×C9×M16C2211yescharacteristic
10C9×#117C2211yescharacteristic
11C2×C42×C9C2211yescharacteristic
12#63488C2211yescharacteristic
13C2×C4⋊Dic9C2211yescharacteristic
14C2×C4⋊Dic9C2211yescharacteristic
15C2×#3667C2211yescharacteristic
16#63452—21no—
17#63450—21no—
18#63440—22no—
19#63432—21no—
20#63431—21no—
21C9⋊#95—22no—
22#63378—21no—
23#63377—21no—
24#63367—21no—
25#63366—21no—
26#5519—31no—
27#5121—31no—
28#4995—31no—
29#4936—31no—
30C3×#339D311yescharacteristic
31#4554—31no—
32#4523—31no—
33C22×C4×C9—21no—
34C22×C4×C9C2311yescharacteristic
35C22×Dic9—21no—
36C22×Dic9D412yes—
37C2×Dic18—22no—
38C9×M16—21no—
39C9×M16Q812yescomplemented
40C2×C8×C9—21no—
41C9×C4⋊C4D411yescharacteristic
42C9×C4⋊C4D411yescharacteristic
43C9×C22⋊C4—21no—
44C42×C9—21no—
45C42×C9—21no—
46C42×C9Q812yescomplemented
47#3676—21no—
48C4⋊Dic9—22no—
49C4⋊Dic9—21no—
50C4⋊Dic9—21no—
51C4⋊Dic9—21no—
52C4⋊Dic9—21no—
53C4⋊Dic9D411yescharacteristic
54C4⋊Dic9D411yescharacteristic
55Dic9⋊C4—22no—
56Dic9⋊C4—22no—
57C4×Dic9—21no—
58#3667—21no—
59#3667Q812yescomplemented
60C2×C9⋊C8—21no—
61#2061—91noSylow
62C2×C3×M16C2×D311yescharacteristic
63C3×#117C2×D311yescharacteristic
64C2×C3×C42C2×D311yescharacteristic
65#926—31no—
66C2×C4⋊Dic3—31no—
67C2×C4⋊Dic3—31no—
68C2×#208—31no—
69#890—61no—
70#888—61no—
71#878—62no—
72#870—61no—
73#869—61no—
74C3⋊#95—62no—
75#818—61no—
76#817—61no—
77#808—61no—
78#807—61no—
79C23×C9C2×D411yescharacteristic
80C2×C4×C9—21no—
81C2×C4×C9—21no—
82C2×C4×C9—22no—
83C2×C4×C9—41no—
84C2×C4×C9—41no—
85C2×C4×C9C2×D411yescharacteristic
86C2×C4×C9C2×D411yescharacteristic
87C2×C4×C9C2×Q811yescharacteristic
88C2×C4×C9C2×Q811yescharacteristic
89C2×C4×C9C2×Q811yescharacteristic
90C2×C4×C9#4111yescharacteristic
91C2×Dic9—21no—
92C2×Dic9—21no—
93C2×Dic9—22no—
94C2×Dic9—42no—
95C2×Dic9—42no—
96C2×Dic9—41no—
97Dic18—82no—
98C8×C9—22no—
99C9⋊C8—22no—
100#544—91no—
101#428—91no—
102#428—91no—
103#382—91no—
104#343—91no—
105#339—91no—
106#339D911yescharacteristic
107C22×C3×C4—21no—
108C22×C3×C4C22×D311yescharacteristic
109C22×Dic3—32no—
110C22×Dic3—61no—
111C2×Dic6—62no—
112C3×M16—21no—
113C3×M16Dic612yes—
114C2×C3×C8—21no—
115C3×C4⋊C4D1211yescharacteristic
116C3×C4⋊C4D1211yescharacteristic
117C3×C22⋊C4—21no—
118C3×C42—21no—
119C3×C42—21no—
120C3×C42Dic612yes—
121#217—61no—
122C4⋊Dic3—31no—
123C4⋊Dic3—31no—
124C4⋊Dic3—62no—
125C4⋊Dic3—61no—
126C4⋊Dic3—61no—
127C4⋊Dic3—61no—
128C4⋊Dic3—61no—
129Dic3⋊C4—62no—
130Dic3⋊C4—62no—
131C4×Dic3—61no—
132#208—32no—
133#208—61no—
134C2×C3⋊C8—61no—
135C22×C9—21no—
136C22×C9—21no—
137C22×C9#12011yescharacteristic
138C22×C9C22⋊Q811yescharacteristic
139C22×C9C4⋊Q811yescharacteristic
140C4×C9—42no—
141C4×C9—41no—
142C4×C9—41no—
143C4×C9C22⋊Q811yescharacteristic
144C4×C9C22⋊Q811yescharacteristic
145C4×C9C4⋊Q811yescharacteristic
146C4×C9C4⋊Q811yescharacteristic
147Dic9—41no—
148Dic9—41no—
149Dic9—42no—
150Dic9—81no—
151C2×M16—91no—
152C2×M16C2×D911yescharacteristic
153C4⋊Q8—181no—
154C4⋊Q8—181no—
155#125—181no—
156#125—181no—
157C22⋊Q8—182no—
158#117—91no—
159#117C2×D911yescharacteristic
160C2×C4⋊C4—91no—
161C2×C4⋊C4—91no—
162C2×C42C2×D911yescharacteristic
163#107—181no—
164#107—181no—
165#106—181no—
166#106—181no—
167#95—182no—
168C23×C3D3×D411yescharacteristic
169C2×C3×C4—22no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—41no—
173C2×C3×C4—41no—
174C2×C3×C4C2×Dic611yescharacteristic
175C2×C3×C4C2×Dic611yescharacteristic
176C2×C3×C4C2×D1211yescharacteristic
177C2×C3×C4D3×D411yescharacteristic
178C2×C3×C4#23711yescharacteristic
179C2×C3×C4D3×Q811yescharacteristic
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—62no—
183C2×Dic3—122no—
184C2×Dic3—122no—
185C2×Dic3—121no—
186Dic6—242no—
187C3×C8—22no—
188C3⋊C8—62no—
189C2×C9—21no—
190C2×C9—21no—
191C2×C9#39511yescharacteristic
192C2×C9#45411yescharacteristic
193C2×C9#45511yescharacteristic
194C2×Q8—182no—
195C22×C4—21no—
196C22×C4—92no—
197C22×C4—181no—
198C22×C4C22×D911yescharacteristic
199M16—21no—
200M16—92no—
201M16—181no—
202M16Dic1812yescomplemented
203C2×C8—21no—
204C2×C8—181no—
205C4⋊C4—91no—
206C4⋊C4—91no—
207C4⋊C4—182no—
208C4⋊C4—182no—
209C4⋊C4—182no—
210C4⋊C4—181no—
211C4⋊C4—181no—
212C4⋊C4—181no—
213C4⋊C4—181no—
214C4⋊C4D3611yescharacteristic
215C4⋊C4D3611yescharacteristic
216C22⋊C4—21no—
217C22⋊C4—181no—
218C42—21no—
219C42—21no—
220C42—181no—
221C42Dic1812yescomplemented
222C22×C3—21no—
223C22×C3—21no—
224C22×C3#87811yescharacteristic
225C22×C3#88211yescharacteristic
226C22×C3#88811yescharacteristic
227C3×C4—42no—
228C3×C4—41no—
229C3×C4—41no—
230C3×C4#86911yescharacteristic
231C3×C4#87811yescharacteristic
232C3×C4#88811yescharacteristic
233C3×C4#89711yescharacteristic
234Dic3—121no—
235Dic3—122no—
236Dic3—121no—
237Dic3—241no—
238C9#206111yescharacteristic, complemented, Sylow
239C23D4×D911yescharacteristic
240Q8—722no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—181no—
247C2×C4—181no—
248C2×C4—182no—
249C2×C4—362no—
250C2×C4—362no—
251C2×C4—361no—
252C2×C4C2×Dic1811yescharacteristic
253C2×C4C2×Dic1811yescharacteristic
254C2×C4C2×D3611yescharacteristic
255C2×C4D4×D911yescharacteristic
256C2×C4#369911yescharacteristic
257C2×C4Q8×D911yescharacteristic
258C8—22no—
259C8—182no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3#465611yescharacteristic
263C2×C3#482511yescharacteristic
264C2×C3#482711yescharacteristic
265C22—21no—
266C22—21no—
267C22#6344011yescharacteristic
268C22#6344411yescharacteristic
269C22#6345011yescharacteristic
270C4—42no—
271C4—41no—
272C4—41no—
273C4—362no—
274C4—361no—
275C4—361no—
276C4—721no—
277C4#6343111yescharacteristic
278C4#6344011yescharacteristic
279C4#6345011yescharacteristic
280C4#6345911yescharacteristic
281C3#6873611yescharacteristic
282C2—21no—
283C2—21no—
284C2#1058833611yescharacteristic
285C2#1058850511yescharacteristic
286C2#1058850711yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#339C2
socleC22×C3#882
prime radicalC23×C3D3×D4
hypercenter#339D9
hypocenterC9#2061
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
39. C9×M16Q8semidirect
46. C42×C9Q8semidirect
59. #3667Q8semidirect
202. M16Dic18semidirect
221. C42Dic18semidirect
238. C9#2061semidirect

Maximal subgroups

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

subgroupindex
#105896212
#105888052
#105886792
#105886162
C9×#3392
#105882342
#105882012
#687363