Finite Group Databasebeta

← #11778014

Subgroups — #11778014

Order 1152.

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

normal subgroups only

This group has 474 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
1C9×#543C211yesmaximal, characteristic, complemented
2#10588729C212yesmaximal, complemented
3#10588640C211yesmaximal, characteristic
4#10588215C212yesmaximal, complemented
5#10588202C211yesmaximal, characteristic, complemented
6#71892—31nomaximal
7C22×#611—21no—
8C22×D36C2211yescharacteristic
9C9×C22⋊Q8—22no—
10C9×C22⋊Q8—21no—
11C9×C22⋊Q8—22no—
12C9×C22⋊Q8C2212yes—
13C2×C9×C22⋊C4—21no—
14C2×C9×C22⋊C4C2211yescharacteristic
15C2×#3675—22no—
16C2×(C2×D9)⋊C4—21no—
17C9⋊#95C2211yescharacteristic
18#63389C2212yes—
19#63369—22no—
20C3×#543D311yescharacteristic
21#5046—32no—
22#4960—31no—
23#4538—32no—
24#4525—31no—
25C24×C9D411yescharacteristic
26C23×D9—21no—
27C2×Q8×C9—21no—
28C2×Q8×C9D412yescomplemented
29C22×C4×C9—21no—
30C22×C4×C9—21no—
31C22×C4×C9D411yescharacteristic
32C22×C4×C9C2311yescharacteristic
33C2×#611—42no—
34C2×#611—42no—
35C2×#611—42no—
36C22×Dic9—21no—
37C2×D36—22no—
38C2×D36—42no—
39C9×C4⋊C4—21no—
40C9×C4⋊C4—22no—
41C9×C4⋊C4—22no—
42C9×C4⋊C4D412yescomplemented
43C9×C22⋊C4—22no—
44C9×C22⋊C4—22no—
45C9×C22⋊C4—22no—
46#3675—44no—
47(C2×D9)⋊C4—42no—
48C2×C9⋊C8—22no—
49#1596—91noSylow
50C22×#67—61no—
51C22×D12—31no—
52C3×C22⋊Q8—22no—
53C3×C22⋊Q8—21no—
54C3×C22⋊Q8—22no—
55C3×C22⋊Q8C2×D312yes—
56C2×C3×C22⋊C4—21no—
57C2×C3×C22⋊C4C2×D311yescharacteristic
58C2×#215—62no—
59C2×(C2×D3)⋊C4—61no—
60C3⋊#95—31no—
61#830—32no—
62#809—62no—
63C23×C9—21no—
64C23×C9—21no—
65C23×C9—41no—
66C23×C9—41no—
67C23×C9SD1612yescomplemented
68C23×C9C2×D411yescharacteristic
69C22×D9—22no—
70C22×D9—41no—
71C22×D9—41no—
72C22×D9—41no—
73C22×D9—41no—
74C22×D9—41no—
75C22×D9—41no—
76Q8×C9—42no—
77Q8×C9—81no—
78C2×C4×C9—22no—
79C2×C4×C9—21no—
80C2×C4×C9—22no—
81C2×C4×C9—41no—
82C2×C4×C9—41no—
83C2×C4×C9—81no—
84C2×C4×C9—81no—
85C2×C4×C9C2×D412yes—
86#611—48no—
87C2×Dic9—22no—
88C2×Dic9—41no—
89C2×Dic9—41no—
90D36—24no—
91D36—42no—
92C9⋊C8—42no—
93#543D911yescharacteristic, complemented
94#450—92no—
95#392—91no—
96#328—92no—
97#323—91no—
98C24×C3#6711yescharacteristic
99C23×D3—61no—
100C2×C3×Q8—21no—
101C2×C3×Q8#6712yes—
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C22×C3×C4#6711yescharacteristic
105C22×C3×C4C22×D311yescharacteristic
106C2×#67—122no—
107C2×#67—122no—
108C2×#67—122no—
109C22×Dic3—61no—
110C2×D12—62no—
111C2×D12—122no—
112C3×C4⋊C4—21no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4#6712yes—
116C3×C22⋊C4—22no—
117C3×C22⋊C4—22no—
118C3×C22⋊C4—22no—
119#215—124no—
120(C2×D3)⋊C4—122no—
121C2×C3⋊C8—62no—
122C22×C9—21no—
123C22×C9—21no—
124C22×C9—22no—
125C22×C9—42no—
126C22×C9—41no—
127C22×C9—41no—
128C22×C9—81no—
129C22×C9#12011yescharacteristic
130C22×C9C2×SD1611yescharacteristic
131C22×C9#13711yescharacteristic
132C2×D9—42no—
133C2×D9—42no—
134C2×D9—42no—
135C2×D9—81no—
136C2×D9—81no—
137C2×D9—81no—
138C2×D9—81no—
139C4×C9—22no—
140C4×C9—41no—
141C4×C9—42no—
142C4×C9—42no—
143Dic9—42no—
144C22×D4—91no—
145C22×D4—181no—
146C2×SD16—182no—
147C22⋊Q8—22no—
148C22⋊Q8—21no—
149C22⋊Q8—22no—
150C22⋊Q8C2×D912yes—
151C2×C22⋊C4—21no—
152C2×C22⋊C4—181no—
153C2×C22⋊C4C2×D911yescharacteristic
154#102—182no—
155C22⋊C8—92no—
156#95—91no—
157C23×C3—21no—
158C23×C3—21no—
159C23×C3—41no—
160C23×C3—41no—
161C23×C3#21512yes—
162C23×C3C2×#6711yescharacteristic
163C22×D3—62no—
164C22×D3—121no—
165C22×D3—121no—
166C22×D3—121no—
167C22×D3—121no—
168C22×D3—121no—
169C22×D3—121no—
170C3×Q8—42no—
171C3×Q8—81no—
172C2×C3×C4—22no—
173C2×C3×C4—21no—
174C2×C3×C4—22no—
175C2×C3×C4—41no—
176C2×C3×C4—41no—
177C2×C3×C4—81no—
178C2×C3×C4—81no—
179C2×C3×C4C2×#6712yes—
180#67—128no—
181C2×Dic3—62no—
182C2×Dic3—121no—
183C2×Dic3—121no—
184D12—64no—
185D12—122no—
186C3⋊C8—122no—
187C2×C9—21no—
188C2×C9—21no—
189C2×C9—42no—
190C2×C9#44811yescharacteristic
191C2×C9#45311yescharacteristic
192C2×C9B(4,𝔽2)11yescharacteristic
193D9—82no—
194C24—181no—
195C24#61111yescharacteristic
196C2×Q8—21no—
197C2×Q8#61112yescomplemented
198C2×D4—182no—
199C2×D4—362no—
200C2×D4—362no—
201C2×D4—362no—
202C2×D4—362no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—181no—
206C22×C4#61111yescharacteristic
207C22×C4C22×D911yescharacteristic
208SD16—364no—
209C2×C8—182no—
210C4⋊C4—21no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4#61112yescomplemented
214C22⋊C4—22no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—362no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—22no—
221C22×C3—42no—
222C22×C3—41no—
223C22×C3—41no—
224C22×C3—81no—
225C22×C3C2×#21511yescharacteristic
226C22×C3#94211yescharacteristic
227C22×C3#95311yescharacteristic
228C2×D3—122no—
229C2×D3—122no—
230C2×D3—122no—
231C2×D3—241no—
232C2×D3—241no—
233C2×D3—241no—
234C2×D3—241no—
235C3×C4—22no—
236C3×C4—41no—
237C3×C4—42no—
238C3×C4—42no—
239Dic3—122no—
240C9#159611yescharacteristic, complemented, Sylow
241C23—21no—
242C23—21no—
243C23—41no—
244C23—41no—
245C23—182no—
246C23—361no—
247C23—361no—
248C23—361no—
249C23—361no—
250C23—361no—
251C23—361no—
252C23#367512yescomplemented
253C23C2×#61111yescharacteristic
254Q8—42no—
255Q8—81no—
256D4—184no—
257D4—362no—
258D4—368no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—182no—
267C2×C4—361no—
268C2×C4—361no—
269C2×C4C2×#61112yes—
270C8—362no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—42no—
274C2×C3#522711yescharacteristic
275C2×C3#524111yescharacteristic
276C2×C3#524411yescharacteristic
277D3—242no—
278C22—21no—
279C22—21no—
280C22—22no—
281C22—42no—
282C22—41no—
283C22—41no—
284C22—81no—
285C22—362no—
286C22—362no—
287C22—362no—
288C22—721no—
289C22—721no—
290C22—721no—
291C22—721no—
292C22C2×#367511yescharacteristic
293C22#6350511yescharacteristic
294C22#6351511yescharacteristic
295C4—22no—
296C4—41no—
297C4—42no—
298C4—42no—
299C4—362no—
300C3#7189211yescharacteristic
301C2—21no—
302C2—21no—
303C2—42no—
304C2—722no—
305C2#1058890811yescharacteristic
306C2#1058892211yescharacteristic
307C2#1058892411yescharacteristic
subgroupG/H
centerC22#63515
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#543C2
socleC22×C3#953
prime radical#10588640C2
hypercenter#543D9
hypocenterC9#1596
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
1. C9×#543C2semidirect
2. #10588729C2semidirect
4. #10588215C2semidirect
5. #10588202C2semidirect
28. C2×Q8×C9D4semidirect
42. C9×C4⋊C4D4semidirect
67. C23×C9SD16semidirect
93. #543D9semidirect
197. C2×Q8#611semidirect
213. C4⋊C4#611semidirect
240. C9#1596semidirect
252. C23#3675semidirect

Maximal subgroups

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

subgroupindex
C9×#5432
#105887292
#105886402
#105882152
#105882022
#718923