Finite Group Databasebeta

← #11791354

Subgroups — #11791354

Order 1152.

414 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C22×#3674C211yesmaximal, characteristic
2C2×C9×#101C211yesmaximal, characteristic
3#10588906C211yesmaximal, characteristic
4C2×#63382C211yesmaximal, characteristic
5#10588804C211yesmaximal, characteristic
6C2×#63381C211yesmaximal, characteristic
7#10588797C211yesmaximal, characteristic
8#70108—31nomaximal
9C22×Q8×C9C2211yescharacteristic
10C22×Dic18C2211yescharacteristic
11C2×C9×M16C2211yescharacteristic
12C2×C9×M16C2211yescharacteristic
13C2×#3674—21no—
14C2×#3674—21no—
15C2×#3674—22no—
16C2×#3674C414yescomplemented
17#63488C2211yescharacteristic
18C2×#3667C2211yescharacteristic
19C22×C9⋊C8C2211yescharacteristic
20C9×#101—22no—
21#63395—22no—
22#63382—22no—
23#63381—22no—
24#63376—22no—
25#63375—21no—
26C8×Dic9—21no—
27C22×#216—31no—
28C2×C3×#101D311yescharacteristic
29#5225—31no—
30C2×#824—31no—
31C2×#822—31no—
32#5122—31no—
33#5120—31no—
34C2×Q8×C9—21no—
35C2×Q8×C9—21no—
36C2×Q8×C9—21no—
37C2×Q8×C9—21no—
38C2×Q8×C9—21no—
39C2×Q8×C9C2×C412yes—
40C22×C4×C9—21no—
41C22×C4×C9C2311yescharacteristic
42C22×Dic9—21no—
43C2×Dic18—21no—
44C2×Dic18—21no—
45C2×Dic18—21no—
46C2×Dic18—21no—
47C2×Dic18—21no—
48C2×Dic18C2×C412yes—
49C9×M16—21no—
50C9×M16—21no—
51C9×M16—21no—
52C9×M16D412yes—
53C2×C8×C9—21no—
54C2×C8×C9—21no—
55#3676—21no—
56#3674—24no—
57#3674—24no—
58C4⋊Dic9D412yes—
59C4×Dic9—21no—
60#3667—21no—
61#3667—21no—
62C2×C9⋊C8—21no—
63C2×C9⋊C8C2×C412yes—
64C2×C9⋊C8D411yescharacteristic
65C2×C9⋊C8D411yescharacteristic
66C2×C9⋊C8D412yes—
67#1979—91noSylow
68C22×C3×Q8C2×D311yescharacteristic
69C22×Dic6—31no—
70C2×C3×M16C2×D311yescharacteristic
71C2×C3×M16C2×D311yescharacteristic
72C2×#216—34no—
73C2×#216—61no—
74C2×#216—61no—
75C2×#216—62no—
76#926—31no—
77C2×#208—31no—
78C22×C3⋊C8—31no—
79C3×#101—22no—
80#835—62no—
81#824—62no—
82#822—62no—
83#816—62no—
84#815—61no—
85C8×Dic3—61no—
86C23×C9#4111yescharacteristic
87Q8×C9—22no—
88Q8×C9—22no—
89Q8×C9—41no—
90Q8×C9—41no—
91C2×C4×C9—22no—
92C2×C4×C9—41no—
93C2×C4×C9—41no—
94C2×C4×C9C22×C411yescharacteristic
95C2×C4×C9C2×D411yescharacteristic
96C2×C4×C9C2×D411yescharacteristic
97C2×C4×C9C2×D411yescharacteristic
98C2×C4×C9C2×D411yescharacteristic
99C2×C4×C9#4111yescharacteristic
100C2×Dic9—22no—
101C2×Dic9—22no—
102C2×Dic9—41no—
103C2×Dic9—41no—
104Dic18—22no—
105Dic18—22no—
106Dic18—41no—
107Dic18—41no—
108C8×C9—22no—
109C8×C9—41no—
110C9⋊C8—41no—
111C9⋊C8C22⋊C412yes—
112C9⋊C8C22⋊C412yes—
113C22×Q16—91no—
114C2×#108—91no—
115#419—91no—
116#419—91no—
117C2×#101—91no—
118C2×#101D911yescharacteristic
119#405—91no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×Q8—21no—
124C2×C3×Q8—21no—
125C2×C3×Q8C4×D312yes—
126C22×C3×C4—21no—
127C22×C3×C4C22×D311yescharacteristic
128C22×Dic3—61no—
129C2×Dic6—32no—
130C2×Dic6—61no—
131C2×Dic6—61no—
132C2×Dic6—61no—
133C2×Dic6—61no—
134C2×Dic6—61no—
135C3×M16—21no—
136C3×M16—21no—
137C3×M16—21no—
138C3×M16#6712yes—
139C2×C3×C8—21no—
140C2×C3×C8—21no—
141#217—61no—
142#216—64no—
143#216—64no—
144C4⋊Dic3—32no—
145C4×Dic3—61no—
146#208—61no—
147#208—61no—
148C2×C3⋊C8—32no—
149C2×C3⋊C8—31no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—32no—
152C2×C3⋊C8—61no—
153C22×C9—22no—
154C22×C9C4×D411yescharacteristic
155C22×C9#12111yescharacteristic
156C22×C9#12411yescharacteristic
157C4×C9—42no—
158C4×C9C2×C22⋊C411yescharacteristic
159C4×C9C4×D411yescharacteristic
160C4×C9#12111yescharacteristic
161C4×C9#12711yescharacteristic
162Dic9—42no—
163Dic9—42no—
164C22×Q8—91no—
165C22×Q8C2×D911yescharacteristic
166C2×Q16—94no—
167C2×Q16—181no—
168C2×Q16—181no—
169C2×Q16—182no—
170C2×M16—91no—
171C2×M16C2×D911yescharacteristic
172C2×M16C2×D911yescharacteristic
173C22×C8—91no—
174#117—91no—
175#108—182no—
176#103—182no—
177#103—182no—
178#101—22no—
179#101—182no—
180#97—181no—
181C4×C8—181no—
182C23×C3#23511yescharacteristic
183C3×Q8—22no—
184C3×Q8—22no—
185C3×Q8—41no—
186C3×Q8—41no—
187C2×C3×C4—22no—
188C2×C3×C4—41no—
189C2×C3×C4—41no—
190C2×C3×C4C2×C4×D311yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4#23711yescharacteristic
195C2×C3×C4C2×#6711yescharacteristic
196C2×Dic3—62no—
197C2×Dic3—62no—
198C2×Dic3—121no—
199C2×Dic3—121no—
200Dic6—62no—
201Dic6—62no—
202Dic6—121no—
203Dic6—121no—
204C3×C8—22no—
205C3×C8—41no—
206C3⋊C8—32no—
207C3⋊C8—32no—
208C3⋊C8—121no—
209C2×C9—21no—
210C2×C9—21no—
211C2×C9#39011yescharacteristic
212C2×C9#47312yes—
213C2×Q8—21no—
214C2×Q8—21no—
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—21no—
218C2×Q8—92no—
219C2×Q8—181no—
220C2×Q8—181no—
221C2×Q8—181no—
222C2×Q8—181no—
223C2×Q8—181no—
224C2×Q8C4×D912yes—
225C22×C4—21no—
226C22×C4—181no—
227C22×C4C22×D911yescharacteristic
228Q16—184no—
229Q16—184no—
230M16—21no—
231M16—21no—
232M16—21no—
233M16—181no—
234M16—181no—
235M16#61112yes—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—92no—
239C2×C8—91no—
240C2×C8—91no—
241C2×C8—92no—
242C2×C8—181no—
243C4⋊C4—92no—
244C22⋊C4—181no—
245C42—181no—
246C22×C3—22no—
247C22×C3#88411yescharacteristic
248C22×C3#88511yescharacteristic
249C22×C3C4×#6711yescharacteristic
250C3×C4—42no—
251C3×C4D3×C22⋊C411yescharacteristic
252C3×C4#67⋊C411yescharacteristic
253C3×C4#93911yescharacteristic
254C3×C4#94011yescharacteristic
255Dic3—122no—
256Dic3—122no—
257C9#197911yescharacteristic, complemented, Sylow
258C23#369711yescharacteristic
259Q8—22no—
260Q8—22no—
261Q8—41no—
262Q8—41no—
263Q8—182no—
264Q8—182no—
265Q8—361no—
266Q8—361no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—182no—
271C2×C4—182no—
272C2×C4—361no—
273C2×C4—361no—
274C2×C4C2×C4×D911yescharacteristic
275C2×C4D4×D911yescharacteristic
276C2×C4D4×D911yescharacteristic
277C2×C4D4×D911yescharacteristic
278C2×C4#369911yescharacteristic
279C2×C4C2×#61111yescharacteristic
280C8—22no—
281C8—41no—
282C8—92no—
283C8—92no—
284C8—361no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3#475512yes—
288C2×C3#495711yescharacteristic
289C22—22no—
290C22#6344611yescharacteristic
291C22#6344711yescharacteristic
292C22C4×#61111yescharacteristic
293C4—42no—
294C4—362no—
295C4—362no—
296C4C22⋊C4×D911yescharacteristic
297C4#611⋊C411yescharacteristic
298C4#6350111yescharacteristic
299C4#6350211yescharacteristic
300C3#7010811yescharacteristic
301C2—21no—
302C2—21no—
303C2#1058843512yes—
304C2#1058863711yescharacteristic
subgroupG/H
centerC22#63446
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC2×C9×#101C2
socleC22×C3#884
prime radicalC23×C3#235
cosocleC22×C4×C9C23
hypercenterC2×#101D9
hypocenterC9#1979
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
16. C2×#3674C4semidirect
257. C9#1979semidirect

Maximal subgroups

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

subgroupindex
C22×#36742
C2×C9×#1012
#105889062
C2×#633822
#105888042
C2×#633812
#105887972
#701083