Finite Group Databasebeta

← #11786871

Subgroups — #11786871

Order 1152.

447 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63449C211yesmaximal, characteristic
2C2×#63376C211yesmaximal, characteristic
3#10588664C211yesmaximal, characteristic
4C2×#63368C211yesmaximal, characteristic
5C2×#63366C211yesmaximal, characteristic
6C9×#340C211yesmaximal, characteristic
7#10588228C211yesmaximal, characteristic
8#68906—31nomaximal
9C22×Dic18C2211yescharacteristic
10C22×C8×C9C2211yescharacteristic
11C2×C9×C4⋊C4C2211yescharacteristic
12C2×C9×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic9—21no—
14C2×C4⋊Dic9C2211yescharacteristic
15C2×Dic9⋊C4—21no—
16C2×C4×Dic9—21no—
17C2×C4×Dic9C2211yescharacteristic
18C22×C9⋊C8C2211yescharacteristic
19#63449—22no—
20#63449—22no—
21C9⋊#95—21no—
22#63376—22no—
23#63368C414yescomplemented
24#63366—22no—
25C2×#887—31no—
26C2×#816—31no—
27#4984—31no—
28C2×#810—31no—
29C2×#807—31no—
30C3×#340D311yescharacteristic
31#4550—31no—
32C22×C4×C9—21no—
33C22×C4×C9—21no—
34C22×C4×C9C2311yescharacteristic
35C22×Dic9—21no—
36C22×Dic9—21no—
37C22×Dic9D411yescharacteristic
38C22×Dic9D411yescharacteristic
39C2×Dic18—21no—
40C2×Dic18—21no—
41C2×Dic18—21no—
42C2×Dic18C2×C412yes—
43C2×Dic18D412yes—
44C2×Dic18Q812yes—
45C2×C8×C9—21no—
46C2×C8×C9—21no—
47C2×C8×C9—21no—
48C9×C4⋊C4—21no—
49C9×C4⋊C4—21no—
50C9×C4⋊C4C2×C412yes—
51C9×C4⋊C4D412yes—
52C4⋊Dic9—21no—
53C4⋊Dic9—21no—
54C4⋊Dic9—42no—
55Dic9⋊C4—24no—
56C4×Dic9—24no—
57C4×Dic9—21no—
58C4×Dic9—21no—
59C2×C9⋊C8—21no—
60C2×C9⋊C8—21no—
61C2×C9⋊C8C2×C412yes—
62#1863—91noSylow
63C22×Dic6—31no—
64C22×C3×C8C2×D311yescharacteristic
65C2×C3×C4⋊C4C2×D311yescharacteristic
66C2×C3×C4⋊C4C2×D311yescharacteristic
67C2×C4⋊Dic3—31no—
68C2×C4⋊Dic3—61no—
69C2×Dic3⋊C4—61no—
70C2×C4×Dic3—31no—
71C2×C4×Dic3—61no—
72C22×C3⋊C8—31no—
73#887—62no—
74#887—62no—
75C3⋊#95—61no—
76#816—62no—
77#810—34no—
78#807—62no—
79C23×C9C2×D411yescharacteristic
80C2×C4×C9—22no—
81C2×C4×C9—22no—
82C2×C4×C9—41no—
83C2×C4×C9—41no—
84C2×C4×C9—41no—
85C2×C4×C9—41no—
86C2×C4×C9C22×C411yescharacteristic
87C2×C4×C9C2×D411yescharacteristic
88C2×C4×C9C2×D411yescharacteristic
89C2×C4×C9C2×Q811yescharacteristic
90C2×C4×C9#4111yescharacteristic
91C2×C4×C9#4111yescharacteristic
92C2×Dic9—22no—
93C2×Dic9—21no—
94C2×Dic9—22no—
95C2×Dic9—22no—
96C2×Dic9—21no—
97C2×Dic9—21no—
98C2×Dic9—21no—
99C2×Dic9—21no—
100C2×Dic9—41no—
101C2×Dic9—41no—
102C2×Dic9—41no—
103C2×Dic9Q1612yes—
104Dic18—22no—
105Dic18—22no—
106Dic18—22no—
107Dic18C4⋊C414yescomplemented
108C8×C9—41no—
109C9⋊C8—22no—
110C2×C4×Q8—91no—
111C2×#107—91no—
112C2×#103—91no—
113C2×#103—91no—
114#389—91no—
115#340D911yescharacteristic
116#336—91no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4C22×D311yescharacteristic
120C22×Dic3—31no—
121C22×Dic3—31no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124C2×Dic6—32no—
125C2×Dic6—32no—
126C2×Dic6—32no—
127C2×Dic6—61no—
128C2×Dic6—61no—
129C2×Dic6—61no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4C4×D312yes—
136C3×C4⋊C4D1212yes—
137C4⋊Dic3—61no—
138C4⋊Dic3—61no—
139C4⋊Dic3—122no—
140Dic3⋊C4—64no—
141C4×Dic3—64no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C2×C3⋊C8—32no—
145C2×C3⋊C8—61no—
146C2×C3⋊C8—61no—
147C22×C9C4×D411yescharacteristic
148C22×C9#12011yescharacteristic
149C22×C9C22⋊Q811yescharacteristic
150C22×C9C2×Q1611yescharacteristic
151C22×C9#13511yescharacteristic
152C22×C9AGL(1,ℤ/8)11yescharacteristic
153C22×C9#13711yescharacteristic
154C4×C9—42no—
155C4×C9—42no—
156C4×C9C2×C4⋊C411yescharacteristic
157C4×C9C4×D411yescharacteristic
158C4×C9C22⋊Q811yescharacteristic
159C4×C9#12311yescharacteristic
160Dic9—24no—
161Dic9—22no—
162Dic9—41no—
163Dic9—81no—
164C22×Q8—91no—
165C22×C8—91no—
166C22×C8C2×D911yescharacteristic
167C4×Q8—182no—
168C4×Q8—182no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4—181no—
171C2×C4⋊C4—181no—
172C2×C4⋊C4C2×D911yescharacteristic
173C2×C4⋊C4C2×D911yescharacteristic
174C2×C42—91no—
175C2×C42—181no—
176#107—182no—
177#103—94no—
178#103—182no—
179#95—181no—
180C23×C3D3×D411yescharacteristic
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—41no—
184C2×C3×C4—41no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×C3×C4C2×C4×D311yescharacteristic
188C2×C3×C4C2×D1211yescharacteristic
189C2×C3×C4#23511yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4#23711yescharacteristic
192C2×C3×C4D3×Q811yescharacteristic
193C2×Dic3—32no—
194C2×Dic3—62no—
195C2×Dic3—61no—
196C2×Dic3—62no—
197C2×Dic3—62no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—121no—
203C2×Dic3—121no—
204C2×Dic3—121no—
205Dic6—34no—
206Dic6—62no—
207Dic6—62no—
208Dic6—62no—
209C3×C8—41no—
210C3⋊C8—62no—
211C2×C9#38511yescharacteristic
212C2×C9C4×Q1611yescharacteristic
213C2×C9#44011yescharacteristic
214C2×C9#44911yescharacteristic
215C2×C9#45111yescharacteristic
216C2×C9#47711yescharacteristic
217C2×C9#47911yescharacteristic
218C2×Q8—92no—
219C2×Q8—92no—
220C2×Q8—92no—
221C2×Q8—181no—
222C2×Q8—181no—
223C2×Q8—181no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—181no—
229C22×C4—181no—
230C22×C4C22×D911yescharacteristic
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—92no—
235C2×C8—181no—
236C2×C8—181no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—184no—
240C4⋊C4—181no—
241C4⋊C4—181no—
242C4⋊C4—362no—
243C4⋊C4C4×D912yes—
244C4⋊C4D3612yes—
245C42—184no—
246C42—181no—
247C42—181no—
248C22×C3#67⋊C411yescharacteristic
249C22×C3#88211yescharacteristic
250C22×C3#89611yescharacteristic
251C22×C3#91111yescharacteristic
252C22×C3#91511yescharacteristic
253C22×C3#91611yescharacteristic
254C22×C3D3×Q1611yescharacteristic
255C3×C4—42no—
256C3×C4—42no—
257C3×C4C4×D1211yescharacteristic
258C3×C4#88311yescharacteristic
259C3×C4D3×C4⋊C411yescharacteristic
260C3×C4#89711yescharacteristic
261Dic3—64no—
262Dic3—62no—
263Dic3—121no—
264Dic3—241no—
265C9#186311yescharacteristic, complemented, Sylow
266C23D4×D911yescharacteristic
267Q8—94no—
268Q8—182no—
269Q8—182no—
270Q8—182no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—92no—
278C2×C4—182no—
279C2×C4—181no—
280C2×C4—182no—
281C2×C4—182no—
282C2×C4—181no—
283C2×C4—181no—
284C2×C4—181no—
285C2×C4—181no—
286C2×C4—361no—
287C2×C4—361no—
288C2×C4—361no—
289C2×C4C2×C4×D911yescharacteristic
290C2×C4C2×D3611yescharacteristic
291C2×C4#369711yescharacteristic
292C2×C4D4×D911yescharacteristic
293C2×C4#369911yescharacteristic
294C2×C4Q8×D911yescharacteristic
295C8—41no—
296C8—182no—
297C2×C3#466811yescharacteristic
298C2×C3#475711yescharacteristic
299C2×C3#478111yescharacteristic
300C2×C3#479011yescharacteristic
301C2×C3#480911yescharacteristic
302C2×C3#485711yescharacteristic
303C2×C3#487511yescharacteristic
304C22#611⋊C411yescharacteristic
305C22#6344411yescharacteristic
306C22#6345811yescharacteristic
307C22#6347311yescharacteristic
308C22#6347711yescharacteristic
309C22#6347811yescharacteristic
310C22Q16×D911yescharacteristic
311C4—42no—
312C4—42no—
313C4—182no—
314C4—184no—
315C4—361no—
316C4—721no—
317C4C4×D3611yescharacteristic
318C4#6344511yescharacteristic
319C4C4⋊C4×D911yescharacteristic
320C4#6345911yescharacteristic
321C3#6890611yescharacteristic
322C2#1058834811yescharacteristic
323C2#1058843711yescharacteristic
324C2#1058846111yescharacteristic
325C2#1058847011yescharacteristic
326C2#1058848911yescharacteristic
327C2#1058853711yescharacteristic
328C2#1058855511yescharacteristic
subgroupG/H
centerC23D4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#340C2
socle, prime radicalC23×C3D3×D4
cosocleC22×C4×C9C23
hypercenter#340D9
hypocenterC9#1863
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
23. #63368C4semidirect
107. Dic18C4⋊C4semidirect
265. C9#1863semidirect

Maximal subgroups

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

subgroupindex
C2×#634492
C2×#633762
#105886642
C2×#633682
C2×#633662
C9×#3402
#105882282
#689063