Finite Group Databasebeta

← #11878930

Subgroups — #11878930

Order 1152.

591 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 591 conjugacy classes of subgroups — too many to draw. Only its 146 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#10589830C211yesmaximal, characteristic, complemented
2#10589818C211yesmaximal, characteristic
3C9×#492C211yesmaximal, characteristic, complemented
4#10588853C214yesmaximal, complemented
5#10588846C214yesmaximal, complemented
6#10588765C211yesmaximal, characteristic, complemented
7#10588750C211yesmaximal, characteristic, complemented
8#10588367C211yesmaximal, characteristic, complemented
9#10588361C211yesmaximal, characteristic, complemented
10#81767—31nomaximal
11C2×#3699C2212yes—
12C2×C9×SD16C2214yes—
13C9×C4⋊Q8C2211yescharacteristic
14C9×#127C2211yescharacteristic
15#63508C2212yes—
16Q8×Dic9C2212yes—
17C2×#3674C2214yes—
18#63500—21no—
19#63500—21no—
20#63498C2212yes—
21D4×Dic9—21no—
22D4×Dic9—21no—
23#63459—21no—
24#63454—21no—
25#63452—21no—
26#63449—21no—
27C42×D9C2211yescharacteristic
28#63431C2211yescharacteristic
29#63431C2211yescharacteristic
30C4×C8×C9C2211yescharacteristic
31#63392C2214yes—
32(C2×D9)⋊C8C2212yes—
33#63376C2214yes—
34Dic9⋊C8C2212yes—
35C4×C9⋊C8C2211yescharacteristic
36#5728—31no—
37#5716—31no—
38C3×#492D311yescharacteristic
39#5173—34no—
40#5166—34no—
41#5092—31no—
42#5070—31no—
43#4685—31no—
44#4681—31no—
45C2×Q8×C9C2312yes—
46C2×D4×C9—21no—
47C2×D4×C9—21no—
48C2×D4×C9C2312yes—
49C2×#611—22no—
50C22×Dic9—22no—
51#3699—44no—
52C2×C4×D9D411yescharacteristic
53C2×C4×D9D411yescharacteristic
54C2×C4×D9C2311yescharacteristic
55C2×Dic18—21no—
56C2×Dic18C2312yes—
57C9×SD16—44no—
58C2×C8×C9C2312yes—
59C9×C4⋊C4—21no—
60C9×C4⋊C4—21no—
61C42×C9C2311yescharacteristic
62#3676—22no—
63#3676—22no—
64#3674—44no—
65(C2×D9)⋊C4—22no—
66C4⋊Dic9—21no—
67C4⋊Dic9—21no—
68C4⋊Dic9—21no—
69C4⋊Dic9—22no—
70C4⋊Dic9C2312yes—
71Dic9⋊C4—22no—
72C4×Dic9—22no—
73C4×Dic9D411yescharacteristic
74C4×Dic9D411yescharacteristic
75C4×Dic9C2311yescharacteristic
76C2×C9⋊C8C2312yes—
77#3210—91noSylow
78C2×#237—32no—
79C2×C3×SD16C2×D314yes—
80C3×C4⋊Q8C2×D311yescharacteristic
81C3×#127C2×D311yescharacteristic
82#946—32no—
83Q8×Dic3—32no—
84C2×#216—34no—
85#938—61no—
86#938—61no—
87#936—32no—
88D4×Dic3—61no—
89D4×Dic3—61no—
90#897—61no—
91#892—61no—
92#890—61no—
93#887—61no—
94C42×D3—31no—
95#869—31no—
96#869—31no—
97C3×C4×C8C2×D311yescharacteristic
98#832—34no—
99(C2×D3)⋊C8—32no—
100#816—34no—
101Dic3⋊C8—32no—
102C4×C3⋊C8—31no—
103C23×C9—22no—
104C22×D9C2×D411yescharacteristic
105Q8×C9—24no—
106D4×C9—24no—
107D4×C9—42no—
108D4×C9—42no—
109C2×C4×C9—22no—
110C2×C4×C9C2×D411yescharacteristic
111C2×C4×C9C2×D411yescharacteristic
112C2×C4×C9C2411yescharacteristic
113#611—44no—
114C2×Dic9—22no—
115C2×Dic9—22no—
116C2×Dic9—44no—
117C2×Dic9C2×D411yescharacteristic
118C2×Dic9C2×D411yescharacteristic
119C2×Dic9C2×D411yescharacteristic
120C4×D9—22no—
121C4×D9—22no—
122C4×D9—22no—
123Dic18—24no—
124Dic18—42no—
125C8×C9—22no—
126C9⋊C8—22no—
127#533—91no—
128#532—91no—
129#494—91no—
130#492D911yescharacteristic, complemented
131#487—91no—
132#486—91no—
133#464—94no—
134#452—94no—
135#431—91no—
136C2×C3×Q8C22×D312yes—
137C2×C3×D4—21no—
138C2×C3×D4—21no—
139C2×C3×D4C22×D312yes—
140C2×#67—62no—
141C22×Dic3—62no—
142#237—124no—
143C2×C4×D3—31no—
144C2×C4×D3—31no—
145C2×C4×D3—31no—
146C2×Dic6—32no—
147C2×Dic6—61no—
148C3×SD16—44no—
149C2×C3×C8C22×D312yes—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C42C22×D311yescharacteristic
153#217—62no—
154#217—62no—
155#216—124no—
156(C2×D3)⋊C4—62no—
157C4⋊Dic3—32no—
158C4⋊Dic3—62no—
159C4⋊Dic3—61no—
160C4⋊Dic3—61no—
161C4⋊Dic3—61no—
162Dic3⋊C4—62no—
163C4×Dic3—31no—
164C4×Dic3—31no—
165C4×Dic3—31no—
166C4×Dic3—62no—
167C2×C3⋊C8—32no—
168C22×C9—42no—
169C22×C9—42no—
170C22×C9—42no—
171C22×C9C22×D411yescharacteristic
172C2×D9—21no—
173C2×D9—21no—
174C2×D9—21no—
175C4×C9—42no—
176C4×C9#13512yes—
177C4×C9#13712yes—
178C4×C9H(5,𝔽2)12yes—
179Dic9—21no—
180Dic9—21no—
181Dic9—21no—
182Dic9—42no—
183Dic9—42no—
184C2×#41—92no—
185C2×Q16—94no—
186C2×SD16C2×D914yes—
187C4⋊Q8—91no—
188C4⋊Q8—91no—
189C4⋊Q8C2×D911yescharacteristic
190#127C2×D911yescharacteristic
191#125—181no—
192#124—92no—
193C22⋊Q8—92no—
194C22⋊Q8—181no—
195#121—181no—
196#121—181no—
197C4×Q8—92no—
198C4×Q8—181no—
199C4×D4—181no—
200C4×D4—181no—
201#117—181no—
202C2×C42—91no—
203C4⋊C8—92no—
204#103—94no—
205#102—94no—
206C22⋊C8—92no—
207C4×C8—91no—
208C4×C8C2×D911yescharacteristic
209C23×C3—22no—
210C22×D3—31no—
211C3×Q8—24no—
212C3×D4—24no—
213C3×D4—42no—
214C3×D4—42no—
215C2×C3×C4—22no—
216C2×C3×C4D3×D411yescharacteristic
217C2×C3×C4D3×D411yescharacteristic
218C2×C3×C4C23×D311yescharacteristic
219#67—124no—
220C2×Dic3—31no—
221C2×Dic3—31no—
222C2×Dic3—31no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—124no—
226C4×D3—62no—
227C4×D3—62no—
228C4×D3—62no—
229Dic6—64no—
230Dic6—122no—
231C3×C8—22no—
232C3⋊C8—62no—
233C2×C9—82no—
234C2×C9#53511yescharacteristic
235C2×C9C2×#13511yescharacteristic
236C2×C9C2×#13711yescharacteristic
237D9—41no—
238#41—364no—
239C2×Q8—92no—
240C2×Q8—181no—
241C2×Q8C22×D912yes—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—182no—
245C2×D4C22×D912yes—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—182no—
250Q16—364no—
251SD16—44no—
252C2×C8—92no—
253C2×C8C22×D912yes—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—92no—
257C4⋊C4—182no—
258C4⋊C4—182no—
259C4⋊C4—181no—
260C4⋊C4—181no—
261C4⋊C4—181no—
262C22⋊C4—182no—
263C22⋊C4—182no—
264C22⋊C4—182no—
265C42—91no—
266C42—91no—
267C42—91no—
268C42—182no—
269C42C22×D911yescharacteristic
270C22×C3—42no—
271C22×C3—42no—
272C22×C3—42no—
273C22×C3C2×D3×D411yescharacteristic
274C2×D3—61no—
275C2×D3—61no—
276C2×D3—61no—
277C3×C4—42no—
278C3×C4#91512yes—
279C3×C4#91612yes—
280C3×C4#100412yes—
281Dic3—61no—
282Dic3—61no—
283Dic3—61no—
284Dic3—122no—
285Dic3—122no—
286C9#321011yescharacteristic, complemented, Sylow
287C23—22no—
288C23—91no—
289Q8—24no—
290Q8—184no—
291Q8—362no—
292D4—24no—
293D4—42no—
294D4—42no—
295D4—364no—
296C2×C4—22no—
297C2×C4—91no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—364no—
306C2×C4D4×D911yescharacteristic
307C2×C4D4×D911yescharacteristic
308C2×C4C23×D911yescharacteristic
309C8—22no—
310C8—182no—
311C2×C3—82no—
312C2×C3#571511yescharacteristic
313C2×C3C2×#91511yescharacteristic
314C2×C3C2×#91611yescharacteristic
315D3—121no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—181no—
320C22—181no—
321C22—181no—
322C22C2×D4×D911yescharacteristic
323C4—42no—
324C4—181no—
325C4—181no—
326C4—181no—
327C4—362no—
328C4—362no—
329C4#6347712yes—
330C4#6347812yes—
331C4#6371012yes—
332C3#8176711yescharacteristic
333C2—82no—
334C2—361no—
335C2#1058981711yescharacteristic
336C2C2×#6347711yescharacteristic
337C2C2×#6347811yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#492C2
socleC22×C3C2×D3×D4
prime radical#10589818C2
hypercenter#492D9
hypocenterC9#3210
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #10589830C2semidirect
3. C9×#492C2semidirect
4. #10588853C2semidirect
5. #10588846C2semidirect
6. #10588765C2semidirect
7. #10588750C2semidirect
8. #10588367C2semidirect
9. #10588361C2semidirect
130. #492D9semidirect
286. C9#3210semidirect

Maximal subgroups

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

subgroupindex
#105898302
#105898182
C9×#4922
#105888532
#105888462
#105887652
#105887502
#105883672
#105883612
#817673