Finite Group Databasebeta

← #11878699

Subgroups — #11878699

Order 1152.

642 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 154 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#10589827C211yesmaximal, characteristic
2D9×C4⋊Q8C211yesmaximal, characteristic, complemented
3C9×#487C211yesmaximal, characteristic, complemented
4#10588770C211yesmaximal, characteristic, complemented
5#10588766C211yesmaximal, characteristic, complemented
6#10588498C214yesmaximal, complemented
7#10588486C214yesmaximal, complemented
8#10588375C211yesmaximal, characteristic, complemented
9#10588367C211yesmaximal, characteristic, complemented
10#81602—31nomaximal
11C2×#3701—21no—
12C2×Q8×D9C2212yes—
13C9×C4⋊Q8C2211yescharacteristic
14C9×C4⋊Q8C2211yescharacteristic
15#63509—21no—
16#63506C2212yes—
17C2×#3675C2214yes—
18C2×#3664C2214yes—
19#63457—21no—
20#63457C2212yes—
21#63455—21no—
22#63455C2212yes—
23C4⋊C4×D9—21no—
24C4⋊C4×D9—21no—
25#63450—21no—
26#63450—21no—
27#63436C2211yescharacteristic
28C42×D9C2211yescharacteristic
29#63431C2211yescharacteristic
30C9×#103C2214yes—
31C4×C8×C9C2211yescharacteristic
32(C2×D9)⋊C8C2212yes—
33Dic9⋊C8C2212yes—
34#63368C2214yes—
35C4×C9⋊C8C2211yescharacteristic
36#5725—31no—
37D3×C4⋊Q8—31no—
38C3×#487D311yescharacteristic
39#5093—31no—
40#5085—31no—
41#4818—34no—
42#4806—34no—
43#4693—31no—
44#4685—31no—
45C2×Q8×C9—21no—
46C2×Q8×C9C2312yes—
47#3701—44no—
48Q8×D9—44no—
49C2×D36—22no—
50C2×D36—21no—
51C2×D36—21no—
52C2×D36C2312yes—
53C2×C4×D9—22no—
54C2×C4×D9—22no—
55C2×C4×D9D411yescharacteristic
56C2×C4×D9D411yescharacteristic
57C2×C4×D9C2311yescharacteristic
58C2×Dic18—22no—
59C2×Dic18C2312yes—
60C2×C8×C9C2312yes—
61C9×C4⋊C4—21no—
62C9×C4⋊C4—21no—
63C9×C4⋊C4—21no—
64C9×C4⋊C4C2312yes—
65C42×C9C2311yescharacteristic
66#3675—44no—
67(C2×D9)⋊C4—22no—
68(C2×D9)⋊C4—22no—
69C4⋊Dic9—21no—
70C4⋊Dic9—21no—
71Dic9⋊C4—22no—
72Dic9⋊C4—22no—
73C4×Dic9D411yescharacteristic
74C4×Dic9D411yescharacteristic
75C4×Dic9C2311yescharacteristic
76C2×C9⋊C8C2312yes—
77#3664—44no—
78#3206—91noSylow
79C2×#239—61no—
80C2×D3×Q8—32no—
81C3×C4⋊Q8C2×D311yescharacteristic
82C3×C4⋊Q8C2×D311yescharacteristic
83#947—61no—
84#944—32no—
85C2×#215—34no—
86C2×#204—34no—
87#895—32no—
88#895—61no—
89#893—32no—
90#893—61no—
91D3×C4⋊C4—61no—
92D3×C4⋊C4—61no—
93#888—61no—
94#888—61no—
95#874—31no—
96C42×D3—31no—
97#869—31no—
98C3×#103C2×D314yes—
99C3×C4×C8C2×D311yescharacteristic
100(C2×D3)⋊C8—32no—
101Dic3⋊C8—32no—
102#810—34no—
103C4×C3⋊C8—31no—
104C22×D9—22no—
105C22×D9C2×D411yescharacteristic
106Q8×C9—24no—
107Q8×C9—42no—
108C2×C4×C9—22no—
109C2×C4×C9—22no—
110C2×C4×C9C2×D411yescharacteristic
111C2×C4×C9C2×D411yescharacteristic
112C2×C4×C9C2411yescharacteristic
113C2×Dic9—22no—
114C2×Dic9C2×D411yescharacteristic
115C2×Dic9C2×D411yescharacteristic
116C2×Dic9C2×D411yescharacteristic
117D36—24no—
118D36—44no—
119D36—42no—
120D36—42no—
121C4×D9—22no—
122C4×D9—22no—
123C4×D9—44no—
124C4×D9—44no—
125C4×D9SD1614yescomplemented
126Dic18—24no—
127Dic18—44no—
128C8×C9—22no—
129C9⋊C8—22no—
130#532—91no—
131C2×C4⋊Q8—91no—
132#492—91no—
133#492—91no—
134#487—91no—
135#487D911yescharacteristic, complemented
136#461—94no—
137#448—94no—
138#431—91no—
139C2×C3×Q8—21no—
140C2×C3×Q8C22×D312yes—
141#239—124no—
142D3×Q8—124no—
143C2×D12—32no—
144C2×D12—62no—
145C2×D12—61no—
146C2×D12—61no—
147C2×C4×D3—31no—
148C2×C4×D3—31no—
149C2×C4×D3—31no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×Dic6—32no—
153C2×Dic6—62no—
154C2×C3×C8C22×D312yes—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4C22×D312yes—
159C3×C42C22×D311yescharacteristic
160#215—124no—
161(C2×D3)⋊C4—62no—
162(C2×D3)⋊C4—62no—
163C4⋊Dic3—61no—
164C4⋊Dic3—61no—
165Dic3⋊C4—62no—
166Dic3⋊C4—62no—
167C4×Dic3—31no—
168C4×Dic3—31no—
169C4×Dic3—31no—
170C2×C3⋊C8—32no—
171#204—124no—
172C22×C9C22×D411yescharacteristic
173C2×D9—21no—
174C2×D9—21no—
175C2×D9—42no—
176C2×D9—42no—
177C2×D9—42no—
178C2×D9C2×SD1612yes—
179C4×C9—42no—
180C4×C9—42no—
181C4×C9C2×SD1612yes—
182C4×C9#13712yes—
183C4×C9H(5,𝔽2)12yes—
184Dic9—21no—
185Dic9—21no—
186Dic9—42no—
187Dic9C2×SD1612yes—
188C2×#41—181no—
189C22×Q8—92no—
190C2×SD16—94no—
191C2×SD16—94no—
192C4⋊Q8—92no—
193C4⋊Q8—91no—
194C4⋊Q8—181no—
195C4⋊Q8—181no—
196C4⋊Q8C2×D911yescharacteristic
197C4⋊Q8C2×D911yescharacteristic
198#127—91no—
199#124—181no—
200#121—92no—
201#121—181no—
202C4×D4—92no—
203C4×D4—181no—
204C2×C4⋊C4—181no—
205C2×C4⋊C4—181no—
206C2×C42—91no—
207C4⋊C8—92no—
208#103—94no—
209#103C2×D914yes—
210C22⋊C8—92no—
211C4×C8—91no—
212C4×C8C2×D911yescharacteristic
213C22×D3—31no—
214C22×D3—62no—
215C3×Q8—24no—
216C3×Q8—42no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4D3×D411yescharacteristic
220C2×C3×C4D3×D411yescharacteristic
221C2×C3×C4C23×D311yescharacteristic
222C2×Dic3—31no—
223C2×Dic3—31no—
224C2×Dic3—31no—
225C2×Dic3—62no—
226D12—64no—
227D12—124no—
228D12—122no—
229D12—122no—
230C4×D3—34no—
231C4×D3—62no—
232C4×D3—62no—
233C4×D3—124no—
234C4×D3—124no—
235Dic6—64no—
236Dic6—124no—
237C3×C8—22no—
238C3⋊C8—62no—
239C2×C9#53511yescharacteristic
240C2×C9C22×SD1611yescharacteristic
241C2×C9C2×#13711yescharacteristic
242D9—22no—
243D9—82no—
244#41—364no—
245C2×Q8—21no—
246C2×Q8—92no—
247C2×Q8—182no—
248C2×Q8—364no—
249C2×Q8C22×D912yes—
250C2×D4—92no—
251C2×D4—182no—
252C2×D4—181no—
253C2×D4—181no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—182no—
258C22×C4—182no—
259SD16—364no—
260SD16—364no—
261C2×C8—92no—
262C2×C8C22×D912yes—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—182no—
267C4⋊C4—182no—
268C4⋊C4—181no—
269C4⋊C4—181no—
270C4⋊C4C22×D912yes—
271C22⋊C4—182no—
272C22⋊C4—182no—
273C42—91no—
274C42—91no—
275C42—91no—
276C42C22×D911yescharacteristic
277C22×C3C2×D3×D411yescharacteristic
278C2×D3—32no—
279C2×D3—61no—
280C2×D3—61no—
281C2×D3—122no—
282C2×D3—122no—
283C2×D3—122no—
284C3×C4—42no—
285C3×C4—42no—
286C3×C4D3×SD1612yes—
287C3×C4#91812yes—
288C3×C4#100912yes—
289Dic3—32no—
290Dic3—61no—
291Dic3—61no—
292Dic3—122no—
293C9#320611yescharacteristic, complemented, Sylow
294C23—91no—
295C23—182no—
296Q8—24no—
297Q8—42no—
298Q8—184no—
299Q8—364no—
300D4—184no—
301D4—364no—
302D4—362no—
303D4—362no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—91no—
307C2×C4—94no—
308C2×C4—91no—
309C2×C4—91no—
310C2×C4—182no—
311C2×C4—182no—
312C2×C4—182no—
313C2×C4—364no—
314C2×C4—364no—
315C2×C4D4×D911yescharacteristic
316C2×C4D4×D911yescharacteristic
317C2×C4C23×D911yescharacteristic
318C8—22no—
319C8—182no—
320C2×C3#567411yescharacteristic
321C2×C3C2×D3×SD1611yescharacteristic
322C2×C3C2×#91811yescharacteristic
323D3—62no—
324D3—242no—
325C22—92no—
326C22—181no—
327C22—181no—
328C22—362no—
329C22—362no—
330C22—362no—
331C22C2×D4×D911yescharacteristic
332C4—42no—
333C4—42no—
334C4—92no—
335C4—181no—
336C4—181no—
337C4—362no—
338C4SD16×D912yes—
339C4#6348012yes—
340C4#6371512yes—
341C3#8160211yescharacteristic
342C2—182no—
343C2—722no—
344C2#1058977611yescharacteristic
345C2C2×SD16×D911yescharacteristic
346C2C2×#6348011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#487C2
socleC22×C3C2×D3×D4
prime radical#10589827C2
hypercenter#487D9
hypocenterC9#3206
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. D9×C4⋊Q8C2semidirect
3. C9×#487C2semidirect
4. #10588770C2semidirect
5. #10588766C2semidirect
6. #10588498C2semidirect
7. #10588486C2semidirect
8. #10588375C2semidirect
9. #10588367C2semidirect
125. C4×D9SD16semidirect
135. #487D9semidirect
293. C9#3206semidirect

Maximal subgroups

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

subgroupindex
#105898272
D9×C4⋊Q82
C9×#4872
#105887702
#105887662
#105884982
#105884862
#105883752
#105883672
#816023