Finite Group Databasebeta

← #11878684

Subgroups — #11878684

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
1D9×C4⋊Q8C211yesmaximal, characteristic, complemented
2#10589818C211yesmaximal, characteristic
3C9×#492C211yesmaximal, characteristic, complemented
4#10588850C214yesmaximal, complemented
5#10588842C214yesmaximal, complemented
6#10588759C211yesmaximal, characteristic, complemented
7#10588753C211yesmaximal, characteristic, complemented
8#10588367C211yesmaximal, characteristic, complemented
9#10588361C211yesmaximal, characteristic, complemented
10#81764—31nomaximal
11C2×Q8×D9C2212yes—
12C2×#3699—21no—
13C2×C9×SD16C2214yes—
14C9×C4⋊Q8C2211yescharacteristic
15C9×#127C2211yescharacteristic
16#63506C2212yes—
17#63500—21no—
18#63500C2212yes—
19#63498—21no—
20D4×Dic9—21no—
21D4×Dic9C2212yes—
22C2×#3672C2214yes—
23C4⋊C4×D9—21no—
24C4⋊C4×D9—21no—
25#63450—21no—
26#63450—21no—
27C42×D9C2211yescharacteristic
28#63431C2211yescharacteristic
29#63431C2211yescharacteristic
30C4×C8×C9C2211yescharacteristic
31#63395C2214yes—
32(C2×D9)⋊C8C2212yes—
33#63376C2214yes—
34Dic9⋊C8C2212yes—
35C4×C9⋊C8C2211yescharacteristic
36D3×C4⋊Q8—31no—
37#5716—31no—
38C3×#492D311yescharacteristic
39#5170—34no—
40#5162—34no—
41#5079—31no—
42#5076—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—
51Q8×D9—44no—
52#3699—44no—
53C2×C4×D9—22no—
54C2×C4×D9D411yescharacteristic
55C2×C4×D9D411yescharacteristic
56C2×C4×D9C2311yescharacteristic
57C2×Dic18—21no—
58C2×Dic18—22no—
59C2×Dic18C2312yes—
60C9×SD16—44no—
61C2×C8×C9C2312yes—
62C9×C4⋊C4—21no—
63C9×C4⋊C4—21no—
64C42×C9C2311yescharacteristic
65#3676—22no—
66#3676—22no—
67#3672—44no—
68C4⋊Dic9—21no—
69C4⋊Dic9—21no—
70C4⋊Dic9—21no—
71C4⋊Dic9C2312yes—
72Dic9⋊C4—22no—
73Dic9⋊C4—22no—
74C4×Dic9D411yescharacteristic
75C4×Dic9D411yescharacteristic
76C4×Dic9C2311yescharacteristic
77C2×C9⋊C8C2312yes—
78#3206—91noSylow
79C2×D3×Q8—32no—
80C2×#237—61no—
81C2×C3×SD16C2×D314yes—
82C3×C4⋊Q8C2×D311yescharacteristic
83C3×#127C2×D311yescharacteristic
84#944—32no—
85#938—32no—
86#938—61no—
87#936—61no—
88D4×Dic3—32no—
89D4×Dic3—61no—
90C2×#214—34no—
91D3×C4⋊C4—61no—
92D3×C4⋊C4—61no—
93#888—61no—
94#888—61no—
95C42×D3—31no—
96#869—31no—
97#869—31no—
98C3×C4×C8C2×D311yescharacteristic
99#835—34no—
100(C2×D3)⋊C8—32no—
101#816—34no—
102Dic3⋊C8—32no—
103C4×C3⋊C8—31no—
104C23×C9—22no—
105C22×D9C2×D411yescharacteristic
106Q8×C9—24no—
107D4×C9—24no—
108D4×C9—42no—
109D4×C9—42no—
110C2×C4×C9—22no—
111C2×C4×C9C2×D411yescharacteristic
112C2×C4×C9C2×D411yescharacteristic
113C2×C4×C9C2411yescharacteristic
114#611—44no—
115C2×Dic9—22no—
116C2×Dic9—22no—
117C2×Dic9—44no—
118C2×Dic9C2×D411yescharacteristic
119C2×Dic9C2×D411yescharacteristic
120C2×Dic9C2×D411yescharacteristic
121C4×D9—22no—
122C4×D9—22no—
123C4×D9—44no—
124C4×D9SD1614yescomplemented
125Dic18—24no—
126Dic18—44no—
127Dic18—42no—
128C8×C9—22no—
129C9⋊C8—22no—
130#532—91no—
131C2×C4⋊Q8—91no—
132#492—91no—
133#492D911yescharacteristic, complemented
134#487—91no—
135#487—91no—
136#461—94no—
137#448—94no—
138#431—91no—
139C2×C3×Q8C22×D312yes—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4C22×D312yes—
143C2×#67—62no—
144C22×Dic3—62no—
145D3×Q8—124no—
146#237—124no—
147C2×C4×D3—31no—
148C2×C4×D3—31no—
149C2×C4×D3—31no—
150C2×C4×D3—62no—
151C2×Dic6—32no—
152C2×Dic6—62no—
153C2×Dic6—61no—
154C3×SD16—44no—
155C2×C3×C8C22×D312yes—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C42C22×D311yescharacteristic
159#217—62no—
160#217—62no—
161#214—124no—
162C4⋊Dic3—32no—
163C4⋊Dic3—61no—
164C4⋊Dic3—61no—
165C4⋊Dic3—61no—
166Dic3⋊C4—62no—
167Dic3⋊C4—62no—
168C4×Dic3—31no—
169C4×Dic3—31no—
170C4×Dic3—31no—
171C2×C3⋊C8—32no—
172C22×C9—42no—
173C22×C9—42no—
174C22×C9—42no—
175C22×C9C22×D411yescharacteristic
176C2×D9—21no—
177C2×D9—21no—
178C2×D9C2×SD1612yes—
179C4×C9—42no—
180C4×C9C2×SD1612yes—
181C4×C9#13712yes—
182C4×C9H(5,𝔽2)12yes—
183Dic9—21no—
184Dic9—21no—
185Dic9—42no—
186Dic9—42no—
187Dic9C2×SD1612yes—
188C2×#41—181no—
189C22×Q8—92no—
190C2×SD16—94no—
191C2×SD16C2×D914yes—
192C4⋊Q8—92no—
193C4⋊Q8—91no—
194C4⋊Q8—91no—
195C4⋊Q8—181no—
196C4⋊Q8—181no—
197C4⋊Q8C2×D911yescharacteristic
198#127C2×D911yescharacteristic
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#103—94no—
210C22⋊C8—92no—
211C4×C8—91no—
212C4×C8C2×D911yescharacteristic
213C23×C3—22no—
214C22×D3—31no—
215C3×Q8—24no—
216C3×D4—24no—
217C3×D4—42no—
218C3×D4—42no—
219C2×C3×C4—22no—
220C2×C3×C4D3×D411yescharacteristic
221C2×C3×C4D3×D411yescharacteristic
222C2×C3×C4C23×D311yescharacteristic
223#67—124no—
224C2×Dic3—31no—
225C2×Dic3—31no—
226C2×Dic3—31no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—124no—
230C4×D3—34no—
231C4×D3—62no—
232C4×D3—62no—
233C4×D3—124no—
234Dic6—64no—
235Dic6—124no—
236Dic6—122no—
237C3×C8—22no—
238C3⋊C8—62no—
239C2×C9—82no—
240C2×C9#53511yescharacteristic
241C2×C9C22×SD1611yescharacteristic
242C2×C9C2×#13711yescharacteristic
243D9—22no—
244#41—364no—
245C2×Q8—92no—
246C2×Q8—182no—
247C2×Q8—181no—
248C2×Q8—364no—
249C2×Q8C22×D912yes—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—182no—
253C2×D4C22×D912yes—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—182no—
258C22×C4—182no—
259SD16—44no—
260SD16—364no—
261C2×C8—92no—
262C2×C8C22×D912yes—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—92no—
266C4⋊C4—182no—
267C4⋊C4—182no—
268C4⋊C4—181no—
269C4⋊C4—181no—
270C4⋊C4—181no—
271C22⋊C4—182no—
272C22⋊C4—182no—
273C42—91no—
274C42—91no—
275C42—91no—
276C42C22×D911yescharacteristic
277C22×C3—42no—
278C22×C3—42no—
279C22×C3—42no—
280C22×C3C2×D3×D411yescharacteristic
281C2×D3—32no—
282C2×D3—61no—
283C2×D3—61no—
284C3×C4—42no—
285C3×C4D3×SD1612yes—
286C3×C4#91512yes—
287C3×C4#100412yes—
288Dic3—32no—
289Dic3—61no—
290Dic3—61no—
291Dic3—122no—
292Dic3—122no—
293C9#320611yescharacteristic, complemented, Sylow
294C23—22no—
295C23—91no—
296Q8—24no—
297Q8—184no—
298Q8—364no—
299Q8—362no—
300D4—24no—
301D4—42no—
302D4—42no—
303D4—364no—
304C2×C4—22no—
305C2×C4—91no—
306C2×C4—94no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—182no—
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—82no—
321C2×C3#571511yescharacteristic
322C2×C3C2×D3×SD1611yescharacteristic
323C2×C3C2×#91511yescharacteristic
324D3—62no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—92no—
329C22—181no—
330C22—181no—
331C22C2×D4×D911yescharacteristic
332C4—42no—
333C4—92no—
334C4—181no—
335C4—181no—
336C4—362no—
337C4—362no—
338C4SD16×D912yes—
339C4#6347712yes—
340C4#6371012yes—
341C3#8176411yescharacteristic
342C2—82no—
343C2—182no—
344C2#1058981711yescharacteristic
345C2C2×SD16×D911yescharacteristic
346C2C2×#6347711yescharacteristic
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#3206
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. D9×C4⋊Q8C2semidirect
3. C9×#492C2semidirect
4. #10588850C2semidirect
5. #10588842C2semidirect
6. #10588759C2semidirect
7. #10588753C2semidirect
8. #10588367C2semidirect
9. #10588361C2semidirect
124. C4×D9SD16semidirect
133. #492D9semidirect
293. C9#3206semidirect

Maximal subgroups

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

subgroupindex
D9×C4⋊Q82
#105898182
C9×#4922
#105888502
#105888422
#105887592
#105887532
#105883672
#105883612
#817643