Finite Group Databasebeta

← #11897631

Subgroups — #11897631

Order 1152.

510 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589824C211yesmaximal, characteristic, complemented
2#10589645C211yesmaximal, characteristic
3C9×#476C211yesmaximal, characteristic
4#10588758C211yesmaximal, characteristic, complemented
5C4×#3672C211yesmaximal, characteristic
6#10588537C212yesmaximal, complemented
7#10588536C212yesmaximal, complemented
8#10588514C211yesmaximal, characteristic, complemented
9#10588509C211yesmaximal, characteristic, complemented
10#10588439C212yesmaximal
11#10588437C212yesmaximal
12#81056—31nomaximal
13C9×C4⋊Q8C2211yescharacteristic
14C4×D4×C9C2211yescharacteristic
15#63506—22no—
16D4×Dic9C2212yes—
17C2×#3672C2211yescharacteristic
18C2×C4⋊Dic9—21no—
19#63486—21no—
20#63452C2212yes—
21#63450—21no—
22#63450C2212yes—
23#63449—21no—
24#63449C2212yes—
25#63440—22no—
26#63431C2211yescharacteristic
27C4×Dic18C2211yescharacteristic
28C4×Dic18C2211yescharacteristic
29C9×#106C2212yes—
30C9×C4⋊C8C2211yescharacteristic
31C9×#102C2212yes—
32#63392C2211yescharacteristic
33#63378C2212yes—
34#63376C2212yes—
35#63375C2212yes—
36Dic9⋊C8C2212yes—
37#63368C2211yescharacteristic
38#63367C2211yescharacteristic
39#63366C2212yes—
40#63366C2212yes—
41C4×C9⋊C8C2211yescharacteristic
42#5722—31no—
43#5543—31no—
44C3×#476D311yescharacteristic
45#5078—31no—
46C4×#214—31no—
47#4857—32no—
48#4856—32no—
49#4850—31no—
50#4831—31no—
51#4759—32no—
52#4757—32no—
53C2×Q8×C9—21no—
54C2×D4×C9C2311yescharacteristic
55C22×C4×C9—21no—
56C22×Dic9—22no—
57C2×Dic18—21no—
58C2×Dic18—22no—
59C2×Dic18D411yescharacteristic
60C2×Dic18C2311yescharacteristic
61C2×C8×C9C2312yes—
62C9×C4⋊C4—21no—
63C9×C4⋊C4C2311yescharacteristic
64C9×C4⋊C4C2312yes—
65C9×C22⋊C4—21no—
66C42×C9C2311yescharacteristic
67#3676—22no—
68#3672Q814yescomplemented
69C4⋊Dic9—21no—
70C4⋊Dic9—22no—
71C4⋊Dic9D411yescharacteristic
72C4⋊Dic9C2312yes—
73C4⋊Dic9C2311yescharacteristic
74Dic9⋊C4—21no—
75Dic9⋊C4—22no—
76Dic9⋊C4—22no—
77Dic9⋊C4—22no—
78Dic9⋊C4D412yes—
79C4×Dic9—21no—
80C4×Dic9—22no—
81C4×Dic9C2312yes—
82C2×C9⋊C8C2311yescharacteristic
83C2×C9⋊C8C2311yescharacteristic
84#3385—91noSylow
85C3×C4⋊Q8C2×D311yescharacteristic
86C3×C4×D4C2×D311yescharacteristic
87#944—62no—
88D4×Dic3—32no—
89C2×#214—31no—
90C2×C4⋊Dic3—61no—
91#924—61no—
92#890—32no—
93#888—32no—
94#888—61no—
95#887—32no—
96#887—61no—
97#878—62no—
98#869—31no—
99C4×Dic6—31no—
100C4×Dic6—31no—
101C3×#106C2×D312yes—
102C3×C4⋊C8C2×D311yescharacteristic
103C3×#102C2×D312yes—
104#832—31no—
105#818—32no—
106#816—32no—
107#815—32no—
108Dic3⋊C8—32no—
109#810—31no—
110#808—31no—
111#807—32no—
112#807—32no—
113C4×C3⋊C8—31no—
114C23×C9—21no—
115Q8×C9—81no—
116D4×C9—21no—
117D4×C9C2×Q812yes—
118C2×C4×C9—22no—
119C2×C4×C9—21no—
120C2×C4×C9—42no—
121C2×C4×C9C2×D411yescharacteristic
122C2×C4×C9C2×D411yescharacteristic
123C2×C4×C9C2411yescharacteristic
124C2×Dic9—21no—
125C2×Dic9—21no—
126C2×Dic9—22no—
127C2×Dic9—82no—
128C2×Dic9C2×D412yes—
129C2×Dic9C2×D412yes—
130Dic18—22no—
131Dic18—21no—
132Dic18—82no—
133Dic18—81no—
134Dic18C2×Q812yes—
135C8×C9—22no—
136C9⋊C8—21no—
137C9⋊C8C2×Q812yes—
138Q82—91no—
139#554—91no—
140#501—92no—
141#500—91no—
142#479—92no—
143#477—91no—
144#476D911yescharacteristic
145#474—92no—
146#446—91no—
147#440—92no—
148C4×SD16—91no—
149C2×C3×Q8—21no—
150C2×C3×D4C22×D311yescharacteristic
151C22×C3×C4—21no—
152C22×Dic3—62no—
153C2×Dic6—31no—
154C2×Dic6—31no—
155C2×Dic6—62no—
156C2×Dic6—61no—
157C2×C3×C8C22×D312yes—
158C3×C4⋊C4—21no—
159C3×C4⋊C4C22×D312yes—
160C3×C4⋊C4C22×D311yescharacteristic
161C3×C22⋊C4—21no—
162C3×C42C22×D311yescharacteristic
163#217—62no—
164#214—34no—
165C4⋊Dic3—31no—
166C4⋊Dic3—32no—
167C4⋊Dic3—31no—
168C4⋊Dic3—62no—
169C4⋊Dic3—61no—
170Dic3⋊C4—32no—
171Dic3⋊C4—62no—
172Dic3⋊C4—62no—
173Dic3⋊C4—62no—
174Dic3⋊C4—61no—
175C4×Dic3—32no—
176C4×Dic3—62no—
177C4×Dic3—61no—
178C2×C3⋊C8—31no—
179C2×C3⋊C8—31no—
180C22×C9—22no—
181C22×C9—41no—
182C22×C9—41no—
183C22×C9C22×D411yescharacteristic
184C4×C9—21no—
185C4×C9—41no—
186C4×C9—42no—
187C4×C9#13712yes—
188C4×C9C22×Q811yescharacteristic
189C4×C92−1+411yescharacteristic
190Dic9—22no—
191Dic9—22no—
192Dic9—22no—
193Dic9—41no—
194Dic9—42no—
195C2×SD16—91no—
196C4⋊Q8—92no—
197C4⋊Q8—91no—
198C4⋊Q8—181no—
199C4⋊Q8—182no—
200C4⋊Q8C2×D911yescharacteristic
201#125—92no—
202C22⋊Q8—182no—
203C22⋊Q8—181no—
204C4×Q8—91no—
205C4×Q8—92no—
206C4×Q8—91no—
207C4×Q8—181no—
208C4×D4—92no—
209C4×D4C2×D911yescharacteristic
210C2×C4⋊C4—181no—
211#107—92no—
212#107—92no—
213#107—92no—
214#106—91no—
215#106C2×D912yes—
216C4⋊C8—92no—
217C4⋊C8C2×D911yescharacteristic
218#103—92no—
219#103—91no—
220#102—91no—
221#102C2×D912yes—
222#97—92no—
223C4×C8—91no—
224C23×C3—21no—
225C3×Q8—81no—
226C3×D4—21no—
227C3×D4D3×Q812yes—
228C2×C3×C4—22no—
229C2×C3×C4—21no—
230C2×C3×C4—42no—
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4C23×D311yescharacteristic
234C2×Dic3—32no—
235C2×Dic3—32no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—62no—
239C2×Dic3—242no—
240Dic6—32no—
241Dic6—62no—
242Dic6—61no—
243Dic6—242no—
244Dic6—241no—
245C3×C8—22no—
246C3⋊C8—32no—
247C3⋊C8—61no—
248C2×C9—42no—
249C2×C9D4×Q811yescharacteristic
250C2×C9C2×#13711yescharacteristic
251C2×C9#57611yescharacteristic
252C2×Q8—21no—
253C2×Q8—91no—
254C2×Q8—91no—
255C2×Q8—182no—
256C2×Q8—181no—
257C2×D4C22×D911yescharacteristic
258C22×C4—21no—
259C22×C4—182no—
260SD16—94no—
261C2×C8—91no—
262C2×C8—91no—
263C2×C8C22×D912yes—
264C4⋊C4—21no—
265C4⋊C4—91no—
266C4⋊C4—92no—
267C4⋊C4—91no—
268C4⋊C4—92no—
269C4⋊C4—182no—
270C4⋊C4—182no—
271C4⋊C4—182no—
272C4⋊C4—182no—
273C4⋊C4—181no—
274C4⋊C4—181no—
275C4⋊C4C22×D912yes—
276C4⋊C4C22×D911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—182no—
279C42—92no—
280C42—182no—
281C42—181no—
282C42C22×D911yescharacteristic
283C22×C3—22no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3C2×D3×D411yescharacteristic
287C3×C4—21no—
288C3×C4—41no—
289C3×C4—42no—
290C3×C4#91512yes—
291C3×C4C2×D3×Q811yescharacteristic
292C3×C4#101011yescharacteristic
293Dic3—62no—
294Dic3—62no—
295Dic3—62no—
296Dic3—121no—
297Dic3—122no—
298C9#338511yescharacteristic, complemented, Sylow
299C23—21no—
300Q8—81no—
301Q8—92no—
302Q8—181no—
303Q8—182no—
304Q8—721no—
305Q8—722no—
306D4—21no—
307D4Q8×D912yes—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—92no—
312C2×C4—92no—
313C2×C4—181no—
314C2×C4—181no—
315C2×C4—182no—
316C2×C4—722no—
317C2×C4D4×D911yescharacteristic
318C2×C4D4×D911yescharacteristic
319C2×C4C23×D911yescharacteristic
320C8—22no—
321C8—92no—
322C8—181no—
323C2×C3—42no—
324C2×C3#563211yescharacteristic
325C2×C3C2×#91511yescharacteristic
326C2×C3#577411yescharacteristic
327C22—22no—
328C22—41no—
329C22—41no—
330C22C2×D4×D911yescharacteristic
331C4—21no—
332C4—41no—
333C4—42no—
334C4—182no—
335C4—182no—
336C4—182no—
337C4—362no—
338C4—361no—
339C4#6347712yes—
340C4C2×Q8×D911yescharacteristic
341C4#6371611yescharacteristic
342C3#8105611yescharacteristic
343C2—42no—
344C2#1058973411yescharacteristic
345C2C2×#6347711yescharacteristic
346C2#1058987611yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#476C2
socleC22×C3C2×D3×D4
prime radicalC2×C3×D4C22×D3
hypercenter#476D9
hypocenterC9#3385
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #10589824C2semidirect
4. #10588758C2semidirect
6. #10588537C2semidirect
7. #10588536C2semidirect
8. #10588514C2semidirect
9. #10588509C2semidirect
68. #3672Q8semidirect
298. C9#3385semidirect

Maximal subgroups

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

subgroupindex
#105898242
#105896452
C9×#4762
#105887582
C4×#36722
#105885372
#105885362
#105885142
#105885092
#105884392
#105884372
#810563