Finite Group Databasebeta

← #11869017

Subgroups — #11869017

Order 1152.

543 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#544C211yesmaximal, characteristic
2#10589618C211yesmaximal, characteristic
3#10588767C212yesmaximal, complemented
4#10588764C212yesmaximal, complemented
5#10588745C212yesmaximal, complemented
6#10588745C212yesmaximal, complemented
7#10588681C211yesmaximal, characteristic
8#10588677C211yesmaximal, characteristic
9#10588676C211yesmaximal, characteristic
10C2×#63368C211yesmaximal, characteristic
11#10588644C211yesmaximal, characteristic
12#83480—31nomaximal
13C22×Dic18C2211yescharacteristic
14C9×C4⋊Q8—21no—
15C9×C4⋊Q8C2212yes—
16C9×#125—21no—
17C9×#125C2212yes—
18C9×C22⋊Q8—22no—
19C9×#117C2211yescharacteristic
20C9×#117C2211yescharacteristic
21C2×C9×C4⋊C4C2211yescharacteristic
22#63488C2211yescharacteristic
23C2×#3667C2211yescharacteristic
24C22×C9⋊C8C2211yescharacteristic
25#63449—21no—
26#63449—21no—
27#63439—22no—
28C4×Dic18C2212yes—
29C4×Dic18C2212yes—
30#63368C2212yes—
31#63368C2212yes—
32#63368C2212yes—
33#63368C2212yes—
34#63367C2211yescharacteristic
35#63367C2211yescharacteristic
36#63367C2212yes—
37#63366C2211yescharacteristic
38#63366C2211yescharacteristic
39#63366C2212yes—
40C4⋊(C9⋊C8)C2212yes—
41C4⋊(C9⋊C8)C2212yes—
42C3×#544D311yescharacteristic
43#5516—31no—
44#5094—32no—
45#5091—32no—
46#5063—32no—
47#5063—32no—
48#5004—31no—
49#4999—31no—
50#4998—31no—
51C2×#810—31no—
52#4964—31no—
53C2×Q8×C9—22no—
54C22×C4×C9—21no—
55C22×C4×C9C2311yescharacteristic
56C22×Dic9—21no—
57C2×Dic18—21no—
58C2×Dic18—22no—
59C2×Dic18Q814yescomplemented
60C2×Dic18C2312yes—
61C9×C4⋊C4—21no—
62C9×C4⋊C4—22no—
63C9×C4⋊C4—22no—
64C9×C4⋊C4—22no—
65C9×C4⋊C4D411yescharacteristic
66C9×C4⋊C4D411yescharacteristic
67C9×C4⋊C4C2312yes—
68C9×C4⋊C4C2311yescharacteristic
69C9×C4⋊C4C2311yescharacteristic
70C9×C22⋊C4—21no—
71C9×C22⋊C4D412yes—
72C42×C9—21no—
73C42×C9C2312yes—
74#3676—21no—
75C4⋊Dic9C2311yescharacteristic
76C4⋊Dic9C2311yescharacteristic
77Dic9⋊C4—22no—
78Dic9⋊C4—22no—
79C4×Dic9—21no—
80C4×Dic9—22no—
81C4×Dic9—22no—
82#3667—22no—
83C2×C9⋊C8—22no—
84C2×C9⋊C8C2311yescharacteristic
85C2×C9⋊C8C2312yes—
86C2×C9⋊C8C2311yescharacteristic
87#3082—91noSylow
88C22×Dic6—31no—
89C3×C4⋊Q8—21no—
90C3×C4⋊Q8C2×D312yes—
91C3×#125—21no—
92C3×#125C2×D312yes—
93C3×C22⋊Q8—22no—
94C3×#117C2×D311yescharacteristic
95C3×#117C2×D311yescharacteristic
96C2×C3×C4⋊C4C2×D311yescharacteristic
97#926—31no—
98C2×#208—31no—
99C22×C3⋊C8—31no—
100#887—61no—
101#887—61no—
102#877—62no—
103C4×Dic6—32no—
104C4×Dic6—32no—
105#810—32no—
106#810—32no—
107#810—32no—
108#810—32no—
109#808—32no—
110#808—31no—
111#808—31no—
112#807—32no—
113#807—31no—
114#807—31no—
115C4⋊(C3⋊C8)—32no—
116C4⋊(C3⋊C8)—32no—
117C23×C9C2×D411yescharacteristic
118Q8×C9—82no—
119C2×C4×C9—21no—
120C2×C4×C9—21no—
121C2×C4×C9—22no—
122C2×C4×C9—81no—
123C2×C4×C9C2×D412yes—
124C2×C4×C9C2×D412yes—
125C2×C4×C9C2×D411yescharacteristic
126C2×C4×C9C2×Q812yes—
127C2×C4×C9#4112yes—
128C2×C4×C9C2411yescharacteristic
129C2×Dic9—24no—
130C2×Dic9—22no—
131C2×Dic9—21no—
132C2×Dic9—21no—
133Dic18—24no—
134Dic18—22no—
135Dic18C2×Q814yes—
136C9⋊C8—21no—
137C9⋊C8—21no—
138C9⋊C8—22no—
139#544D911yescharacteristic
140#519—91no—
141#479—92no—
142#479—92no—
143#477—92no—
144#475—92no—
145#428—91no—
146#427—91no—
147#424—91no—
148#419—91no—
149C2×#103—91no—
150C2×C3×Q8—22no—
151C22×C3×C4—21no—
152C22×C3×C4C22×D311yescharacteristic
153C22×Dic3—61no—
154C2×Dic6—34no—
155C2×Dic6—32no—
156C2×Dic6—62no—
157C2×Dic6—61no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—22no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4#6711yescharacteristic
163C3×C4⋊C4#6711yescharacteristic
164C3×C4⋊C4C22×D312yes—
165C3×C4⋊C4C22×D311yescharacteristic
166C3×C4⋊C4C22×D311yescharacteristic
167C3×C22⋊C4—21no—
168C3×C22⋊C4#6712yes—
169C3×C42—21no—
170C3×C42C22×D312yes—
171#217—61no—
172C4⋊Dic3—31no—
173C4⋊Dic3—31no—
174Dic3⋊C4—62no—
175Dic3⋊C4—62no—
176C4×Dic3—62no—
177C4×Dic3—62no—
178C4×Dic3—61no—
179#208—62no—
180C2×C3⋊C8—31no—
181C2×C3⋊C8—32no—
182C2×C3⋊C8—31no—
183C2×C3⋊C8—62no—
184C22×C9—21no—
185C22×C9—21no—
186C22×C9C22⋊Q812yes—
187C22×C9C22×D411yescharacteristic
188C4×C9—22no—
189C4×C9—22no—
190C4×C9—42no—
191C4×C9—41no—
192C4×C9—41no—
193C4×C9C22⋊Q812yes—
194C4×C9C22×Q811yescharacteristic
195C4×C9C2×#4111yescharacteristic
196Dic9—24no—
197Dic9—41no—
198Dic9—41no—
199C22×Q8—91no—
200C2×M16—91no—
201C22×C8—91no—
202C4⋊Q8—21no—
203C4⋊Q8C2×D912yes—
204#125—21no—
205#125C2×D912yes—
206C22⋊Q8—22no—
207C4×Q8—92no—
208C4×Q8—92no—
209C4×Q8—181no—
210C4×Q8—181no—
211#117—91no—
212#117—182no—
213#117C2×D911yescharacteristic
214#117C2×D911yescharacteristic
215C2×C4⋊C4C2×D911yescharacteristic
216#107—91no—
217#107—91no—
218#107—92no—
219#106—91no—
220#106—91no—
221#106—92no—
222C4⋊C8—92no—
223C4⋊C8—92no—
224#103—92no—
225#103—92no—
226#103—92no—
227#103—92no—
228C23×C3C2×#6711yescharacteristic
229C3×Q8—82no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—22no—
233C2×C3×C4—81no—
234C2×C3×C4D3×Q812yes—
235C2×C3×C4#23912yes—
236C2×C3×C4C2×#6712yes—
237C2×C3×C4C2×#6712yes—
238C2×C3×C4C2×#6711yescharacteristic
239C2×C3×C4C23×D311yescharacteristic
240C2×Dic3—64no—
241C2×Dic3—62no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244Dic6—34no—
245Dic6—64no—
246Dic6—62no—
247C3⋊C8—61no—
248C3⋊C8—61no—
249C3⋊C8—62no—
250C2×C9—22no—
251C2×C9C2×C22⋊Q811yescharacteristic
252C2×C9#57711yescharacteristic
253C2×C9#57811yescharacteristic
254C2×Q8—22no—
255C2×Q8—94no—
256C2×Q8—92no—
257C2×Q8—182no—
258C2×Q8—181no—
259C22×C4—21no—
260C22×C4—181no—
261C22×C4C22×D911yescharacteristic
262M16—182no—
263C2×C8—91no—
264C2×C8—92no—
265C2×C8—91no—
266C2×C8—182no—
267C4⋊C4—21no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—91no—
272C4⋊C4—91no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C4⋊C4#61111yescharacteristic
276C4⋊C4#61111yescharacteristic
277C4⋊C4C22×D912yes—
278C4⋊C4C22×D911yescharacteristic
279C4⋊C4C22×D911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—181no—
282C22⋊C4#61112yes—
283C42—21no—
284C42—181no—
285C42—182no—
286C42—182no—
287C42C22×D912yes—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3#94612yes—
291C22×C3C22×#6711yescharacteristic
292C3×C4—22no—
293C3×C4—22no—
294C3×C4—42no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4#94612yes—
298C3×C4C2×D3×Q811yescharacteristic
299C3×C4C2×#23911yescharacteristic
300Dic3—64no—
301Dic3—121no—
302Dic3—121no—
303C9#308211yescharacteristic, complemented, Sylow
304C23C2×#61111yescharacteristic
305Q8—82no—
306Q8—94no—
307Q8—184no—
308Q8—182no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—81no—
313C2×C4—184no—
314C2×C4—182no—
315C2×C4—181no—
316C2×C4—181no—
317C2×C4Q8×D912yes—
318C2×C4#370112yes—
319C2×C4C2×#61112yes—
320C2×C4C2×#61112yes—
321C2×C4C2×#61111yescharacteristic
322C2×C4C23×D911yescharacteristic
323C8—181no—
324C8—181no—
325C8—182no—
326C2×C3—22no—
327C2×C3C2×#94611yescharacteristic
328C2×C3#583611yescharacteristic
329C2×C3#583811yescharacteristic
330C22—21no—
331C22—21no—
332C22#6350812yes—
333C22C22×#61111yescharacteristic
334C4—22no—
335C4—22no—
336C4—42no—
337C4—41no—
338C4—41no—
339C4—184no—
340C4—361no—
341C4—361no—
342C4#6350812yes—
343C4C2×Q8×D911yescharacteristic
344C4C2×#370111yescharacteristic
345C3#8348011yescharacteristic
346C2—22no—
347C2C2×#6350811yescharacteristic
348C2#1058993811yescharacteristic
349C2#1058994011yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#544C2
socleC22×C3C22×#67
prime radicalC23×C3C2×#67
hypercenter#544D9
hypocenterC9#3082
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #10588767C2semidirect
4. #10588764C2semidirect
5. #10588745C2semidirect
6. #10588745C2semidirect
59. C2×Dic18Q8semidirect
303. C9#3082semidirect

Maximal subgroups

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

subgroupindex
C9×#5442
#105896182
#105887672
#105887642
#105887452
#105886812
#105886772
#105886762
C2×#633682
#105886442
#834803