Finite Group Databasebeta

← #11786673

Subgroups — #11786673

Order 1152.

453 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#520C211yesmaximal, characteristic
2#10588916C211yesmaximal, characteristic
3C2×#63396C211yesmaximal, characteristic
4#10588679C211yesmaximal, characteristic, complemented
5#10588655C211yesmaximal, characteristic, complemented
6#10588208C211yesmaximal, characteristic, complemented
7#10588207C211yesmaximal, characteristic, complemented
8#71664—31nomaximal
9C2×C9×#41C2211yescharacteristic
10C4×Q8×C9—21no—
11C4×D4×C9—21no—
12C4×D4×C9—22no—
13C9×#117—21no—
14C9×#117C2211yescharacteristic
15C2×C9×C4⋊C4—21no—
16C2×C9×C4⋊C4C2211yescharacteristic
17C2×C4⋊Dic9C2211yescharacteristic
18C2×Dic9⋊C4—22no—
19C2×C4×Dic9C2211yescharacteristic
20C2×#3667C2211yescharacteristic
21C2×#3667C2211yescharacteristic
22#63396C414yescomplemented
23#63395—21no—
24#63392—21no—
25#63367—21no—
26#63366—21no—
27C3×#520D311yescharacteristic
28C2×#837—31no—
29#5232—31no—
30#4995—31no—
31#4975—31no—
32#4532—31no—
33#4530—31no—
34C9×#41—21no—
35C9×#41—21no—
36C9×#41C2×C412yes—
37C9×#41Q812yes—
38C2×Q8×C9D411yescharacteristic
39C2×D4×C9—21no—
40C2×D4×C9D411yescharacteristic
41C22×C4×C9—21no—
42C22×C4×C9—22no—
43C22×C4×C9D412yes—
44C22×C4×C9C2311yescharacteristic
45C22×Dic9—21no—
46C22×Dic9—21no—
47C9×C4⋊C4—22no—
48C9×C4⋊C4—21no—
49C9×C4⋊C4—21no—
50C9×C4⋊C4D411yescharacteristic
51C9×C4⋊C4D411yescharacteristic
52C9×C22⋊C4—22no—
53C9×C22⋊C4—21no—
54C42×C9—22no—
55C42×C9—21no—
56C4⋊Dic9—21no—
57C4⋊Dic9—21no—
58Dic9⋊C4—44no—
59C4×Dic9—21no—
60C4×Dic9C2×C412yescomplemented
61#3667—21no—
62#3667—21no—
63#3667—21no—
64#3667C2×C412yescomplemented
65C2×C9⋊C8—21no—
66C2×C9⋊C8—21no—
67#1859—91noSylow
68C2×C3×#41C2×D311yescharacteristic
69C3×C4×Q8—21no—
70C3×C4×D4—21no—
71C3×C4×D4—22no—
72C3×#117—21no—
73C3×#117C2×D311yescharacteristic
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4C2×D311yescharacteristic
76C2×C4⋊Dic3—31no—
77C2×Dic3⋊C4—62no—
78C2×C4×Dic3—31no—
79C2×#208—31no—
80C2×#208—31no—
81#837—34no—
82#835—61no—
83#832—61no—
84#808—61no—
85#807—61no—
86C23×C9—21no—
87C23×C9C2×D411yescharacteristic
88Q8×C9—21no—
89Q8×C9C4⋊C412yescomplemented
90D4×C9—22no—
91D4×C9—22no—
92D4×C9—21no—
93D4×C9C4⋊C412yescomplemented
94C2×C4×C9—21no—
95C2×C4×C9—22no—
96C2×C4×C9—22no—
97C2×C4×C9—21no—
98C2×C4×C9—22no—
99C2×C4×C9—21no—
100C2×C4×C9—42no—
101C2×C4×C9—82no—
102C2×C4×C9C22×C411yescharacteristic
103C2×C4×C9C2×D411yescharacteristic
104C2×C4×C9C2×D411yescharacteristic
105C2×C4×C9C2×Q811yescharacteristic
106C2×C4×C9#4111yescharacteristic
107C2×C4×C9#4111yescharacteristic
108C2×Dic9—22no—
109C2×Dic9—22no—
110C2×Dic9—22no—
111C2×Dic9—42no—
112C2×Dic9—41no—
113C9⋊C8—22no—
114C9⋊C8—41no—
115#520D911yescharacteristic
116#428—91no—
117C2×#104—91no—
118#417—91no—
119#384—91no—
120#343—91no—
121#339—91no—
122C3×#41—21no—
123C3×#41—21no—
124C3×#41Dic612yes—
125C3×#41C4×D312yes—
126C2×C3×Q8#6711yescharacteristic
127C2×C3×D4—21no—
128C2×C3×D4#6711yescharacteristic
129C22×C3×C4—21no—
130C22×C3×C4—22no—
131C22×C3×C4#6712yes—
132C22×C3×C4C22×D311yescharacteristic
133C22×Dic3—61no—
134C22×Dic3—61no—
135C3×C4⋊C4—22no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4#6711yescharacteristic
139C3×C4⋊C4#6711yescharacteristic
140C3×C22⋊C4—22no—
141C3×C22⋊C4—21no—
142C3×C42—22no—
143C3×C42—21no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146Dic3⋊C4—124no—
147C4×Dic3—32no—
148C4×Dic3—61no—
149#208—32no—
150#208—61no—
151#208—61no—
152#208—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—61no—
155C22×C9—21no—
156C22×C9—21no—
157C22×C9—22no—
158C22×C9—41no—
159C22×C9—41no—
160C22×C9C4×D411yescharacteristic
161C22×C9#12011yescharacteristic
162C22×C9C22⋊Q811yescharacteristic
163C4×C9—22no—
164C4×C9—42no—
165C4×C9—41no—
166C4×C9—41no—
167C4×C9C2×C4⋊C411yescharacteristic
168C4×C9C4×D411yescharacteristic
169C4×C9C22⋊Q811yescharacteristic
170C4×C9#12311yescharacteristic
171Dic9—24no—
172Dic9—81no—
173C2×#41C2×D911yescharacteristic
174C2×M16—91no—
175C2×M16—91no—
176C4×Q8—21no—
177C4×D4—21no—
178C4×D4—22no—
179#117—21no—
180#117C2×D911yescharacteristic
181C2×C4⋊C4—21no—
182C2×C4⋊C4—91no—
183C2×C4⋊C4—182no—
184C2×C4⋊C4C2×D911yescharacteristic
185C2×C42—91no—
186#107—181no—
187#106—181no—
188#104—94no—
189#103—181no—
190#102—181no—
191C23×C3—21no—
192C23×C3C2×#6711yescharacteristic
193C3×Q8—21no—
194C3×Q8Dic3⋊C412yes—
195C3×D4—22no—
196C3×D4—22no—
197C3×D4—21no—
198C3×D4Dic3⋊C412yes—
199C2×C3×C4—21no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—21no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—42no—
206C2×C3×C4—82no—
207C2×C3×C4C2×Dic611yescharacteristic
208C2×C3×C4C2×C4×D311yescharacteristic
209C2×C3×C4#23511yescharacteristic
210C2×C3×C4#23511yescharacteristic
211C2×C3×C4C2×#6711yescharacteristic
212C2×C3×C4C2×#6711yescharacteristic
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—122no—
217C2×Dic3—121no—
218C3⋊C8—62no—
219C3⋊C8—121no—
220C2×C9—21no—
221C2×C9—21no—
222C2×C9—42no—
223C2×C9#38511yescharacteristic
224C2×C9#45311yescharacteristic
225C2×C9#45611yescharacteristic
226#41—21no—
227#41—21no—
228#41Dic1812yes—
229#41C4×D912yes—
230C2×Q8#61111yescharacteristic
231C2×D4—21no—
232C2×D4#61111yescharacteristic
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—181no—
236C22×C4—181no—
237C22×C4#61112yes—
238C22×C4C22×D911yescharacteristic
239M16—92no—
240M16—181no—
241M16—181no—
242M16—181no—
243C2×C8—181no—
244C2×C8—181no—
245C4⋊C4—22no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—181no—
249C4⋊C4—181no—
250C4⋊C4—364no—
251C4⋊C4#61111yescharacteristic
252C4⋊C4#61111yescharacteristic
253C22⋊C4—22no—
254C22⋊C4—21no—
255C42—22no—
256C42—21no—
257C42—92no—
258C42—181no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—22no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3#92411yescharacteristic
265C22×C3C4×#6711yescharacteristic
266C22×C3#95311yescharacteristic
267C3×C4—22no—
268C3×C4—42no—
269C3×C4—41no—
270C3×C4—41no—
271C3×C4C2×Dic3⋊C411yescharacteristic
272C3×C4#92411yescharacteristic
273C3×C4C4×#6711yescharacteristic
274C3×C4#92911yescharacteristic
275Dic3—64no—
276Dic3—241no—
277C9#185911yescharacteristic, complemented, Sylow
278C23—21no—
279C23C2×#61111yescharacteristic
280Q8—21no—
281Q8Dic9⋊C412yescomplemented
282D4—22no—
283D4—22no—
284D4—21no—
285D4Dic9⋊C412yescomplemented
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—82no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4—362no—
298C2×C4—361no—
299C2×C4C2×Dic1811yescharacteristic
300C2×C4C2×C4×D911yescharacteristic
301C2×C4#369711yescharacteristic
302C2×C4#369711yescharacteristic
303C2×C4C2×#61111yescharacteristic
304C2×C4C2×#61111yescharacteristic
305C8—182no—
306C8—361no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—42no—
310C2×C3#521011yescharacteristic
311C2×C3#524111yescharacteristic
312C2×C3#524611yescharacteristic
313C22—21no—
314C22—21no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22#6348611yescharacteristic
319C22C4×#61111yescharacteristic
320C22#6351511yescharacteristic
321C4—22no—
322C4—42no—
323C4—41no—
324C4—41no—
325C4—184no—
326C4—721no—
327C4C2×Dic9⋊C411yescharacteristic
328C4#6348611yescharacteristic
329C4C4×#61111yescharacteristic
330C4#6349111yescharacteristic
331C3#7166411yescharacteristic
332C2—21no—
333C2—21no—
334C2—42no—
335C2#1058889011yescharacteristic
336C2#1058892211yescharacteristic
337C2#1058892511yescharacteristic
subgroupG/H
centerC22#63515
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#520C2
socleC22×C3#953
prime radicalC2×C3×#41C2×D3
cosocleC22×C4×C9C23
hypercenter#520D9
hypocenterC9#1859
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #520

Complements

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

NH ≅ G/Ntype
4. #10588679C2semidirect
5. #10588655C2semidirect
6. #10588208C2semidirect
7. #10588207C2semidirect
22. #63396C4semidirect
60. C4×Dic9C2×C4semidirect
64. #3667C2×C4semidirect
89. Q8×C9C4⋊C4semidirect
93. D4×C9C4⋊C4semidirect
277. C9#1859semidirect
281. Q8Dic9⋊C4semidirect
285. D4Dic9⋊C4semidirect

Maximal subgroups

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

subgroupindex
C9×#5202
#105889162
C2×#633962
#105886792
#105886552
#105882082
#105882072
#716643