Finite Group Databasebeta

← #11778502

Subgroups — #11778502

Order 1152.

324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C9×#539C211yesmaximal, characteristic
2#10588723C211yesmaximal, characteristic, complemented
3#10588713C211yesmaximal, characteristic
4#10588661C211yesmaximal, characteristic, complemented
5#10588215C211yesmaximal, characteristic, complemented
6#10588214C211yesmaximal, characteristic
7#10588205C211yesmaximal, characteristic, complemented
8#71886—31nomaximal
9C9×#126—21no—
10C9×#125—21no—
11C9×#123—21no—
12C9×#123—21no—
13C9×C22⋊Q8—21no—
14C9×C22⋊Q8C2211yescharacteristic
15C9×#121C2211yescharacteristic
16C4×D4×C9—21no—
17C2×C9×C4⋊C4C2211yescharacteristic
18C2×C4⋊Dic9C2211yescharacteristic
19C2×Dic9⋊C4—21no—
20#63395—21no—
21#63392—21no—
22C9⋊#95—21no—
23C9⋊#95C2211yescharacteristic
24#63389C2211yescharacteristic
25#63389C2211yescharacteristic
26#63367—21no—
27#63366—21no—
28C3×#539D311yescharacteristic
29#5043—31no—
30#5033—31no—
31#4981—31no—
32#4538—31no—
33#4537—31no—
34#4528—31no—
35C2×Q8×C9D411yescharacteristic
36C2×D4×C9—21no—
37C2×D4×C9D411yescharacteristic
38C22×C4×C9—21no—
39C22×C4×C9D411yescharacteristic
40C22×C4×C9D411yescharacteristic
41C22×C4×C9C2311yescharacteristic
42C22×Dic9—21no—
43C22×Dic9—21no—
44C9×C4⋊C4—21no—
45C9×C4⋊C4—21no—
46C9×C4⋊C4—21no—
47C9×C4⋊C4—21no—
48C9×C4⋊C4—21no—
49C9×C4⋊C4—21no—
50C9×C4⋊C4D411yescharacteristic
51C9×C4⋊C4D411yescharacteristic
52C9×C22⋊C4—21no—
53C9×C22⋊C4—21no—
54C9×C22⋊C4—21no—
55C9×C22⋊C4—21no—
56C9×C22⋊C4—21no—
57C42×C9—21no—
58C4⋊Dic9—21no—
59C4⋊Dic9—21no—
60Dic9⋊C4—42no—
61C2×C9⋊C8—21no—
62C2×C9⋊C8—21no—
63#1609—91noSylow
64C3×#126—21no—
65C3×#125—21no—
66C3×#123—21no—
67C3×#123—21no—
68C3×C22⋊Q8—21no—
69C3×C22⋊Q8C2×D311yescharacteristic
70C3×#121C2×D311yescharacteristic
71C3×C4×D4—21no—
72C2×C3×C4⋊C4C2×D311yescharacteristic
73C2×C4⋊Dic3—31no—
74C2×Dic3⋊C4—61no—
75#835—61no—
76#832—61no—
77C3⋊#95—31no—
78C3⋊#95—61no—
79#830—31no—
80#830—31no—
81#808—61no—
82#807—61no—
83C23×C9—21no—
84C23×C9C2×D411yescharacteristic
85Q8×C9—41no—
86D4×C9—41no—
87D4×C9—41no—
88D4×C9—41no—
89C2×C4×C9—21no—
90C2×C4×C9—21no—
91C2×C4×C9—21no—
92C2×C4×C9—21no—
93C2×C4×C9—21no—
94C2×C4×C9—21no—
95C2×C4×C9—21no—
96C2×C4×C9—41no—
97C2×C4×C9—41no—
98C2×C4×C9—81no—
99C2×C4×C9C2×D411yescharacteristic
100C2×C4×C9C2×D411yescharacteristic
101C2×Dic9—22no—
102C2×Dic9—41no—
103C2×Dic9—41no—
104C2×Dic9—41no—
105C2×Dic9—41no—
106C2×Dic9—41no—
107C9⋊C8—41no—
108C9⋊C8—41no—
109#539D911yescharacteristic
110#483—91no—
111#480—91no—
112#398—91no—
113#328—91no—
114#327—91no—
115#324—91no—
116C2×C3×Q8#6711yescharacteristic
117C2×C3×D4—21no—
118C2×C3×D4#6711yescharacteristic
119C22×C3×C4—21no—
120C22×C3×C4#6711yescharacteristic
121C22×C3×C4#6711yescharacteristic
122C22×C3×C4C22×D311yescharacteristic
123C22×Dic3—61no—
124C22×Dic3—61no—
125C3×C4⋊C4—21no—
126C3×C4⋊C4—21no—
127C3×C4⋊C4—21no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4#6711yescharacteristic
132C3×C4⋊C4#6711yescharacteristic
133C3×C22⋊C4—21no—
134C3×C22⋊C4—21no—
135C3×C22⋊C4—21no—
136C3×C22⋊C4—21no—
137C3×C22⋊C4—21no—
138C3×C42—21no—
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141Dic3⋊C4—122no—
142C2×C3⋊C8—61no—
143C2×C3⋊C8—61no—
144C22×C9—21no—
145C22×C9—21no—
146C22×C9—41no—
147C22×C9—41no—
148C22×C9—41no—
149C22×C9#12011yescharacteristic
150C22×C9#13511yescharacteristic
151C22×C9AGL(1,ℤ/8)11yescharacteristic
152C4×C9—21no—
153C4×C9—21no—
154C4×C9—41no—
155C4×C9—41no—
156C4×C9—41no—
157C4×C9—41no—
158C4×C9—41no—
159Dic9—42no—
160Dic9—81no—
161#126—21no—
162#125—21no—
163#123—21no—
164#123—21no—
165C22⋊Q8—21no—
166C22⋊Q8C2×D911yescharacteristic
167#121C2×D911yescharacteristic
168C4×D4—21no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4—181no—
171C2×C4⋊C4C2×D911yescharacteristic
172#107—181no—
173#106—181no—
174#103—181no—
175#102—181no—
176C22⋊C8—91no—
177C22⋊C8—91no—
178#95—91no—
179#95—181no—
180C23×C3—21no—
181C23×C3C2×#6711yescharacteristic
182C3×Q8—41no—
183C3×D4—41no—
184C3×D4—41no—
185C3×D4—41no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—81no—
196C2×C3×C4C2×#6711yescharacteristic
197C2×C3×C4C2×#6711yescharacteristic
198C2×Dic3—62no—
199C2×Dic3—121no—
200C2×Dic3—121no—
201C2×Dic3—121no—
202C2×Dic3—121no—
203C2×Dic3—121no—
204C3⋊C8—121no—
205C3⋊C8—121no—
206C2×C9—21no—
207C2×C9—21no—
208C2×C9—81no—
209C2×C9#44911yescharacteristic
210C2×C9#45611yescharacteristic
211C2×C9#45811yescharacteristic
212C2×Q8#61111yescharacteristic
213C2×D4—21no—
214C2×D4#61111yescharacteristic
215C22×C4—21no—
216C22×C4—181no—
217C22×C4—181no—
218C22×C4#61111yescharacteristic
219C22×C4#61111yescharacteristic
220C22×C4C22×D911yescharacteristic
221C2×C8—181no—
222C2×C8—181no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—181no—
230C4⋊C4—181no—
231C4⋊C4—362no—
232C4⋊C4#61111yescharacteristic
233C4⋊C4#61111yescharacteristic
234C22⋊C4—21no—
235C22⋊C4—21no—
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—21no—
239C42—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—41no—
243C22×C3—41no—
244C22×C3—41no—
245C22×C3#94911yescharacteristic
246C22×C3#95011yescharacteristic
247C22×C3#95311yescharacteristic
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—41no—
251C3×C4—41no—
252C3×C4—41no—
253C3×C4—41no—
254C3×C4—41no—
255Dic3—122no—
256Dic3—241no—
257C9#160911yescharacteristic, complemented, Sylow
258C23—21no—
259C23C2×#61111yescharacteristic
260Q8—41no—
261D4—41no—
262D4—41no—
263D4—41no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—81no—
274C2×C4—182no—
275C2×C4—361no—
276C2×C4—361no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4—361no—
280C2×C4C2×#61111yescharacteristic
281C2×C4C2×#61111yescharacteristic
282C8—361no—
283C8—361no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—81no—
287C2×C3#523811yescharacteristic
288C2×C3#524311yescharacteristic
289C2×C3#524611yescharacteristic
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22#6351211yescharacteristic
296C22#6351311yescharacteristic
297C22#6351511yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—362no—
306C4—721no—
307C3#7188611yescharacteristic
308C2—21no—
309C2—21no—
310C2—81no—
311C2#1058891911yescharacteristic
312C2#1058892311yescharacteristic
313C2#1058892511yescharacteristic
subgroupG/H
centerC22#63515
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#539C2
socleC22×C3#953
prime radicalC3×#121C2×D3
hypercenter#539D9
hypocenterC9#1609
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
2. #10588723C2semidirect
4. #10588661C2semidirect
5. #10588215C2semidirect
7. #10588205C2semidirect
257. C9#1609semidirect

Maximal subgroups

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

subgroupindex
C9×#5392
#105887232
#105887132
#105886612
#105882152
#105882142
#105882052
#718863