Finite Group Databasebeta

← #11779522

Subgroups — #11779522

Order 1152.

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

normal subgroups only

This group has 351 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
1#10589828C211yesmaximal, characteristic
2#10588766C211yesmaximal, characteristic, complemented
3#10588526C211yesmaximal, characteristic, complemented
4#10588526C211yesmaximal, characteristic, complemented
5C9×#332C211yesmaximal, characteristic, complemented
6#10588162C211yesmaximal, characteristic, complemented
7#10588162C211yesmaximal, characteristic, complemented
8#68434—31nomaximal
9C2×#3701—21no—
10C9×C4⋊Q8C2211yescharacteristic
11#63508—21no—
12#63457—21no—
13#63456—22no—
14C4⋊C4×D9—21no—
15C4×D36C2211yescharacteristic
16C4×D36C2211yescharacteristic
17#63431C2211yescharacteristic
18C9×C4⋊C8C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20#63380—21no—
21#63380—21no—
22#63377—21no—
23#63377—21no—
24#63368—22no—
25C4×C9⋊C8C2211yescharacteristic
26#5726—31no—
27#5093—31no—
28#4842—31no—
29#4842—31no—
30C3×#332D311yescharacteristic
31#4483—31no—
32#4483—31no—
33C2×Q8×C9—21no—
34#3701—42no—
35#3701—42no—
36C2×D36—22no—
37C2×D36D411yescharacteristic
38C2×D36D411yescharacteristic
39C2×C4×D9—22no—
40C2×C4×D9—21no—
41C2×C4×D9—21no—
42C2×Dic18—21no—
43C2×C8×C9—21no—
44C2×C8×C9—21no—
45C9×C4⋊C4—21no—
46C9×C4⋊C4D412yes—
47C42×C9C2311yescharacteristic
48(C2×D9)⋊C4—22no—
49(C2×D9)⋊C4—21no—
50(C2×D9)⋊C4—21no—
51C4⋊Dic9—21no—
52C4⋊Dic9—21no—
53C4⋊Dic9D411yescharacteristic
54C4⋊Dic9D411yescharacteristic
55Dic9⋊C4—22no—
56C2×C9⋊C8—21no—
57#1635—91noSylow
58C2×#239—61no—
59C3×C4⋊Q8C2×D311yescharacteristic
60#946—61no—
61#895—61no—
62#894—62no—
63D3×C4⋊C4—61no—
64C4×D12—31no—
65C4×D12—31no—
66#869—31no—
67C3×C4⋊C8C2×D311yescharacteristic
68C3×C4⋊C8C2×D311yescharacteristic
69#821—61no—
70#821—61no—
71#817—61no—
72#817—61no—
73#810—62no—
74C4×C3⋊C8—31no—
75C22×D9—21no—
76C22×D9—21no—
77Q8×C9—41no—
78Q8×C9—41no—
79C2×C4×C9—22no—
80C2×C4×C9C2×D411yescharacteristic
81C2×C4×C9C2×D411yescharacteristic
82C2×C4×C9C2×D411yescharacteristic
83C2×Dic9—21no—
84C2×Dic9—21no—
85C2×Dic9—41no—
86D36—21no—
87D36—21no—
88D36—21no—
89D36—44no—
90D36SD1612yes—
91C4×D9—44no—
92C4×D9—41no—
93C4×D9—41no—
94C4×D9—41no—
95C4×D9—41no—
96Dic18—42no—
97C8×C9—41no—
98C8×C9—41no—
99C9⋊C8—41no—
100#547—91no—
101#487—91no—
102#476—91no—
103#476—91no—
104#332D911yescharacteristic, complemented
105D4⋊C8—91no—
106D4⋊C8—91no—
107C2×C3×Q8—21no—
108#239—122no—
109#239—122no—
110C2×D12—31no—
111C2×D12—31no—
112C2×D12—62no—
113C2×C4×D3—62no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×Dic6—61no—
117C2×C3×C8—21no—
118C2×C3×C8—21no—
119C3×C4⋊C4—21no—
120C3×C4⋊C4D1212yes—
121C3×C42C22×D311yescharacteristic
122(C2×D3)⋊C4—62no—
123(C2×D3)⋊C4—61no—
124(C2×D3)⋊C4—61no—
125C4⋊Dic3—31no—
126C4⋊Dic3—31no—
127C4⋊Dic3—61no—
128C4⋊Dic3—61no—
129Dic3⋊C4—62no—
130C2×C3⋊C8—61no—
131C22×C9#12011yescharacteristic
132C2×D9—22no—
133C2×D9—41no—
134C2×D9—41no—
135C2×D9—41no—
136C2×D9—41no—
137C2×D9—41no—
138C4×C9—21no—
139C4×C9—42no—
140C4×C9C2×SD1611yescharacteristic
141C4×C9#13511yescharacteristic
142C4×C9AGL(1,ℤ/8)11yescharacteristic
143C4×C9#13711yescharacteristic
144Dic9—41no—
145Dic9—41no—
146Dic9—81no—
147C2×#41—181no—
148C4⋊Q8—91no—
149C4⋊Q8C2×D911yescharacteristic
150#123—182no—
151C22⋊Q8—181no—
152#121—181no—
153C4×D4—91no—
154C4×D4—91no—
155C2×C4⋊C4—181no—
156#106—181no—
157#106—181no—
158C4⋊C8C2×D911yescharacteristic
159C4⋊C8C2×D911yescharacteristic
160#103—182no—
161#102—181no—
162#102—181no—
163C4×C8—91no—
164C22×D3—61no—
165C22×D3—61no—
166C3×Q8—41no—
167C3×Q8—41no—
168C2×C3×C4—22no—
169C2×C3×C4C2×D1211yescharacteristic
170C2×C3×C4D3×D411yescharacteristic
171C2×C3×C4D3×D411yescharacteristic
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—121no—
175D12—32no—
176D12—61no—
177D12—61no—
178D12—61no—
179D12—124no—
180C4×D3—124no—
181C4×D3—121no—
182C4×D3—121no—
183C4×D3—121no—
184C4×D3—121no—
185Dic6—122no—
186C3×C8—41no—
187C3×C8—41no—
188C3⋊C8—121no—
189C2×C9#45011yescharacteristic
190C2×C9#45211yescharacteristic
191C2×C9#45411yescharacteristic
192D9—42no—
193D9—81no—
194#41—362no—
195#41—362no—
196C2×Q8—21no—
197C2×Q8—181no—
198C2×D4—91no—
199C2×D4—91no—
200C2×D4—182no—
201C22×C4—182no—
202C22×C4—181no—
203C22×C4—181no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—181no—
207C4⋊C4—21no—
208C4⋊C4—91no—
209C4⋊C4—91no—
210C4⋊C4—182no—
211C4⋊C4—181no—
212C4⋊C4—181no—
213C4⋊C4D3612yes—
214C22⋊C4—182no—
215C22⋊C4—181no—
216C22⋊C4—181no—
217C42C22×D911yescharacteristic
218C22×C3#88211yescharacteristic
219C2×D3—62no—
220C2×D3—121no—
221C2×D3—121no—
222C2×D3—121no—
223C2×D3—121no—
224C2×D3—121no—
225C3×C4—21no—
226C3×C4—42no—
227C3×C4#91111yescharacteristic
228C3×C4D3×SD1611yescharacteristic
229C3×C4#91611yescharacteristic
230C3×C4#91811yescharacteristic
231Dic3—121no—
232Dic3—121no—
233Dic3—241no—
234C9#163511yescharacteristic, complemented, Sylow
235C23—181no—
236C23—181no—
237Q8—41no—
238Q8—41no—
239Q8—362no—
240D4—92no—
241D4—181no—
242D4—181no—
243D4—181no—
244D4—364no—
245C2×C4—22no—
246C2×C4—181no—
247C2×C4—181no—
248C2×C4—364no—
249C2×C4—361no—
250C2×C4—361no—
251C2×C4—361no—
252C2×C4—361no—
253C2×C4—361no—
254C2×C4C2×D3611yescharacteristic
255C2×C4D4×D911yescharacteristic
256C2×C4D4×D911yescharacteristic
257C8—41no—
258C8—41no—
259C8—361no—
260C2×C3#475311yescharacteristic
261C2×C3#477611yescharacteristic
262C2×C3#480811yescharacteristic
263D3—122no—
264D3—241no—
265C22—182no—
266C22—361no—
267C22—361no—
268C22—361no—
269C22—361no—
270C22—361no—
271C22#6344411yescharacteristic
272C4—21no—
273C4—42no—
274C4—361no—
275C4—361no—
276C4—721no—
277C4#6347311yescharacteristic
278C4SD16×D911yescharacteristic
279C4#6347811yescharacteristic
280C4#6348011yescharacteristic
281C3#6843411yescharacteristic
282C2—362no—
283C2—721no—
284C2#1058843311yescharacteristic
285C2#1058845611yescharacteristic
286C2#1058848811yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#332C2
socleC22×C3#882
prime radical#10589828C2
hypercenter#332D9
hypocenterC9#1635
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #10588766C2semidirect
3. #10588526C2semidirect
4. #10588526C2semidirect
5. C9×#332C2semidirect
6. #10588162C2semidirect
7. #10588162C2semidirect
104. #332D9semidirect
234. C9#1635semidirect

Maximal subgroups

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

subgroupindex
#105898282
#105887662
#105885262
C9×#3322
#105881622
#684343