Finite Group Databasebeta

← #11779997

Subgroups — #11779997

Order 1152.

300 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 76 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#10589824C211yesmaximal, characteristic
2#10588759C211yesmaximal, characteristic
3#10588515C211yesmaximal, characteristic
4#10588513C211yesmaximal, characteristic
5C9×#333C211yesmaximal, characteristic
6#10588160C211yesmaximal, characteristic
7#10588160C211yesmaximal, characteristic
8#68507—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10#63506—22no—
11C2×Dic36—21no—
12#63450—21no—
13#63450—21no—
14#63449—21no—
15#63449—21no—
16#63431C2211yescharacteristic
17C4×Dic18C2211yescharacteristic
18C4×Dic18C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20C9×C4⋊C8C2211yescharacteristic
21#63395—22no—
22#63377—21no—
23#63376—21no—
24#63376—21no—
25C4×C9⋊C8C2211yescharacteristic
26#5722—31no—
27#5079—31no—
28#4851—31no—
29#4849—31no—
30C3×#333D311yescharacteristic
31#4484—31no—
32#4484—31no—
33C2×Q8×C9D412yes—
34C2×Dic18—21no—
35C2×Dic18—22no—
36C2×Dic18D411yescharacteristic
37C2×Dic18D411yescharacteristic
38C2×C8×C9—21no—
39C2×C8×C9—21no—
40C9×C4⋊C4—21no—
41C9×C4⋊C4—21no—
42C42×C9C2311yescharacteristic
43C4⋊Dic9—21no—
44C4⋊Dic9—21no—
45C4⋊Dic9D411yescharacteristic
46C4⋊Dic9D411yescharacteristic
47Dic9⋊C4—22no—
48Dic9⋊C4—22no—
49Dic9⋊C4—21no—
50Dic9⋊C4—21no—
51C4×Dic9—22no—
52C4×Dic9—21no—
53C4×Dic9—21no—
54C2×C9⋊C8—21no—
55Dic36—42no—
56#1645—91noSylow
57C3×C4⋊Q8C2×D311yescharacteristic
58#944—62no—
59C2×Dic12—61no—
60#888—61no—
61#888—61no—
62#887—61no—
63#887—61no—
64#869—31no—
65C4×Dic6—31no—
66C4×Dic6—31no—
67C3×C4⋊C8C2×D311yescharacteristic
68C3×C4⋊C8C2×D311yescharacteristic
69#835—62no—
70#817—61no—
71#816—61no—
72#816—61no—
73C4×C3⋊C8—31no—
74Q8×C9—42no—
75C2×C4×C9—22no—
76C2×C4×C9C2×D411yescharacteristic
77C2×C4×C9C2×D411yescharacteristic
78C2×C4×C9C2×D411yescharacteristic
79C2×Dic9—21no—
80C2×Dic9—21no—
81C2×Dic9—21no—
82C2×Dic9—21no—
83C2×Dic9—41no—
84Dic18—21no—
85Dic18—21no—
86Dic18—41no—
87Dic18—41no—
88Dic18—82no—
89Dic18SD1612yes—
90Dic18Q1612yescomplemented
91C8×C9—41no—
92C8×C9—41no—
93C9⋊C8—41no—
94Q82—91no—
95#487—91no—
96#475—91no—
97#462—91no—
98#333D911yescharacteristic
99Q8⋊C8—91no—
100Q8⋊C8—91no—
101C2×C3×Q8D1212yes—
102C2×Dic6—31no—
103C2×Dic6—31no—
104C2×Dic6—61no—
105C2×Dic6—62no—
106C2×C3×C8—21no—
107C2×C3×C8—21no—
108C3×C4⋊C4—21no—
109C3×C4⋊C4—21no—
110C3×C42C22×D311yescharacteristic
111C4⋊Dic3—31no—
112C4⋊Dic3—31no—
113C4⋊Dic3—61no—
114C4⋊Dic3—61no—
115Dic3⋊C4—62no—
116Dic3⋊C4—62no—
117Dic3⋊C4—61no—
118Dic3⋊C4—61no—
119C4×Dic3—62no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C2×C3⋊C8—61no—
123Dic12—122no—
124C22×C9#12011yescharacteristic
125C4×C9—21no—
126C4×C9—42no—
127C4×C9C2×SD1611yescharacteristic
128C4×C9C2×Q1611yescharacteristic
129C4×C9#13711yescharacteristic
130C4×C9#13711yescharacteristic
131Dic9—22no—
132Dic9—22no—
133Dic9—41no—
134Dic9—41no—
135Dic9—81no—
136C2×Q16—181no—
137C4⋊Q8—91no—
138C4⋊Q8—181no—
139C4⋊Q8—181no—
140C4⋊Q8—182no—
141C4⋊Q8C2×D911yescharacteristic
142C4×Q8—91no—
143C4×Q8—91no—
144C4×Q8—181no—
145C4×Q8—181no—
146#106—181no—
147C4⋊C8C2×D911yescharacteristic
148C4⋊C8C2×D911yescharacteristic
149#103—181no—
150#103—181no—
151#103—182no—
152C4×C8—91no—
153C3×Q8—42no—
154C2×C3×C4—22no—
155C2×C3×C4C2×D1211yescharacteristic
156C2×C3×C4D3×D411yescharacteristic
157C2×C3×C4D3×D411yescharacteristic
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—121no—
163Dic6—32no—
164Dic6—32no—
165Dic6—61no—
166Dic6—61no—
167Dic6—121no—
168Dic6—121no—
169Dic6—242no—
170C3×C8—41no—
171C3×C8—41no—
172C3⋊C8—121no—
173C2×C9#44811yescharacteristic
174C2×C9#45111yescharacteristic
175C2×C9#45511yescharacteristic
176C2×Q8—91no—
177C2×Q8—91no—
178C2×Q8—182no—
179C2×Q8—181no—
180C2×Q8D3612yes—
181Q16—362no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—181no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—91no—
188C4⋊C4—91no—
189C4⋊C4—182no—
190C4⋊C4—182no—
191C4⋊C4—181no—
192C4⋊C4—181no—
193C4⋊C4—181no—
194C4⋊C4—181no—
195C42—182no—
196C42—181no—
197C42—181no—
198C42C22×D911yescharacteristic
199C22×C3#88211yescharacteristic
200C3×C4—21no—
201C3×C4—42no—
202C3×C4D3×SD1611yescharacteristic
203C3×C4#91511yescharacteristic
204C3×C4D3×Q1611yescharacteristic
205C3×C4#91811yescharacteristic
206Dic3—62no—
207Dic3—62no—
208Dic3—121no—
209Dic3—121no—
210Dic3—241no—
211C9#164511yescharacteristic, complemented, Sylow
212Q8—42no—
213Q8—92no—
214Q8—92no—
215Q8—181no—
216Q8—181no—
217Q8—361no—
218Q8—361no—
219Q8—722no—
220C2×C4—22no—
221C2×C4—181no—
222C2×C4—181no—
223C2×C4—181no—
224C2×C4—181no—
225C2×C4—361no—
226C2×C4C2×D3611yescharacteristic
227C2×C4D4×D911yescharacteristic
228C2×C4D4×D911yescharacteristic
229C8—41no—
230C8—41no—
231C8—361no—
232C2×C3#474611yescharacteristic
233C2×C3#480611yescharacteristic
234C2×C3#480911yescharacteristic
235C22#6344411yescharacteristic
236C4—21no—
237C4—42no—
238C4—182no—
239C4—182no—
240C4—361no—
241C4—361no—
242C4—721no—
243C4SD16×D911yescharacteristic
244C4#6347711yescharacteristic
245C4Q16×D911yescharacteristic
246C4#6348011yescharacteristic
247C3#6850711yescharacteristic
248C2#1058842611yescharacteristic
249C2#1058848611yescharacteristic
250C2#1058848911yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#333C2
socle, prime radicalC22×C3#882
hypercenter#333D9
hypocenterC9#1645
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
90. Dic18Q16semidirect
211. C9#1645semidirect

Maximal subgroups

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

subgroupindex
#105898242
#105887592
#105885152
#105885132
C9×#3332
#105881602
#685073