Finite Group Databasebeta

← #11779991

Subgroups — #11779991

Order 1152.

300 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 80 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
1Q8×Dic18C211yesmaximal, characteristic
2C9×#475C211yesmaximal, characteristic
3#10588766C211yesmaximal, characteristic
4#10588763C211yesmaximal, characteristic
5#10588212C211yesmaximal, characteristic
6#10588160C211yesmaximal, characteristic
7#10588158C211yesmaximal, characteristic
8#71129—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C4×Q8×C9C2211yescharacteristic
11Q8×Dic9—21no—
12C2×#3674—21no—
13#63450—22no—
14#63450—21no—
15#63431—21no—
16#63431C2211yescharacteristic
17C4×Dic18—21no—
18C4×Dic18C2211yescharacteristic
19C9×#106—21no—
20C9×C4⋊C8C2211yescharacteristic
21C9×#103—21no—
22#63395—21no—
23#63368—22no—
24C4⋊(C9⋊C8)C2211yescharacteristic
25C4×C9⋊C8C2211yescharacteristic
26Q8×Dic6—31no—
27C3×#475D311yescharacteristic
28#5093—31no—
29#5090—31no—
30#4535—31no—
31#4484—31no—
32#4481—31no—
33C2×Q8×C9—21no—
34C2×Q8×C9D411yescharacteristic
35C2×Dic18—22no—
36C2×Dic18D411yescharacteristic
37C2×Dic18D412yes—
38C2×C8×C9—21no—
39C9×C4⋊C4—21no—
40C9×C4⋊C4—21no—
41C9×C4⋊C4—21no—
42C9×C4⋊C4D411yescharacteristic
43C42×C9—21no—
44C42×C9C2311yescharacteristic
45#3674—42no—
46C4⋊Dic9—22no—
47C4⋊Dic9—21no—
48C4⋊Dic9—21no—
49C4⋊Dic9D411yescharacteristic
50Dic9⋊C4—22no—
51Dic9⋊C4—21no—
52C4×Dic9—22no—
53C4×Dic9—21no—
54C2×C9⋊C8—21no—
55C2×C9⋊C8—21no—
56#1645—91noSylow
57C3×C4⋊Q8C2×D311yescharacteristic
58C3×C4×Q8C2×D311yescharacteristic
59Q8×Dic3—61no—
60C2×#216—61no—
61#888—62no—
62#888—61no—
63#869—31no—
64#869—61no—
65C4×Dic6—31no—
66C4×Dic6—61no—
67C3×#106—21no—
68C3×C4⋊C8C2×D311yescharacteristic
69C3×#103—21no—
70#835—61no—
71#810—62no—
72C4⋊(C3⋊C8)—31no—
73C4×C3⋊C8—31no—
74Q8×C9—21no—
75Q8×C9—41no—
76Q8×C9—41no—
77Q8×C9Q1612yescomplemented
78C2×C4×C9—21no—
79C2×C4×C9—21no—
80C2×C4×C9—41no—
81C2×C4×C9C2×D411yescharacteristic
82C2×C4×C9C2×D411yescharacteristic
83C2×C4×C9C2×D411yescharacteristic
84C2×Dic9—21no—
85C2×Dic9—22no—
86C2×Dic9—21no—
87Dic18—21no—
88Dic18—42no—
89Dic18—82no—
90Dic18SD1612yes—
91C8×C9—41no—
92C9⋊C8—41no—
93C9⋊C8—41no—
94Q82—91no—
95#487—91no—
96#475D911yescharacteristic
97#462—91no—
98#333—91no—
99Q8⋊C8—91no—
100Q8⋊C8—91no—
101C2×C3×Q8—21no—
102C2×C3×Q8#6711yescharacteristic
103C2×Dic6—31no—
104C2×Dic6—32no—
105C2×Dic6—62no—
106C2×C3×C8—21no—
107C3×C4⋊C4—21no—
108C3×C4⋊C4—21no—
109C3×C4⋊C4—21no—
110C3×C4⋊C4#6711yescharacteristic
111C3×C42—21no—
112C3×C42C22×D311yescharacteristic
113#216—122no—
114C4⋊Dic3—31no—
115C4⋊Dic3—62no—
116C4⋊Dic3—61no—
117C4⋊Dic3—61no—
118Dic3⋊C4—62no—
119Dic3⋊C4—61no—
120C4×Dic3—62no—
121C4×Dic3—61no—
122C2×C3⋊C8—61no—
123C2×C3⋊C8—61no—
124C22×C9#12011yescharacteristic
125C4×C9—22no—
126C4×C9—21no—
127C4×C9—41no—
128C4×C9—81no—
129C4×C9C2×SD1611yescharacteristic
130C4×C9C2×Q1611yescharacteristic
131C4×C9#13711yescharacteristic
132C4×C9#13711yescharacteristic
133Dic9—22no—
134Dic9—42no—
135Dic9—41no—
136C2×Q16—181no—
137C4⋊Q8—91no—
138C4⋊Q8—181no—
139C4⋊Q8—182no—
140C4⋊Q8—181no—
141C4⋊Q8C2×D911yescharacteristic
142C4×Q8—91no—
143C4×Q8—181no—
144C4×Q8—181no—
145C4×Q8C2×D911yescharacteristic
146#106—21no—
147C4⋊C8—91no—
148C4⋊C8C2×D911yescharacteristic
149#103—21no—
150#103—182no—
151#103—181no—
152C4×C8—91no—
153C3×Q8—21no—
154C3×Q8—41no—
155C3×Q8—41no—
156C3×Q8#21612yes—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—41no—
160C2×C3×C4D3×D411yescharacteristic
161C2×C3×C4D3×D411yescharacteristic
162C2×C3×C4C2×#6711yescharacteristic
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—62no—
166Dic6—32no—
167Dic6—61no—
168Dic6—122no—
169Dic6—242no—
170C3×C8—41no—
171C3⋊C8—121no—
172C3⋊C8—121no—
173C2×C9#44811yescharacteristic
174C2×C9#45111yescharacteristic
175C2×C9#45511yescharacteristic
176C2×Q8—21no—
177C2×Q8—91no—
178C2×Q8—92no—
179C2×Q8—182no—
180C2×Q8#61111yescharacteristic
181Q16—362no—
182C2×C8—21no—
183C2×C8—181no—
184C2×C8—181no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—91no—
189C4⋊C4—182no—
190C4⋊C4—182no—
191C4⋊C4—181no—
192C4⋊C4—181no—
193C4⋊C4—181no—
194C4⋊C4#61111yescharacteristic
195C42—21no—
196C42—182no—
197C42—181no—
198C42C22×D911yescharacteristic
199C22×C3#93711yescharacteristic
200C3×C4—21no—
201C3×C4—22no—
202C3×C4—41no—
203C3×C4—81no—
204C3×C4D3×SD1611yescharacteristic
205C3×C4#91511yescharacteristic
206C3×C4C2×#21611yescharacteristic
207C3×C4#95111yescharacteristic
208Dic3—62no—
209Dic3—122no—
210Dic3—121no—
211C9#164511yescharacteristic, complemented, Sylow
212Q8—21no—
213Q8—41no—
214Q8—41no—
215Q8—92no—
216Q8—181no—
217Q8—362no—
218Q8—722no—
219Q8#367412yescomplemented
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—181no—
224C2×C4—181no—
225C2×C4—182no—
226C2×C4D4×D911yescharacteristic
227C2×C4D4×D911yescharacteristic
228C2×C4C2×#61111yescharacteristic
229C8—41no—
230C8—361no—
231C8—361no—
232C2×C3#505011yescharacteristic
233C2×C3#517011yescharacteristic
234C2×C3#520211yescharacteristic
235C22#6349911yescharacteristic
236C4—22no—
237C4—21no—
238C4—41no—
239C4—81no—
240C4—182no—
241C4—362no—
242C4—361no—
243C4SD16×D911yescharacteristic
244C4#6347711yescharacteristic
245C4C2×#367411yescharacteristic
246C4#6351111yescharacteristic
247C3#7112911yescharacteristic
248C2#1058872611yescharacteristic
249C2#1058885011yescharacteristic
250C2#1058888311yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#475C2
socle, prime radicalC22×C3#937
hypercenter#475D9
hypocenterC9#1645
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
77. Q8×C9Q16semidirect
211. C9#1645semidirect
219. Q8#3674semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic182
C9×#4752
#105887662
#105887632
#105882122
#105881602
#105881582
#711293