Finite Group Databasebeta

← #3028⋊C9 #11919595

Subgroups — #3028⋊C9 #11919595

Order 1152.

290 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 31 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#10593125C211yesmaximal, characteristic
2#458⋊C9C212yesmaximal, complemented
3C3×#3028C311yesmaximal, characteristic
4#63703C2211yescharacteristic
5Q8×C22⋊C9—41nomaximal
6C3×#585C2×C311yescharacteristic
7C3×#536—31no—
8C3×#458—32no—
9C3×#458C2×C312yes—
10C3×#410—31no—
11#41⋊C9—81no—
12C4×C22⋊C9—41no—
13C4×C22⋊C9—42no—
14C4×C22⋊C9—81no—
15#3028C911yescharacteristic, complemented, Sylow
16C3×2−1+4—61no—
17C3×H(5,𝔽2)—31no—
18C3×H(5,𝔽2)—61no—
19C3×H(5,𝔽2)C22×C311yescharacteristic
20C2×C3×#41—31no—
21C2×C3×#41—61no—
22C2×C3×#41—61no—
23C22×C3×Q8A411yescharacteristic
24C3×C4⋊Q8—61no—
25C3×#124—61no—
26C3×#123—32no—
27C3×#123—32no—
28C3×C22⋊Q8—61no—
29C3×C22⋊Q8—61no—
30C3×#117—31no—
31C3×#99—32no—
32C3×#99—32no—
33C2×C22⋊C9—41no—
34C2×C22⋊C9—81no—
35Q8×C9—161no—
36Q8⋊C9—81no—
37#585C2×C911yescharacteristic
38#536—31no—
39#458—32no—
40#458C2×C912yes—
41#410—31no—
42C3×#41—21no—
43C3×#41—62no—
44C3×#41—62no—
45C3×#41—61no—
46C3×#41—62no—
47C3×#41—61no—
48C3×#41—62no—
49C3×#41—62no—
50C3×#41—61no—
51C2×C3×Q8—31no—
52C2×C3×Q8—61no—
53C2×C3×Q8—61no—
54C2×C3×Q8—61no—
55C2×C3×Q8—61no—
56C2×C3×D4—31no—
57C2×C3×D4—31no—
58C2×C3×D4—31no—
59C2×C3×D4—61no—
60C2×C3×D4—62no—
61C2×C3×D4—61no—
62C2×C3×D4—61no—
63C2×C3×D4—61no—
64C22×C3×C4—21no—
65C22×C3×C4—31no—
66C22×C3×C4—31no—
67C22×C3×C4—61no—
68C22×C3×C4C2×A411yescharacteristic
69C22×C3×C4C2×A412yes—
70C3×C4⋊C4—61no—
71C3×C4⋊C4—62no—
72C3×C4⋊C4—62no—
73C3×C22⋊C4—32no—
74C3×C22⋊C4—62no—
75C3×C22⋊C4—62no—
76C3×C42—61no—
77C22⋊C9—41no—
78C22⋊C9—81no—
79C4×C9—162no—
80C4×C9—161no—
812−1+4—61no—
82H(5,𝔽2)—31no—
83H(5,𝔽2)—61no—
84H(5,𝔽2)C22×C911yescharacteristic
85C2×#41—31no—
86C2×#41—61no—
87C2×#41—61no—
88C22×Q8C22⋊C911yescharacteristic, complemented
89C4⋊Q8—61no—
90#124—61no—
91#123—32no—
92#123—32no—
93C22⋊Q8—61no—
94C22⋊Q8—61no—
95#117—31no—
96#99—32no—
97#99—32no—
98C23×C3—21no—
99C23×C3—31no—
100C23×C3—31no—
101C23×C3—61no—
102C23×C3C22×A411yescharacteristic
103C3×Q8—21no—
104C3×Q8—41no—
105C3×Q8—62no—
106C3×Q8—61no—
107C3×Q8—121no—
108C3×D4—62no—
109C3×D4—62no—
110C3×D4—62no—
111C3×D4—61no—
112C3×D4—61no—
113C3×D4—62no—
114C2×C3×C4—31no—
115C2×C3×C4—31no—
116C2×C3×C4—31no—
117C2×C3×C4—31no—
118C2×C3×C4—61no—
119C2×C3×C4—61no—
120C2×C3×C4—62no—
121C2×C3×C4—62no—
122C2×C3×C4—61no—
123C2×C3×C4—61no—
124C2×C3×C4—61no—
125C2×C3×C4—61no—
126C2×C3×C4—62no—
127C2×C9—161no—
128#41—21no—
129#41—62no—
130#41—62no—
131#41—61no—
132#41—62no—
133#41—61no—
134#41—62no—
135#41—62no—
136#41—61no—
137C2×Q8—31no—
138C2×Q8—61no—
139C2×Q8—61no—
140C2×Q8—61no—
141C2×Q8—61no—
142C2×D4—31no—
143C2×D4—31no—
144C2×D4—31no—
145C2×D4—61no—
146C2×D4—62no—
147C2×D4—61no—
148C2×D4—61no—
149C2×D4—61no—
150C22×C4—21no—
151C22×C4—31no—
152C22×C4—31no—
153C22×C4—61no—
154C22×C4C2×C22⋊C911yescharacteristic
155C22×C4C2×C22⋊C912yes—
156C4⋊C4—61no—
157C4⋊C4—62no—
158C4⋊C4—62no—
159C22⋊C4—32no—
160C22⋊C4—62no—
161C22⋊C4—62no—
162C42—61no—
163C22×C3—31no—
164C22×C3—41no—
165C22×C3—61no—
166C22×C3—61no—
167C22×C3—81no—
168C22×C3—121no—
169C22×C3—121no—
170C22×C3—241no—
171C3×C4—31no—
172C3×C4—42no—
173C3×C4—61no—
174C3×C4—61no—
175C3×C4—122no—
176C3×C4#120⋊C311yescharacteristic
177C9—161noSylow
178C23—21no—
179C23—31no—
180C23—31no—
181C23—61no—
182C23C22×C22⋊C911yescharacteristic
183Q8—21no—
184Q8—41no—
185Q8—62no—
186Q8—61no—
187Q8—121no—
188D4—62no—
189D4—62no—
190D4—62no—
191D4—61no—
192D4—61no—
193D4—62no—
194C2×C4—31no—
195C2×C4—31no—
196C2×C4—31no—
197C2×C4—31no—
198C2×C4—61no—
199C2×C4—61no—
200C2×C4—62no—
201C2×C4—62no—
202C2×C4—61no—
203C2×C4—61no—
204C2×C4—61no—
205C2×C4—61no—
206C2×C4—62no—
207C2×C3—61no—
208C2×C3—121no—
209C2×C3—121no—
210C2×C3C2×#120⋊C311yescharacteristic
211C22—31no—
212C22—41no—
213C22—61no—
214C22—61no—
215C22—81no—
216C22—121no—
217C22—121no—
218C22—241no—
219C4—31no—
220C4—42no—
221C4—61no—
222C4—61no—
223C4—122no—
224C4#120⋊C911yescharacteristic
225C3#3028⋊C311yescharacteristic
226C2—61no—
227C2—121no—
228C2—121no—
229C2C2×#120⋊C911yescharacteristic
subgroupG/H
center, socleC2×C3C2×#120⋊C3
commutator, hypocenterH(5,𝔽2)C22×C9
FrattiniC23×C3C22×A4
FittingC3×#3028C3
prime radicalC3×#585C2×C3
cosocleC3×H(5,𝔽2)C22×C3
hypercenterC3×C4#120⋊C3
LCSG ▷ H(5,𝔽2)
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
2. #458⋊C9C2semidirect
15. #3028C9semidirect
88. C22×Q8C22⋊C9semidirect

Maximal subgroups

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

subgroupindex
#105931252
#458⋊C92
C3×#30283
Q8×C22⋊C94