Finite Group Databasebeta

← #15675421

Subgroups — #15675421

Order 2944.

236 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 41 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#13093129C211yesmaximal, characteristic, complemented
2#13092600C211yesmaximal, characteristic, complemented
3#13092590C211yesmaximal, characteristic, complemented
4#13092215C211yesmaximal, characteristic, complemented
5#13092214C211yesmaximal, characteristic, complemented
6#13092213C211yesmaximal, characteristic, complemented
7C23×#454C211yesmaximal, characteristic, complemented
8C23×2−1+4C2211yescharacteristic
9C23×AGL(1,ℤ/8)—21no—
10C23×#124C2211yescharacteristic
11#10625122—21no—
12#10625120—21no—
13#10625118C2211yescharacteristic
14#10625115C2211yescharacteristic
15#10625110—21no—
16#10625056—21no—
17#10625055—21no—
18(C22⋊D23)⋊C4—21no—
19#10625048—21no—
20#10625043—21no—
21C23×#104—21no—
22C23×#101C2211yescharacteristic
23#10625019—21no—
24#10625019—21no—
25#10625018C2211yescharacteristic
26#10625018C2211yescharacteristic
27#41×C23—21no—
28#41×C23—21no—
29#41×C23—21no—
30#41×C23—41no—
31C2×Q8×C23—41no—
32C2×Q8×C23C2311yescharacteristic
33C2×D4×C23D411yescharacteristic
34C2×C22⋊D23—21no—
35C2×C22⋊D23—21no—
36C22×Dic23—21no—
37C2×D92D411yescharacteristic
38C2×C4×D23—21no—
39C2×Dic46D411yescharacteristic
40SD16×C23—41no—
41D8×C23—41no—
42M16×C23—21no—
43C22⋊C4×C23—21no—
44C22⋊C4×C23—21no—
45C42×C23D411yescharacteristic
46C22⋊Dic23—21no—
47#67275—41no—
48#67274—41no—
49#67273—41no—
50#67272—41no—
51(C2×D23)⋊C4—21no—
52(C2×D23)⋊C4—21no—
53(C2×D23)⋊C4—21no—
54Dic23⋊C4—21no—
55Dic23⋊C4—21no—
56Dic23⋊C4—21no—
57C4×Dic23—21no—
58C4×Dic23D411yescharacteristic
59C4×Dic23D411yescharacteristic
60#67267—21no—
61#67267—21no—
62C23×C23—21no—
63C22×D23—21no—
64Q8×C23—21no—
65Q8×C23—21no—
66Q8×C23—21no—
67Q8×C23—41no—
68D4×C23—21no—
69D4×C23—21no—
70D4×C23—21no—
71D4×C23—41no—
72D4×C23—41no—
73C2×C4×C23—21no—
74C2×C4×C23—41no—
75C2×C4×C23—41no—
76C2×C4×C23—41no—
77C2×C4×C23C2×D411yescharacteristic
78C2×C4×C23C2×D411yescharacteristic
79C2×C4×C23C2×D411yescharacteristic
80C22⋊D23—42no—
81C22⋊D23—81no—
82C2×Dic23—21no—
83C2×Dic23—21no—
84C2×Dic23—21no—
85C2×Dic23—42no—
86D92—41no—
87C4×D23—42no—
88Dic46—41no—
89C8×C23—41no—
90C23⋊C8—41no—
91C23⋊C8—41no—
92#2204—231nomaximal, Sylow
93C22×C23—41no—
94C22×C23—41no—
95C22×C23—41no—
96C22×C23—41no—
97C22×C23#12011yescharacteristic
98C2×D23—41no—
99C2×D23—41no—
100C2×D23—41no—
101C4×C23—21no—
102C4×C23—21no—
103C4×C23—21no—
104C4×C23—41no—
105C4×C23—41no—
106Dic23—22no—
107Dic23—41no—
108Dic23—41no—
109#555—231no—
110#456—231no—
111#454—231no—
112#454D2311yescharacteristic, complemented
113#356—231no—
114#355—231no—
115#355—231no—
116C2×C23—21no—
117C2×C23—81no—
118C2×C23—81no—
119C2×C23B(4,𝔽2)11yescharacteristic
120D23—81no—
1212−1+4C2×D2311yescharacteristic
122#137—461no—
123AGL(1,ℤ/8)—21no—
124AGL(1,ℤ/8)—461no—
125C4⋊Q8—231no—
126#124—231no—
127#124—461no—
128#124C2×D2311yescharacteristic
129#121—461no—
130#121—461no—
131C4×D4—461no—
132#117—461no—
133#117—461no—
134#104—21no—
135#104—461no—
136#104—461no—
137#101—231no—
138#101—231no—
139#101C2×D2311yescharacteristic
140C23#220411yescharacteristic, complemented, Sylow
141#41—21no—
142#41—21no—
143#41—21no—
144#41—41no—
145C2×Q8—41no—
146C2×Q8—231no—
147C2×Q8C22×D2311yescharacteristic
148C2×D4—231no—
149C2×D4—461no—
150C2×D4—461no—
151C2×D4C22⋊D2311yescharacteristic
152C22×C4—461no—
153C22×C4—461no—
154Q16—921no—
155SD16—41no—
156SD16—921no—
157SD16—921no—
158D8—41no—
159D8—921no—
160M16—21no—
161M16—461no—
162M16—461no—
163C4⋊C4—461no—
164C4⋊C4—461no—
165C4⋊C4—461no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—461no—
169C22⋊C4—461no—
170C22⋊C4—461no—
171C22⋊C4—461no—
172C42—231no—
173C42—231no—
174C42—461no—
175C42C22⋊D2311yescharacteristic
176C23—21no—
177C23—461no—
178Q8—21no—
179Q8—21no—
180Q8—21no—
181Q8—41no—
182Q8—921no—
183D4—21no—
184D4—21no—
185D4—21no—
186D4—41no—
187D4—41no—
188D4—921no—
189D4—922no—
190D4—1841no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—461no—
196C2×C4—461no—
197C2×C4—461no—
198C2×C4—922no—
199C2×C4—922no—
200C2×C4D4×D2311yescharacteristic
201C2×C4D4×D2311yescharacteristic
202C2×C4C2×C22⋊D2311yescharacteristic
203C8—41no—
204C8—921no—
205C8—921no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—921no—
211C22—921no—
212C22—921no—
213C22#1062510811yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—41no—
218C4—41no—
219C4—462no—
220C4—921no—
221C4—921no—
222C2—21no—
223C2—81no—
224C2—81no—
225C2—1841no—
226C2#1309260311yescharacteristic
subgroupG/H
centerC2#13092603
commutator, cosocleC2×Q8×C23C23
FrattiniC2×Q8C22×D23
FittingC23×#454C2
socleC2×C23B(4,𝔽2)
hypercenter#454D23
hypocenterC23#2204
LCSG ▷ C2×Q8×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #13093129C2semidirect
2. #13092600C2semidirect
3. #13092590C2semidirect
4. #13092215C2semidirect
5. #13092214C2semidirect
6. #13092213C2semidirect
7. C23×#454C2semidirect
112. #454D23semidirect
140. C23#2204semidirect

Maximal subgroups

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

subgroupindex
#130931292
#130926002
#130925902
#130922152
#130922142
#130922132
C23×#4542
#220423