Finite Group Databasebeta

← #15674432

Subgroups — #15674432

Order 2944.

362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#10625122C211yesmaximal, characteristic
2#13092988C211yesmaximal, characteristic
3C2×#10625040C211yesmaximal, characteristic, complemented
4#13092427C211yesmaximal, characteristic, complemented
5C2×#10625006C211yesmaximal, characteristic, complemented
6#13092177C211yesmaximal, characteristic, complemented
7C2×C23×#104C211yesmaximal, characteristic
8C2×#41×C23C2211yescharacteristic
9C22×Dic46C2211yescharacteristic
10C22×Dic46C2211yescharacteristic
11C2×M16×C23C2211yescharacteristic
12C2×C42×C23C2211yescharacteristic
13#10625122—22no—
14#10625122—22no—
15#10625115—21no—
16C2×#67275—21no—
17#10625107—21no—
18#10625106—22no—
19C2×#67273—21no—
20#10625097C2211yescharacteristic
21C2×C4⋊Dic23—22no—
22#10625095—22no—
23C2×#67267C2211yescharacteristic
24#10625040—22no—
25#10625040—22no—
26C23×#104—22no—
27#10625006—22no—
28#10624998—22no—
29#41×C23—21no—
30#41×C23—21no—
31#41×C23—21no—
32#41×C23—21no—
33C2×Q8×C23D411yescharacteristic
34C2×D4×C23—21no—
35C2×D4×C23D411yescharacteristic
36C22×C4×C23—21no—
37C22×C4×C23—21no—
38C22×C4×C23C2311yescharacteristic
39C22×Dic23—21no—
40C22×Dic23D412yes—
41C2×Dic46—21no—
42C2×Dic46—21no—
43C2×Dic46—21no—
44C2×Dic46—21no—
45C2×Dic46—21no—
46C2×Dic46—21no—
47C2×Dic46—21no—
48C2×Dic46—21no—
49C2×Dic46—21no—
50C2×Dic46—21no—
51C2×Dic46—21no—
52C2×Dic46D412yes—
53M16×C23—21no—
54M16×C23—21no—
55C2×C8×C23—21no—
56C42×C23—21no—
57C42×C23D412yes—
58C22⋊Dic23—24no—
59C22⋊Dic23—21no—
60#67275—24no—
61#67273—24no—
62C4⋊Dic23—28no—
63C4⋊Dic23D412yes—
64Dic23⋊C4—24no—
65C4×Dic23—21no—
66#67267—21no—
67#67267D412yes—
68C2×C23⋊C8—21no—
69C23×C23—21no—
70C23×C23C2×D411yescharacteristic
71Q8×C23—21no—
72Q8×C23—21no—
73D4×C23—21no—
74D4×C23—21no—
75D4×C23—41no—
76D4×C23—41no—
77C2×C4×C23—24no—
78C2×C4×C23—22no—
79C2×C4×C23—21no—
80C2×C4×C23—41no—
81C2×C4×C23—41no—
82C2×C4×C23C2×D411yescharacteristic
83C2×C4×C23C2×D411yescharacteristic
84C2×C4×C23C2×D411yescharacteristic
85C2×C4×C23C2×D411yescharacteristic
86C2×C4×C23C2×D411yescharacteristic
87C2×C4×C23#4111yescharacteristic
88C2×Dic23—22no—
89C2×Dic23—22no—
90C2×Dic23—22no—
91C2×Dic23—22no—
92C2×Dic23—22no—
93C2×Dic23—41no—
94C2×Dic23—41no—
95Dic46—22no—
96Dic46—22no—
97Dic46—41no—
98Dic46—41no—
99Dic46—41no—
100Dic46—41no—
101Dic46—41no—
102Dic46—41no—
103C8×C23—41no—
104C23⋊C8—22no—
105#2005—231nomaximal, Sylow
106C22×C23—22no—
107C22×C23—41no—
108C22×C23—42no—
109C22×C23#12011yescharacteristic
110C22×C23#12011yescharacteristic
111C22×C23#12111yescharacteristic
112C4×C23—24no—
113C4×C23—41no—
114C4×C23#12011yescharacteristic
115C4×C23#12111yescharacteristic
116C4×C23#12111yescharacteristic
117C4×C23#12711yescharacteristic
118Dic23—42no—
119Dic23—42no—
120Dic23—42no—
121C2×#137—231no—
122#536—231no—
123C2×C4⋊Q8—231no—
124C2×#104D2311yescharacteristic
125#419—231no—
126C2×#101—231no—
127#339—231no—
128C2×C23—21no—
129C2×C23—21no—
130C2×C23—81no—
131C2×C23#39211yescharacteristic
132C2×C23#45612yes—
133C2×#41C2×D2311yescharacteristic
134C22×Q8—231no—
135C22×Q8—231no—
136#137—462no—
137#137—462no—
138C2×Q16—461no—
139C2×SD16—461no—
140C2×M16—231no—
141C2×M16C2×D2311yescharacteristic
142C4⋊Q8—462no—
143C4⋊Q8—461no—
144C4⋊Q8—462no—
145#124—461no—
146#123—462no—
147C22⋊Q8—462no—
148#117—231no—
149C2×C4⋊C4—462no—
150C2×C42C2×D2311yescharacteristic
151#104—22no—
152#103—462no—
153#101—462no—
154C23#200511yescharacteristic, complemented, Sylow
155#41—21no—
156#41—21no—
157#41—21no—
158#41—21no—
159C2×Q8—232no—
160C2×Q8—461no—
161C2×Q8—461no—
162C2×Q8—461no—
163C2×Q8—461no—
164C2×Q8—461no—
165C2×Q8—461no—
166C2×Q8—461no—
167C2×Q8—461no—
168C2×Q8—461no—
169C2×Q8—461no—
170C2×Q8—461no—
171C2×Q8D9211yescharacteristic
172C2×D4—21no—
173C2×D4D9211yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—232no—
177C22×C4—461no—
178C22×C4C22×D2311yescharacteristic
179Q16—464no—
180SD16—464no—
181M16—21no—
182M16—21no—
183M16—232no—
184M16—461no—
185C2×C8—21no—
186C2×C8—461no—
187C4⋊C4—232no—
188C4⋊C4—468no—
189C4⋊C4—464no—
190C22⋊C4—464no—
191C22⋊C4—461no—
192C42—21no—
193C42—461no—
194C42C22⋊D2312yes—
195C23—21no—
196C23D4×D2311yescharacteristic
197Q8—21no—
198Q8—21no—
199Q8—462no—
200Q8—462no—
201Q8—921no—
202Q8—921no—
203Q8—921no—
204Q8—921no—
205Q8—921no—
206Q8—921no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—462no—
217C2×C4—462no—
218C2×C4—462no—
219C2×C4—462no—
220C2×C4—462no—
221C2×C4—921no—
222C2×C4—921no—
223C2×C4C2×D9211yescharacteristic
224C2×C4#6728811yescharacteristic
225C2×C4D4×D2311yescharacteristic
226C2×C4D4×D2311yescharacteristic
227C2×C4D4×D2311yescharacteristic
228C2×C4C2×C22⋊D2311yescharacteristic
229C8—41no—
230C8—462no—
231C22—22no—
232C22—41no—
233C22—42no—
234C22#1062505311yescharacteristic
235C22#1062505511yescharacteristic
236C22#1062510811yescharacteristic
237C4—24no—
238C4—41no—
239C4—922no—
240C4—922no—
241C4—922no—
242C4#1062505311yescharacteristic
243C4#1062505511yescharacteristic
244C4#1062510111yescharacteristic
245C4#1062511111yescharacteristic
246C2—21no—
247C2—21no—
248C2—81no—
249C2#1309232611yescharacteristic
250C2#1309260112yes—
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC2×C23×#104C2
socleC22×C23#120
prime radicalC2×#41×C23C22
hypercenterC2×#104D23
hypocenterC23#2005
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
3. C2×#10625040C2semidirect
4. #13092427C2semidirect
5. C2×#10625006C2semidirect
6. #13092177C2semidirect
154. C23#2005semidirect

Maximal subgroups

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

subgroupindex
C2×#106251222
#130929882
C2×#106250402
#130924272
C2×#106250062
#130921772
C2×C23×#1042
#200523