Finite Group Databasebeta

← #27207074

Subgroups — #27207074

Order 13184.

398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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#20268506C211yesmaximal, characteristic, complemented
2#20268445C211yesmaximal, characteristic, complemented
3#20268142C211yesmaximal, characteristic, complemented
4#20268134C212yesmaximal, complemented
5#20268081C211yesmaximal, characteristic, complemented
6#20268019C212yesmaximal, complemented
7#20267996C211yesmaximal, characteristic, complemented
8#20267933C212yesmaximal, complemented
9C8×D412C211yesmaximal, characteristic, complemented
10#20267784C212yesmaximal, complemented
11C4×D8×C103C211yesmaximal, characteristic, complemented
12C2×#13110104C2212yes—
13C2×#13110093C2212yes—
14C2×C8×D103C2212yes—
15#15693021C2211yescharacteristic
16#15693021C2211yescharacteristic
17#15693007—22no—
18#15693005—22no—
19#15693001C2212yes—
20#15692995—21no—
21#15692995—21no—
22#15692992C2212yes—
23C4×D412C2211yescharacteristic
24#15692980—21no—
25#15692979C2212yes—
26C2×C4⋊Dic103—21no—
27#15692952C2212yes—
28C4⋊(C103⋊C8)C2211yescharacteristic
29#15692946C2212yes—
30#15692946C2212yes—
31#15692944C2212yes—
32#15692942C2212yes—
33(C2×D103)⋊C8C2212yes—
34C2×D8×C103C2211yescharacteristic
35C4×D4×C103C2211yescharacteristic
36C4×D4×C103C2211yescharacteristic
37#107×C103C2211yescharacteristic
38#102×C103C2211yescharacteristic
39#102×C103C2211yescharacteristic
40C4×C8×C103C2211yescharacteristic
41#13110104—24no—
42#13110104—42no—
43C2×Dic206—21no—
44C2×Dic206C2312yes—
45C2×D412D411yescharacteristic
46C2×C22⋊D103—22no—
47C2×C22⋊D103—22no—
48C22×Dic103—22no—
49C2×C4×D103C2312yes—
50#13110093—42no—
51C2×C103⋊C8C2312yes—
52C8×D103—42no—
53C4⋊Dic103—21no—
54C4⋊Dic103—21no—
55C4⋊Dic103—21no—
56C4⋊Dic103—22no—
57C4⋊Dic103D411yescharacteristic
58C4⋊Dic103C2312yes—
59C22⋊Dic103—22no—
60(C2×D103)⋊C4—22no—
61(C2×D103)⋊C4—22no—
62(C2×D103)⋊C4D412yes—
63C4×Dic103—22no—
64C2×D4×C103C2311yescharacteristic
65C2×D4×C103C2311yescharacteristic
66C22×C4×C103—21no—
67C22×C4×C103—21no—
68D8×C103—22no—
69C2×C8×C103C2311yescharacteristic
70C2×C8×C103C2311yescharacteristic
71C4⋊C4×C103C2311yescharacteristic
72C4⋊C4×C103C2311yescharacteristic
73C22⋊C4×C103—21no—
74C22⋊C4×C103—21no—
75C42×C103C2311yescharacteristic
76C23×C103—21no—
77C23×C103—21no—
78C22×D103C2×D412yes—
79D4×C103—21no—
80D4×C103—21no—
81D4×C103—21no—
82D4×C103#4112yes—
83C2×C4×C103—21no—
84C2×C4×C103—21no—
85C2×C4×C103—42no—
86C2×C4×C103—42no—
87C2×C4×C103C2×D411yescharacteristic
88C2×C4×C103C2×D411yescharacteristic
89C2×C4×C103C2411yescharacteristic
90C22⋊D103—44no—
91C22⋊D103—82no—
92C2×Dic103—22no—
93C2×Dic103—22no—
94C2×Dic103—44no—
95C2×Dic103C2×D412yes—
96D412—22no—
97C4×D103—22no—
98C4×D103—22no—
99Dic206—22no—
100Dic206—22no—
101Dic206—81no—
102C8×C103—21no—
103C8×C103—21no—
104C103⋊C8—22no—
105C22×C103—22no—
106C22×C103—41no—
107C22×C103—41no—
108C22×C103—41no—
109C22×C103—41no—
110C22×C103—41no—
111C22×C103C22×D411yescharacteristic
112C2×D103—22no—
113C2×D103—22no—
114C2×D103—22no—
115C4×C103—21no—
116C4×C103—41no—
117C4×C103—41no—
118C4×C103#13512yes—
119C4×C103C2×#4111yescharacteristic
120C4×C103H(5,𝔽2)11yescharacteristic
121Dic103—22no—
122Dic103—42no—
123Dic103—42no—
124C2×C103—42no—
125C2×C103—81no—
126C2×C103#54611yescharacteristic
127C2×C103C2×#13511yescharacteristic
128C2×C103#57711yescharacteristic
129D103—42no—
130#3303—1031nomaximal, Sylow
131C103#330311yescharacteristic, complemented, Sylow
132#555—1031no—
133#547—1031no—
134#487—1031no—
135#485—1032no—
136#476—1031no—
137#465—1032no—
138#461—1031no—
139#449—1032no—
140C4×D8D10311yescharacteristic, complemented
141C8×D4—1031no—
142#416—1032no—
143C2×#41—1032no—
144C2×SD16—1032no—
145C2×D8C2×D10311yescharacteristic
146C22×C8—1032no—
147C4⋊Q8—1031no—
148C4⋊Q8—1031no—
149#124—2062no—
150#123—2062no—
151C22⋊Q8—1032no—
152#121—1032no—
153#121—2061no—
154#121—2061no—
155C4×D4—1031no—
156C4×D4C2×D10311yescharacteristic
157C4×D4C2×D10311yescharacteristic
158#117—1032no—
159#117—2061no—
160C2×C4⋊C4—2061no—
161#107C2×D10311yescharacteristic
162#106—1032no—
163C4⋊C8—1031no—
164#103—1032no—
165#103—1032no—
166#103—1032no—
167#102—1032no—
168#102C2×D10311yescharacteristic
169#102C2×D10311yescharacteristic
170C22⋊C8—1032no—
171C4×C8C2×D10311yescharacteristic
172#41—4122no—
173#41—2064no—
174C2×Q8—1032no—
175C2×Q8—2061no—
176C2×D4—1031no—
177C2×D4—2062no—
178C2×D4—2062no—
179C2×D4C22×D10311yescharacteristic
180C2×D4C22×D10311yescharacteristic
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—1032no—
184C22×C4—2062no—
185SD16—4122no—
186D8—22no—
187C2×C8—1032no—
188C2×C8—4122no—
189C2×C8C22×D10311yescharacteristic
190C2×C8C22×D10311yescharacteristic
191C4⋊C4—1031no—
192C4⋊C4—1032no—
193C4⋊C4—2062no—
194C4⋊C4—2061no—
195C4⋊C4—2061no—
196C4⋊C4—2061no—
197C4⋊C4C22×D10311yescharacteristic
198C4⋊C4C22×D10311yescharacteristic
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—1032no—
202C22⋊C4—2062no—
203C22⋊C4—2062no—
204C22⋊C4—2062no—
205C42—2062no—
206C42C22×D10311yescharacteristic
207C23—21no—
208C23—21no—
209C23—1032no—
210Q8—8241no—
211Q8—2062no—
212Q8—2062no—
213D4—21no—
214D4—21no—
215D4—21no—
216D4—8242no—
217D4—4124no—
218D4—2062no—
219D4#1311010512yes—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—1032no—
225C2×C4—4124no—
226C2×C4—2062no—
227C2×C4—2062no—
228C2×C4—2062no—
229C2×C4—2062no—
230C2×C4D4×D10311yescharacteristic
231C2×C4D4×D10311yescharacteristic
232C2×C4C23×D10311yescharacteristic
233C8—21no—
234C8—21no—
235C8—2062no—
236C22—22no—
237C22—41no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—2062no—
243C22—2062no—
244C22—2062no—
245C22C2×D4×D10311yescharacteristic
246C4—21no—
247C4—41no—
248C4—41no—
249C4—4122no—
250C4—4122no—
251C4—2062no—
252C4#1569304012yes—
253C4C2×#1311010511yescharacteristic
254C4#1569306711yescharacteristic
255C2—42no—
256C2—81no—
257C2—4122no—
258C2#2026843711yescharacteristic
259C2C2×#1569304011yescharacteristic
260C2#2026859811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC4×D8×C103C2
socleC22×C103C22×D4
hypercenterC4×D8D103
hypocenterC103#3303
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20268506C2semidirect
2. #20268445C2semidirect
3. #20268142C2semidirect
4. #20268134C2semidirect
5. #20268081C2semidirect
6. #20268019C2semidirect
7. #20267996C2semidirect
8. #20267933C2semidirect
9. C8×D412C2semidirect
10. #20267784C2semidirect
11. C4×D8×C103C2semidirect
131. C103#3303semidirect
140. C4×D8D103semidirect

Maximal subgroups

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

subgroupindex
#202685062
#202684452
#202681422
#202681342
#202680812
#202680192
#202679962
#202679332
C8×D4122
#202677842
C4×D8×C1032
#3303103