Finite Group Databasebeta

← #27205792

Subgroups — #27205792

Order 13184.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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#20268392C212yesmaximal, complemented
2#20268191C211yesmaximal, characteristic, complemented
3#20268166C211yesmaximal, characteristic, complemented
4#20268154C212yesmaximal, complemented
5#20268045C211yesmaximal, characteristic, complemented
6#20268041C211yesmaximal, characteristic, complemented
7#20268026C212yesmaximal, complemented
8#20267904C211yesmaximal, characteristic, complemented
9C4×#13110090C212yesmaximal, complemented
10#20267748C211yesmaximal, characteristic, complemented
11#442×C103C211yesmaximal, characteristic, complemented
12C2×D824C2211yescharacteristic
13C2×#13110090C2212yes—
14C2×#13110088C2211yescharacteristic
15C2×C8×D103C2211yescharacteristic
16#15693017C2212yes—
17#15693012C2212yes—
18#15693004—22no—
19#15693003—22no—
20#15692996C2212yes—
21#15692995—22no—
22#15692994—22no—
23#15692992C2212yes—
24C4×D412C2212yes—
25#15692978C2211yescharacteristic
26#15692954C2212yes—
27#15692953C2211yescharacteristic
28#15692943C2212yes—
29#15692942C2212yes—
30#15692941C2212yes—
31#15692931C2211yescharacteristic
32C4×C103⋊C8C2211yescharacteristic
33C8×Dic103C2211yescharacteristic
34C2×D8×C103C2211yescharacteristic
35C4×D4×C103C2212yes—
36#106×C103C2211yescharacteristic
37#102×C103C2212yes—
38#97×C103C2211yescharacteristic
39C2×D412—22no—
40C2×D412C2312yes—
41C2×C22⋊D103—22no—
42C2×C22⋊D103—22no—
43C2×C22⋊D103—22no—
44C2×C4×D103—22no—
45C2×C4×D103C2311yescharacteristic
46D824—22no—
47#13110090—24no—
48#13110088—22no—
49C2×C103⋊C8C2311yescharacteristic
50C2×C103⋊C8C2311yescharacteristic
51C8×D103—22no—
52C4⋊Dic103—22no—
53C4⋊Dic103C2312yes—
54Dic103⋊C4—22no—
55Dic103⋊C4D412yes—
56C22⋊Dic103—22no—
57(C2×D103)⋊C4—22no—
58(C2×D103)⋊C4—22no—
59(C2×D103)⋊C4D412yes—
60C4×Dic103C2311yescharacteristic
61C2×D4×C103C2312yes—
62C22×C4×C103—22no—
63D8×C103—22no—
64C2×C8×C103C2311yescharacteristic
65C2×C8×C103C2311yescharacteristic
66C4⋊C4×C103C2312yes—
67C22⋊C4×C103—22no—
68C42×C103C2311yescharacteristic
69C23×C103—22no—
70C22×D103—22no—
71C22×D103C2×D411yescharacteristic
72D4×C103—22no—
73D4×C103—22no—
74C2×C4×C103—22no—
75C2×C4×C103—82no—
76C2×C4×C103C2×D412yes—
77C2×C4×C103C2411yescharacteristic
78C22⋊D103—82no—
79C22⋊D103—82no—
80C22⋊D103—82no—
81C2×Dic103—22no—
82C2×Dic103C2×D412yes—
83C2×Dic103C2×D411yescharacteristic
84D412—22no—
85D412—22no—
86D412—82no—
87C4×D103—21no—
88C4×D103—21no—
89C4×D103—82no—
90C8×C103—21no—
91C8×C103#4112yes—
92C103⋊C8—21no—
93C103⋊C8#4112yes—
94C22×C103—42no—
95C22×C103—42no—
96C22×C103—42no—
97C22×C103C22×D411yescharacteristic
98C2×D103—21no—
99C2×D103—22no—
100C2×D103—42no—
101C2×D103—42no—
102C2×D103—42no—
103C4×C103—22no—
104C4×C103—42no—
105C4×C103C2×#4111yescharacteristic
106C4×C103C2×#4111yescharacteristic
107Dic103—21no—
108Dic103—22no—
109Dic103—42no—
110C2×C103—82no—
111C2×C103#53211yescharacteristic
112C2×C103#57612yes—
113D103—41no—
114D103—82no—
115#3176—1031nomaximal, Sylow
116C103#317611yescharacteristic, complemented, Sylow
117#540—1032no—
118#499—1031no—
119#493—1031no—
120#490—1032no—
121#469—1031no—
122#469—1031no—
123#466—1032no—
124#442—1031no—
125#442D10311yescharacteristic, complemented
126C4×D8—1032no—
127#405—1031no—
128C2×D8—1032no—
129C2×D8—1031no—
130C2×D8C2×D10311yescharacteristic
131C2×M16—1031no—
132C22×C8—1031no—
133#127—1032no—
134#125—1032no—
135#123—2062no—
136#123—2062no—
137#121—1032no—
138#121—1032no—
139#121—2062no—
140#121—2062no—
141C4×D4—1032no—
142C4×D4C2×D10312yes—
143#117—1031no—
144#107—1032no—
145#106—1031no—
146#106C2×D10311yescharacteristic
147#102—1032no—
148#102—1032no—
149#102—1032no—
150#102C2×D10312yes—
151#97—1031no—
152#97C2×D10311yescharacteristic
153C4×C8—1031no—
154C4×C8—1031no—
155C2×D4—1032no—
156C2×D4—2062no—
157C2×D4—2062no—
158C2×D4—2062no—
159C2×D4—2062no—
160C2×D4C22×D10312yes—
161C22×C4—22no—
162C22×C4—1031no—
163C22×C4—2062no—
164D8—22no—
165D8—2064no—
166D8—2062no—
167M16—2062no—
168C2×C8—1031no—
169C2×C8—1031no—
170C2×C8—2062no—
171C2×C8C22×D10311yescharacteristic
172C2×C8C22×D10311yescharacteristic
173C4⋊C4—1032no—
174C4⋊C4—1032no—
175C4⋊C4—2062no—
176C4⋊C4—2062no—
177C4⋊C4C22×D10312yes—
178C22⋊C4—22no—
179C22⋊C4—1032no—
180C22⋊C4—2062no—
181C22⋊C4—2062no—
182C22⋊C4—2062no—
183C42—1031no—
184C42C22×D10311yescharacteristic
185C23—22no—
186C23—1031no—
187C23—2062no—
188D4—22no—
189D4—22no—
190D4—8242no—
191D4—8242no—
192D4—8242no—
193D4—8242no—
194D4—2062no—
195D4—2062no—
196C2×C4—22no—
197C2×C4—82no—
198C2×C4—8242no—
199C2×C4—1032no—
200C2×C4—1031no—
201C2×C4—2062no—
202C2×C4—2061no—
203C2×C4—2061no—
204C2×C4D4×D10312yes—
205C2×C4C23×D10311yescharacteristic
206C8—21no—
207C8—1032no—
208C8—2061no—
209C8#1311010512yes—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—4122no—
214C22—4122no—
215C22—4122no—
216C22—2061no—
217C22—2062no—
218C22C2×D4×D10311yescharacteristic
219C4—22no—
220C4—42no—
221C4—4122no—
222C4—2061no—
223C4—2062no—
224C4#41×D10311yescharacteristic
225C4C2×#1311010511yescharacteristic
226C2—82no—
227C2—8242no—
228C2—4121no—
229C2#2026833811yescharacteristic
230C2#2026859512yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#442×C103C2
socleC22×C103C22×D4
hypercenter#442D103
hypocenterC103#3176
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #20268392C2semidirect
2. #20268191C2semidirect
3. #20268166C2semidirect
4. #20268154C2semidirect
5. #20268045C2semidirect
6. #20268041C2semidirect
7. #20268026C2semidirect
8. #20267904C2semidirect
9. C4×#13110090C2semidirect
10. #20267748C2semidirect
11. #442×C103C2semidirect
116. C103#3176semidirect
125. #442D103semidirect

Maximal subgroups

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

subgroupindex
#202683922
#202681912
#202681662
#202681542
#202680452
#202680412
#202680262
#202679042
C4×#131100902
#202677482
#442×C1032
#3176103