Finite Group Databasebeta

← #27198429

Subgroups — #27198429

Order 13184.

568 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 143 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×#15692986C211yesmaximal, characteristic, complemented
2C2×(C22⋊D103)⋊C4C211yesmaximal, characteristic
3#20267732C212yesmaximal, complemented
4#20267717C211yesmaximal, characteristic, complemented
5#20267706C212yesmaximal
6#20267704C211yesmaximal, characteristic, complemented
7#20267703C211yesmaximal, characteristic, complemented
8C22⋊C4×Dic103C212yesmaximal, complemented
9#20267638C212yesmaximal, complemented
10#20267636C211yesmaximal, characteristic, complemented
11#397×C103C211yesmaximal, characteristic, complemented
12C22×Dic206C2211yescharacteristic
13C22×C22⋊D103C2211yescharacteristic
14C23×Dic103C2211yescharacteristic
15C22×C4×D103C2211yescharacteristic
16#15692986—24no—
17(C22⋊D103)⋊C4—24no—
18C2×Dic103⋊C4C2212yes—
19C2×Dic103⋊C4C2211yescharacteristic
20C2×C22⋊Dic103C2212yes—
21C2×(C2×D103)⋊C4C2212yes—
22C2×(C2×D103)⋊C4C2212yes—
23C2×(C2×D103)⋊C4C2211yescharacteristic
24C2×C4×Dic103C2212yes—
25C2×C4×Dic103C2212yes—
26C2×C4×Dic103C2211yescharacteristic
27C103⋊#95C2211yescharacteristic
28C103⋊#95C2212yes—
29C103⋊#95C2212yes—
30C103⋊#95C2212yes—
31C103⋊#95C2212yes—
32C2×C4⋊C4×C103C2211yescharacteristic
33C2×C22⋊C4×C103C2212yes—
34C2×C22⋊C4×C103C2211yescharacteristic
35#95×C103C2211yescharacteristic
36#95×C103C2212yes—
37C23×D103C2311yescharacteristic
38C2×Dic206—22no—
39C2×Dic206—24no—
40C2×C22⋊D103—22no—
41C2×C22⋊D103—22no—
42C2×C22⋊D103—22no—
43C22×Dic103—22no—
44C22×Dic103—24no—
45C22×Dic103C2311yescharacteristic
46C22×Dic103C2312yes—
47C22×Dic103C2311yescharacteristic
48C22×Dic103C2312yes—
49C22×Dic103C2311yescharacteristic
50C2×C4×D103—22no—
51C2×C4×D103—24no—
52Dic103⋊C4—22no—
53Dic103⋊C4—24no—
54C22⋊Dic103—24no—
55(C2×D103)⋊C4—24no—
56(C2×D103)⋊C4—22no—
57(C2×D103)⋊C4—24no—
58C4×Dic103—24no—
59C4×Dic103—24no—
60C4×Dic103D414yes—
61C24×C103C2311yescharacteristic
62C22×C4×C103C2312yes—
63C22×C4×C103C2311yescharacteristic
64C22×C4×C103C2312yes—
65C22×C4×C103C2311yescharacteristic
66C4⋊C4×C103—22no—
67C22⋊C4×C103—24no—
68C22⋊C4×C103—22no—
69C23×C103—21no—
70C23×C103—22no—
71C23×C103—22no—
72C23×C103—21no—
73C23×C103#4112yes—
74C23×C103C2411yescharacteristic
75C22×D103—21no—
76C22×D103—22no—
77C22×D103—22no—
78C22×D103—21no—
79C22×D103#4112yes—
80C2×C4×C103—22no—
81C2×C4×C103—21no—
82C2×C4×C103—22no—
83C2×C4×C103—22no—
84C2×C4×C103—22no—
85C2×C4×C103—22no—
86C2×C4×C103—22no—
87C2×C4×C103—22no—
88C2×C4×C103—22no—
89C2×C4×C103C2×D412yes—
90C22⋊D103—28no—
91C2×Dic103—22no—
92C2×Dic103—21no—
93C2×Dic103—21no—
94C2×Dic103—22no—
95C2×Dic103—21no—
96C2×Dic103—22no—
97C2×Dic103—22no—
98C2×Dic103—22no—
99C2×Dic103—22no—
100C2×Dic103—44no—
101C2×Dic103C2×D412yes—
102C2×Dic103C2×D412yes—
103C2×Dic103#4114yes—
104C2×Dic103#4114yes—
105C4×D103—44no—
106Dic206—28no—
107C22×C103—22no—
108C22×C103—24no—
109C22×C103—41no—
110C22×C103—41no—
111C22×C103—42no—
112C22×C103C22×D411yescharacteristic
113C22×C103C2×#4111yescharacteristic
114C22×C103C2×#4112yes—
115C22×C103C2×#4112yes—
116C22×C103C2×#4111yescharacteristic
117C2×D103—22no—
118C2×D103—24no—
119C2×D103—41no—
120C2×D103—41no—
121C2×D103—42no—
122C4×C103—22no—
123C4×C103—42no—
124C4×C103—41no—
125C4×C103—42no—
126Dic103—24no—
127Dic103—22no—
128Dic103—41no—
129Dic103—42no—
130Dic103#12414yes—
131C2×C103—42no—
132C2×C103#52511yescharacteristic
133C2×C103#52511yescharacteristic
134C2×C103C2×#12411yescharacteristic
135C2×C103#52912yes—
136C2×C103#52912yes—
137D103—42no—
138#2398—1031nomaximal, Sylow
139C103#239811yescharacteristic, complemented, Sylow
140C2×C4×Q8—1031no—
141C2×C4×D4—1031no—
142#400—1032no—
143#397—1031no—
144#397D10311yescharacteristic, complemented
145#394—1032no—
146#393—1031no—
147#393—1031no—
148C4×C22⋊C4—1032no—
149C4×C22⋊C4—1032no—
150#376—1031no—
151C22×Q8—1031no—
152C22×D4—1031no—
153C23×C4—1031no—
154C23×C4—1031no—
155C4×Q8—2064no—
156C4×D4—2064no—
157C2×C4⋊C4—1031no—
158C2×C4⋊C4—1032no—
159C2×C4⋊C4C2×D10311yescharacteristic
160C2×C22⋊C4—1032no—
161C2×C22⋊C4—1031no—
162C2×C22⋊C4—1032no—
163C2×C22⋊C4—1032no—
164C2×C22⋊C4C2×D10311yescharacteristic
165C2×C22⋊C4C2×D10312yes—
166C2×C42—1031no—
167C2×C42—1032no—
168C2×C42—1032no—
169#95—1031no—
170#95—1032no—
171#95—1032no—
172#95—1032no—
173#95—1032no—
174#95C2×D10311yescharacteristic
175#95C2×D10312yes—
176C24—1031no—
177C24C22×D10311yescharacteristic
178C2×Q8—2064no—
179C2×Q8—2062no—
180C2×D4—2062no—
181C2×D4—2062no—
182C2×D4—2062no—
183C22×C4—1031no—
184C22×C4—1032no—
185C22×C4—1031no—
186C22×C4—1032no—
187C22×C4—1031no—
188C22×C4—2062no—
189C22×C4—2064no—
190C22×C4—2062no—
191C22×C4—2064no—
192C22×C4C22×D10312yes—
193C22×C4C22×D10311yescharacteristic
194C22×C4C22×D10312yes—
195C22×C4C22×D10311yescharacteristic
196C4⋊C4—22no—
197C4⋊C4—2062no—
198C4⋊C4—2064no—
199C22⋊C4—24no—
200C22⋊C4—22no—
201C22⋊C4—2064no—
202C22⋊C4—2064no—
203C22⋊C4—2064no—
204C22⋊C4—2062no—
205C42—1034no—
206C42—2064no—
207C42—2064no—
208C23—21no—
209C23—22no—
210C23—22no—
211C23—21no—
212C23—1032no—
213C23—2061no—
214C23—2062no—
215C23—2062no—
216C23—2061no—
217C23#1311010412yes—
218C23C23×D10311yescharacteristic
219Q8—2068no—
220D4—2068no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—1032no—
231C2×C4—1034no—
232C2×C4—1032no—
233C2×C4—1034no—
234C2×C4—4124no—
235C2×C4—4124no—
236C2×C4—2061no—
237C2×C4—2062no—
238C2×C4—2062no—
239C2×C4—2062no—
240C2×C4—2062no—
241C2×C4—2062no—
242C2×C4—2061no—
243C2×C4—2062no—
244C2×C4—2061no—
245C2×C4D4×D10312yes—
246C22—22no—
247C22—24no—
248C22—41no—
249C22—41no—
250C22—42no—
251C22—4121no—
252C22—4121no—
253C22—4122no—
254C22—2062no—
255C22—2064no—
256C22C2×D4×D10311yescharacteristic
257C22#41×D10312yes—
258C22#41×D10311yescharacteristic
259C22#41×D10312yes—
260C22C2×#1311010411yescharacteristic
261C4—22no—
262C4—42no—
263C4—41no—
264C4—42no—
265C4—1034no—
266C4—4121no—
267C4—4122no—
268C4—2064no—
269C4—2062no—
270C2—42no—
271C2—4122no—
272C2#2026829911yescharacteristic
273C2#2026830111yescharacteristic
274C2#124×D10311yescharacteristic
275C2#2026831812yes—
276C2#2026832412yes—
subgroupG/H
center, FrattiniC23C23×D103
commutator, socle, cosocleC23×C103C24
Fitting#397×C103C2
prime radicalC22×C22⋊D103C22
hypercenter#397D103
hypocenterC103#2398
LCSG ▷ C23×C103 ▷ C103
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#15692986C2semidirect
3. #20267732C2semidirect
4. #20267717C2semidirect
6. #20267704C2semidirect
7. #20267703C2semidirect
8. C22⋊C4×Dic103C2semidirect
9. #20267638C2semidirect
10. #20267636C2semidirect
11. #397×C103C2semidirect
139. C103#2398semidirect
144. #397D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929862
C2×(C22⋊D103)⋊C42
#202677322
#202677172
#202677062
#202677042
#202677032
C22⋊C4×Dic1032
#202676382
#202676362
#397×C1032
#2398103