Finite Group Databasebeta

← #27195574

Subgroups — #27195574

Order 13184.

360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C22×#13110088C211yesmaximal, characteristic
2C2×#15692997C211yesmaximal, characteristic
3C2×#15692945C211yesmaximal, characteristic, complemented
4#20267648C211yesmaximal, characteristic
5#20267554C211yesmaximal, characteristic, complemented
6#20267553C211yesmaximal, characteristic, complemented
7C2×#103×C103C211yesmaximal, characteristic, complemented
8C22×C4×D103C2211yescharacteristic
9C2×#13110088—22no—
10C2×#13110088—22no—
11C2×#13110088—22no—
12C22×C103⋊C8C2211yescharacteristic
13#15692997—22no—
14#15692997C414yescomplemented
15C2×C4⋊Dic103C2211yescharacteristic
16C2×C4⋊Dic103C2211yescharacteristic
17C2×Dic103⋊C4—21no—
18C2×(C2×D103)⋊C4—21no—
19C2×(C2×D103)⋊C4—21no—
20#15692945—22no—
21C103⋊#95—21no—
22C22×Q8×C103C2211yescharacteristic
23C22×C8×C103C2211yescharacteristic
24C2×C4⋊C4×C103C2211yescharacteristic
25#103×C103—22no—
26C23×D103D411yescharacteristic
27C22×Dic103—21no—
28C22×Dic103—21no—
29C22×Dic103D411yescharacteristic
30C2×C4×D103—21no—
31C2×C4×D103—21no—
32C2×C4×D103—21no—
33C2×C4×D103—21no—
34C2×C4×D103C2×C412yes—
35C2×C4×D103D412yes—
36#13110088—28no—
37C2×C103⋊C8—21no—
38C2×C103⋊C8—21no—
39C2×C103⋊C8D412yes—
40C4⋊Dic103—21no—
41C4⋊Dic103—21no—
42C4⋊Dic103—21no—
43C4⋊Dic103C2×C412yes—
44Dic103⋊C4—24no—
45(C2×D103)⋊C4—24no—
46(C2×D103)⋊C4—42no—
47C2×Q8×C103—21no—
48C2×Q8×C103—21no—
49C2×Q8×C103—21no—
50C2×Q8×C103—21no—
51C2×Q8×C103—21no—
52C2×Q8×C103C2×C412yes—
53C22×C4×C103—21no—
54C22×C4×C103—21no—
55C22×C4×C103C2311yescharacteristic
56C2×C8×C103—21no—
57C2×C8×C103—21no—
58C2×C8×C103D412yes—
59C4⋊C4×C103—21no—
60C4⋊C4×C103—21no—
61C23×C103C2×D411yescharacteristic
62C22×D103—21no—
63C22×D103—21no—
64C22×D103—21no—
65C22×D103—21no—
66C22×D103—21no—
67C22×D103—21no—
68C22×D103C22⋊C412yes—
69Q8×C103—22no—
70Q8×C103—22no—
71Q8×C103—41no—
72Q8×C103—41no—
73C2×C4×C103—22no—
74C2×C4×C103—41no—
75C2×C4×C103—41no—
76C2×C4×C103—41no—
77C2×C4×C103—41no—
78C2×C4×C103—41no—
79C2×C4×C103C22×C411yescharacteristic
80C2×C4×C103C2×D411yescharacteristic
81C2×C4×C103C2×D411yescharacteristic
82C2×C4×C103C2×D411yescharacteristic
83C2×C4×C103#4111yescharacteristic
84C2×C4×C103#4111yescharacteristic
85C2×Dic103—21no—
86C2×Dic103—21no—
87C2×Dic103—22no—
88C2×Dic103—41no—
89C2×Dic103—41no—
90C2×Dic103—41no—
91C2×Dic103—41no—
92C2×Dic103—41no—
93C2×Dic103C22⋊C412yes—
94C4×D103—22no—
95C4×D103—22no—
96C4×D103—22no—
97C4×D103—22no—
98C8×C103—22no—
99C103⋊C8—22no—
100C22×C103C2×C22⋊C411yescharacteristic
101C22×C103#12111yescharacteristic
102C22×C103#12111yescharacteristic
103C22×C103AGL(1,ℤ/8)11yescharacteristic
104C22×C103#13711yescharacteristic
105C22×C103#13711yescharacteristic
106C22×C103#13711yescharacteristic
107C2×D103—22no—
108C2×D103—22no—
109C2×D103—22no—
110C2×D103—41no—
111C2×D103—41no—
112C2×D103—41no—
113C2×D103—41no—
114C4×C103—42no—
115C4×C103—81no—
116C4×C103C4×D411yescharacteristic
117C4×C103C4×D411yescharacteristic
118C4×C103#12011yescharacteristic
119C4×C103#12311yescharacteristic
120Dic103—22no—
121Dic103—42no—
122Dic103—81no—
123C2×C103#38611yescharacteristic
124C2×C103#41711yescharacteristic
125C2×C103#41911yescharacteristic
126C2×C103#46811yescharacteristic
127C2×C103#46811yescharacteristic
128C2×C103#47011yescharacteristic
129C2×C103#47011yescharacteristic
130D103—42no—
131#1894—1031nomaximal, Sylow
132C103#189411yescharacteristic, complemented, Sylow
133C22×M16—1031no—
134C2×C22⋊Q8—1031no—
135C2×#103—1031no—
136C2×#103D10311yescharacteristic, complemented
137#380—1031no—
138#340—1031no—
139#340—1031no—
140C22×Q8C2×D10311yescharacteristic
141C23×C4—1031no—
142C2×M16—2062no—
143C2×M16—2062no—
144C2×M16—2062no—
145C22×C8—1031no—
146C22×C8C2×D10311yescharacteristic
147C22⋊Q8—1034no—
148C22⋊Q8—2062no—
149C2×C4⋊C4—1031no—
150C2×C4⋊C4—1031no—
151C2×C4⋊C4—2061no—
152C2×C4⋊C4C2×D10311yescharacteristic
153C2×C22⋊C4—2061no—
154C2×C22⋊C4—2061no—
155#103—22no—
156#103—2062no—
157#95—2061no—
158C24—1031no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8C4×D10312yes—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—1031no—
168C22×C4—1032no—
169C22×C4—1032no—
170C22×C4—2061no—
171C22×C4—2061no—
172C22×C4—2061no—
173C22×C4—2061no—
174C22×C4—2061no—
175C22×C4—2061no—
176C22×C4C22×D10311yescharacteristic
177M16—2068no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—1032no—
181C2×C8—2061no—
182C2×C8—2061no—
183C2×C8C22⋊D10312yes—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—1032no—
187C4⋊C4—2064no—
188C4⋊C4—2061no—
189C4⋊C4—2061no—
190C4⋊C4—2061no—
191C22⋊C4—4122no—
192C22⋊C4—2064no—
193C23—1032no—
194C23—2061no—
195C23—2061no—
196C23—2061no—
197C23—2061no—
198C23—2061no—
199C23—2061no—
200C23D4×D10311yescharacteristic
201Q8—22no—
202Q8—22no—
203Q8—41no—
204Q8—41no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—1032no—
212C2×C4—4121no—
213C2×C4—4121no—
214C2×C4—4121no—
215C2×C4—4121no—
216C2×C4—4121no—
217C2×C4—2062no—
218C2×C4—2061no—
219C2×C4—2061no—
220C2×C4—2062no—
221C2×C4—2062no—
222C2×C4—2062no—
223C2×C4—2062no—
224C2×C4C2×C4×D10311yescharacteristic
225C2×C4D4×D10311yescharacteristic
226C2×C4D4×D10311yescharacteristic
227C2×C4C2×C22⋊D10311yescharacteristic
228C2×C4#1311010411yescharacteristic
229C2×C4#1311010511yescharacteristic
230C8—22no—
231C8—2062no—
232C22—4121no—
233C22—4121no—
234C22—4121no—
235C22—4121no—
236C22—2062no—
237C22—2062no—
238C22—2062no—
239C22C22⋊C4×D10311yescharacteristic
240C22#1569299211yescharacteristic
241C22#1569299411yescharacteristic
242C22#1569304811yescharacteristic
243C22#1569305011yescharacteristic
244C22#1569305311yescharacteristic
245C22#1569305311yescharacteristic
246C4—42no—
247C4—81no—
248C4—8241no—
249C4—4122no—
250C4—2062no—
251C4(C22⋊D103)⋊C411yescharacteristic
252C4C4×C22⋊D10311yescharacteristic
253C4#1569298911yescharacteristic
254C4#1569300311yescharacteristic
255C2—4122no—
256C2#2026766711yescharacteristic
257C2#2026779111yescharacteristic
258C2#2026779811yescharacteristic
259C2#2026803411yescharacteristic
260C2#2026804011yescharacteristic
261C2#2026804611yescharacteristic
262C2#2026804811yescharacteristic
subgroupG/H
centerC23D4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×#103×C103C2
socleC23×C103C2×D4
prime radicalC23×D103D4
cosocleC22×C4×C103C23
hypercenterC2×#103D103
hypocenterC103#1894
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#15692945C2semidirect
5. #20267554C2semidirect
6. #20267553C2semidirect
7. C2×#103×C103C2semidirect
14. #15692997C4semidirect
132. C103#1894semidirect
136. C2×#103D103semidirect

Maximal subgroups

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

subgroupindex
C22×#131100882
C2×#156929972
C2×#156929452
#202676482
#202675542
#202675532
C2×#103×C1032
#1894103