Finite Group Databasebeta

← #27195450

Subgroups — #27195450

Order 13184.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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×#15693001C211yesmaximal, characteristic
2C2×C4⋊C4×D103C211yesmaximal, characteristic
3C2×#15692946C211yesmaximal, characteristic, complemented
4C2×#15692944C211yesmaximal, characteristic, complemented
5C2×(C2×D103)⋊C8C211yesmaximal, characteristic
6#20267553C211yesmaximal, characteristic, complemented
7#340×C103C211yesmaximal, characteristic, complemented
8C22×Dic206C2211yescharacteristic
9C22×C4×D103—21no—
10C22×C4×D103C2211yescharacteristic
11C22×C103⋊C8C2211yescharacteristic
12#15693001—22no—
13#15693001C414yescomplemented
14C2×C4⋊Dic103—21no—
15C2×C4⋊Dic103C2211yescharacteristic
16C2×Dic103⋊C4—21no—
17C4⋊C4×D103—22no—
18C4⋊C4×D103—22no—
19C2×(C2×D103)⋊C4—21no—
20#15692946—22no—
21#15692944—22no—
22(C2×D103)⋊C8—22no—
23C22×C8×C103C2211yescharacteristic
24C2×C4⋊C4×C103C2211yescharacteristic
25C2×C4⋊C4×C103C2211yescharacteristic
26C23×D103D411yescharacteristic
27C2×Dic206—21no—
28C2×Dic206—21no—
29C2×Dic206—21no—
30C2×Dic206—21no—
31C2×Dic206—21no—
32C2×Dic206C2×C412yescomplemented
33C22×Dic103—21no—
34C22×Dic103—21no—
35C22×Dic103D411yescharacteristic
36C2×C4×D103—21no—
37C2×C4×D103—21no—
38C2×C4×D103—21no—
39C2×C4×D103—21no—
40C2×C4×D103—24no—
41C2×C4×D103—42no—
42C2×C4×D103—42no—
43C2×C4×D103C2×C412yes—
44C2×C4×D103D412yes—
45C2×C103⋊C8—21no—
46C2×C103⋊C8—21no—
47C2×C103⋊C8—21no—
48C4⋊Dic103—21no—
49C4⋊Dic103—24no—
50C4⋊Dic103D412yes—
51Dic103⋊C4—24no—
52(C2×D103)⋊C4—24no—
53C22×C4×C103—21no—
54C22×C4×C103—21no—
55C22×C4×C103C2311yescharacteristic
56C2×C8×C103—21no—
57C2×C8×C103—21no—
58C2×C8×C103—21no—
59C4⋊C4×C103—21no—
60C4⋊C4×C103—21no—
61C4⋊C4×C103C2×C412yescomplemented
62C4⋊C4×C103D412yes—
63C23×C103C2×D411yescharacteristic
64C22×D103—21no—
65C22×D103—21no—
66C22×D103—21no—
67C22×D103—21no—
68C22×D103C22⋊C412yes—
69C22×D103SD1612yes—
70C22×D103Q1612yes—
71C2×C4×C103—22no—
72C2×C4×C103—22no—
73C2×C4×C103—41no—
74C2×C4×C103—41no—
75C2×C4×C103—41no—
76C2×C4×C103—41no—
77C2×C4×C103C22×C411yescharacteristic
78C2×C4×C103C2×D411yescharacteristic
79C2×C4×C103C2×D411yescharacteristic
80C2×C4×C103C2×D411yescharacteristic
81C2×C4×C103#4111yescharacteristic
82C2×C4×C103#4111yescharacteristic
83C2×Dic103—21no—
84C2×Dic103—21no—
85C2×Dic103—22no—
86C2×Dic103—22no—
87C2×Dic103—41no—
88C2×Dic103—41no—
89C2×Dic103—41no—
90C2×Dic103—41no—
91C2×Dic103C22⋊C412yes—
92C4×D103—22no—
93C4×D103—22no—
94C4×D103—22no—
95C4×D103—22no—
96C4×D103—48no—
97Dic206—22no—
98Dic206—22no—
99Dic206—41no—
100Dic206—41no—
101C8×C103—41no—
102C103⋊C8—41no—
103C22×C103C2×C22⋊C411yescharacteristic
104C22×C103#12011yescharacteristic
105C22×C103#12311yescharacteristic
106C22×C103C2×SD1611yescharacteristic
107C22×C103C2×Q1611yescharacteristic
108C22×C103AGL(1,ℤ/8)11yescharacteristic
109C22×C103#13711yescharacteristic
110C2×D103—22no—
111C2×D103—22no—
112C2×D103—22no—
113C2×D103—22no—
114C2×D103—22no—
115C2×D103—22no—
116C2×D103#10314yescomplemented
117C4×C103—42no—
118C4×C103—42no—
119C4×C103C4×D411yescharacteristic
120C4×C103C4×D411yescharacteristic
121C4×C103#12111yescharacteristic
122C4×C103#12111yescharacteristic
123Dic103—22no—
124Dic103—42no—
125Dic103—42no—
126C2×C103#38611yescharacteristic
127C2×C103C2×#10311yescharacteristic
128C2×C103#41711yescharacteristic
129C2×C103#45011yescharacteristic
130C2×C103#45111yescharacteristic
131C2×C103#48311yescharacteristic
132C2×C103#48411yescharacteristic
133D103—24no—
134#1872—1031nomaximal, Sylow
135C103#187211yescharacteristic, complemented, Sylow
136C2×C22⋊Q8—1031no—
137C22×C4⋊C4—1031no—
138C2×#103—1031no—
139C2×#103—1031no—
140C2×C22⋊C8—1031no—
141#340—1031no—
142#340D10311yescharacteristic, complemented
143C22×Q8—1031no—
144C23×C4—1031no—
145C23×C4—2061no—
146C22×C8—1031no—
147C22×C8C2×D10311yescharacteristic
148C22⋊Q8—1034no—
149C22⋊Q8—2062no—
150C2×C4⋊C4—1031no—
151C2×C4⋊C4—2062no—
152C2×C4⋊C4—2061no—
153C2×C4⋊C4—2061no—
154C2×C4⋊C4—2062no—
155C2×C4⋊C4C2×D10311yescharacteristic
156C2×C4⋊C4C2×D10311yescharacteristic
157C2×C22⋊C4—2061no—
158#103—2062no—
159#103—2062no—
160C22⋊C8—2062no—
161C24—1031no—
162C2×Q8—1032no—
163C2×Q8—2061no—
164C2×Q8—2061no—
165C2×Q8—2061no—
166C2×Q8—2061no—
167C2×Q8—2061no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—1031no—
171C22×C4—1032no—
172C22×C4—1032no—
173C22×C4—4122no—
174C22×C4—4122no—
175C22×C4—2064no—
176C22×C4—2061no—
177C22×C4—2061no—
178C22×C4—2061no—
179C22×C4—2061no—
180C22×C4—2061no—
181C22×C4—2061no—
182C22×C4C22×D10311yescharacteristic
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—2061no—
187C2×C8—2061no—
188C2×C8—2061no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—1032no—
192C4⋊C4—2064no—
193C4⋊C4—2064no—
194C4⋊C4—2061no—
195C4⋊C4C4×D10312yescomplemented
196C4⋊C4D41212yes—
197C22⋊C4—2064no—
198C23—1032no—
199C23—1032no—
200C23—1032no—
201C23—2061no—
202C23—2061no—
203C23—2061no—
204C23—2061no—
205C23D4×D10311yescharacteristic
206Q8—4121no—
207Q8—4121no—
208Q8—2062no—
209Q8—2062no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—1032no—
217C2×C4—4128no—
218C2×C4—4121no—
219C2×C4—4121no—
220C2×C4—4121no—
221C2×C4—4121no—
222C2×C4—2062no—
223C2×C4—2062no—
224C2×C4—2061no—
225C2×C4—2061no—
226C2×C4—2062no—
227C2×C4—2062no—
228C2×C4—2062no—
229C2×C4—2062no—
230C2×C4C2×C4×D10311yescharacteristic
231C2×C4D4×D10311yescharacteristic
232C2×C4D4×D10311yescharacteristic
233C2×C4C2×D41211yescharacteristic
234C2×C4#1311010511yescharacteristic
235C2×C4#1311010611yescharacteristic
236C8—41no—
237C8—4121no—
238C22—1034no—
239C22—2062no—
240C22—2062no—
241C22—2062no—
242C22—2062no—
243C22—2062no—
244C22—2062no—
245C22C22⋊C4×D10311yescharacteristic
246C22#1569299111yescharacteristic
247C22#1569300611yescharacteristic
248C22SD16×D10311yescharacteristic
249C22Q16×D10311yescharacteristic
250C22#1569304511yescharacteristic
251C22#1569305011yescharacteristic
252C4—42no—
253C4—42no—
254C4—4122no—
255C4—4122no—
256C4—2062no—
257C4#1569298311yescharacteristic
258C4C4×D41211yescharacteristic
259C4#1569299411yescharacteristic
260C4#1569299611yescharacteristic
261C2—2064no—
262C2#2026766911yescharacteristic
263C2#103×D10311yescharacteristic
264C2#2026778911yescharacteristic
265C2#2026794311yescharacteristic
266C2#2026794811yescharacteristic
267C2#2026812311yescharacteristic
268C2#2026812811yescharacteristic
subgroupG/H
centerC23D4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#340×C103C2
socleC23×C103C2×D4
prime radicalC23×D103D4
cosocleC22×C4×C103C23
hypercenter#340D103
hypocenterC103#1872
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
3. C2×#15692946C2semidirect
4. C2×#15692944C2semidirect
6. #20267553C2semidirect
7. #340×C103C2semidirect
13. #15693001C4semidirect
32. C2×Dic206C2×C4semidirect
61. C4⋊C4×C103C2×C4semidirect
116. C2×D103#103semidirect
135. C103#1872semidirect
142. #340D103semidirect
195. C4⋊C4C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930012
C2×C4⋊C4×D1032
C2×#156929462
C2×#156929442
C2×(C2×D103)⋊C82
#202675532
#340×C1032
#1872103