Finite Group Databasebeta

← #27196343

Subgroups — #27196343

Order 13184.

316 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 85 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×#15692952C211yesmaximal, characteristic, complemented
3C2×#15692946C211yesmaximal, characteristic, complemented
4C2×#15692944C211yesmaximal, characteristic, complemented
5C2×(C2×D103)⋊C8C211yesmaximal, characteristic
6#20267648C211yesmaximal, characteristic
7#340×C103C211yesmaximal, characteristic, complemented
8C22×Dic206C2211yescharacteristic
9C22×C4×D103C2211yescharacteristic
10C22×C103⋊C8C2211yescharacteristic
11#15693001—22no—
12#15693001—22no—
13C2×C4⋊Dic103—21no—
14C2×C4⋊Dic103C2211yescharacteristic
15C2×(C2×D103)⋊C4—21no—
16C2×(C2×D103)⋊C4—21no—
17#15692952—22no—
18#15692946—22no—
19#15692944—22no—
20(C2×D103)⋊C8—22no—
21C103⋊#95—21no—
22C22×C8×C103C2211yescharacteristic
23C2×C4⋊C4×C103C2211yescharacteristic
24C2×C4⋊C4×C103C2211yescharacteristic
25C23×D103D411yescharacteristic
26C2×Dic206—21no—
27C2×Dic206—21no—
28C2×Dic206—21no—
29C2×Dic206—21no—
30C2×Dic206—21no—
31C2×Dic206D412yes—
32C22×Dic103—21no—
33C22×Dic103—21no—
34C22×Dic103D411yescharacteristic
35C2×C4×D103—21no—
36C2×C4×D103—21no—
37C2×C4×D103—21no—
38C2×C4×D103—21no—
39C2×C4×D103—21no—
40C2×C4×D103—21no—
41C2×C103⋊C8—21no—
42C2×C103⋊C8—21no—
43C2×C103⋊C8D412yes—
44C4⋊Dic103—24no—
45C4⋊Dic103—21no—
46C4⋊Dic103—21no—
47(C2×D103)⋊C4—24no—
48(C2×D103)⋊C4—42no—
49C22×C4×C103—21no—
50C22×C4×C103—21no—
51C22×C4×C103C2311yescharacteristic
52C2×C8×C103—21no—
53C2×C8×C103—21no—
54C2×C8×C103—21no—
55C4⋊C4×C103—21no—
56C4⋊C4×C103—21no—
57C4⋊C4×C103—21no—
58C4⋊C4×C103D412yes—
59C23×C103C2×D411yescharacteristic
60C22×D103—21no—
61C22×D103—21no—
62C22×D103—21no—
63C22×D103—21no—
64C22×D103—21no—
65C22×D103—21no—
66C22×D103SD1612yes—
67C2×C4×C103—22no—
68C2×C4×C103—41no—
69C2×C4×C103—41no—
70C2×C4×C103—41no—
71C2×C4×C103—41no—
72C2×C4×C103—41no—
73C2×C4×C103C2×D411yescharacteristic
74C2×C4×C103C2×D411yescharacteristic
75C2×C4×C103C2×D411yescharacteristic
76C2×C4×C103#4111yescharacteristic
77C2×C4×C103#4111yescharacteristic
78C2×C4×C103#4111yescharacteristic
79C2×Dic103—22no—
80C2×Dic103—21no—
81C2×Dic103—21no—
82C2×Dic103—21no—
83C2×Dic103—41no—
84C2×Dic103—41no—
85C2×Dic103—41no—
86C2×Dic103—41no—
87C2×Dic103—41no—
88C4×D103—41no—
89C4×D103—41no—
90C4×D103—41no—
91C4×D103—41no—
92Dic206—22no—
93Dic206—22no—
94Dic206—41no—
95Dic206—41no—
96C8×C103—41no—
97C103⋊C8—22no—
98C22×C103#12011yescharacteristic
99C22×C103#12111yescharacteristic
100C22×C103#12311yescharacteristic
101C22×C103C2×SD1611yescharacteristic
102C22×C103#13511yescharacteristic
103C22×C103#13711yescharacteristic
104C22×C103#13711yescharacteristic
105C2×D103—22no—
106C2×D103—22no—
107C2×D103—22no—
108C2×D103—41no—
109C2×D103—41no—
110C2×D103—41no—
111C2×D103—41no—
112C4×C103—42no—
113C4×C103—81no—
114C4×C103#12111yescharacteristic
115C4×C103#12111yescharacteristic
116C4×C103#12311yescharacteristic
117C4×C103#12411yescharacteristic
118Dic103—42no—
119Dic103—41no—
120Dic103—81no—
121C2×C103#39411yescharacteristic
122C2×C103#44811yescharacteristic
123C2×C103#45211yescharacteristic
124C2×C103#46511yescharacteristic
125C2×C103#47011yescharacteristic
126C2×C103#48311yescharacteristic
127C2×C103#48511yescharacteristic
128D103—42no—
129#2035—1031nomaximal, Sylow
130C103#203511yescharacteristic, complemented, Sylow
131C2×C22⋊Q8—1031no—
132C2×#106—1031no—
133C2×#103—1031no—
134C2×#103—1031no—
135C2×C22⋊C8—1031no—
136#380—1031no—
137#340D10311yescharacteristic, complemented
138C22×Q8—1031no—
139C23×C4—1031no—
140C22×C8—1031no—
141C22×C8C2×D10311yescharacteristic
142C22⋊Q8—2062no—
143C22⋊Q8—2062no—
144C2×C4⋊C4—1031no—
145C2×C4⋊C4—2061no—
146C2×C4⋊C4C2×D10311yescharacteristic
147C2×C4⋊C4C2×D10311yescharacteristic
148C2×C22⋊C4—2061no—
149C2×C22⋊C4—2061no—
150#106—2062no—
151#103—2062no—
152#103—2062no—
153C22⋊C8—2062no—
154#95—2061no—
155C24—1031no—
156C2×Q8—1032no—
157C2×Q8—2061no—
158C2×Q8—2061no—
159C2×Q8—2061no—
160C2×Q8—2061no—
161C2×Q8—2061no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—1031no—
165C22×C4—2061no—
166C22×C4—2061no—
167C22×C4—2061no—
168C22×C4—2061no—
169C22×C4—2061no—
170C22×C4—2061no—
171C22×C4—2061no—
172C22×C4—2061no—
173C22×C4C22×D10311yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—1032no—
178C2×C8—2061no—
179C2×C8—2061no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—2064no—
184C4⋊C4—2061no—
185C4⋊C4—2061no—
186C4⋊C4D41212yes—
187C22⋊C4—4122no—
188C22⋊C4—2064no—
189C23—1032no—
190C23—2061no—
191C23—2061no—
192C23—2061no—
193C23—2061no—
194C23—2061no—
195C23—2061no—
196C23D4×D10311yescharacteristic
197Q8—4121no—
198Q8—4121no—
199Q8—2062no—
200Q8—2062no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—4121no—
208C2×C4—4121no—
209C2×C4—4121no—
210C2×C4—4121no—
211C2×C4—4121no—
212C2×C4—4121no—
213C2×C4—4121no—
214C2×C4—4121no—
215C2×C4—4121no—
216C2×C4—2062no—
217C2×C4—2061no—
218C2×C4—2061no—
219C2×C4—2061no—
220C2×C4D4×D10311yescharacteristic
221C2×C4D4×D10311yescharacteristic
222C2×C4C2×D41211yescharacteristic
223C2×C4#1311010511yescharacteristic
224C2×C4#1311010511yescharacteristic
225C2×C4#1311010611yescharacteristic
226C8—41no—
227C8—2062no—
228C22—4121no—
229C22—4121no—
230C22—4121no—
231C22—4121no—
232C22—2062no—
233C22—2062no—
234C22—2062no—
235C22#1569299111yescharacteristic
236C22#1569299411yescharacteristic
237C22#1569300611yescharacteristic
238C22SD16×D10311yescharacteristic
239C22#1569304011yescharacteristic
240C22#1569305011yescharacteristic
241C22#1569305311yescharacteristic
242C4—42no—
243C4—81no—
244C4—8241no—
245C4—4121no—
246C4—4122no—
247C4#1569299411yescharacteristic
248C4#1569299611yescharacteristic
249C4#1569300611yescharacteristic
250C4#1569300911yescharacteristic
251C2—4122no—
252C2#2026770911yescharacteristic
253C2#2026793111yescharacteristic
254C2#2026795411yescharacteristic
255C2#2026801911yescharacteristic
256C2#2026804811yescharacteristic
257C2#2026812311yescharacteristic
258C2#2026813411yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#340×C103C2
socleC23×C103C2×D4
prime radicalC23×D103D4
hypercenter#340D103
hypocenterC103#2035
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#15692952C2semidirect
3. C2×#15692946C2semidirect
4. C2×#15692944C2semidirect
7. #340×C103C2semidirect
130. C103#2035semidirect
137. #340D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930012
C2×#156929522
C2×#156929462
C2×#156929442
C2×(C2×D103)⋊C82
#202676482
#340×C1032
#2035103