Finite Group Databasebeta

← #27196340

Subgroups — #27196340

Order 13184.

316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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×#15693000C211yesmaximal, characteristic
2C2×#15692952C211yesmaximal, characteristic, complemented
3C2×#15692944C211yesmaximal, characteristic, complemented
4C2×#15692944C211yesmaximal, characteristic, complemented
5C2×C22⋊(C103⋊C8)C211yesmaximal, characteristic
6#20267553C211yesmaximal, characteristic, complemented
7#380×C103C211yesmaximal, characteristic
8C22×Dic206C2211yescharacteristic
9C22×C103⋊C8C2211yescharacteristic
10C22×C103⋊C8C2211yescharacteristic
11#15693000—22no—
12#15693000—22no—
13C2×C4⋊Dic103C2211yescharacteristic
14C2×Dic103⋊C4—21no—
15C2×C22⋊Dic103—21no—
16#15692952—22no—
17#15692944—22no—
18#15692944—22no—
19C22⋊(C103⋊C8)—22no—
20C23×C4×C103C2211yescharacteristic
21C2×C4⋊C4×C103C2211yescharacteristic
22C2×C4⋊C4×C103C2211yescharacteristic
23C2×C22⋊C4×C103—21no—
24#95×C103—21no—
25C2×Dic206—21no—
26C2×Dic206—21no—
27C2×Dic206—21no—
28C2×Dic206—21no—
29C2×Dic206—21no—
30C2×Dic206D412yes—
31C22×Dic103—21no—
32C22×Dic103—21no—
33C2×C103⋊C8—21no—
34C2×C103⋊C8—21no—
35C2×C103⋊C8—21no—
36C2×C103⋊C8—21no—
37C2×C103⋊C8—21no—
38C2×C103⋊C8D412yes—
39C4⋊Dic103—21no—
40C4⋊Dic103D412yes—
41Dic103⋊C4—24no—
42C22⋊Dic103—24no—
43C24×C103D411yescharacteristic
44C22×C4×C103—21no—
45C22×C4×C103—21no—
46C22×C4×C103—21no—
47C22×C4×C103—21no—
48C22×C4×C103—21no—
49C22×C4×C103—21no—
50C22×C4×C103—21no—
51C22×C4×C103—21no—
52C22×C4×C103D411yescharacteristic
53C22×C4×C103C2311yescharacteristic
54C4⋊C4×C103—21no—
55C4⋊C4×C103—21no—
56C4⋊C4×C103—21no—
57C4⋊C4×C103—21no—
58C22⋊C4×C103—42no—
59C23×C103—21no—
60C23×C103—21no—
61C23×C103—21no—
62C23×C103—21no—
63C23×C103—21no—
64C23×C103—21no—
65C23×C103SD1612yes—
66C23×C103C2×D411yescharacteristic
67C2×C4×C103—21no—
68C2×C4×C103—21no—
69C2×C4×C103—21no—
70C2×C4×C103—41no—
71C2×C4×C103—41no—
72C2×C4×C103—41no—
73C2×C4×C103—41no—
74C2×C4×C103—41no—
75C2×C4×C103—41no—
76C2×C4×C103—41no—
77C2×C4×C103—41no—
78C2×C4×C103—41no—
79C2×C4×C103—41no—
80C2×C4×C103C2×D411yescharacteristic
81C2×C4×C103C2×D411yescharacteristic
82C2×C4×C103C2×D411yescharacteristic
83C2×C4×C103#4111yescharacteristic
84C2×C4×C103#4111yescharacteristic
85C2×C4×C103#4111yescharacteristic
86C2×Dic103—22no—
87C2×Dic103—22no—
88C2×Dic103—41no—
89C2×Dic103—41no—
90C2×Dic103—41no—
91C2×Dic103—41no—
92Dic206—22no—
93Dic206—22no—
94Dic206—41no—
95Dic206—41no—
96C103⋊C8—22no—
97C103⋊C8—41no—
98C22×C103—22no—
99C22×C103—22no—
100C22×C103—22no—
101C22×C103—41no—
102C22×C103—41no—
103C22×C103—41no—
104C22×C103—41no—
105C22×C103#12011yescharacteristic
106C22×C103#12111yescharacteristic
107C22×C103#12311yescharacteristic
108C22×C103C2×SD1611yescharacteristic
109C22×C103#13511yescharacteristic
110C22×C103#13711yescharacteristic
111C22×C103#13711yescharacteristic
112C4×C103—41no—
113C4×C103—81no—
114C4×C103—81no—
115C4×C103#12111yescharacteristic
116C4×C103#12111yescharacteristic
117C4×C103#12311yescharacteristic
118C4×C103#12411yescharacteristic
119Dic103—42no—
120Dic103—42no—
121C2×C103—42no—
122C2×C103#39411yescharacteristic
123C2×C103#44811yescharacteristic
124C2×C103#45211yescharacteristic
125C2×C103#46511yescharacteristic
126C2×C103#47011yescharacteristic
127C2×C103#48311yescharacteristic
128C2×C103#48511yescharacteristic
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#380D10311yescharacteristic
137#340—1031no—
138C22×Q8—1031no—
139C23×C4C2×D10311yescharacteristic
140C22×C8—1031no—
141C22×C8—1031no—
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—21no—
149C2×C22⋊C4—2061no—
150#106—2062no—
151#103—2062no—
152#103—2062no—
153C22⋊C8—2062no—
154#95—21no—
155C24C22⋊D10311yescharacteristic
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—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—2061no—
171C22×C4—2061no—
172C22×C4C22⋊D10311yescharacteristic
173C22×C4C22×D10311yescharacteristic
174C2×C8—1032no—
175C2×C8—2061no—
176C2×C8—2061no—
177C2×C8—2061no—
178C2×C8—2061no—
179C2×C8—2061no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—1032no—
185C4⋊C4—2064no—
186C4⋊C4—2061no—
187C22⋊C4—42no—
188C22⋊C4—2064no—
189C23—21no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23#1311009312yes—
196C23C2×C22⋊D10311yescharacteristic
197Q8—4121no—
198Q8—4121no—
199Q8—2062no—
200Q8—2062no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—4121no—
215C2×C4—4121no—
216C2×C4—4121no—
217C2×C4—4121no—
218C2×C4—2062no—
219C2×C4—2062no—
220C2×C4D4×D10311yescharacteristic
221C2×C4D4×D10311yescharacteristic
222C2×C4D4×D10311yescharacteristic
223C2×C4#1311010411yescharacteristic
224C2×C4#1311010511yescharacteristic
225C2×C4#1311010511yescharacteristic
226C8—4121no—
227C8—2062no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22#1569298911yescharacteristic
236C22#1569299311yescharacteristic
237C22#1569300411yescharacteristic
238C22C2×#1311009311yescharacteristic
239C22#1569304111yescharacteristic
240C22#1569305111yescharacteristic
241C22#1569305211yescharacteristic
242C4—41no—
243C4—81no—
244C4—81no—
245C4—4122no—
246C4—4122no—
247C4#1569299411yescharacteristic
248C4#1569299411yescharacteristic
249C4#1569300311yescharacteristic
250C4#1569300711yescharacteristic
251C2—42no—
252C2#2026770611yescharacteristic
253C2#2026792911yescharacteristic
254C2#2026795111yescharacteristic
255C2#2026801811yescharacteristic
256C2#2026804711yescharacteristic
257C2#2026812111yescharacteristic
258C2#2026813211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#380×C103C2
socleC23×C103C2×D4
prime radicalC24×C103D4
hypercenter#380D103
hypocenterC103#2035
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#15692952C2semidirect
3. C2×#15692944C2semidirect
4. C2×#15692944C2semidirect
6. #20267553C2semidirect
130. C103#2035semidirect

Maximal subgroups

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

subgroupindex
C2×#156930002
C2×#156929522
C2×#156929442
C2×C22⋊(C103⋊C8)2
#202675532
#380×C1032
#2035103