Finite Group Databasebeta

← #27195238

Subgroups — #27195238

Order 13184.

300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 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×#15692979C211yesmaximal, characteristic
2C2×(C2×D103)⋊C8C211yesmaximal, characteristic
3#20267648C211yesmaximal, characteristic
4#20267554C211yesmaximal, characteristic, complemented
5#20267553C211yesmaximal, characteristic, complemented
6#20267553C211yesmaximal, characteristic, complemented
7#340×C103C211yesmaximal, characteristic, complemented
8C22×C4×D103C2211yescharacteristic
9C22×C103⋊C8C2211yescharacteristic
10#15692979—22no—
11#15692979C414yescomplemented
12C2×C4⋊Dic103C2211yescharacteristic
13C2×C4⋊Dic103C2211yescharacteristic
14C2×(C2×D103)⋊C4—21no—
15C2×(C2×D103)⋊C4—21no—
16C2×C4×Dic103—21no—
17(C2×D103)⋊C8—22no—
18C103⋊#95—21no—
19C22×C8×C103C2211yescharacteristic
20C2×C4⋊C4×C103C2211yescharacteristic
21C2×C4⋊C4×C103C2211yescharacteristic
22C23×D103D411yescharacteristic
23C22×Dic103—21no—
24C22×Dic103—21no—
25C22×Dic103D411yescharacteristic
26C2×C4×D103—21no—
27C2×C4×D103—21no—
28C2×C4×D103—21no—
29C2×C4×D103—21no—
30C2×C4×D103C2×C412yes—
31C2×C4×D103D412yes—
32C2×C103⋊C8—21no—
33C2×C103⋊C8—21no—
34C2×C103⋊C8—21no—
35C4⋊Dic103—21no—
36C4⋊Dic103—21no—
37C4⋊Dic103—21no—
38C4⋊Dic103C2×C412yes—
39(C2×D103)⋊C4—24no—
40(C2×D103)⋊C4—42no—
41C4×Dic103—24no—
42C22×C4×C103—21no—
43C22×C4×C103—21no—
44C22×C4×C103C2311yescharacteristic
45C2×C8×C103—21no—
46C2×C8×C103—21no—
47C2×C8×C103—21no—
48C4⋊C4×C103—21no—
49C4⋊C4×C103—21no—
50C4⋊C4×C103—21no—
51C4⋊C4×C103C2×C412yes—
52C23×C103C2×D411yescharacteristic
53C22×D103—21no—
54C22×D103—21no—
55C22×D103—21no—
56C22×D103—21no—
57C22×D103—21no—
58C22×D103—21no—
59C22×D103C22⋊C412yes—
60C2×C4×C103—22no—
61C2×C4×C103—41no—
62C2×C4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103C22×C411yescharacteristic
67C2×C4×C103C2×D411yescharacteristic
68C2×C4×C103#4111yescharacteristic
69C2×C4×C103#4111yescharacteristic
70C2×C4×C103#4111yescharacteristic
71C2×C4×C103#4111yescharacteristic
72C2×Dic103—21no—
73C2×Dic103—21no—
74C2×Dic103—22no—
75C2×Dic103—41no—
76C2×Dic103—41no—
77C2×Dic103—41no—
78C2×Dic103—41no—
79C2×Dic103—41no—
80C2×Dic103C22⋊C412yes—
81C4×D103—22no—
82C4×D103—22no—
83C4×D103—22no—
84C4×D103—22no—
85C8×C103—41no—
86C103⋊C8—41no—
87C22×C103C2×C22⋊C411yescharacteristic
88C22×C103#12311yescharacteristic
89C22×C103#12311yescharacteristic
90C22×C103#13511yescharacteristic
91C22×C103#13511yescharacteristic
92C22×C103AGL(1,ℤ/8)11yescharacteristic
93C22×C103#13711yescharacteristic
94C2×D103—22no—
95C2×D103—22no—
96C2×D103—22no—
97C2×D103—41no—
98C2×D103—41no—
99C2×D103—41no—
100C2×D103—41no—
101C4×C103—42no—
102C4×C103—81no—
103C4×C103#11711yescharacteristic
104C4×C103#11711yescharacteristic
105C4×C103#12311yescharacteristic
106C4×C103#12311yescharacteristic
107Dic103—22no—
108Dic103—42no—
109Dic103—81no—
110C2×C103#38111yescharacteristic
111C2×C103#41611yescharacteristic
112C2×C103#41711yescharacteristic
113C2×C103#48211yescharacteristic
114C2×C103#48211yescharacteristic
115C2×C103#48511yescharacteristic
116C2×C103#48511yescharacteristic
117D103—42no—
118#1825—1031nomaximal, Sylow
119C103#182511yescharacteristic, complemented, Sylow
120C2×#117—1031no—
121C2×C22⋊C8—1031no—
122#380—1031no—
123#340—1031no—
124#340—1031no—
125#340—1031no—
126#340D10311yescharacteristic, complemented
127C23×C4—1031no—
128C22×C8—1031no—
129C22×C8C2×D10311yescharacteristic
130#117—1034no—
131#117—2062no—
132C2×C4⋊C4—1031no—
133C2×C4⋊C4—1031no—
134C2×C4⋊C4C2×D10311yescharacteristic
135C2×C4⋊C4C2×D10311yescharacteristic
136C2×C22⋊C4—2061no—
137C2×C22⋊C4—2061no—
138C2×C42—2061no—
139C22⋊C8—2062no—
140#95—2061no—
141C24—1031no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—1031no—
145C22×C4—1032no—
146C22×C4—1032no—
147C22×C4—2061no—
148C22×C4—2061no—
149C22×C4—2061no—
150C22×C4—2061no—
151C22×C4—2061no—
152C22×C4—2061no—
153C22×C4C22×D10311yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—2061no—
158C2×C8—2061no—
159C2×C8—2061no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—1032no—
164C4⋊C4—2061no—
165C4⋊C4—2061no—
166C4⋊C4—2061no—
167C4⋊C4C4×D10312yes—
168C22⋊C4—4122no—
169C22⋊C4—2064no—
170C42—2064no—
171C23—1032no—
172C23—2061no—
173C23—2061no—
174C23—2061no—
175C23—2061no—
176C23—2061no—
177C23—2061no—
178C23D4×D10311yescharacteristic
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—1032no—
186C2×C4—4121no—
187C2×C4—4121no—
188C2×C4—4121no—
189C2×C4—4121no—
190C2×C4—4121no—
191C2×C4—2062no—
192C2×C4—2061no—
193C2×C4—2061no—
194C2×C4—2062no—
195C2×C4—2062no—
196C2×C4—2062no—
197C2×C4—2062no—
198C2×C4C2×C4×D10311yescharacteristic
199C2×C4D4×D10311yescharacteristic
200C2×C4#1311010411yescharacteristic
201C2×C4#1311010511yescharacteristic
202C2×C4#1311010511yescharacteristic
203C2×C4#1311010611yescharacteristic
204C8—41no—
205C8—4121no—
206C22—4121no—
207C22—4121no—
208C22—4121no—
209C22—4121no—
210C22—2062no—
211C22—2062no—
212C22—2062no—
213C22C22⋊C4×D10311yescharacteristic
214C22#1569300311yescharacteristic
215C22#1569300611yescharacteristic
216C22#1569304211yescharacteristic
217C22#1569304411yescharacteristic
218C22#1569304511yescharacteristic
219C22#1569305011yescharacteristic
220C4—42no—
221C4—81no—
222C4—8241no—
223C4—4122no—
224C4—2062no—
225C4#1569297811yescharacteristic
226C4#1569297911yescharacteristic
227C4#1569300311yescharacteristic
228C4#1569300611yescharacteristic
229C2—4122no—
230C2#2026765311yescharacteristic
231C2#2026778611yescharacteristic
232C2#2026778911yescharacteristic
233C2#2026811411yescharacteristic
234C2#2026811811yescharacteristic
235C2#2026813111yescharacteristic
236C2#2026813511yescharacteristic
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#1825
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
4. #20267554C2semidirect
5. #20267553C2semidirect
6. #20267553C2semidirect
7. #340×C103C2semidirect
11. #15692979C4semidirect
119. C103#1825semidirect
126. #340D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929792
C2×(C2×D103)⋊C82
#202676482
#202675542
#202675532
#340×C1032
#1825103