Finite Group Databasebeta

← #27195342

Subgroups — #27195342

Order 13184.

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

normal subgroups only

This group has 316 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
1C2×#15692979C211yesmaximal, characteristic
2C2×#15692954C211yesmaximal, characteristic, complemented
3C2×(C2×D103)⋊C8C211yesmaximal, characteristic
4#20267648C211yesmaximal, characteristic
5#20267554C211yesmaximal, characteristic, complemented
6#20267553C211yesmaximal, characteristic, complemented
7C2×#106×C103C211yesmaximal, characteristic, complemented
8C22×C4×D103C2211yescharacteristic
9C22×C103⋊C8C2211yescharacteristic
10#15692979—22no—
11#15692979—22no—
12C2×C4⋊Dic103C2211yescharacteristic
13C2×C4⋊Dic103C2211yescharacteristic
14C2×(C2×D103)⋊C4—21no—
15C2×(C2×D103)⋊C4—21no—
16C2×C4×Dic103—21no—
17#15692954—22no—
18(C2×D103)⋊C8C414yescomplemented
19C103⋊#95—21no—
20C22×C8×C103C2211yescharacteristic
21C2×C4⋊C4×C103C2211yescharacteristic
22C2×C4⋊C4×C103C2211yescharacteristic
23#106×C103—22no—
24C23×D103D411yescharacteristic
25C22×Dic103—21no—
26C22×Dic103—21no—
27C22×Dic103D411yescharacteristic
28C2×C4×D103—21no—
29C2×C4×D103—21no—
30C2×C4×D103—21no—
31C2×C4×D103—21no—
32C2×C4×D103C2×C412yes—
33C2×C4×D103Q812yes—
34C2×C103⋊C8—21no—
35C2×C103⋊C8—21no—
36C2×C103⋊C8C2×C412yes—
37C4⋊Dic103—21no—
38C4⋊Dic103—21no—
39C4⋊Dic103—21no—
40C4⋊Dic103D412yes—
41(C2×D103)⋊C4—24no—
42(C2×D103)⋊C4—42no—
43C4×Dic103—24no—
44C22×C4×C103—21no—
45C22×C4×C103—21no—
46C22×C4×C103C2311yescharacteristic
47C2×C8×C103—21no—
48C2×C8×C103—21no—
49C2×C8×C103C2×C412yes—
50C4⋊C4×C103—21no—
51C4⋊C4×C103—21no—
52C4⋊C4×C103—21no—
53C4⋊C4×C103D412yes—
54C23×C103C2×D411yescharacteristic
55C22×D103—21no—
56C22×D103—21no—
57C22×D103—21no—
58C22×D103—21no—
59C22×D103—21no—
60C22×D103—21no—
61C22×D103C4⋊C412yes—
62C2×C4×C103—22no—
63C2×C4×C103—41no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103—41no—
67C2×C4×C103—41no—
68C2×C4×C103C22×C411yescharacteristic
69C2×C4×C103C2×D411yescharacteristic
70C2×C4×C103C2×D411yescharacteristic
71C2×C4×C103C2×Q811yescharacteristic
72C2×C4×C103#4111yescharacteristic
73C2×C4×C103#4111yescharacteristic
74C2×Dic103—21no—
75C2×Dic103—21no—
76C2×Dic103—22no—
77C2×Dic103—41no—
78C2×Dic103—41no—
79C2×Dic103—41no—
80C2×Dic103—41no—
81C2×Dic103—41no—
82C2×Dic103C4⋊C412yes—
83C4×D103—22no—
84C4×D103—22no—
85C4×D103—22no—
86C4×D103—22no—
87C8×C103—22no—
88C103⋊C8—22no—
89C22×C103C2×C4⋊C411yescharacteristic
90C22×C103#12011yescharacteristic
91C22×C103#12311yescharacteristic
92C22×C103#13511yescharacteristic
93C22×C103#13511yescharacteristic
94C22×C103AGL(1,ℤ/8)11yescharacteristic
95C22×C103#13711yescharacteristic
96C2×D103—22no—
97C2×D103—22no—
98C2×D103—22no—
99C2×D103—41no—
100C2×D103—41no—
101C2×D103—41no—
102C2×D103—41no—
103C4×C103—42no—
104C4×C103—81no—
105C4×C103C4×D411yescharacteristic
106C4×C103C4×D411yescharacteristic
107C4×C103C22⋊Q811yescharacteristic
108C4×C103C22⋊Q811yescharacteristic
109Dic103—22no—
110Dic103—42no—
111Dic103—81no—
112C2×C103#38511yescharacteristic
113C2×C103#42711yescharacteristic
114C2×C103#42811yescharacteristic
115C2×C103#44911yescharacteristic
116C2×C103#45211yescharacteristic
117C2×C103#48211yescharacteristic
118C2×C103#48511yescharacteristic
119D103—42no—
120#1854—1031nomaximal, Sylow
121C103#185411yescharacteristic, complemented, Sylow
122C2×#117—1031no—
123C2×#107—1031no—
124C2×#106D10311yescharacteristic, complemented
125C2×C22⋊C8—1031no—
126#380—1031no—
127#340—1031no—
128#340—1031no—
129C23×C4—1031no—
130C22×C8—1031no—
131C22×C8C2×D10311yescharacteristic
132#117—2062no—
133#117—2062no—
134C2×C4⋊C4—1031no—
135C2×C4⋊C4—1031no—
136C2×C4⋊C4C2×D10311yescharacteristic
137C2×C4⋊C4C2×D10311yescharacteristic
138C2×C22⋊C4—2061no—
139C2×C22⋊C4—2061no—
140C2×C42—2061no—
141#107—2062no—
142#106—22no—
143C22⋊C8—1034no—
144#95—2061no—
145C24—1031no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—1031no—
149C22×C4—1032no—
150C22×C4—1032no—
151C22×C4—2061no—
152C22×C4—2061no—
153C22×C4—2061no—
154C22×C4—2061no—
155C22×C4—2061no—
156C22×C4—2061no—
157C22×C4C22×D10311yescharacteristic
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—1032no—
161C2×C8—2061no—
162C2×C8—2061no—
163C2×C8C4×D10312yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—1032no—
168C4⋊C4—2061no—
169C4⋊C4—2061no—
170C4⋊C4—2061no—
171C4⋊C4C22⋊D10312yes—
172C22⋊C4—4122no—
173C22⋊C4—2064no—
174C42—2064no—
175C23—1032no—
176C23—2061no—
177C23—2061no—
178C23—2061no—
179C23—2061no—
180C23—2061no—
181C23—2061no—
182C23D4×D10311yescharacteristic
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—1032no—
190C2×C4—4121no—
191C2×C4—4121no—
192C2×C4—4121no—
193C2×C4—4121no—
194C2×C4—4121no—
195C2×C4—2062no—
196C2×C4—2061no—
197C2×C4—2061no—
198C2×C4—2062no—
199C2×C4—2062no—
200C2×C4—2062no—
201C2×C4—2062no—
202C2×C4C2×C4×D10311yescharacteristic
203C2×C4D4×D10311yescharacteristic
204C2×C4C2×C22⋊D10311yescharacteristic
205C2×C4Q8×D10311yescharacteristic
206C2×C4#1311010511yescharacteristic
207C2×C4#1311010611yescharacteristic
208C8—22no—
209C8—2062no—
210C22—4121no—
211C22—4121no—
212C22—4121no—
213C22—4121no—
214C22—2062no—
215C22—2062no—
216C22—2062no—
217C22C4⋊C4×D10311yescharacteristic
218C22#1569298911yescharacteristic
219C22#1569300611yescharacteristic
220C22#1569304211yescharacteristic
221C22#1569304211yescharacteristic
222C22#1569304811yescharacteristic
223C22#1569305011yescharacteristic
224C4—42no—
225C4—81no—
226C4—8241no—
227C4—4122no—
228C4—2062no—
229C4C4×C22⋊D10311yescharacteristic
230C4#1569298311yescharacteristic
231C4#1569299711yescharacteristic
232C4#1569299911yescharacteristic
233C2—4122no—
234C2#2026766211yescharacteristic
235C2#2026782611yescharacteristic
236C2#2026783011yescharacteristic
237C2#2026793511yescharacteristic
238C2#2026795011yescharacteristic
239C2#2026811711yescharacteristic
240C2#2026813511yescharacteristic
subgroupG/H
centerC23D4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×#106×C103C2
socleC23×C103C2×D4
prime radicalC23×D103D4
cosocleC22×C4×C103C23
hypercenterC2×#106D103
hypocenterC103#1854
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#15692954C2semidirect
5. #20267554C2semidirect
6. #20267553C2semidirect
7. C2×#106×C103C2semidirect
18. (C2×D103)⋊C8C4semidirect
121. C103#1854semidirect
124. C2×#106D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929792
C2×#156929542
C2×(C2×D103)⋊C82
#202676482
#202675542
#202675532
C2×#106×C1032
#1854103