Finite Group Databasebeta

← #27169634

Subgroups — #27169634

Order 12928.

334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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
1#20265688C211yesmaximal, characteristic
2#20265141C211yesmaximal, characteristic, complemented
3#20264913C212yesmaximal, complemented
4#20264910C212yesmaximal, complemented
5C2×#95×C101C211yesmaximal, characteristic, complemented
6C2×#13108074C411yescharacteristic, complemented
7C2×#13108058—21no—
8#15692238—21no—
9#15692234C411yescharacteristic, complemented
10#15692234C2211yescharacteristic
11#15692229C411yescharacteristic, complemented
12#15692229C2211yescharacteristic
13#15692224—21no—
14C4×C22⋊D101—21no—
15C4×C22⋊D101—21no—
16#15692214C411yescharacteristic, complemented
17C22⋊#11717579—21no—
18C22⋊#11717579C2212yes—
19C23×C4×C101—21no—
20C23×C4×C101C2211yescharacteristic
21#95×C101—21no—
22#95×C101C2212yes—
23#13108074—42no—
24C2×Dic202C2×C411yescharacteristic, complemented
25C2×D404C2×C411yescharacteristic, complemented
26C2×C22⋊D101—21no—
27C2×C22⋊D101—21no—
28C2×C22⋊D101—21no—
29C2×C4×D101—21no—
30#13108058—42no—
31C2×#11717579—22no—
32C4⋊Dic101C2×C411yescharacteristic, complemented
33C4⋊Dic101C2×C411yescharacteristic, complemented
34#13108053—21no—
35#13108053—21no—
36C22⋊Dic101—21no—
37C22⋊Dic101—21no—
38C22⋊Dic101—21no—
39#13108051—21no—
40#13108051—21no—
41C4×Dic101—21no—
42C24×C101D411yescharacteristic
43C22×C4×C101—24no—
44C22×C4×C101—22no—
45C22×C4×C101—42no—
46C22×C4×C101—42no—
47C22×C4×C101—42no—
48C22×C4×C101C2×C411yescharacteristic
49C22×C4×C101C2×C411yescharacteristic
50C22×C4×C101D411yescharacteristic
51C22×C4×C101D411yescharacteristic
52C22×C4×C101D411yescharacteristic
53C22×C4×C101C2311yescharacteristic
54C23×C101—22no—
55C23×C101—22no—
56C23×C101—21no—
57C23×C101—21no—
58C23×C101C22⋊C411yescharacteristic
59C23×C101C22⋊C411yescharacteristic
60C23×C101C2×D411yescharacteristic
61C22×D101—21no—
62C2×C4×C101—22no—
63C2×C4×C101—22no—
64C2×C4×C101—24no—
65C2×C4×C101—41no—
66C2×C4×C101—41no—
67C2×C4×C101—41no—
68C2×C4×C101—41no—
69C2×C4×C101—48no—
70C2×C4×C101—42no—
71C2×C4×C101—42no—
72C2×C4×C101C22⋊C411yescharacteristic
73C2×C4×C101C22⋊C411yescharacteristic
74C2×C4×C101C22×C411yescharacteristic
75C2×C4×C101C2×D411yescharacteristic
76C22⋊D101—42no—
77C22⋊D101—42no—
78C22⋊D101—41no—
79C22⋊D101—41no—
80C2×Dic101—21no—
81C2×Dic101—21no—
82C2×Dic101—21no—
83D404—41no—
84C4×D101—42no—
85Dic202—41no—
86#11717579—42no—
87C22×C101—24no—
88C22×C101—24no—
89C22×C101—21no—
90C22×C101—21no—
91C22×C101—21no—
92C22×C101—21no—
93C22×C101—21no—
94C22×C101—21no—
95C22×C101#9912yes—
96C22×C101#10412yes—
97C22×C101C2×C22⋊C411yescharacteristic
98C22×C101AGL(1,ℤ/8)11yescharacteristic
99C22×C101#13711yescharacteristic
100C2×D101—41no—
101C2×D101—41no—
102C2×D101—41no—
103C4×C101—21no—
104C4×C101—21no—
105C4×C101—21no—
106C4×C101—21no—
107C4×C101—44no—
108Dic101—41no—
109Dic101—41no—
110Dic101—41no—
111C2×C101—21no—
112C2×C101—22no—
113C2×C101—22no—
114C2×C101—21no—
115C2×C101C2×#9911yescharacteristic
116C2×C101#41711yescharacteristic
117C2×C101C2×#10411yescharacteristic
118D101—81no—
119#1504—1011nomaximal, Sylow
120C101#150411yescharacteristic, complemented, Sylow
121#525—1011no—
122#407—1011no—
123C2×#95D10111yescharacteristic, complemented
124#328—1012no—
125#327—1012no—
126C2×#41—1011no—
127C23×C4—21no—
128C23×C4C2×D10111yescharacteristic
129C2×M16—2021no—
130#123—2021no—
131C22⋊Q8—1011no—
132C22⋊Q8—1011no—
133#121—1011no—
134#121—1011no—
135#120—2021no—
136C4×D4—2021no—
137C4×D4—2021no—
138#117—1011no—
139C22⋊C8—1012no—
140C22⋊C8—2021no—
141#95—21no—
142#95C2×D10112yes—
143C24C22⋊D10111yescharacteristic
144#41—4042no—
145C2×Q8—1011no—
146C2×D4—1011no—
147C2×D4—2021no—
148C2×D4—2021no—
149C2×D4—2021no—
150C22×C4—24no—
151C22×C4—22no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—2021no—
156C22×C4C4×D10111yescharacteristic
157C22×C4C4×D10111yescharacteristic
158C22×C4D40411yescharacteristic
159C22×C4D40411yescharacteristic
160C22×C4C22⋊D10111yescharacteristic
161C22×C4C22×D10111yescharacteristic
162M16—4042no—
163C2×C8—2022no—
164C4⋊C4—1011no—
165C4⋊C4—1011no—
166C4⋊C4—2021no—
167C4⋊C4—2021no—
168C22⋊C4—2021no—
169C22⋊C4—2021no—
170C22⋊C4—2021no—
171C22⋊C4—2021no—
172C22⋊C4—2021no—
173C42—2021no—
174C23—22no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—2021no—
179C23#1310805111yescharacteristic
180C23#1310805111yescharacteristic
181C23C2×C22⋊D10111yescharacteristic
182Q8—4041no—
183D4—4041no—
184D4—4042no—
185D4—4042no—
186D4—4041no—
187D4—4041no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—48no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—4042no—
199C2×C4—2021no—
200C2×C4—2021no—
201C2×C4—2021no—
202C2×C4#1310805111yescharacteristic
203C2×C4#1310805111yescharacteristic
204C2×C4C2×C4×D10111yescharacteristic
205C2×C4C2×D40411yescharacteristic
206C8—4042no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—4041no—
216C22—4041no—
217C22—4041no—
218C22#1569216912yes—
219C22#1569218312yes—
220C22C2×#1310805111yescharacteristic
221C22#1569228111yescharacteristic
222C22#1569228611yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—44no—
228C4—4041no—
229C4—4041no—
230C4—4041no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2—21no—
235C2—8081no—
236C2C2×#1569216911yescharacteristic
237C2#2026517611yescharacteristic
238C2C2×#1569218311yescharacteristic
subgroupG/H
centerC22C2×#13108051
commutatorC2×C4×C101C22×C4
FrattiniC22×C4C22×D101
FittingC2×#95×C101C2
socleC22×C101C2×C22⋊C4
prime radical#20265688C2
cosocleC22×C4×C101C23
hypercenterC2×#95D101
hypocenterC101#1504
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. #20265141C2semidirect
3. #20264913C2semidirect
4. #20264910C2semidirect
5. C2×#95×C101C2semidirect
6. C2×#13108074C4semidirect
9. #15692234C4semidirect
11. #15692229C4semidirect
16. #15692214C4semidirect
24. C2×Dic202C2×C4semidirect
25. C2×D404C2×C4semidirect
32. C4⋊Dic101C2×C4semidirect
33. C4⋊Dic101C2×C4semidirect
120. C101#1504semidirect
123. C2×#95D101semidirect

Maximal subgroups

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

subgroupindex
#202656882
#202651412
#202649132
#202649102
C2×#95×C1012
#1504101