Finite Group Databasebeta

← #27183059

Subgroups — #27183059

Order 12928.

398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 115 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#20265893C211yesmaximal, characteristic, complemented
2#20265830C211yesmaximal, characteristic, complemented
3#20265517C212yesmaximal, complemented
4#20265464C211yesmaximal, characteristic, complemented
5#20265409C212yesmaximal, complemented
6#20265379C211yesmaximal, characteristic, complemented
7#20265325C212yesmaximal, complemented
8C4×D808C211yesmaximal, characteristic, complemented
9C8×D404C211yesmaximal, characteristic, complemented
10#20265172C212yesmaximal, complemented
11#487×C101C211yesmaximal, characteristic, complemented
12C2×#13108075C2212yes—
13C2×#13108061C2212yes—
14C2×D808C2211yescharacteristic
15C2×C8×D101C2212yes—
16#15692244—22no—
17#15692240—22no—
18#15692231C2212yes—
19#15692230—21no—
20#15692230—21no—
21#15692230C2212yes—
22C4×D404C2211yescharacteristic
23C4×D404C2211yescharacteristic
24C4×D404C2211yescharacteristic
25#15692213—21no—
26#15692213C2212yes—
27C4⋊C4×D101—21no—
28#15692189C2211yescharacteristic
29#15692186C2212yes—
30C4⋊#11717579C2211yescharacteristic
31#15692179C2212yes—
32#15692177C2211yescharacteristic
33#15692177C2211yescharacteristic
34#15692175C2212yes—
35#15692167C2212yes—
36C4⋊Q8×C101C2211yescharacteristic
37C4⋊Q8×C101C2211yescharacteristic
38#103×C101C2212yes—
39#103×C101C2212yes—
40C4×C8×C101C2211yescharacteristic
41#13108075—24no—
42#13108075—42no—
43C2×D404—22no—
44C2×D404—22no—
45C2×D404D411yescharacteristic
46C2×D404C2311yescharacteristic
47C2×D404C2311yescharacteristic
48C2×C4×D101—21no—
49C2×C4×D101—21no—
50C2×C4×D101—22no—
51C2×C4×D101C2312yes—
52#13108061—42no—
53D808—22no—
54C2×#11717579C2312yes—
55C8×D101—42no—
56C4⋊Dic101D411yescharacteristic
57C4⋊Dic101C2311yescharacteristic
58C4⋊Dic101C2311yescharacteristic
59#13108053—22no—
60#13108051—22no—
61#13108051—22no—
62#13108051—21no—
63#13108051—21no—
64#13108051—22no—
65#13108051D412yes—
66C4×Dic101—22no—
67C2×Q8×C101—21no—
68C2×Q8×C101C2312yes—
69C2×C8×C101C2311yescharacteristic
70C2×C8×C101C2311yescharacteristic
71C4⋊C4×C101—21no—
72C4⋊C4×C101—21no—
73C4⋊C4×C101—21no—
74C4⋊C4×C101C2312yes—
75C42×C101C2311yescharacteristic
76C22×D101—21no—
77C22×D101—21no—
78C22×D101C2×D412yes—
79Q8×C101—22no—
80Q8×C101—22no—
81Q8×C101—81no—
82C2×C4×C101—22no—
83C2×C4×C101—22no—
84C2×C4×C101C2×D411yescharacteristic
85C2×C4×C101C2×D411yescharacteristic
86C2×C4×C101C2411yescharacteristic
87C2×Dic101—21no—
88C2×Dic101—21no—
89C2×Dic101C2×D412yes—
90D404—22no—
91D404—21no—
92D404—21no—
93D404—21no—
94D404—44no—
95D404—82no—
96D404#4112yes—
97C4×D101—22no—
98C4×D101—22no—
99C4×D101—44no—
100C4×D101—42no—
101C4×D101—42no—
102C8×C101—21no—
103C8×C101—21no—
104#11717579—22no—
105C22×C101C22×D411yescharacteristic
106C2×D101—22no—
107C2×D101—22no—
108C2×D101—22no—
109C2×D101—22no—
110C2×D101—41no—
111C2×D101—41no—
112C2×D101—41no—
113C2×D101—41no—
114C2×D101—41no—
115C4×C101—21no—
116C4×C101—42no—
117C4×C101—42no—
118C4×C101#13512yes—
119C4×C101C2×#4111yescharacteristic
120C4×C101H(5,𝔽2)11yescharacteristic
121Dic101—22no—
122Dic101—41no—
123Dic101—41no—
124C2×C101#54611yescharacteristic
125C2×C101C2×#13511yescharacteristic
126C2×C101#57711yescharacteristic
127D101—42no—
128D101—42no—
129D101—81no—
130#3303—1011nomaximal, Sylow
131C101#330311yescharacteristic, complemented, Sylow
132#555—1011no—
133#547—1011no—
134#487D10111yescharacteristic, complemented
135#485—1012no—
136#476—1011no—
137#465—1012no—
138#461—1011no—
139#449—1012no—
140C4×D8—1011no—
141C8×D4—1011no—
142#416—1012no—
143C2×#41—1012no—
144C2×SD16—1012no—
145C2×D8—1011no—
146C22×C8—1012no—
147C4⋊Q8C2×D10111yescharacteristic
148C4⋊Q8C2×D10111yescharacteristic
149#124—2022no—
150#123—2022no—
151C22⋊Q8—1012no—
152#121—1012no—
153#121—2021no—
154#121—2021no—
155C4×D4—1011no—
156C4×D4—1011no—
157C4×D4—1011no—
158#117—1012no—
159#117—2021no—
160C2×C4⋊C4—2021no—
161#107—1011no—
162#106—1012no—
163C4⋊C8—1011no—
164#103—1012no—
165#103C2×D10112yes—
166#103C2×D10112yes—
167#102—1011no—
168#102—1011no—
169#102—1012no—
170C22⋊C8—1012no—
171C4×C8C2×D10111yescharacteristic
172#41—4042no—
173#41—2024no—
174C2×Q8—21no—
175C2×Q8C22×D10112yes—
176C2×D4—1011no—
177C2×D4—1011no—
178C2×D4—1011no—
179C2×D4—2022no—
180C2×D4—2022no—
181C22×C4—1012no—
182C22×C4—2022no—
183C22×C4—2021no—
184C22×C4—2021no—
185SD16—4042no—
186D8—2022no—
187C2×C8—1012no—
188C2×C8—4042no—
189C2×C8C22×D10111yescharacteristic
190C2×C8C22×D10111yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—1011no—
195C4⋊C4—1011no—
196C4⋊C4—1011no—
197C4⋊C4—2022no—
198C4⋊C4C22×D10112yes—
199C22⋊C4—1012no—
200C22⋊C4—2022no—
201C22⋊C4—2022no—
202C22⋊C4—2022no—
203C22⋊C4—2021no—
204C22⋊C4—2021no—
205C42—2022no—
206C42C22×D10111yescharacteristic
207C23—1012no—
208C23—2021no—
209C23—2021no—
210Q8—22no—
211Q8—22no—
212Q8—81no—
213D4—8082no—
214D4—1012no—
215D4—4044no—
216D4—2021no—
217D4—2021no—
218D4—2021no—
219D4—2022no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—1012no—
223C2×C4—4044no—
224C2×C4—4042no—
225C2×C4—4042no—
226C2×C4—2021no—
227C2×C4—2021no—
228C2×C4—2022no—
229C2×C4—2022no—
230C2×C4D4×D10111yescharacteristic
231C2×C4D4×D10111yescharacteristic
232C2×C4C23×D10111yescharacteristic
233C8—21no—
234C8—21no—
235C8—2022no—
236C22—4041no—
237C22—4041no—
238C22—4041no—
239C22—4041no—
240C22—4041no—
241C22—2022no—
242C22—2022no—
243C22—2022no—
244C22—2022no—
245C22C2×D4×D10111yescharacteristic
246C4—21no—
247C4—42no—
248C4—42no—
249C4—4041no—
250C4—4041no—
251C4—2022no—
252C4#1569227812yes—
253C4#41×D10111yescharacteristic
254C4#1569230111yescharacteristic
255C2—8081no—
256C2—4042no—
257C2—4042no—
258C2#2026582011yescharacteristic
259C2C2×#1569227811yescharacteristic
260C2#2026598311yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#487×C101C2
socleC22×C101C22×D4
hypercenter#487D101
hypocenterC101#3303
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #20265893C2semidirect
2. #20265830C2semidirect
3. #20265517C2semidirect
4. #20265464C2semidirect
5. #20265409C2semidirect
6. #20265379C2semidirect
7. #20265325C2semidirect
8. C4×D808C2semidirect
9. C8×D404C2semidirect
10. #20265172C2semidirect
11. #487×C101C2semidirect
131. C101#3303semidirect
134. #487D101semidirect

Maximal subgroups

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

subgroupindex
#202658932
#202658302
#202655172
#202654642
#202654092
#202653792
#202653252
C4×D8082
C8×D4042
#202651722
#487×C1012
#3303101