Finite Group Databasebeta

← #27174300

Subgroups — #27174300

Order 12928.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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×#15692234C211yesmaximal, characteristic
2#20265081C212yesmaximal, complemented
3#20265074C212yesmaximal, complemented
4#20265071C212yesmaximal
5#20265065C212yesmaximal
6#20265064C212yesmaximal, complemented
7#20265062C212yesmaximal, complemented
8#20265037C211yesmaximal, characteristic
9#381×C101C211yesmaximal, characteristic
10C22×Dic202C2211yescharacteristic
11#15692234C418yescomplemented
12C2×C4⋊Dic101C2212yes—
13C2×C4⋊Dic101C2211yescharacteristic
14C2×#13108053C2212yes—
15C2×#13108053C2212yes—
16C2×#13108053C2212yes—
17C2×C22⋊Dic101C2211yescharacteristic
18C2×C22⋊Dic101C2211yescharacteristic
19C2×C22⋊Dic101C2212yes—
20C2×C4×Dic101C2212yes—
21C2×C4×Dic101C2212yes—
22#15692162C2212yes—
23#15692162C2212yes—
24#15692162C2212yes—
25#15692162C2212yes—
26#15692162C2212yes—
27C23×C4×C101C2211yescharacteristic
28C2×C22⋊C4×C101C2212yes—
29#95×C101C2212yes—
30#95×C101C2211yescharacteristic
31#95×C101C2211yescharacteristic
32C2×Dic202—42no—
33C2×Dic202C2×C414yes—
34C22×Dic101C2312yes—
35C22×Dic101C2312yes—
36C22×Dic101C2312yes—
37C22×Dic101C2312yes—
38C4⋊Dic101—42no—
39C4⋊Dic101C2×C414yes—
40#13108053—42no—
41#13108053—42no—
42#13108053C2×C418yes—
43C22⋊Dic101—41no—
44C22⋊Dic101—41no—
45C22⋊Dic101C2×C418yes—
46C4×Dic101—42no—
47C4×Dic101—42no—
48C24×C101C2311yescharacteristic
49C22×C4×C101—42no—
50C22×C4×C101C2×C414yes—
51C22×C4×C101C2312yes—
52C22×C4×C101C2312yes—
53C22×C4×C101C2311yescharacteristic
54C22×C4×C101C2311yescharacteristic
55C22⋊C4×C101—42no—
56C23×C101—22no—
57C23×C101—21no—
58C23×C101—22no—
59C23×C101—21no—
60C23×C101C22×C412yes—
61C23×C101C2411yescharacteristic
62C2×C4×C101—22no—
63C2×C4×C101—22no—
64C2×C4×C101—22no—
65C2×C4×C101—22no—
66C2×C4×C101—22no—
67C2×C4×C101—22no—
68C2×C4×C101—22no—
69C2×C4×C101—22no—
70C2×C4×C101—44no—
71C2×C4×C101C22×C412yes—
72C2×C4×C101C22×C412yes—
73C2×Dic101—22no—
74C2×Dic101—22no—
75C2×Dic101—22no—
76C2×Dic101—22no—
77C2×Dic101—22no—
78C2×Dic101—22no—
79C2×Dic101—22no—
80C2×Dic101—22no—
81C2×Dic101—22no—
82C2×Dic101—22no—
83C2×Dic101C22×C414yes—
84C2×Dic101C22×C414yes—
85Dic202—44no—
86C22×C101—22no—
87C22×C101—22no—
88C22×C101—22no—
89C22×C101—42no—
90C22×C101—42no—
91C22×C101C23×C411yescharacteristic
92C22×C101H(5,𝔽2)12yes—
93C22×C101H(5,𝔽2)11yescharacteristic
94C22×C1012−1+412yes—
95C22×C1012−1+411yescharacteristic
96C4×C101—22no—
97C4×C101—22no—
98C4×C101—42no—
99C4×C101—42no—
100Dic101—24no—
101Dic101—24no—
102Dic101—42no—
103Dic101—42no—
104C2×C101—42no—
105C2×C101#51811yescharacteristic
106C2×C101#51911yescharacteristic
107C2×C101#52011yescharacteristic
108C2×C101#56212yes—
109C2×C101#56312yes—
110#2378—1011nomaximal, Sylow
111C101#237811yescharacteristic, complemented, Sylow
112C2×C22⋊Q8—1011no—
113#391—1012no—
114#389—1012no—
115#388—1012no—
116#388—1012no—
117#387—1012no—
118#387—1012no—
119#381D10111yescharacteristic
120#380—1011no—
121C22×Q8—1011no—
122C23×C4C2×D10111yescharacteristic
123C22⋊Q8—1018no—
124C2×C4⋊C4—1011no—
125C2×C4⋊C4—1012no—
126C2×C4⋊C4—1012no—
127C2×C4⋊C4—1012no—
128C2×C4⋊C4—1012no—
129C2×C22⋊C4—1012no—
130C2×C22⋊C4—1011no—
131C2×C22⋊C4—1011no—
132C2×C22⋊C4C2×D10112yes—
133C2×C42—1012no—
134C2×C42—1012no—
135#95—1012no—
136#95—1012no—
137#95—1012no—
138#95—1012no—
139#95—1012no—
140#95C2×D10111yescharacteristic
141#95C2×D10112yes—
142#95C2×D10111yescharacteristic
143C24C22×D10111yescharacteristic
144C2×Q8—1014no—
145C2×Q8—4042no—
146C22×C4—42no—
147C22×C4—1012no—
148C22×C4—1012no—
149C22×C4—1012no—
150C22×C4—1012no—
151C22×C4C4×D10114yes—
152C22×C4C22×D10112yes—
153C22×C4C22×D10112yes—
154C22×C4C22×D10111yescharacteristic
155C22×C4C22×D10111yescharacteristic
156C4⋊C4—1018no—
157C4⋊C4—1014no—
158C4⋊C4—4042no—
159C4⋊C4—4042no—
160C4⋊C4—4042no—
161C22⋊C4—42no—
162C22⋊C4—1018no—
163C22⋊C4—4041no—
164C22⋊C4—4041no—
165C42—4042no—
166C42—4042no—
167C23—22no—
168C23—21no—
169C23—22no—
170C23—21no—
171C23C2×C4×D10112yes—
172C23C23×D10111yescharacteristic
173Q8—4044no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—1014no—
184C2×C4—1014no—
185C2×C4—2022no—
186C2×C4—2022no—
187C2×C4—2022no—
188C2×C4—2022no—
189C2×C4—2022no—
190C2×C4—2022no—
191C2×C4—2022no—
192C2×C4—2022no—
193C2×C4—2022no—
194C2×C4—2022no—
195C2×C4C2×C4×D10112yes—
196C2×C4C2×C4×D10112yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D10111yescharacteristic
203C22#1569230012yes—
204C22#1569230111yescharacteristic
205C22#1569230212yes—
206C22#1569230211yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—4042no—
212C4—4042no—
213C4—2024no—
214C4—2024no—
215C2—42no—
216C2#2026565011yescharacteristic
217C2#2026565411yescharacteristic
218C2#2026565711yescharacteristic
219C2#2026592412yes—
220C2#2026593012yes—
subgroupG/H
center, FrattiniC23C23×D101
commutatorC22×C101C23×C4
Fitting#381×C101C2
socle, cosocleC23×C101C24
prime radicalC24×C101C23
hypercenter#381D101
hypocenterC101#2378
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #20265081C2semidirect
3. #20265074C2semidirect
6. #20265064C2semidirect
7. #20265062C2semidirect
11. #15692234C4semidirect
111. C101#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#156922342
#202650812
#202650742
#202650712
#202650652
#202650642
#202650622
#202650372
#381×C1012
#2378101