Finite Group Databasebeta

← #27182578

Subgroups — #27182578

Order 12928.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#20265789C211yesmaximal, characteristic, complemented
2#20265481C212yesmaximal, complemented
3#20265477C212yesmaximal, complemented
4#20265421C212yesmaximal, complemented
5#20265404C212yesmaximal, complemented
6#20265382C212yesmaximal, complemented
7#20265374C212yesmaximal, complemented
8#20265204C211yesmaximal, characteristic, complemented
9#540×C101C211yesmaximal, characteristic
10C2×#13108062C2212yes—
11C2×#13108062C2212yes—
12C2×#13108058C2211yescharacteristic
13C22×#11717579C2211yescharacteristic
14#15692255C2211yescharacteristic
15#15692248—22no—
16#15692247C2211yescharacteristic
17#15692245—22no—
18#15692234C2212yes—
19C4×Dic202C2212yes—
20#15692188C2212yes—
21#15692186C2212yes—
22C4⋊#11717579C2212yes—
23C4⋊#11717579C2212yes—
24#15692178C2212yes—
25#15692178C2212yes—
26#15692176C2212yes—
27#15692176C2212yes—
28#127×C101C2211yescharacteristic
29#125×C101C2211yescharacteristic
30#123×C101—22no—
31#121×C101—22no—
32#121×C101C2212yes—
33C4×D4×C101C2212yes—
34#117×C101C2211yescharacteristic
35C2×Dic202C2312yes—
36#13108062—42no—
37#13108062—42no—
38#13108058—41no—
39C2×#11717579—41no—
40C2×#11717579C2312yes—
41C2×#11717579C2312yes—
42C4⋊Dic101—22no—
43C4⋊Dic101C2312yes—
44#13108053—22no—
45#13108053—22no—
46#13108053—22no—
47C22⋊Dic101—22no—
48C4×Dic101—22no—
49C2×D4×C101—22no—
50C2×D4×C101—22no—
51C2×D4×C101C2312yes—
52C22×C4×C101—22no—
53C22×C4×C101C2311yescharacteristic
54C4⋊C4×C101—22no—
55C4⋊C4×C101D412yes—
56C4⋊C4×C101C2312yes—
57C22⋊C4×C101—22no—
58C22⋊C4×C101—22no—
59C22⋊C4×C101D412yes—
60C42×C101C2311yescharacteristic
61C42×C101C2311yescharacteristic
62C23×C101—22no—
63C23×C101C2×D411yescharacteristic
64D4×C101—22no—
65D4×C101—22no—
66D4×C101—82no—
67D4×C101—82no—
68C2×C4×C101—21no—
69C2×C4×C101—21no—
70C2×C4×C101—22no—
71C2×C4×C101—82no—
72C2×C4×C101C2×D412yes—
73C2×C4×C101C2×D412yes—
74C2×C4×C101C2×D411yescharacteristic
75C2×C4×C101C2411yescharacteristic
76C2×Dic101—22no—
77C2×Dic101—22no—
78Dic202—22no—
79Dic202—22no—
80#11717579—22no—
81#11717579—22no—
82C22×C101—21no—
83C22×C101—22no—
84C22×C101—42no—
85C22×C101—42no—
86C22×C101—42no—
87C22×C101C22×D411yescharacteristic
88C4×C101—21no—
89C4×C101—22no—
90C4×C101—22no—
91C4×C101—42no—
92C4×C101H(5,𝔽2)11yescharacteristic
93C4×C1012−1+411yescharacteristic
94Dic101—42no—
95Dic101—42no—
96C2×C101—41no—
97C2×C101—82no—
98C2×C101#53711yescharacteristic
99C2×C101#57712yes—
100#3260—1011nomaximal, Sylow
101C101#326011yescharacteristic, complemented, Sylow
102#541—1011no—
103#540D10111yescharacteristic
104#479—1012no—
105#478—1012no—
106#468—1012no—
107#465—1012no—
108#461—1012no—
109#460—1012no—
110#424—1011no—
111C2×SD16—1012no—
112C2×SD16—1012no—
113C2×M16—1011no—
114C22×C8—1011no—
115C4⋊Q8—1011no—
116#127C2×D10111yescharacteristic
117#126—2022no—
118#125—1011no—
119#125—2022no—
120#125C2×D10111yescharacteristic
121#123—22no—
122C22⋊Q8—1012no—
123#121—22no—
124#121C2×D10112yes—
125C4×Q8—1012no—
126C4×D4C2×D10112yes—
127#117C2×D10111yescharacteristic
128#107—1012no—
129#106—1012no—
130C4⋊C8—1012no—
131C4⋊C8—1012no—
132#103—1012no—
133#103—1012no—
134#102—1012no—
135#102—1012no—
136C2×Q8—1012no—
137C2×D4—22no—
138C2×D4—22no—
139C2×D4C22×D10112yes—
140C22×C4—22no—
141C22×C4C22×D10111yescharacteristic
142SD16—4042no—
143SD16—4042no—
144M16—4041no—
145C2×C8—1012no—
146C2×C8—1012no—
147C2×C8—4041no—
148C4⋊C4—22no—
149C4⋊C4—1012no—
150C4⋊C4—2022no—
151C4⋊C4—2022no—
152C4⋊C4—2022no—
153C4⋊C4—2022no—
154C4⋊C4C22⋊D10112yes—
155C4⋊C4C22×D10112yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—2022no—
159C22⋊C4C22⋊D10112yes—
160C42—2022no—
161C42C22×D10111yescharacteristic
162C42C22×D10111yescharacteristic
163C23—22no—
164C23C2×C22⋊D10111yescharacteristic
165Q8—2022no—
166Q8—2022no—
167D4—22no—
168D4—22no—
169D4—82no—
170D4—82no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—82no—
175C2×C4—2022no—
176C2×C4—2022no—
177C2×C4C2×C22⋊D10112yes—
178C2×C4C2×C22⋊D10112yes—
179C2×C4C2×C22⋊D10111yescharacteristic
180C2×C4C23×D10111yescharacteristic
181C8—2022no—
182C8—2022no—
183C22—22no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22C22×C22⋊D10111yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—42no—
193C4—4042no—
194C4—4042no—
195C4#1569230111yescharacteristic
196C4#1569230211yescharacteristic
197C2—41no—
198C2—82no—
199C2#2026575511yescharacteristic
200C2#2026598812yes—
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting, prime radical#540×C101C2
socleC22×C101C22×D4
hypercenter#540D101
hypocenterC101#3260
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20265789C2semidirect
2. #20265481C2semidirect
3. #20265477C2semidirect
4. #20265421C2semidirect
5. #20265404C2semidirect
6. #20265382C2semidirect
7. #20265374C2semidirect
8. #20265204C2semidirect
101. C101#3260semidirect

Maximal subgroups

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

subgroupindex
#202657892
#202654812
#202654772
#202654212
#202654042
#202653822
#202653742
#202652042
#540×C1012
#3260101