Finite Group Databasebeta

← #27187003

Subgroups — #27187003

Order 12928.

292 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D101⋊(C4⋊C8)C211yesmaximal, characteristic
2C2×#15692318C212yesmaximal
3#20266121C211yesmaximal, characteristic
4#20266050C212yesmaximal
5C4×Q8×D101C211yesmaximal, characteristic
6C2×D101⋊C8C2212yes—
7C2×C4⋊#87938C2212yes—
8#15692322—21no—
9C4⋊#11717581—21no—
10#15692318—24no—
11(C2×#87938)⋊C4—21no—
12(C2×#87938)⋊C4—21no—
13C2×Q8×D101C2211yescharacteristic
14Q8×Dic101C411yescharacteristic, complemented
15C4×Dic202—21no—
16C4×Dic202C411yescharacteristic, complemented
17#15692220—21no—
18#15692220C411yescharacteristic, complemented
19C4⋊C4×D101—21no—
20C4⋊C4×D101C2211yescharacteristic
21C42×D101—21no—
22C42×D101C2211yescharacteristic
23C4×Q8×C101C411yescharacteristic, complemented
24C22×#87938—22no—
25D101⋊C8—22no—
26D101⋊C8—22no—
27C2×#11717581—22no—
28C4⋊#87938—22no—
29C4⋊#87938—22no—
30C2×Dic202—21no—
31C2×Dic202C2×C411yescharacteristic
32Q8×D101—21no—
33Q8×D101—21no—
34Q8×D101D412yes—
35Q8×D101Q812yes—
36C2×C4×D101—21no—
37C2×C4×D101—21no—
38C2×C4×D101D411yescharacteristic
39C2×C4×D101D411yescharacteristic
40C2×C4×D101C2311yescharacteristic
41C4⋊Dic101—21no—
42C4⋊Dic101C2×C411yescharacteristic
43#13108053—21no—
44#13108053—21no—
45#13108053—21no—
46C4×Dic101—21no—
47C4×Dic101—21no—
48C4×Dic101—21no—
49C4×Dic101C2×C411yescharacteristic
50C4×Dic101D411yescharacteristic
51C4×Dic101D411yescharacteristic
52C2×Q8×C101C2×C411yescharacteristic
53C4⋊C4×C101—21no—
54C4⋊C4×C101C2×C411yescharacteristic
55C42×C101—21no—
56C42×C101C2×C411yescharacteristic
57C22×D101C2×D411yescharacteristic
58C2×#87938—42no—
59C2×#87938—42no—
60C2×#87938—42no—
61Q8×C101—21no—
62Q8×C101C4⋊C412yes—
63C2×C4×C101—21no—
64C2×C4×C101—21no—
65C2×C4×C101C22⋊C411yescharacteristic
66C2×C4×C101C22⋊C411yescharacteristic
67C2×C4×C101C22×C411yescharacteristic
68C2×Dic101—21no—
69C2×Dic101—21no—
70C2×Dic101C22⋊C411yescharacteristic
71C2×Dic101C22⋊C411yescharacteristic
72C2×Dic101C2×D411yescharacteristic
73C4×D101—22no—
74C4×D101—22no—
75C4×D101—22no—
76C4×D101—22no—
77C4×D101—42no—
78C4×D101C2×D411yescharacteristic
79C4×D101C2×Q811yescharacteristic
80C4×D101#4111yescharacteristic
81C4×D101#4111yescharacteristic
82Dic202—21no—
83Dic202—22no—
84Dic202—22no—
85Dic202C4⋊C412yes—
86#11717581—42no—
87C22×C101C2×C22⋊C411yescharacteristic
88C2×D101#12111yescharacteristic
89C2×D101C22⋊Q811yescharacteristic
90C2×D101#13512yes—
91C2×D101#13712yes—
92#87938—82no—
93C4×C101—22no—
94C4×C101—21no—
95C4×C101—21no—
96C4×C101—41no—
97C4×C101C2×C4⋊C411yescharacteristic
98C4×C101#11711yescharacteristic
99Dic101—22no—
100Dic101—21no—
101Dic101—21no—
102Dic101—41no—
103Dic101#12111yescharacteristic
104Dic101C22⋊Q811yescharacteristic
105C2×C101#38011yescharacteristic
106C2×C101#41611yescharacteristic
107C2×C101#41911yescharacteristic
108D101#46412yes—
109D101#47912yes—
110#1805—1011nomaximal, Sylow
111C101#180511yescharacteristic, complemented, Sylow
112C2×C4×Q8—1011no—
113C2×C4⋊C8—1011no—
114C2×#103—1012no—
115#382—1011no—
116#340—1012no—
117C22×Q8—1011no—
118C22×C8—1012no—
119C4×Q8—1011no—
120C4×Q8—1011no—
121C4×Q8—1011no—
122C4×Q8—2021no—
123C4×Q8—2021no—
124C4×Q8#8793811yescharacteristic, complemented
125C2×C4⋊C4—1011no—
126C2×C4⋊C4—1012no—
127C2×C4⋊C4—2021no—
128C2×C42—1011no—
129C2×C42—2021no—
130C4⋊C8—2021no—
131C4⋊C8—2021no—
132#103—2024no—
133#95—2021no—
134#95—2021no—
135C2×Q8—1012no—
136C2×Q8—1012no—
137C2×Q8—1011no—
138C2×Q8—2021no—
139C2×Q8—2021no—
140C2×Q8—2021no—
141C2×Q8C2×#8793811yescharacteristic
142C22×C4—1011no—
143C22×C4—1011no—
144C22×C4—1011no—
145C22×C4—2021no—
146C22×C4—2021no—
147C22×C4—2022no—
148C2×C8—2022no—
149C2×C8—2022no—
150C2×C8—2022no—
151C4⋊C4—21no—
152C4⋊C4—1011no—
153C4⋊C4—2021no—
154C4⋊C4—2021no—
155C4⋊C4—2021no—
156C4⋊C4—2022no—
157C4⋊C4—2022no—
158C4⋊C4—2021no—
159C4⋊C4C2×#8793811yescharacteristic
160C42—21no—
161C42—1011no—
162C42—1011no—
163C42—1011no—
164C42—2021no—
165C42—2021no—
166C42—2021no—
167C42C2×#8793811yescharacteristic
168C23—1011no—
169Q8—21no—
170Q8—1012no—
171Q8—2022no—
172Q8—2022no—
173Q8—2021no—
174Q8C4⋊#8793812yes—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—1011no—
178C2×C4—1011no—
179C2×C4—1011no—
180C2×C4—1011no—
181C2×C4—1011no—
182C2×C4—1011no—
183C2×C4—1011no—
184C2×C4—4042no—
185C2×C4—4042no—
186C2×C4—4042no—
187C2×C4—4042no—
188C2×C4—2022no—
189C2×C4—2022no—
190C2×C4—2022no—
191C2×C4—2022no—
192C2×C4—2021no—
193C2×C4—2021no—
194C2×C4C22⋊#8793811yescharacteristic
195C2×C4C22⋊#8793811yescharacteristic
196C2×C4C22×#8793811yescharacteristic
197C8—4042no—
198C22—1011no—
199C22—1011no—
200C22—1012no—
201C22—1012no—
202C22C2×C22⋊#8793811yescharacteristic
203C4—22no—
204C4—21no—
205C4—21no—
206C4—41no—
207C4—8082no—
208C4—1011no—
209C4—1011no—
210C4—4041no—
211C4—2022no—
212C4—2021no—
213C4—2021no—
214C4C2×C4⋊#8793811yescharacteristic
215C4#1569233411yescharacteristic
216C2—1012no—
217C2—1012no—
218C2#2026611911yescharacteristic
219C2#2026616711yescharacteristic
220C2#2026617011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4×Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D101C2×D4
cosocleC2×C4×D101C23
hypercenterC4×Q8#87938
hypocenterC101#1805
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
14. Q8×Dic101C4semidirect
16. C4×Dic202C4semidirect
18. #15692220C4semidirect
23. C4×Q8×C101C4semidirect
111. C101#1805semidirect
124. C4×Q8#87938semidirect

Maximal subgroups

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

subgroupindex
D101⋊(C4⋊C8)2
C2×#156923182
#202661212
#202660502
C4×Q8×D1012
#1805101