Finite Group Databasebeta

← #27171107

Subgroups — #27171107

Order 12928.

536 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 121 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#20265194C212yesmaximal, complemented
2#20265186C212yesmaximal, complemented
3#20265161C211yesmaximal, characteristic, complemented
4#20265151C211yesmaximal, characteristic, complemented
5C2×2−1+4×C101C211yesmaximal, characteristic
6C2×#13108058C2212yes—
7#15692214C2212yes—
8#15692182—24no—
9#15692179—24no—
10#15692174—21no—
11#15692172—21no—
12#15692170—22no—
132−1+4×C101—24no—
142−1+4×C101—24no—
15C2×#41×C101—21no—
16C2×#41×C101—22no—
17C2×#41×C101C412yescomplemented
18C2×#41×C101C2211yescharacteristic
19C2×#41×C101C2211yescharacteristic
20C22×Q8×C101—21no—
21C22×Q8×C101C412yescomplemented
22C22×Q8×C101C2211yescharacteristic
23#13108058—22no—
24#13108058—22no—
25C2×#11717579—22no—
26C4⋊Dic101—22no—
27C22⋊Dic101—22no—
28C4×Dic101—22no—
29#41×C101—216no—
30#41×C101—28no—
31#41×C101—24no—
32#41×C101—24no—
33#41×C101—22no—
34#41×C101—22no—
35#41×C101—22no—
36#41×C101D414yes—
37C2×Q8×C101—28no—
38C2×Q8×C101—24no—
39C2×Q8×C101—24no—
40C2×Q8×C101—22no—
41C2×Q8×C101—21no—
42C2×Q8×C101—22no—
43C2×Q8×C101C2×C411yescharacteristic
44C2×Q8×C101C2×C412yes—
45C2×Q8×C101D414yes—
46C2×Q8×C101D411yescharacteristic
47C2×D4×C101—22no—
48C2×D4×C101—21no—
49C2×D4×C101C2×C411yescharacteristic
50C2×D4×C101D412yes—
51C2×D4×C101D411yescharacteristic
52C22×C4×C101—22no—
53C22×C4×C101—21no—
54C22×C4×C101—22no—
55C22×C4×C101—21no—
56C22×C4×C101C2×C412yes—
57C22×C4×C101C2311yescharacteristic
58C23×C101—21no—
59C23×C101C22⋊C412yes—
60C23×C101C2×D411yescharacteristic
61Q8×C101—28no—
62Q8×C101—21no—
63Q8×C101—22no—
64Q8×C101—24no—
65Q8×C101—22no—
66Q8×C101C22⋊C412yes—
67Q8×C101C22⋊C414yes—
68D4×C101—28no—
69D4×C101—24no—
70D4×C101—24no—
71D4×C101—21no—
72D4×C101—22no—
73D4×C101C22⋊C412yes—
74C2×C4×C101—28no—
75C2×C4×C101—28no—
76C2×C4×C101—21no—
77C2×C4×C101—22no—
78C2×C4×C101—24no—
79C2×C4×C101—22no—
80C2×C4×C101—22no—
81C2×C4×C101—24no—
82C2×C4×C101C22⋊C412yes—
83C2×C4×C101C22×C411yescharacteristic
84C2×C4×C101C2×D412yes—
85C2×C4×C101C2×D412yes—
86C2×C4×C101C2×D411yescharacteristic
87C2×Dic101—42no—
88#11717579—42no—
89C22×C101—22no—
90C22×C101—22no—
91C22×C101—41no—
92C22×C101—42no—
93C22×C101—42no—
94C22×C101C2×C22⋊C411yescharacteristic
95C22×C101#12012yes—
96C4×C101—24no—
97C4×C101—22no—
98C4×C101—22no—
99C4×C101C2×C22⋊C411yescharacteristic
100C4×C101C2×C22⋊C411yescharacteristic
101C4×C101#12012yes—
102Dic101—82no—
103C2×C101—22no—
104C2×C101—21no—
105C2×C101—42no—
106C2×C101—42no—
107C2×C101#37911yescharacteristic
108#1796—1011nomaximal, Sylow
109C101#179611yescharacteristic, complemented, Sylow
110C2×2−1+4D10111yescharacteristic
111#421—1012no—
112#419—1012no—
113#413—1011no—
114#410—1011no—
1152−1+4—24no—
1162−1+4—24no—
117C2×#41—21no—
118C2×#41—22no—
119C2×#41Dic10112yescomplemented
120C2×#41C2×D10111yescharacteristic
121C2×#41C2×D10111yescharacteristic
122C22×Q8—21no—
123C22×Q8Dic10112yescomplemented
124C22×Q8C2×D10111yescharacteristic
125C2×M16—1012no—
126#117—1012no—
127#104—2024no—
128#103—2024no—
129#101—2021no—
130#100—2021no—
131#99—2022no—
132#41—216no—
133#41—28no—
134#41—24no—
135#41—24no—
136#41—22no—
137#41—22no—
138#41—22no—
139#41C22⋊D10114yes—
140C2×Q8—28no—
141C2×Q8—24no—
142C2×Q8—24no—
143C2×Q8—22no—
144C2×Q8—21no—
145C2×Q8—22no—
146C2×Q8C2×Dic10111yescharacteristic
147C2×Q8C2×Dic10112yes—
148C2×Q8C22⋊D10114yes—
149C2×Q8C22⋊D10111yescharacteristic
150C2×D4—22no—
151C2×D4—21no—
152C2×D4C2×Dic10111yescharacteristic
153C2×D4C22⋊D10112yes—
154C2×D4C22⋊D10111yescharacteristic
155C22×C4—22no—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—21no—
159C22×C4C2×Dic10112yes—
160C22×C4C22×D10111yescharacteristic
161M16—2022no—
162M16—2022no—
163C2×C8—2022no—
164C4⋊C4—2022no—
165C22⋊C4—2022no—
166C42—2022no—
167C23—21no—
168C23C22⋊Dic10112yes—
169C23C2×C22⋊D10111yescharacteristic
170Q8—28no—
171Q8—21no—
172Q8—22no—
173Q8—24no—
174Q8—22no—
175Q8C22⋊Dic10112yes—
176Q8C22⋊Dic10114yes—
177D4—28no—
178D4—24no—
179D4—24no—
180D4—21no—
181D4—22no—
182D4C22⋊Dic10112yes—
183C2×C4—28no—
184C2×C4—28no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—4042no—
192C2×C4C22⋊Dic10112yes—
193C2×C4C22×Dic10111yescharacteristic
194C2×C4C2×C22⋊D10112yes—
195C2×C4C2×C22⋊D10112yes—
196C2×C4C2×C22⋊D10111yescharacteristic
197C8—4042no—
198C22—22no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22C2×C22⋊Dic10111yescharacteristic
204C22#1569222412yes—
205C4—24no—
206C4—22no—
207C4—22no—
208C4—8082no—
209C4C2×C22⋊Dic10111yescharacteristic
210C4C2×C22⋊Dic10111yescharacteristic
211C4#1569222412yes—
212C2—22no—
213C2—21no—
214C2—42no—
215C2—42no—
216C2#2026503311yescharacteristic
subgroupG/H
centerC2#20265033
commutatorC2×C4×C101C22×C4
FrattiniC22×C4C22×D101
Fitting, prime radicalC2×2−1+4×C101C2
socleC2×C101#379
cosocleC22×C4×C101C23
hypercenterC2×2−1+4D101
hypocenterC101#1796
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20265194C2semidirect
2. #20265186C2semidirect
3. #20265161C2semidirect
4. #20265151C2semidirect
17. C2×#41×C101C4semidirect
21. C22×Q8×C101C4semidirect
109. C101#1796semidirect
119. C2×#41Dic101semidirect
123. C22×Q8Dic101semidirect

Maximal subgroups

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

subgroupindex
#202651942
#202651862
#202651612
#202651512
C2×2−1+4×C1012
#1796101