Finite Group Databasebeta

← #46783785

Subgroups — #46783785

Order 33664.

362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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×#22554503C211yesmaximal, characteristic
2#30682512C211yesmaximal, characteristic
3C2×#22554468C211yesmaximal, characteristic, complemented
4C2×#22554396C211yesmaximal, characteristic
5#30681948C211yesmaximal, characteristic, complemented
6#30681699C211yesmaximal, characteristic, complemented
7C2×#101×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×Dic526C2211yescharacteristic
10#22554503—22no—
11#22554503—22no—
12C2×Dic1052—21no—
13C2×#16862365—21no—
14#22554468—22no—
15#22554468—21no—
16#22554468—22no—
17#22554459—21no—
18#22554453—22no—
19#22554446—22no—
20#22554429C2211yescharacteristic
21C2×Dic263⋊C4—22no—
22C2×C4×Dic263C2211yescharacteristic
23#22554396—22no—
24#22554395—22no—
25C22×Q8×C263C2211yescharacteristic
26C2×M16×C263C2211yescharacteristic
27C2×M16×C263C2211yescharacteristic
28#101×C263—22no—
29#16862376—21no—
30#16862376—21no—
31#16862376—21no—
32#16862376—21no—
33C2×Dic526—21no—
34C2×Dic526—21no—
35C2×Dic526—21no—
36C2×Dic526—21no—
37C2×Dic526—21no—
38C2×Dic526D411yescharacteristic
39C2×Dic526D412yes—
40C2×D1052D411yescharacteristic
41C2×C22⋊D263—21no—
42C22×Dic263—21no—
43C22×Dic263—21no—
44C2×C4×D263—21no—
45Dic1052—24no—
46#16862365—24no—
47C4⋊Dic263D412yes—
48Dic263⋊C4—28no—
49Dic263⋊C4—24no—
50C22⋊Dic263—21no—
51(C2×D263)⋊C4—24no—
52C4×Dic263—21no—
53C4×Dic263—21no—
54C4×Dic263D412yes—
55C2×Q8×C263—21no—
56C2×Q8×C263—21no—
57C2×Q8×C263—21no—
58C2×Q8×C263—21no—
59C2×Q8×C263—21no—
60C2×Q8×C263—21no—
61C22×C4×C263D412yes—
62C22×C4×C263C2311yescharacteristic
63M16×C263—21no—
64M16×C263—21no—
65M16×C263—21no—
66M16×C263D412yes—
67C2×C8×C263—21no—
68C2×C8×C263—21no—
69C22×D263—21no—
70Dic526—22no—
71Dic526—21no—
72Dic526—22no—
73Dic526—21no—
74Dic526—41no—
75Dic526—41no—
76D1052—21no—
77D1052—21no—
78C22⋊D263—41no—
79C22⋊D263—41no—
80C2×Dic263—24no—
81C2×Dic263—22no—
82C2×Dic263—22no—
83C2×Dic263—21no—
84C2×Dic263—22no—
85C2×Dic263—41no—
86C2×Dic263—41no—
87C4×D263—41no—
88C4×D263—41no—
89C23×C263C2×D411yescharacteristic
90Q8×C263—41no—
91Q8×C263—41no—
92Q8×C263—41no—
93Q8×C263—41no—
94C2×C4×C263—22no—
95C2×C4×C263—22no—
96C2×C4×C263—22no—
97C2×C4×C263C2×D411yescharacteristic
98C2×C4×C263C2×D411yescharacteristic
99C2×C4×C263C2×D411yescharacteristic
100C2×C4×C263C2×D411yescharacteristic
101C2×C4×C263C2×D411yescharacteristic
102C2×C4×C263#4111yescharacteristic
103C8×C263—22no—
104C8×C263—41no—
105C22×C263—22no—
106C22×C263#12011yescharacteristic
107C22×C263#12011yescharacteristic
108C22×C263#12111yescharacteristic
109C2×D263—41no—
110C2×D263—42no—
111C4×C263—42no—
112C4×C263#12011yescharacteristic
113C4×C263#12111yescharacteristic
114C4×C263#12111yescharacteristic
115C4×C263#12711yescharacteristic
116Dic263—24no—
117Dic263—41no—
118Dic263—42no—
119Dic263—42no—
120C2×C263—21no—
121C2×C263—21no—
122C2×C263#39211yescharacteristic
123C2×C263#45612yes—
124D263—81no—
125C263#200511yescharacteristic, complemented, Sylow
126#2005—2631nomaximal, Sylow
127C2×#137—2631no—
128#536—2631no—
129C2×C4⋊Q8—2631no—
130C2×#104—2631no—
131#419—2631no—
132C2×#101D26311yescharacteristic, complemented
133#339—2631no—
134C2×#41—2631no—
135C22×Q8—2631no—
136C22×Q8C2×D26311yescharacteristic
137#137—5262no—
138#137—5262no—
139C2×Q16—5261no—
140C2×SD16—5261no—
141C2×M16C2×D26311yescharacteristic
142C2×M16C2×D26311yescharacteristic
143C4⋊Q8—5262no—
144C4⋊Q8—5262no—
145C4⋊Q8—5261no—
146#124—5261no—
147#123—5262no—
148C22⋊Q8—5262no—
149#117—2631no—
150C2×C4⋊C4—5262no—
151C2×C42—2631no—
152#104—5262no—
153#103—5262no—
154#101—22no—
155#41—5261no—
156#41—5261no—
157#41—5261no—
158#41—5261no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—2631no—
166C2×Q8—2632no—
167C2×Q8—5261no—
168C2×Q8—5261no—
169C2×Q8—5261no—
170C2×Q8—5261no—
171C2×Q8—5261no—
172C2×D4—2631no—
173C2×D4—5261no—
174C22×C4—5261no—
175C22×C4—5261no—
176C22×C4—5261no—
177C22×C4D105212yes—
178C22×C4C22×D26311yescharacteristic
179Q16—5264no—
180SD16—5264no—
181M16—21no—
182M16—21no—
183M16—21no—
184M16C22⋊D26312yes—
185C2×C8—21no—
186C2×C8—21no—
187C4⋊C4—2632no—
188C4⋊C4—5268no—
189C4⋊C4—5264no—
190C22⋊C4—5264no—
191C22⋊C4—5261no—
192C42—2632no—
193C42—5261no—
194C42—5261no—
195C23—5261no—
196C23C2×D105211yescharacteristic
197Q8—41no—
198Q8—41no—
199Q8—41no—
200Q8—41no—
201Q8—5262no—
202Q8—5261no—
203Q8—5262no—
204Q8—5261no—
205Q8—10521no—
206Q8—10521no—
207D4—5261no—
208D4—5261no—
209D4—10521no—
210D4—10521no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—5264no—
215C2×C4—5262no—
216C2×C4—5262no—
217C2×C4—5262no—
218C2×C4—5261no—
219C2×C4—10521no—
220C2×C4—10521no—
221C2×C4—10521no—
222C2×C4—10521no—
223C2×C4D4×D26311yescharacteristic
224C2×C4D4×D26311yescharacteristic
225C2×C4D4×D26311yescharacteristic
226C2×C4D4×D26311yescharacteristic
227C2×C4C2×C22⋊D26311yescharacteristic
228C2×C4#1686237611yescharacteristic
229C8—22no—
230C8—41no—
231C22—22no—
232C22—10522no—
233C22—10521no—
234C22#2255444011yescharacteristic
235C22#2255444011yescharacteristic
236C22#2255444411yescharacteristic
237C4—42no—
238C4—5264no—
239C4—10522no—
240C4—10521no—
241C4—10522no—
242C4#2255443811yescharacteristic
243C4#2255444311yescharacteristic
244C4#2255444311yescharacteristic
245C4#2255446611yescharacteristic
246C2—21no—
247C2—21no—
248C2—21041no—
249C2#3068184711yescharacteristic
250C2#3068212312yes—
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#101×C263C2
socleC22×C263#120
prime radicalC2×#16862376C22
hypercenterC2×#101D263
hypocenterC263#2005
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
3. C2×#22554468C2semidirect
5. #30681948C2semidirect
6. #30681699C2semidirect
7. C2×#101×C263C2semidirect
125. C263#2005semidirect
132. C2×#101D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225545032
#306825122
C2×#225544682
C2×#225543962
#306819482
#306816992
C2×#101×C2632
#2005263