Finite Group Databasebeta

← #46784032

Subgroups — #46784032

Order 33664.

266 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 63 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#30682736C211yesmaximal, characteristic
2#30681961C211yesmaximal, characteristic, complemented
3C2×#22554397C211yesmaximal, characteristic, complemented
4C2×#22554396C211yesmaximal, characteristic, complemented
5#30681920C211yesmaximal, characteristic, complemented
6C263⋊#338C211yesmaximal, characteristic, complemented
7#413×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554501—21no—
10#22554500—21no—
11#22554496—21no—
12#22554495—21no—
13#22554490—22no—
14C2×#16862360C2211yescharacteristic
15C2×#16862360C2211yescharacteristic
16C2×C4×Dic263C2211yescharacteristic
17Dic263⋊C8—22no—
18#22554397—21no—
19#22554397—21no—
20#22554396—21no—
21#22554396—21no—
22#22554388—21no—
23#22554386—21no—
24C2×#41×C263C2211yescharacteristic
25C2×M16×C263C2211yescharacteristic
26C2×M16×C263C2211yescharacteristic
27#101×C263—21no—
28#100×C263—21no—
29#16862376—21no—
30#16862376—21no—
31#16862376—21no—
32#16862376—21no—
33C2×Dic526D411yescharacteristic
34C2×D1052D411yescharacteristic
35C2×C22⋊D263—21no—
36C22×Dic263—21no—
37C2×C4×D263—21no—
38#16862366—22no—
39#16862364—22no—
40#16862363—22no—
41#16862361—22no—
42#16862360—21no—
43#16862360—21no—
44#16862360—21no—
45#16862360—21no—
46C2×C263⋊C8—21no—
47C2×C263⋊C8D412yes—
48C4×Dic263—21no—
49C4×Dic263D411yescharacteristic
50C4×Dic263D411yescharacteristic
51#41×C263—21no—
52#41×C263—21no—
53#41×C263—21no—
54#41×C263—21no—
55C2×Q8×C263D411yescharacteristic
56C2×D4×C263—21no—
57C2×D4×C263D411yescharacteristic
58C22×C4×C263—21no—
59C22×C4×C263C2311yescharacteristic
60M16×C263—21no—
61M16×C263—21no—
62M16×C263—21no—
63M16×C263—21no—
64C2×C8×C263—21no—
65C2×C8×C263—21no—
66C22×D263—21no—
67Dic526—21no—
68Dic526—21no—
69D1052—21no—
70D1052—21no—
71C22⋊D263—41no—
72C22⋊D263—41no—
73C2×Dic263—21no—
74C2×Dic263—21no—
75C2×Dic263—21no—
76C2×Dic263—42no—
77C4×D263—41no—
78C4×D263—41no—
79C263⋊C8—22no—
80C263⋊C8—41no—
81C23×C263—21no—
82C23×C263#4111yescharacteristic
83Q8×C263—21no—
84Q8×C263—21no—
85D4×C263—21no—
86D4×C263—21no—
87D4×C263—41no—
88D4×C263—41no—
89C2×C4×C263—21no—
90C2×C4×C263—41no—
91C2×C4×C263—41no—
92C2×C4×C263C2×D411yescharacteristic
93C2×C4×C263C2×D411yescharacteristic
94C2×C4×C263C2×D411yescharacteristic
95C2×C4×C263C2×D411yescharacteristic
96C2×C4×C263#4111yescharacteristic
97C2×C4×C263#4111yescharacteristic
98C8×C263—41no—
99C8×C263—41no—
100C22×C263—41no—
101C22×C263—41no—
102C22×C263—81no—
103C22×C263#12111yescharacteristic
104C22×C263#12311yescharacteristic
105C22×C263#12311yescharacteristic
106C2×D263—41no—
107C2×D263—81no—
108C4×C263—41no—
109C4×C263#12011yescharacteristic
110C4×C263#12111yescharacteristic
111C4×C263#12111yescharacteristic
112C4×C263#12411yescharacteristic
113Dic263—22no—
114Dic263—41no—
115Dic263—41no—
116C2×C263—21no—
117C2×C263—21no—
118C2×C263—21no—
119C2×C263—81no—
120C2×C263#39411yescharacteristic
121D263—81no—
122C263#205011yescharacteristic, complemented, Sylow
123#2050—2631nomaximal, Sylow
124#575—2631no—
125#423—2631no—
126C2×#104—2631no—
127C2×#104—2631no—
128#413—2631no—
129#413D26311yescharacteristic, complemented
130#338—2631no—
131C2×#41—2631no—
132C2×#41C2×D26311yescharacteristic
133#137—5261no—
134#137—5261no—
135AGL(1,ℤ/8)—5261no—
136AGL(1,ℤ/8)—5261no—
137#135—5262no—
138C2×M16—2631no—
139C2×M16—2631no—
140C2×M16C2×D26311yescharacteristic
141C2×M16C2×D26311yescharacteristic
142C2×C42—2631no—
143C4⋊C8—5262no—
144#104—5261no—
145#104—5261no—
146#104—5261no—
147#104—5261no—
148#101—21no—
149#101—5261no—
150#100—21no—
151#100—5261no—
152#41—21no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—5261no—
157#41—5261no—
158#41—5261no—
159#41—5261no—
160C2×Q8—2631no—
161C2×Q8C22⋊D26311yescharacteristic
162C2×D4—21no—
163C2×D4—2631no—
164C2×D4—5261no—
165C2×D4C22⋊D26311yescharacteristic
166C22×C4—21no—
167C22×C4—5261no—
168C22×C4—5261no—
169C22×C4C22×D26311yescharacteristic
170Q16—5262no—
171SD16—5262no—
172SD16—5262no—
173D8—5262no—
174M16—21no—
175M16—21no—
176M16—21no—
177M16—21no—
178M16—5261no—
179M16—5261no—
180M16—5261no—
181M16—5261no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—2632no—
185C2×C8—5261no—
186C42—2631no—
187C42—2631no—
188C42—5261no—
189C23—21no—
190C23—5261no—
191C23#1686237611yescharacteristic
192Q8—21no—
193Q8—21no—
194Q8—5261no—
195Q8—5261no—
196D4—21no—
197D4—21no—
198D4—41no—
199D4—41no—
200D4—5261no—
201D4—5261no—
202D4—10521no—
203D4—10521no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—5261no—
208C2×C4—5261no—
209C2×C4—5261no—
210C2×C4—10522no—
211C2×C4—10521no—
212C2×C4—10521no—
213C2×C4D4×D26311yescharacteristic
214C2×C4D4×D26311yescharacteristic
215C2×C4D4×D26311yescharacteristic
216C2×C4C2×C22⋊D26311yescharacteristic
217C2×C4#1686237511yescharacteristic
218C2×C4#1686237611yescharacteristic
219C8—41no—
220C8—41no—
221C8—5262no—
222C8—10521no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—10521no—
227C22—21041no—
228C22#2255444311yescharacteristic
229C22#2255445211yescharacteristic
230C22#2255445311yescharacteristic
231C4—41no—
232C4—5262no—
233C4—10521no—
234C4—10521no—
235C4#2255443811yescharacteristic
236C4#2255444211yescharacteristic
237C4#2255444311yescharacteristic
238C4#2255445611yescharacteristic
239C2—21no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—21041no—
244C2#3068185311yescharacteristic
subgroupG/H
centerC4#22554456
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#413×C263C2
socleC2×C263#394
prime radical#30682736C2
hypercenter#413D263
hypocenterC263#2050
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #30681961C2semidirect
3. C2×#22554397C2semidirect
4. C2×#22554396C2semidirect
5. #30681920C2semidirect
6. C263⋊#338C2semidirect
7. #413×C263C2semidirect
122. C263#2050semidirect
129. #413D263semidirect

Maximal subgroups

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

subgroupindex
#306827362
#306819612
C2×#225543972
C2×#225543962
#306819202
C263⋊#3382
#413×C2632
#2050263