Finite Group Databasebeta

← #46783805

Subgroups — #46783805

Order 33664.

348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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#30682512C211yesmaximal, characteristic, complemented
3#30681954C211yesmaximal, characteristic, complemented
4#30681947C211yesmaximal, characteristic, complemented
5#30681912C211yesmaximal, characteristic, complemented
6#30681710C211yesmaximal, characteristic, complemented
7C2×#137×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554501—21no—
10#22554500—21no—
11#22554496—21no—
12#22554495—21no—
13#22554490—22no—
14C2×#16862360C2211yescharacteristic
15#22554468—21no—
16#22554459—21no—
17#22554453—22no—
18#22554446—22no—
19#22554429C2211yescharacteristic
20#22554429C2211yescharacteristic
21#22554396—22no—
22#22554394—22no—
23#22554385—22no—
24C2×#41×C263C2211yescharacteristic
25C22×Q8×C263C2211yescharacteristic
26#137×C263—22no—
27#137×C263—22no—
28C2×Q16×C263—21no—
29C2×SD16×C263—21no—
30C2×M16×C263C2211yescharacteristic
31#16862376—21no—
32#16862376—21no—
33#16862376—21no—
34#16862376—21no—
35C2×Dic526D411yescharacteristic
36C2×D1052D411yescharacteristic
37C2×C22⋊D263—21no—
38C2×C4×D263—21no—
39#16862366—22no—
40#16862364—22no—
41#16862363—22no—
42#16862361—22no—
43#16862360—21no—
44#16862360—21no—
45C2×C263⋊C8D412yes—
46C4⋊Dic263—21no—
47C4⋊Dic263—21no—
48Dic263⋊C4—24no—
49C22⋊Dic263—21no—
50C22⋊Dic263D412yes—
51(C2×D263)⋊C4—24no—
52C4×Dic263—21no—
53C4×Dic263—21no—
54#41×C263—21no—
55#41×C263—21no—
56#41×C263—21no—
57#41×C263—21no—
58C2×Q8×C263—21no—
59C2×Q8×C263—21no—
60C2×Q8×C263—21no—
61C2×Q8×C263—21no—
62C2×Q8×C263—21no—
63C2×Q8×C263D412yes—
64C2×Q8×C263D411yescharacteristic
65C2×D4×C263—21no—
66C2×D4×C263D411yescharacteristic
67C22×C4×C263—21no—
68C22×C4×C263—21no—
69C22×C4×C263C2311yescharacteristic
70Q16×C263—24no—
71SD16×C263—24no—
72M16×C263—21no—
73M16×C263D412yes—
74C2×C8×C263—21no—
75C22×D263—21no—
76Dic526—21no—
77Dic526—21no—
78D1052—21no—
79D1052—21no—
80C22⋊D263—41no—
81C22⋊D263—41no—
82C2×Dic263—22no—
83C2×Dic263—21no—
84C2×Dic263—41no—
85C4×D263—41no—
86C4×D263—41no—
87C263⋊C8—22no—
88C23×C263—21no—
89C23×C263C2×D411yescharacteristic
90Q8×C263—22no—
91Q8×C263—21no—
92Q8×C263—21no—
93Q8×C263—22no—
94Q8×C263—41no—
95Q8×C263—41no—
96D4×C263—21no—
97D4×C263—21no—
98D4×C263—41no—
99D4×C263—41no—
100C2×C4×C263—22no—
101C2×C4×C263—21no—
102C2×C4×C263—41no—
103C2×C4×C263—41no—
104C2×C4×C263—41no—
105C2×C4×C263—41no—
106C2×C4×C263C2×D411yescharacteristic
107C2×C4×C263C2×D411yescharacteristic
108C2×C4×C263C2×D411yescharacteristic
109C2×C4×C263C2×D411yescharacteristic
110C2×C4×C263C2×D411yescharacteristic
111C2×C4×C263#4111yescharacteristic
112C8×C263—22no—
113C22×C263—41no—
114C22×C263—41no—
115C22×C263—81no—
116C22×C263#12011yescharacteristic
117C22×C263#12111yescharacteristic
118C22×C263#12711yescharacteristic
119C2×D263—42no—
120C2×D263—41no—
121C4×C263—41no—
122C4×C263—42no—
123C4×C263#12011yescharacteristic
124C4×C263#12011yescharacteristic
125C4×C263#12111yescharacteristic
126C4×C263#12111yescharacteristic
127Dic263—42no—
128Dic263—41no—
129Dic263—81no—
130C2×C263—21no—
131C2×C263—21no—
132C2×C263—21no—
133C2×C263—81no—
134C2×C263#39211yescharacteristic
135D263—81no—
136C263#200911yescharacteristic, complemented, Sylow
137#2009—2631nomaximal, Sylow
138#575—2631no—
139C2×#137D26311yescharacteristic, complemented
140#536—2631no—
141#421—2631no—
142#419—2631no—
143#410—2631no—
144#344—2631no—
145C2×#41—2631no—
146C2×#41C2×D26311yescharacteristic
147C22×Q8C2×D26311yescharacteristic
148#137—22no—
149#137—22no—
150#137—5261no—
151#137—5261no—
152AGL(1,ℤ/8)—5261no—
153AGL(1,ℤ/8)—5261no—
154#135—5262no—
155C2×Q16—21no—
156C2×SD16—21no—
157C2×M16—2631no—
158C2×M16C2×D26311yescharacteristic
159C4⋊Q8—5261no—
160#124—5261no—
161#123—5262no—
162C22⋊Q8—5262no—
163#117—2631no—
164#117—2631no—
165#104—5262no—
166#103—5262no—
167#99—5262no—
168#41—21no—
169#41—21no—
170#41—21no—
171#41—21no—
172#41—5261no—
173#41—5261no—
174#41—5261no—
175#41—5261no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—2631no—
182C2×Q8C22⋊D26312yes—
183C2×Q8C22⋊D26311yescharacteristic
184C2×D4—21no—
185C2×D4—2631no—
186C2×D4—5261no—
187C2×D4C22⋊D26311yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—5261no—
191C22×C4C22×D26311yescharacteristic
192Q16—24no—
193Q16—5262no—
194SD16—24no—
195SD16—5262no—
196SD16—5262no—
197D8—5262no—
198M16—21no—
199M16—5261no—
200M16—5261no—
201M16C22⋊D26312yes—
202C2×C8—21no—
203C2×C8—2632no—
204C4⋊C4—5264no—
205C4⋊C4—5261no—
206C4⋊C4—5261no—
207C22⋊C4—2632no—
208C22⋊C4—5264no—
209C22⋊C4—5261no—
210C42—5261no—
211C42—5261no—
212C23—21no—
213C23—5261no—
214C23D4×D26311yescharacteristic
215Q8—21no—
216Q8—22no—
217Q8—21no—
218Q8—22no—
219Q8—41no—
220Q8—41no—
221Q8—5261no—
222Q8—5261no—
223D4—21no—
224D4—21no—
225D4—41no—
226D4—41no—
227D4—5261no—
228D4—5261no—
229D4—10521no—
230D4—10521no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—5262no—
238C2×C4—5261no—
239C2×C4—10521no—
240C2×C4—10521no—
241C2×C4—10521no—
242C2×C4D4×D26311yescharacteristic
243C2×C4D4×D26311yescharacteristic
244C2×C4C2×C22⋊D26311yescharacteristic
245C2×C4C2×C22⋊D26311yescharacteristic
246C2×C4C2×C22⋊D26311yescharacteristic
247C2×C4#1686237511yescharacteristic
248C8—22no—
249C8—5262no—
250C22—41no—
251C22—41no—
252C22—81no—
253C22—10522no—
254C22—10521no—
255C22#2255443811yescharacteristic
256C22#2255444211yescharacteristic
257C22#2255446611yescharacteristic
258C4—41no—
259C4—42no—
260C4—10522no—
261C4—10521no—
262C4—21041no—
263C4#2255443811yescharacteristic
264C4#2255443911yescharacteristic
265C4#2255444111yescharacteristic
266C4#2255444211yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—21041no—
272C2#3068184611yescharacteristic
subgroupG/H
centerC2#30681846
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#137×C263C2
socleC2×C263#392
prime radical#30682736C2
hypercenterC2×#137D263
hypocenterC263#2009
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. #30682512C2semidirect
3. #30681954C2semidirect
4. #30681947C2semidirect
5. #30681912C2semidirect
6. #30681710C2semidirect
7. C2×#137×C263C2semidirect
136. C263#2009semidirect
139. C2×#137D263semidirect

Maximal subgroups

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

subgroupindex
#306827362
#306825122
#306819542
#306819472
#306819122
#306817102
C2×#137×C2632
#2009263