Finite Group Databasebeta

← #46783790

Subgroups — #46783790

Order 33664.

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

normal subgroups only

This group has 406 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×#22554498C211yesmaximal, characteristic, complemented
2C2×#22554495C211yesmaximal, characteristic, complemented
3#30682516C211yesmaximal, characteristic, complemented
4C2×#22554398C211yesmaximal, characteristic, complemented
5#30681840C211yesmaximal, characteristic, complemented
6#30681706C211yesmaximal, characteristic, complemented
7C2×#104×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×D1052C2211yescharacteristic
10#22554498—22no—
11#22554498—22no—
12#22554495—22no—
13#22554495—22no—
14C2×#16862365—21no—
15C2×#16862363—21no—
16C2×D2104—21no—
17C2×#16862361—21no—
18C2×#16862360C2211yescharacteristic
19#22554449—21no—
20#22554446—21no—
21#22554444—21no—
22#22554442—22no—
23#22554441—21no—
24C2×C4⋊Dic263C2211yescharacteristic
25C2×(C2×D263)⋊C4—22no—
26#22554398—22no—
27C2×#41×C263C2211yescharacteristic
28C2×M16×C263C2211yescharacteristic
29C2×C42×C263C2211yescharacteristic
30#104×C263—22no—
31C23×D263—21no—
32#16862376—21no—
33#16862376—21no—
34#16862376—21no—
35#16862376—21no—
36C2×Dic526D411yescharacteristic
37C2×D1052—21no—
38C2×D1052—21no—
39C2×D1052—21no—
40C2×D1052—21no—
41C2×D1052—21no—
42C2×D1052D411yescharacteristic
43C2×D1052D412yescomplemented
44C2×C22⋊D263—22no—
45C2×C22⋊D263—21no—
46C22×Dic263D412yes—
47C2×C4×D263—21no—
48#16862365—24no—
49#16862363—24no—
50D2104—24no—
51#16862361—24no—
52#16862360—21no—
53#16862360D412yescomplemented
54C2×C263⋊C8—21no—
55C4⋊Dic263—21no—
56C4⋊Dic263—21no—
57Dic263⋊C4—22no—
58C22⋊Dic263—22no—
59(C2×D263)⋊C4—22no—
60(C2×D263)⋊C4—44no—
61#41×C263—21no—
62#41×C263—21no—
63#41×C263—21no—
64#41×C263—21no—
65C2×Q8×C263D411yescharacteristic
66C2×D4×C263—21no—
67C2×D4×C263D411yescharacteristic
68C22×C4×C263—21no—
69C22×C4×C263—21no—
70C22×C4×C263C2311yescharacteristic
71M16×C263—21no—
72M16×C263D412yescomplemented
73C2×C8×C263—21no—
74C42×C263—21no—
75C42×C263—21no—
76C22×D263—21no—
77C22×D263—22no—
78C22×D263—42no—
79C22×D263—42no—
80C22×D263—41no—
81C22×D263—41no—
82Dic526—21no—
83Dic526—21no—
84D1052—22no—
85D1052—21no—
86D1052—22no—
87D1052—21no—
88D1052—41no—
89D1052—41no—
90C22⋊D263—41no—
91C22⋊D263—41no—
92C22⋊D263—82no—
93C2×Dic263—22no—
94C2×Dic263—21no—
95C2×Dic263—42no—
96C4×D263—41no—
97C4×D263—41no—
98C263⋊C8—22no—
99C23×C263—21no—
100C23×C263C2×D411yescharacteristic
101Q8×C263—21no—
102Q8×C263—21no—
103D4×C263—21no—
104D4×C263—21no—
105D4×C263—41no—
106D4×C263—41no—
107C2×C4×C263—22no—
108C2×C4×C263—21no—
109C2×C4×C263—41no—
110C2×C4×C263—41no—
111C2×C4×C263—41no—
112C2×C4×C263—41no—
113C2×C4×C263C2×D411yescharacteristic
114C2×C4×C263C2×D411yescharacteristic
115C2×C4×C263C2×D411yescharacteristic
116C2×C4×C263C2×D411yescharacteristic
117C2×C4×C263C2×D411yescharacteristic
118C2×C4×C263#4111yescharacteristic
119C8×C263—22no—
120C22×C263—21no—
121C22×C263—21no—
122C22×C263—41no—
123C22×C263—41no—
124C22×C263—41no—
125C22×C263#12011yescharacteristic
126C22×C263#12111yescharacteristic
127C22×C263#12711yescharacteristic
128C2×D263—44no—
129C2×D263—41no—
130C2×D263—42no—
131C2×D263—41no—
132C2×D263—41no—
133C2×D263—82no—
134C2×D263—81no—
135C2×D263—81no—
136C4×C263—42no—
137C4×C263—41no—
138C4×C263#12011yescharacteristic
139C4×C263#12011yescharacteristic
140C4×C263#12111yescharacteristic
141C4×C263#12111yescharacteristic
142Dic263—41no—
143Dic263—42no—
144C2×C263—21no—
145C2×C263—21no—
146C2×C263—81no—
147C2×C263#39211yescharacteristic
148C2×C263#45311yescharacteristic
149C2×C263#45411yescharacteristic
150D263—81no—
151D263—82no—
152C263#200611yescharacteristic, complemented, Sylow
153#2006—2631nomaximal, Sylow
154C2×AGL(1,ℤ/8)—2631no—
155C2×AGL(1,ℤ/8)—2631no—
156#537—2631no—
157C2×#104—2631no—
158C2×#104D26311yescharacteristic, complemented
159#390—2631no—
160#343—2631no—
161C2×#41—2631no—
162C2×#41C2×D26311yescharacteristic
163C22×D4—2631no—
164AGL(1,ℤ/8)—5262no—
165AGL(1,ℤ/8)—5262no—
166AGL(1,ℤ/8)—5262no—
167AGL(1,ℤ/8)—5262no—
168C2×SD16—5261no—
169C2×SD16—5261no—
170C2×D8—5261no—
171C2×D8—5261no—
172C2×M16—2631no—
173C2×M16C2×D26311yescharacteristic
174C22⋊Q8—5261no—
175C22⋊Q8—5261no—
176#121—5261no—
177#121—5262no—
178#121—5261no—
179C2×C4⋊C4—2631no—
180C2×C22⋊C4—5262no—
181C2×C42C2×D26311yescharacteristic
182#104—22no—
183#104—5262no—
184C24—5261no—
185#41—21no—
186#41—21no—
187#41—21no—
188#41—21no—
189#41—5261no—
190#41—5261no—
191#41—5261no—
192#41—5261no—
193C2×Q8—2631no—
194C2×Q8D105211yescharacteristic
195C2×D4—21no—
196C2×D4—2631no—
197C2×D4—2632no—
198C2×D4—5261no—
199C2×D4—5262no—
200C2×D4—5261no—
201C2×D4—5261no—
202C2×D4—5261no—
203C2×D4—5261no—
204C2×D4—5261no—
205C2×D4D105211yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—2632no—
209C22×C4—5261no—
210C22×C4C22×D26311yescharacteristic
211SD16—5264no—
212SD16—5264no—
213D8—5264no—
214D8—5264no—
215M16—21no—
216M16—2632no—
217M16—5261no—
218M16C22⋊D26312yescomplemented
219C2×C8—21no—
220C2×C8—5261no—
221C4⋊C4—5262no—
222C4⋊C4—5261no—
223C4⋊C4—5261no—
224C22⋊C4—5262no—
225C22⋊C4—5262no—
226C22⋊C4—10524no—
227C42—21no—
228C42—21no—
229C23—21no—
230C23—5261no—
231C23—5262no—
232C23—10522no—
233C23—10522no—
234C23—10521no—
235C23—10521no—
236C23D4×D26311yescharacteristic
237Q8—21no—
238Q8—21no—
239Q8—5261no—
240Q8—5261no—
241D4—21no—
242D4—21no—
243D4—41no—
244D4—41no—
245D4—5261no—
246D4—5262no—
247D4—5262no—
248D4—5261no—
249D4—10521no—
250D4—10521no—
251D4—10521no—
252D4—10521no—
253D4—21042no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—5262no—
261C2×C4—5261no—
262C2×C4—10521no—
263C2×C4—10521no—
264C2×C4—10522no—
265C2×C4D4×D26311yescharacteristic
266C2×C4D4×D26311yescharacteristic
267C2×C4D4×D26311yescharacteristic
268C2×C4C2×C22⋊D26311yescharacteristic
269C2×C4C2×D105211yescharacteristic
270C2×C4#1686237611yescharacteristic
271C8—22no—
272C8—5262no—
273C22—21no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—10524no—
279C22—10521no—
280C22—10521no—
281C22—10522no—
282C22—10521no—
283C22—21042no—
284C22—21041no—
285C22—21041no—
286C22#2255444011yescharacteristic
287C22#2255444311yescharacteristic
288C22#2255446611yescharacteristic
289C4—42no—
290C4—41no—
291C4—10521no—
292C4—10522no—
293C4#2255443811yescharacteristic
294C4#2255444011yescharacteristic
295C4#2255444311yescharacteristic
296C4#2255444411yescharacteristic
297C2—21no—
298C2—21no—
299C2—81no—
300C2—21042no—
301C2—21041no—
302C2#3068184711yescharacteristic
303C2#3068210711yescharacteristic
304C2#3068211211yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#104×C263C2
socleC22×C263#120
hypercenterC2×#104D263
hypocenterC263#2006
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#22554498C2semidirect
2. C2×#22554495C2semidirect
3. #30682516C2semidirect
4. C2×#22554398C2semidirect
5. #30681840C2semidirect
6. #30681706C2semidirect
7. C2×#104×C263C2semidirect
43. C2×D1052D4semidirect
53. #16862360D4semidirect
72. M16×C263D4semidirect
152. C263#2006semidirect
158. C2×#104D263semidirect
218. M16C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544982
C2×#225544952
#306825162
C2×#225543982
#306818402
#306817062
C2×#104×C2632
#2006263