Finite Group Databasebeta

← #46783795

Subgroups — #46783795

Order 33664.

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

normal subgroups only

This group has 370 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, complemented
2C2×#22554500C211yesmaximal, characteristic, complemented
3#30682516C211yesmaximal, characteristic
4C2×#22554398C211yesmaximal, characteristic, complemented
5#30681844C211yesmaximal, characteristic, complemented
6#30681706C211yesmaximal, characteristic, complemented
7C2×#104×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×Dic526C2211yescharacteristic
10#22554503—22no—
11#22554503—22no—
12#22554500—22no—
13#22554500—22no—
14C2×Dic1052—21no—
15C2×#16862366—21no—
16C2×#16862365—21no—
17C2×#16862364—21no—
18C2×#16862360C2211yescharacteristic
19#22554449—21no—
20#22554446—21no—
21#22554444—21no—
22#22554442—22no—
23#22554441—21no—
24C2×C4⋊Dic263C2211yescharacteristic
25#22554398—22no—
26C263⋊#95—22no—
27C2×#41×C263C2211yescharacteristic
28C2×M16×C263C2211yescharacteristic
29C2×C42×C263C2211yescharacteristic
30#104×C263—22no—
31#16862376—21no—
32#16862376—21no—
33#16862376—21no—
34#16862376—21no—
35C2×Dic526—21no—
36C2×Dic526—21no—
37C2×Dic526—21no—
38C2×Dic526—21no—
39C2×Dic526—21no—
40C2×Dic526D411yescharacteristic
41C2×Dic526D412yescomplemented
42C2×D1052D411yescharacteristic
43C2×C22⋊D263—22no—
44C2×C22⋊D263—21no—
45C22×Dic263—21no—
46C22×Dic263D412yes—
47C2×C4×D263—21no—
48Dic1052—24no—
49#16862366—24no—
50#16862365—24no—
51#16862364—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#41×C263—21no—
61#41×C263—21no—
62#41×C263—21no—
63#41×C263—21no—
64C2×Q8×C263D411yescharacteristic
65C2×D4×C263—21no—
66C2×D4×C263D411yescharacteristic
67C22×C4×C263—21no—
68C22×C4×C263—21no—
69C22×C4×C263C2311yescharacteristic
70M16×C263—21no—
71M16×C263D412yescomplemented
72C2×C8×C263—21no—
73C42×C263—21no—
74C42×C263—21no—
75C22×D263—21no—
76Dic526—22no—
77Dic526—22no—
78Dic526—21no—
79Dic526—21no—
80Dic526—41no—
81Dic526—41no—
82D1052—21no—
83D1052—21no—
84C22⋊D263—41no—
85C22⋊D263—41no—
86C22⋊D263—82no—
87C2×Dic263—22no—
88C2×Dic263—21no—
89C2×Dic263—22no—
90C2×Dic263—41no—
91C2×Dic263—41no—
92C2×Dic263—42no—
93C4×D263—41no—
94C4×D263—41no—
95C263⋊C8—22no—
96C23×C263—21no—
97C23×C263C2×D411yescharacteristic
98Q8×C263—21no—
99Q8×C263—21no—
100D4×C263—21no—
101D4×C263—21no—
102D4×C263—41no—
103D4×C263—41no—
104C2×C4×C263—22no—
105C2×C4×C263—21no—
106C2×C4×C263—41no—
107C2×C4×C263—41no—
108C2×C4×C263—41no—
109C2×C4×C263—41no—
110C2×C4×C263C2×D411yescharacteristic
111C2×C4×C263C2×D411yescharacteristic
112C2×C4×C263C2×D411yescharacteristic
113C2×C4×C263C2×D411yescharacteristic
114C2×C4×C263C2×D411yescharacteristic
115C2×C4×C263#4111yescharacteristic
116C8×C263—22no—
117C22×C263—21no—
118C22×C263—21no—
119C22×C263—41no—
120C22×C263—41no—
121C22×C263—41no—
122C22×C263#12011yescharacteristic
123C22×C263#12111yescharacteristic
124C22×C263#12711yescharacteristic
125C2×D263—41no—
126C2×D263—41no—
127C2×D263—41no—
128C4×C263—42no—
129C4×C263—41no—
130C4×C263#12011yescharacteristic
131C4×C263#12011yescharacteristic
132C4×C263#12111yescharacteristic
133C4×C263#12111yescharacteristic
134Dic263—41no—
135Dic263—42no—
136Dic263—42no—
137C2×C263—21no—
138C2×C263—21no—
139C2×C263—81no—
140C2×C263#39211yescharacteristic
141C2×C263#45511yescharacteristic
142C2×C263#45611yescharacteristic
143D263—81no—
144C263#200711yescharacteristic, complemented, Sylow
145#2007—2631nomaximal, Sylow
146C2×#137—2631no—
147C2×#137—2631no—
148#537—2631no—
149C2×#104—2631no—
150C2×#104D26311yescharacteristic, complemented
151#391—2631no—
152#343—2631no—
153C2×#41—2631no—
154C2×#41C2×D26311yescharacteristic
155C22×Q8—2631no—
156#137—5262no—
157#137—5262no—
158#137—5262no—
159#137—5262no—
160C2×Q16—5261no—
161C2×Q16—5261no—
162C2×SD16—5261no—
163C2×SD16—5261no—
164C2×M16—2631no—
165C2×M16C2×D26311yescharacteristic
166C22⋊Q8—5261no—
167C22⋊Q8—5261no—
168#121—5261no—
169#121—5262no—
170#121—5261no—
171C2×C4⋊C4—2631no—
172C2×C42C2×D26311yescharacteristic
173#104—22no—
174#104—5262no—
175#95—5262no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—21no—
180#41—5261no—
181#41—5261no—
182#41—5261no—
183#41—5261no—
184C2×Q8—2631no—
185C2×Q8—2632no—
186C2×Q8—5261no—
187C2×Q8—5261no—
188C2×Q8—5261no—
189C2×Q8—5261no—
190C2×Q8—5261no—
191C2×Q8D105211yescharacteristic
192C2×D4—21no—
193C2×D4—2631no—
194C2×D4—5261no—
195C2×D4—5262no—
196C2×D4D105211yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—2632no—
200C22×C4—5261no—
201C22×C4—5261no—
202C22×C4C22×D26311yescharacteristic
203Q16—5264no—
204Q16—5264no—
205SD16—5264no—
206SD16—5264no—
207M16—21no—
208M16—2632no—
209M16—5261no—
210M16C22⋊D26312yescomplemented
211C2×C8—21no—
212C2×C8—5261no—
213C4⋊C4—5262no—
214C4⋊C4—5261no—
215C4⋊C4—5261no—
216C22⋊C4—5262no—
217C22⋊C4—5262no—
218C42—21no—
219C42—21no—
220C23—21no—
221C23—5261no—
222C23D4×D26311yescharacteristic
223Q8—21no—
224Q8—21no—
225Q8—5262no—
226Q8—5261no—
227Q8—5262no—
228Q8—5261no—
229Q8—10521no—
230Q8—10521no—
231D4—21no—
232D4—21no—
233D4—41no—
234D4—41no—
235D4—5261no—
236D4—5261no—
237D4—10521no—
238D4—10521no—
239D4—21042no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—5262no—
247C2×C4—5261no—
248C2×C4—5262no—
249C2×C4—10521no—
250C2×C4—10521no—
251C2×C4—10521no—
252C2×C4—10521no—
253C2×C4—10522no—
254C2×C4D4×D26311yescharacteristic
255C2×C4D4×D26311yescharacteristic
256C2×C4D4×D26311yescharacteristic
257C2×C4C2×C22⋊D26311yescharacteristic
258C2×C4C2×D105211yescharacteristic
259C2×C4#1686237611yescharacteristic
260C8—22no—
261C8—5262no—
262C22—21no—
263C22—21no—
264C22—41no—
265C22—41no—
266C22—41no—
267C22—10521no—
268C22—10521no—
269C22—10521no—
270C22#2255444011yescharacteristic
271C22#2255444311yescharacteristic
272C22#2255446611yescharacteristic
273C4—42no—
274C4—41no—
275C4—10522no—
276C4—10521no—
277C4—10522no—
278C4#2255443811yescharacteristic
279C4#2255444011yescharacteristic
280C4#2255444311yescharacteristic
281C4#2255444411yescharacteristic
282C2—21no—
283C2—21no—
284C2—81no—
285C2—21041no—
286C2#3068184711yescharacteristic
287C2#3068211711yescharacteristic
288C2#3068212211yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#104×C263C2
socleC22×C263#120
prime radical#30682516C2
hypercenterC2×#104D263
hypocenterC263#2007
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×#22554503C2semidirect
2. C2×#22554500C2semidirect
4. C2×#22554398C2semidirect
5. #30681844C2semidirect
6. #30681706C2semidirect
7. C2×#104×C263C2semidirect
41. C2×Dic526D4semidirect
53. #16862360D4semidirect
71. M16×C263D4semidirect
144. C263#2007semidirect
150. C2×#104D263semidirect
210. M16C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225545032
C2×#225545002
#306825162
C2×#225543982
#306818442
#306817062
C2×#104×C2632
#2007263