Finite Group Databasebeta

← #46782719

Subgroups — #46782719

Order 33664.

536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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×#22554518C211yesmaximal, characteristic
2#30681956C211yesmaximal, characteristic, complemented
3#30681954C211yesmaximal, characteristic, complemented
4#30681947C211yesmaximal, characteristic, complemented
5#30681920C211yesmaximal, characteristic, complemented
6#30681911C211yesmaximal, characteristic, complemented
7#419×C263C211yesmaximal, characteristic, complemented
8#22554518—22no—
9#22554518—22no—
10#22554518—22no—
11#22554518—22no—
12C2×#16862377—21no—
13C2×#16862377C412yescomplemented
14C2×#16862376—22no—
15C2×#16862376C2211yescharacteristic
16C2×#16862376C2211yescharacteristic
17C2×Q8×D263—21no—
18C2×Q8×D263C412yescomplemented
19C2×#16862360C2211yescharacteristic
20#22554429C2211yescharacteristic
21#22554398—22no—
22#22554396—22no—
23#22554394—22no—
24#22554388—21no—
25#22554386—21no—
26#22554384—22no—
27C22×Q8×C263C2211yescharacteristic
28C2×M16×C263C2211yescharacteristic
29#117×C263C2211yescharacteristic
30#103×C263—22no—
31#16862377—24no—
32#16862377—24no—
33#16862377—24no—
34#16862377—24no—
35#16862376—28no—
36#16862376—28no—
37#16862376—21no—
38#16862376—21no—
39#16862376—21no—
40#16862376—21no—
41#16862376—21no—
42#16862376—21no—
43#16862376D412yes—
44#16862376D412yes—
45C2×Dic526—22no—
46C2×Dic526C2×C411yescharacteristic
47C2×Dic526D411yescharacteristic
48Q8×D263—24no—
49Q8×D263—24no—
50Q8×D263—24no—
51Q8×D263—24no—
52C2×D1052—22no—
53C2×D1052C2×C411yescharacteristic
54C2×D1052D411yescharacteristic
55C2×C22⋊D263—21no—
56C2×C22⋊D263D412yes—
57C2×C4×D263—22no—
58C2×C4×D263—22no—
59C2×C4×D263—21no—
60C2×C4×D263C2×C412yes—
61#16862360—21no—
62#16862360—21no—
63C2×C263⋊C8—21no—
64C4⋊Dic263—21no—
65C22⋊Dic263—21no—
66C4×Dic263—21no—
67C2×Q8×C263—21no—
68C2×Q8×C263—21no—
69C2×Q8×C263—21no—
70C2×Q8×C263C2×C412yes—
71C2×Q8×C263D412yes—
72C2×Q8×C263D412yes—
73C22×C4×C263—21no—
74C22×C4×C263C2311yescharacteristic
75M16×C263—21no—
76M16×C263—21no—
77C2×C8×C263—21no—
78C4⋊C4×C263—21no—
79C22⋊C4×C263—21no—
80C42×C263—21no—
81C22×D263—21no—
82C22×D263C22⋊C412yes—
83Dic526—28no—
84Dic526—21no—
85Dic526—21no—
86Dic526—21no—
87Dic526C22⋊C412yes—
88D1052—28no—
89D1052—21no—
90D1052—21no—
91D1052—21no—
92D1052C22⋊C412yes—
93C22⋊D263—22no—
94C22⋊D263—22no—
95C22⋊D263—22no—
96C22⋊D263—22no—
97C2×Dic263—21no—
98C2×Dic263—41no—
99C2×Dic263C22⋊C412yes—
100C4×D263—28no—
101C4×D263—28no—
102C4×D263—22no—
103C4×D263—22no—
104C4×D263—22no—
105C4×D263—22no—
106C263⋊C8—41no—
107C23×C263C2×D411yescharacteristic
108Q8×C263—22no—
109Q8×C263—22no—
110Q8×C263—22no—
111Q8×C263C22⋊C414yes—
112C2×C4×C263—22no—
113C2×C4×C263—22no—
114C2×C4×C263—22no—
115C2×C4×C263—41no—
116C2×C4×C263C22×C411yescharacteristic
117C2×C4×C263C2×D411yescharacteristic
118C2×C4×C263C2×D411yescharacteristic
119C2×C4×C263C2×D411yescharacteristic
120C2×C4×C263C2×D411yescharacteristic
121C2×C4×C263C2×D411yescharacteristic
122C8×C263—41no—
123C22×C263—41no—
124C22×C263C2×C22⋊C411yescharacteristic
125C22×C263#12011yescharacteristic
126C22×C263#12011yescharacteristic
127C2×D263—22no—
128C2×D263—22no—
129C2×D263—42no—
130C2×D263—42no—
131C4×C263—24no—
132C4×C263—81no—
133C4×C263C2×C22⋊C411yescharacteristic
134C4×C263C2×C22⋊C411yescharacteristic
135C4×C263#12011yescharacteristic
136C4×C263#12011yescharacteristic
137Dic263—22no—
138Dic263—22no—
139Dic263—81no—
140C2×C263—21no—
141C2×C263—21no—
142C2×C263—21no—
143C2×C263#37911yescharacteristic
144D263—42no—
145D263—42no—
146C263#179611yescharacteristic, complemented, Sylow
147#1796—2631nomaximal, Sylow
148C2×2−1+4—2631no—
149#421—2631no—
150#421—2631no—
151#419—2631no—
152#419D26311yescharacteristic, complemented
153#413—2631no—
154#410—2631no—
1552−1+4—5262no—
1562−1+4—5262no—
1572−1+4—5262no—
1582−1+4—5262no—
159C2×#41—2631no—
160C2×#41—2632no—
161C2×#41—2631no—
162C2×#41—5262no—
163C2×#41—5261no—
164C22×Q8—2632no—
165C22×Q8—5261no—
166C22×Q8C2×D26311yescharacteristic
167C2×M16—2631no—
168C2×M16C2×D26311yescharacteristic
169#117—2631no—
170#117C2×D26311yescharacteristic
171#104—5262no—
172#104—5262no—
173#103—22no—
174#103—5262no—
175#101—5261no—
176#100—5261no—
177#99—5262no—
178#41—2632no—
179#41—2632no—
180#41—5268no—
181#41—5268no—
182#41—5264no—
183#41—5264no—
184#41—5264no—
185#41—5264no—
186#41—5261no—
187#41—5261no—
188#41—5261no—
189#41—5261no—
190#41—5261no—
191#41—5261no—
192C2×Q8—21no—
193C2×Q8—21no—
194C2×Q8—21no—
195C2×Q8—2631no—
196C2×Q8—2631no—
197C2×Q8—5262no—
198C2×Q8—5264no—
199C2×Q8—5264no—
200C2×Q8—5264no—
201C2×Q8—5264no—
202C2×Q8C4×D26312yes—
203C2×Q8C22⋊D26312yes—
204C2×Q8D105212yes—
205C2×D4—2632no—
206C2×D4—2631no—
207C2×D4—2631no—
208C2×D4—5262no—
209C2×D4—5261no—
210C22×C4—21no—
211C22×C4—2632no—
212C22×C4—5262no—
213C22×C4—5262no—
214C22×C4—5261no—
215C22×C4C22×D26311yescharacteristic
216M16—21no—
217M16—21no—
218M16—5261no—
219M16—5261no—
220C2×C8—21no—
221C2×C8—5261no—
222C4⋊C4—21no—
223C4⋊C4—5261no—
224C22⋊C4—21no—
225C22⋊C4—5261no—
226C42—21no—
227C42—5261no—
228C23—2632no—
229C23—5261no—
230C23D4×D26311yescharacteristic
231Q8—22no—
232Q8—22no—
233Q8—22no—
234Q8—2632no—
235Q8—5268no—
236Q8—5261no—
237Q8—5261no—
238Q8—5261no—
239Q8(C2×D263)⋊C414yes—
240D4—2632no—
241D4—5268no—
242D4—5262no—
243D4—5262no—
244D4—5262no—
245D4—5262no—
246D4—5261no—
247D4—5261no—
248D4—5261no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—2632no—
254C2×C4—5268no—
255C2×C4—5268no—
256C2×C4—5261no—
257C2×C4—5262no—
258C2×C4—5262no—
259C2×C4—5262no—
260C2×C4—5262no—
261C2×C4—10521no—
262C2×C4C2×C4×D26311yescharacteristic
263C2×C4D4×D26311yescharacteristic
264C2×C4D4×D26311yescharacteristic
265C2×C4D4×D26311yescharacteristic
266C2×C4C2×C22⋊D26311yescharacteristic
267C2×C4C2×D105211yescharacteristic
268C8—41no—
269C8—10521no—
270C22—41no—
271C22—5262no—
272C22—5262no—
273C22—10522no—
274C22—10522no—
275C22C22⋊C4×D26311yescharacteristic
276C22#2255443811yescharacteristic
277C22#2255444011yescharacteristic
278C4—24no—
279C4—81no—
280C4—5262no—
281C4—5262no—
282C4—21041no—
283C4C22⋊C4×D26311yescharacteristic
284C4C2×(C2×D263)⋊C411yescharacteristic
285C4#2255443811yescharacteristic
286C4#2255444011yescharacteristic
287C2—21no—
288C2—21no—
289C2—21no—
290C2—10522no—
291C2—10522no—
292C2#3068179311yescharacteristic
subgroupG/H
centerC2#30681793
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#419×C263C2
socleC2×C263#379
prime radicalC2×#22554518C2
cosocleC22×C4×C263C23
hypercenter#419D263
hypocenterC263#1796
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. #30681956C2semidirect
3. #30681954C2semidirect
4. #30681947C2semidirect
5. #30681920C2semidirect
6. #30681911C2semidirect
7. #419×C263C2semidirect
13. C2×#16862377C4semidirect
18. C2×Q8×D263C4semidirect
146. C263#1796semidirect
152. #419D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225545182
#306819562
#306819542
#306819472
#306819202
#306819112
#419×C2632
#1796263