Finite Group Databasebeta

← #46782709

Subgroups — #46782709

Order 33664.

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

normal subgroups only

This group has 548 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
1#30682774C211yesmaximal, characteristic
2#30681954C211yesmaximal, characteristic, complemented
3#30681934C211yesmaximal, characteristic, complemented
4#30681932C211yesmaximal, characteristic, complemented
5#30681911C211yesmaximal, characteristic, complemented
6#30681906C211yesmaximal, characteristic, complemented
7#421×C263C211yesmaximal, characteristic, complemented
8#22554518—21no—
9#22554517—21no—
10#22554517C412yescomplemented
11#22554516—21no—
12#22554516C412yescomplemented
13#22554515—22no—
14#22554515—21no—
15C2×#16862376—22no—
16C2×#16862376C2211yescharacteristic
17C2×#16862376C2211yescharacteristic
18#41×D263—22no—
19#41×D263—22no—
20C22×C263⋊C8C2211yescharacteristic, complemented
21#22554429C2211yescharacteristic, complemented
22#22554396—22no—
23#22554394—21no—
24#22554393—21no—
25#22554391—21no—
26#22554390—21no—
27#22554384—22no—
28(C2×D263)⋊C8—22no—
29C2×#41×C263C2211yescharacteristic
30C2×M16×C263C2211yescharacteristic, complemented
31#117×C263C2211yescharacteristic, complemented
32#104×C263—22no—
33#16862377—22no—
34#16862377—22no—
35#16862376—24no—
36#16862376—24no—
37#16862376—22no—
38#16862376—22no—
39#16862376—21no—
40#16862376—21no—
41#16862376—21no—
42#16862376—21no—
43#16862376—21no—
44#16862376—21no—
45#16862376C2×C412yes—
46#16862376D412yes—
47#16862375—24no—
48#16862375—22no—
49#16862375—24no—
50#16862375—22no—
51C2×Dic526—22no—
52C2×Dic526C2×C411yescharacteristic
53C2×Dic526D411yescharacteristic
54Q8×D263—22no—
55Q8×D263—22no—
56C2×D1052—22no—
57C2×D1052C2×C411yescharacteristic
58C2×D1052D411yescharacteristic
59C2×C22⋊D263—24no—
60C2×C22⋊D263—21no—
61C2×C22⋊D263D412yes—
62D4×D263—24no—
63D4×D263—22no—
64D4×D263—24no—
65D4×D263—22no—
66C2×C4×D263—24no—
67C2×C4×D263—21no—
68C2×C4×D263D412yes—
69C2×C263⋊C8—21no—
70C2×C263⋊C8—21no—
71C2×C263⋊C8—21no—
72C4⋊Dic263—21no—
73C22⋊Dic263—21no—
74C4×Dic263—21no—
75#41×C263—21no—
76#41×C263—21no—
77#41×C263C2×C412yes—
78#41×C263D412yes—
79C2×Q8×C263D411yescharacteristic
80C2×D4×C263—21no—
81C2×D4×C263D411yescharacteristic
82C22×C4×C263—21no—
83C22×C4×C263C2311yescharacteristic
84M16×C263—21no—
85M16×C263—21no—
86C2×C8×C263—21no—
87C4⋊C4×C263—21no—
88C22⋊C4×C263—21no—
89C42×C263—21no—
90C22×D263—24no—
91C22×D263—21no—
92C22×D263C22⋊C412yes—
93Dic526—24no—
94Dic526—21no—
95Dic526—21no—
96Dic526—21no—
97Dic526C22⋊C412yes—
98D1052—24no—
99D1052—21no—
100D1052—21no—
101D1052—21no—
102D1052C22⋊C412yes—
103C22⋊D263—24no—
104C22⋊D263—24no—
105C22⋊D263—22no—
106C22⋊D263—22no—
107C22⋊D263—22no—
108C22⋊D263—22no—
109C2×Dic263—24no—
110C2×Dic263—21no—
111C2×Dic263—41no—
112C2×Dic263C22⋊C412yes—
113C4×D263—24no—
114C4×D263—24no—
115C4×D263—22no—
116C4×D263—22no—
117C4×D263—22no—
118C4×D263—22no—
119C263⋊C8—41no—
120C23×C263—21no—
121C23×C263C2×D411yescharacteristic
122Q8×C263—21no—
123Q8×C263C22⋊C412yes—
124D4×C263—22no—
125D4×C263—22no—
126D4×C263—21no—
127D4×C263C22⋊C412yes—
128C2×C4×C263—21no—
129C2×C4×C263—22no—
130C2×C4×C263—22no—
131C2×C4×C263—41no—
132C2×C4×C263C22×C411yescharacteristic
133C2×C4×C263C2×D411yescharacteristic
134C2×C4×C263C2×D411yescharacteristic
135C2×C4×C263C2×D411yescharacteristic
136C2×C4×C263C2×D411yescharacteristic
137C2×C4×C263C2×D411yescharacteristic
138C8×C263—41no—
139C22×C263—22no—
140C22×C263—41no—
141C22×C263—81no—
142C22×C263C2×C22⋊C411yescharacteristic
143C22×C263#12011yescharacteristic
144C22×C263#12011yescharacteristic
145C2×D263—22no—
146C2×D263—22no—
147C2×D263—42no—
148C2×D263—81no—
149C2×D263—84no—
150C4×C263—22no—
151C4×C263—81no—
152C4×C263C2×C22⋊C411yescharacteristic
153C4×C263C2×C22⋊C411yescharacteristic
154C4×C263#12011yescharacteristic
155C4×C263#12011yescharacteristic
156Dic263—22no—
157Dic263—22no—
158Dic263—81no—
159C2×C263—21no—
160C2×C263—21no—
161C2×C263—21no—
162C2×C263—42no—
163C2×C263#37911yescharacteristic
164D263—42no—
165D263—42no—
166C263#179411yescharacteristic, complemented, Sylow
167#1794—2631nomaximal, Sylow
168#585—2631no—
169#421—2631no—
170#421D26311yescharacteristic, complemented
171#416—2631no—
172#416—2631no—
173#410—2631no—
174#408—2631no—
1752−1+4—2632no—
1762−1+4—5261no—
1772−1+4—5261no—
178H(5,𝔽2)—2632no—
179H(5,𝔽2)—5262no—
180H(5,𝔽2)—5261no—
181H(5,𝔽2)—5261no—
182C2×#41—2631no—
183C2×#41—2631no—
184C2×#41—5262no—
185C2×#41—5262no—
186C2×#41—5262no—
187C2×#41C2×D26311yescharacteristic
188C2×M16C2×D26311yescharacteristic, complemented
189C22×C8—2631no—
190#117—2631no—
191#117C2×D26311yescharacteristic, complemented
192#104—22no—
193#104—5262no—
194#103—5261no—
195#103—5261no—
196#102—5261no—
197#102—5261no—
198#99—5262no—
199C22⋊C8—5262no—
200#41—21no—
201#41—21no—
202#41—2632no—
203#41—2632no—
204#41—5262no—
205#41—5262no—
206#41—5264no—
207#41—5264no—
208#41—5264no—
209#41—5264no—
210#41—5262no—
211#41—5262no—
212#41—5262no—
213#41—5262no—
214#41—5261no—
215#41—5261no—
216#41—5261no—
217#41—5261no—
218#41—5261no—
219#41—5261no—
220#41C4×D26312yes—
221#41C22⋊D26312yes—
222C2×Q8—2631no—
223C2×Q8—2631no—
224C2×Q8—5262no—
225C2×Q8—5262no—
226C2×Q8—5262no—
227C2×Q8D105211yescharacteristic
228C2×D4—21no—
229C2×D4—2632no—
230C2×D4—2631no—
231C2×D4—2631no—
232C2×D4—5262no—
233C2×D4—5264no—
234C2×D4—5264no—
235C2×D4—5262no—
236C2×D4—5264no—
237C2×D4—5261no—
238C2×D4—5262no—
239C2×D4D105211yescharacteristic
240C22×C4—21no—
241C22×C4—2632no—
242C22×C4—5264no—
243C22×C4—5261no—
244C22×C4C22×D26311yescharacteristic
245M16—21no—
246M16—21no—
247C2×C8—21no—
248C2×C8—5261no—
249C2×C8—5261no—
250C2×C8—5261no—
251C4⋊C4—21no—
252C4⋊C4—5261no—
253C22⋊C4—21no—
254C22⋊C4—5261no—
255C42—21no—
256C42—5261no—
257C23—21no—
258C23—2632no—
259C23—5264no—
260C23—5261no—
261C23D4×D26311yescharacteristic
262Q8—21no—
263Q8—2632no—
264Q8—5264no—
265Q8—5261no—
266Q8—5261no—
267Q8—5261no—
268Q8(C2×D263)⋊C412yes—
269D4—22no—
270D4—22no—
271D4—21no—
272D4—2632no—
273D4—5264no—
274D4—5264no—
275D4—5264no—
276D4—5262no—
277D4—5262no—
278D4—5262no—
279D4—5262no—
280D4—5261no—
281D4—5261no—
282D4—5261no—
283D4(C2×D263)⋊C412yes—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—2632no—
289C2×C4—5264no—
290C2×C4—5264no—
291C2×C4—5264no—
292C2×C4—5261no—
293C2×C4—5262no—
294C2×C4—5262no—
295C2×C4—5262no—
296C2×C4—5262no—
297C2×C4—10521no—
298C2×C4C2×C4×D26311yescharacteristic
299C2×C4D4×D26311yescharacteristic
300C2×C4D4×D26311yescharacteristic
301C2×C4D4×D26311yescharacteristic
302C2×C4C2×C22⋊D26311yescharacteristic
303C2×C4C2×D105211yescharacteristic
304C8—41no—
305C8—10521no—
306C22—22no—
307C22—41no—
308C22—81no—
309C22—5262no—
310C22—5262no—
311C22—10522no—
312C22—21041no—
313C22—21044no—
314C22C22⋊C4×D26311yescharacteristic
315C22#2255443811yescharacteristic
316C22#2255444011yescharacteristic
317C4—22no—
318C4—81no—
319C4—5262no—
320C4—5262no—
321C4—21041no—
322C4C22⋊C4×D26311yescharacteristic
323C4C2×(C2×D263)⋊C411yescharacteristic
324C4#2255443811yescharacteristic
325C4#2255444011yescharacteristic
326C2—21no—
327C2—21no—
328C2—21no—
329C2—42no—
330C2—10522no—
331C2—10522no—
332C2#3068179311yescharacteristic
subgroupG/H
centerC4#22554438
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#421×C263C2
socleC2×C263#379
prime radical#30682774C2
cosocleC22×C4×C263C23
hypercenter#421D263
hypocenterC263#1794
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #30681954C2semidirect
3. #30681934C2semidirect
4. #30681932C2semidirect
5. #30681911C2semidirect
6. #30681906C2semidirect
7. #421×C263C2semidirect
10. #22554517C4semidirect
12. #22554516C4semidirect
20. C22×C263⋊C8C22semidirect
21. #22554429C22semidirect
30. C2×M16×C263C22semidirect
31. #117×C263C22semidirect
166. C263#1794semidirect
170. #421D263semidirect
188. C2×M16C2×D263semidirect
191. #117C2×D263semidirect

Maximal subgroups

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

subgroupindex
#306827742
#306819542
#306819342
#306819322
#306819112
#306819062
#421×C2632
#1794263