Finite Group Databasebeta

← #46782704

Subgroups — #46782704

Order 33664.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22554517C211yesmaximal, characteristic
2C2×#22554397C211yesmaximal, characteristic, complemented
3C2×#22554396C211yesmaximal, characteristic, complemented
4#30681937C211yesmaximal, characteristic, complemented
5C2×#22554388C211yesmaximal, characteristic, complemented
6#30681843C211yesmaximal, characteristic, complemented
7#417×C263C211yesmaximal, characteristic, complemented
8#22554517—22no—
9#22554517—22no—
10#22554517—22no—
11#22554517C414yescomplemented
12C2×#16862376—21no—
13C2×#16862376C2211yescharacteristic
14C2×#16862375—22no—
15C2×#16862375—21no—
16C22×Dic526—21no—
17C22×Dic526C2211yescharacteristic
18C2×Q8×D263—21no—
19C2×#16862360C2211yescharacteristic
20C2×C4×Dic263C2211yescharacteristic
21#22554397—22no—
22#22554396—22no—
23#22554393—21no—
24#22554390—21no—
25#22554388—22no—
26C263⋊#95—22no—
27C2×#41×C263C2211yescharacteristic
28C2×M16×C263C2211yescharacteristic
29C2×C4⋊C4×C263C2211yescharacteristic
30#103×C263—21no—
31#102×C263—21no—
32#16862376—24no—
33#16862376—24no—
34#16862376—21no—
35#16862376—21no—
36#16862376C2×C412yes—
37#16862376D412yes—
38#16862375—28no—
39#16862375—24no—
40#16862375—28no—
41#16862375—24no—
42C2×Dic526—22no—
43C2×Dic526—24no—
44C2×Dic526—24no—
45C2×Dic526—21no—
46C2×Dic526—21no—
47C2×Dic526—21no—
48C2×Dic526—21no—
49C2×Dic526C2×C412yes—
50C2×Dic526D411yescharacteristic
51C2×Dic526D412yes—
52Q8×D263—24no—
53Q8×D263—24no—
54C2×D1052D411yescharacteristic
55C2×C22⋊D263—22no—
56C2×C22⋊D263—21no—
57C22×Dic263—22no—
58C22×Dic263—21no—
59C22×Dic263D412yes—
60C2×C4×D263—22no—
61C2×C4×D263—21no—
62#16862360—21no—
63#16862360—21no—
64C2×C263⋊C8—21no—
65C4×Dic263—21no—
66C4×Dic263—21no—
67#41×C263—21no—
68#41×C263—21no—
69#41×C263C2×C412yes—
70#41×C263D412yes—
71C2×Q8×C263D411yescharacteristic
72C2×D4×C263—21no—
73C2×D4×C263D411yescharacteristic
74C22×C4×C263—21no—
75C22×C4×C263—21no—
76C22×C4×C263C2311yescharacteristic
77M16×C263—21no—
78M16×C263—21no—
79C2×C8×C263—21no—
80C4⋊C4×C263—21no—
81C4⋊C4×C263—21no—
82C22×D263—21no—
83Dic526—28no—
84Dic526—22no—
85Dic526—22no—
86Dic526—22no—
87Dic526—21no—
88Dic526—22no—
89Dic526C22⋊C412yes—
90D1052—21no—
91D1052C22⋊C412yes—
92C22⋊D263—28no—
93C22⋊D263—22no—
94C22⋊D263—22no—
95C2×Dic263—28no—
96C2×Dic263—21no—
97C2×Dic263—22no—
98C2×Dic263—22no—
99C2×Dic263—22no—
100C2×Dic263—41no—
101C2×Dic263—41no—
102C2×Dic263C22⋊C414yes—
103C4×D263—28no—
104C4×D263—22no—
105C4×D263—22no—
106C263⋊C8—41no—
107C23×C263—21no—
108C23×C263C2×D411yescharacteristic
109Q8×C263—21no—
110Q8×C263C22⋊C412yes—
111D4×C263—22no—
112D4×C263—22no—
113D4×C263—21no—
114D4×C263C22⋊C412yes—
115C2×C4×C263—21no—
116C2×C4×C263—22no—
117C2×C4×C263—22no—
118C2×C4×C263—42no—
119C2×C4×C263—41no—
120C2×C4×C263C22×C411yescharacteristic
121C2×C4×C263C2×D411yescharacteristic
122C2×C4×C263C2×D411yescharacteristic
123C2×C4×C263C2×D411yescharacteristic
124C2×C4×C263C2×D411yescharacteristic
125C2×C4×C263C2×D411yescharacteristic
126C8×C263—41no—
127C22×C263—21no—
128C22×C263—21no—
129C22×C263—22no—
130C22×C263—41no—
131C22×C263—41no—
132C22×C263C2×C22⋊C411yescharacteristic
133C22×C263#12011yescharacteristic
134C22×C263#12011yescharacteristic
135C2×D263—22no—
136C2×D263—41no—
137C2×D263—41no—
138C4×C263—22no—
139C4×C263—81no—
140C4×C263C2×C22⋊C411yescharacteristic
141C4×C263C2×C22⋊C411yescharacteristic
142C4×C263#12011yescharacteristic
143C4×C263#12011yescharacteristic
144Dic263—22no—
145Dic263—24no—
146Dic263—42no—
147C2×C263—21no—
148C2×C263—21no—
149C2×C263—42no—
150C2×C263#37911yescharacteristic
151C2×C263#45411yescharacteristic
152C2×C263#45611yescharacteristic
153D263—42no—
154C263#179311yescharacteristic, complemented, Sylow
155#1793—2631nomaximal, Sylow
156C2×2−1+4—2631no—
157C2×#104—2631no—
158C2×#104—2631no—
159#417—2631no—
160#417D26311yescharacteristic, complemented
161C2×#101—2631no—
162#391—2631no—
1632−1+4—2634no—
1642−1+4—5262no—
1652−1+4—5262no—
1662−1+4—5262no—
167C2×#41—2631no—
168C2×#41—5261no—
169C2×#41—5262no—
170C2×#41—5261no—
171C2×#41C2×D26311yescharacteristic
172C22×Q8—2631no—
173C22×Q8—5261no—
174C22×Q8—5261no—
175C2×M16—2631no—
176C2×M16C2×D26311yescharacteristic
177C2×C4⋊C4C2×D26311yescharacteristic
178C2×C42—2631no—
179#104—5262no—
180#104—5262no—
181#103—21no—
182#103—5261no—
183#102—21no—
184#102—5261no—
185#101—5262no—
186#95—5262no—
187#41—21no—
188#41—21no—
189#41—2632no—
190#41—2632no—
191#41—5264no—
192#41—5264no—
193#41—5268no—
194#41—5268no—
195#41—5264no—
196#41—5264no—
197#41—5261no—
198#41—5261no—
199#41C4×D26312yes—
200#41D105212yes—
201C2×Q8—2632no—
202C2×Q8—2632no—
203C2×Q8—2631no—
204C2×Q8—5264no—
205C2×Q8—5262no—
206C2×Q8—5264no—
207C2×Q8—5264no—
208C2×Q8—5264no—
209C2×Q8—5261no—
210C2×Q8—5261no—
211C2×Q8—5261no—
212C2×Q8—5261no—
213C2×Q8C22⋊D26311yescharacteristic
214C2×D4—21no—
215C2×D4—2631no—
216C2×D4—5262no—
217C2×D4—5261no—
218C2×D4C22⋊D26311yescharacteristic
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—2632no—
222C22×C4—5262no—
223C22×C4—5262no—
224C22×C4—5261no—
225C22×C4—5261no—
226C22×C4C22×D26311yescharacteristic
227M16—21no—
228M16—21no—
229M16—5261no—
230M16—5261no—
231C2×C8—21no—
232C2×C8—5261no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C42—5261no—
236C42—5261no—
237C23—21no—
238C23—5261no—
239C23D4×D26311yescharacteristic
240Q8—21no—
241Q8—2632no—
242Q8—5268no—
243Q8—5262no—
244Q8—5262no—
245Q8—5262no—
246Q8—5262no—
247Q8—5261no—
248Q8(C2×D263)⋊C412yes—
249D4—22no—
250D4—22no—
251D4—21no—
252D4—2632no—
253D4—5268no—
254D4—5262no—
255D4—5262no—
256D4—5261no—
257D4(C2×D263)⋊C412yes—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—2634no—
264C2×C4—5268no—
265C2×C4—5268no—
266C2×C4—5262no—
267C2×C4—5261no—
268C2×C4—5262no—
269C2×C4—5262no—
270C2×C4—5262no—
271C2×C4—5262no—
272C2×C4—10521no—
273C2×C4—10521no—
274C2×C4C2×C4×D26311yescharacteristic
275C2×C4D4×D26311yescharacteristic
276C2×C4D4×D26311yescharacteristic
277C2×C4D4×D26311yescharacteristic
278C2×C4C2×C22⋊D26311yescharacteristic
279C2×C4C2×D105211yescharacteristic
280C8—41no—
281C8—10521no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—5262no—
288C22—10521no—
289C22—10521no—
290C22C22⋊C4×D26311yescharacteristic
291C22#2255443811yescharacteristic
292C22#2255444011yescharacteristic
293C4—22no—
294C4—81no—
295C4—5264no—
296C4—5262no—
297C4—10522no—
298C4C22⋊C4×D26311yescharacteristic
299C4C2×(C2×D263)⋊C411yescharacteristic
300C4#2255443811yescharacteristic
301C4#2255444011yescharacteristic
302C2—21no—
303C2—21no—
304C2—42no—
305C2—10522no—
306C2#3068179311yescharacteristic
307C2#3068210911yescharacteristic
308C2#3068211911yescharacteristic
subgroupG/H
centerC22#22554438
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#417×C263C2
socleC22×C263#120
prime radicalC2×#22554517C2
cosocleC22×C4×C263C23
hypercenter#417D263
hypocenterC263#1793
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#22554397C2semidirect
3. C2×#22554396C2semidirect
4. #30681937C2semidirect
5. C2×#22554388C2semidirect
6. #30681843C2semidirect
7. #417×C263C2semidirect
11. #22554517C4semidirect
154. C263#1793semidirect
160. #417D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225545172
C2×#225543972
C2×#225543962
#306819372
C2×#225543882
#306818432
#417×C2632
#1793263