Finite Group Databasebeta

← #46783799

Subgroups — #46783799

Order 33664.

380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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#30682736C211yesmaximal, characteristic, complemented
2C2×#22554495C211yesmaximal, characteristic, complemented
3#30682507C211yesmaximal, characteristic, complemented
4#30681956C211yesmaximal, characteristic, complemented
5#30681942C211yesmaximal, characteristic, complemented
6#30681708C211yesmaximal, characteristic, complemented
7#410×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×D1052C2211yescharacteristic
10#22554501—21no—
11#22554500—21no—
12#22554496—21no—
13#22554495—22no—
14#22554495—21no—
15#22554495—22no—
16#22554490—22no—
17C2×#16862363—21no—
18C2×#16862361—21no—
19C2×#16862360C2211yescharacteristic
20C2×#16862360C2211yescharacteristic
21#22554467—21no—
22#22554458—21no—
23#22554445—22no—
24#22554440—22no—
25#22554398—22no—
26#22554390—22no—
27C2×#41×C263C2211yescharacteristic
28#117×C263C2211yescharacteristic
29#117×C263C2211yescharacteristic
30#99×C263—22no—
31C23×D263—21no—
32#16862376—21no—
33#16862376—21no—
34#16862376—21no—
35#16862376—21no—
36C2×Dic526D411yescharacteristic
37C2×D1052—24no—
38C2×D1052—21no—
39C2×D1052—21no—
40C2×D1052—21no—
41C2×D1052—21no—
42C2×D1052—21no—
43C2×D1052D412yes—
44C2×D1052D411yescharacteristic
45C2×C22⋊D263—21no—
46C2×C4×D263—21no—
47#16862366—22no—
48#16862364—22no—
49#16862363—24no—
50#16862363—22no—
51#16862361—24no—
52#16862361—22no—
53#16862360—21no—
54#16862360—21no—
55#16862360—21no—
56#16862360D412yescomplemented
57C2×C263⋊C8—21no—
58C2×C263⋊C8D412yescomplemented
59(C2×D263)⋊C4—24no—
60#41×C263—21no—
61#41×C263—21no—
62#41×C263—21no—
63#41×C263—21no—
64C2×Q8×C263D411yescharacteristic, complemented
65C2×D4×C263—21no—
66C2×D4×C263D411yescharacteristic, complemented
67C22×C4×C263—21no—
68C22×C4×C263C2311yescharacteristic
69C4⋊C4×C263—21no—
70C4⋊C4×C263—21no—
71C22⋊C4×C263—21no—
72C22⋊C4×C263D412yes—
73C42×C263—21no—
74C42×C263—21no—
75C22×D263—22no—
76C22×D263—21no—
77C22×D263—41no—
78C22×D263—41no—
79C22×D263—82no—
80Dic526—21no—
81Dic526—21no—
82D1052—22no—
83D1052—21no—
84D1052—22no—
85D1052—21no—
86D1052—41no—
87D1052—41no—
88D1052—84no—
89C22⋊D263—41no—
90C22⋊D263—41no—
91C2×Dic263—21no—
92C4×D263—41no—
93C4×D263—41no—
94C263⋊C8—22no—
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×C263C2×D411yescharacteristic
110C2×C4×C263C2×D411yescharacteristic
111C2×C4×C263C2×D411yescharacteristic
112C2×C4×C263C2×D411yescharacteristic
113C2×C4×C263C2×D411yescharacteristic
114C2×C4×C263#4111yescharacteristic
115C22×C263—41no—
116C22×C263—41no—
117C22×C263—81no—
118C22×C263#12011yescharacteristic
119C22×C263#12111yescharacteristic
120C22×C263#12711yescharacteristic
121C2×D263—42no—
122C2×D263—44no—
123C2×D263—41no—
124C2×D263—42no—
125C2×D263—82no—
126C2×D263—82no—
127C4×C263—42no—
128C4×C263—41no—
129C4×C263—81no—
130C4×C263#12011yescharacteristic
131C4×C263#12011yescharacteristic
132C4×C263#12111yescharacteristic
133C4×C263#12111yescharacteristic
134Dic263—41no—
135C2×C263—21no—
136C2×C263—21no—
137C2×C263—21no—
138C2×C263—81no—
139C2×C263#39211yescharacteristic
140D263—81no—
141D263—82no—
142C263#200811yescharacteristic, complemented, Sylow
143#2008—2631nomaximal, Sylow
144#575—2631no—
145C2×AGL(1,ℤ/8)—2631no—
146#535—2631no—
147#421—2631no—
148#418—2631no—
149#410D26311yescharacteristic, complemented
150#344—2631no—
151C2×#41—2631no—
152C2×#41C2×D26311yescharacteristic
153C22×D4—2631no—
154#137—5261no—
155#137—5261no—
156AGL(1,ℤ/8)—5262no—
157AGL(1,ℤ/8)—5262no—
158AGL(1,ℤ/8)—5261no—
159AGL(1,ℤ/8)—5261no—
160#135—5262no—
161C2×SD16—5261no—
162C2×D8—5261no—
163C2×M16—2631no—
164C2×M16—2631no—
165#127—5261no—
166#124—5261no—
167#121—5262no—
168#120—5262no—
169#117C2×D26311yescharacteristic
170#117C2×D26311yescharacteristic
171#104—5262no—
172#102—5262no—
173#99—22no—
174C24—5261no—
175#41—21no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—5261no—
180#41—5261no—
181#41—5261no—
182#41—5261no—
183C2×Q8—2631no—
184C2×Q8D105211yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—2632no—
187C2×D4—2631no—
188C2×D4—5264no—
189C2×D4—5261no—
190C2×D4—5261no—
191C2×D4—5261no—
192C2×D4—5261no—
193C2×D4—5261no—
194C2×D4—5261no—
195C2×D4D105211yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—5261no—
198C22×C4C22×D26311yescharacteristic
199Q16—5262no—
200SD16—5262no—
201SD16—5264no—
202SD16—5262no—
203D8—5264no—
204D8—5262no—
205M16—2632no—
206M16—5261no—
207M16—5261no—
208M16—5261no—
209C2×C8—2632no—
210C2×C8—5261no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—5264no—
215C22⋊C4C22⋊D26312yes—
216C42—21no—
217C42—21no—
218C23—21no—
219C23—5262no—
220C23—5261no—
221C23—10521no—
222C23—10521no—
223C23—21042no—
224C23C2×C22⋊D26311yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—5261no—
228Q8—5261no—
229D4—21no—
230D4—21no—
231D4—41no—
232D4—41no—
233D4—5262no—
234D4—5261no—
235D4—5262no—
236D4—5261no—
237D4—10521no—
238D4—10521no—
239D4—10521no—
240D4—10521no—
241D4—21044no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—5261no—
248C2×C4—10521no—
249C2×C4—10521no—
250C2×C4D4×D26311yescharacteristic
251C2×C4D4×D26311yescharacteristic
252C2×C4D4×D26311yescharacteristic
253C2×C4D4×D26311yescharacteristic
254C2×C4C2×D105211yescharacteristic
255C2×C4#1686237611yescharacteristic
256C8—5262no—
257C8—5262no—
258C22—41no—
259C22—41no—
260C22—81no—
261C22—10522no—
262C22—10524no—
263C22—10521no—
264C22—10522no—
265C22—21042no—
266C22—21042no—
267C22#2255443811yescharacteristic
268C22#2255444411yescharacteristic
269C22#2255446611yescharacteristic
270C4—42no—
271C4—41no—
272C4—81no—
273C4—10521no—
274C4#2255444011yescharacteristic
275C4#2255444011yescharacteristic
276C4#2255444311yescharacteristic
277C4#2255444311yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—81no—
282C2—21042no—
283C2—21041no—
284C2#3068184711yescharacteristic
subgroupG/H
centerC2#30681847
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#410×C263C2
socleC2×C263#392
hypercenter#410D263
hypocenterC263#2008
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #30682736C2semidirect
2. C2×#22554495C2semidirect
3. #30682507C2semidirect
4. #30681956C2semidirect
5. #30681942C2semidirect
6. #30681708C2semidirect
7. #410×C263C2semidirect
56. #16862360D4semidirect
58. C2×C263⋊C8D4semidirect
64. C2×Q8×C263D4semidirect
66. C2×D4×C263D4semidirect
142. C263#2008semidirect
149. #410D263semidirect
184. C2×Q8D1052semidirect
195. C2×D4D1052semidirect

Maximal subgroups

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

subgroupindex
#306827362
C2×#225544952
#306825072
#306819562
#306819422
#306817082
#410×C2632
#2008263