Finite Group Databasebeta

← #46783797

Subgroups — #46783797

Order 33664.

380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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×#22554495C211yesmaximal, characteristic, complemented
2#30682502C211yesmaximal, characteristic, complemented
3#30681955C211yesmaximal, characteristic, complemented
4#30681944C211yesmaximal, characteristic, complemented
5#30681912C211yesmaximal, characteristic, complemented
6#30681709C211yesmaximal, characteristic, complemented
7#575×C263C211yesmaximal, characteristic, complemented
8C22×D1052C2211yescharacteristic
9#22554495—22no—
10#22554495—22no—
11C2×#16862363—21no—
12C2×#16862361—21no—
13C2×#16862360C2211yescharacteristic
14#22554466—21no—
15#22554459—21no—
16#22554444—22no—
17#22554438—22no—
18#22554429C2211yescharacteristic
19#22554429C2211yescharacteristic
20#22554397—22no—
21#22554392—22no—
22#22554385—22no—
23C2×#41×C263C2211yescharacteristic
24C2×#41×C263C2211yescharacteristic
25#137×C263—21no—
26#137×C263—21no—
27AGL(1,ℤ/8)×C263—21no—
28AGL(1,ℤ/8)×C263—21no—
29#135×C263—22no—
30C2×M16×C263C2211yescharacteristic
31C23×D263—21no—
32C2×D1052—21no—
33C2×D1052—21no—
34C2×D1052—21no—
35C2×D1052—21no—
36C2×D1052—21no—
37C2×D1052D412yes—
38C2×C22⋊D263—24no—
39#16862363—24no—
40#16862361—24no—
41#16862360—21no—
42#16862360D412yescomplemented
43C2×C263⋊C8—21no—
44C4⋊Dic263—21no—
45C4⋊Dic263—21no—
46C22⋊Dic263—21no—
47C22⋊Dic263D412yes—
48(C2×D263)⋊C4—24no—
49C4×Dic263—21no—
50C4×Dic263—21no—
51#41×C263—21no—
52#41×C263—21no—
53#41×C263—21no—
54#41×C263—21no—
55#41×C263—21no—
56#41×C263—21no—
57#41×C263—21no—
58#41×C263—21no—
59C2×Q8×C263D411yescharacteristic
60C2×Q8×C263D411yescharacteristic, complemented
61C2×D4×C263—21no—
62C2×D4×C263—21no—
63C2×D4×C263D411yescharacteristic
64C2×D4×C263D411yescharacteristic, complemented
65C22×C4×C263—21no—
66C22×C4×C263—21no—
67C22×C4×C263C2311yescharacteristic
68Q16×C263—22no—
69SD16×C263—22no—
70SD16×C263—22no—
71D8×C263—22no—
72M16×C263—21no—
73M16×C263—21no—
74C2×C8×C263D412yescomplemented
75C22×D263—22no—
76C22×D263—41no—
77C22×D263—41no—
78C22×D263—82no—
79D1052—22no—
80D1052—22no—
81D1052—41no—
82D1052—41no—
83C22⋊D263—84no—
84C2×Dic263—22no—
85C2×Dic263—41no—
86C263⋊C8—22no—
87C23×C263—21no—
88C23×C263—21no—
89C23×C263C2×D411yescharacteristic
90Q8×C263—21no—
91Q8×C263—21no—
92Q8×C263—21no—
93Q8×C263—21no—
94D4×C263—21no—
95D4×C263—21no—
96D4×C263—21no—
97D4×C263—21no—
98D4×C263—41no—
99D4×C263—41no—
100D4×C263—41no—
101D4×C263—41no—
102C2×C4×C263—21no—
103C2×C4×C263—21no—
104C2×C4×C263—41no—
105C2×C4×C263—41no—
106C2×C4×C263—41no—
107C2×C4×C263—41no—
108C2×C4×C263C2×D411yescharacteristic
109C2×C4×C263C2×D411yescharacteristic
110C2×C4×C263C2×D411yescharacteristic
111C2×C4×C263C2×D411yescharacteristic
112C2×C4×C263C2×D411yescharacteristic
113C2×C4×C263#4111yescharacteristic
114C8×C263—22no—
115C22×C263—41no—
116C22×C263—42no—
117C22×C263—41no—
118C22×C263—41no—
119C22×C263—81no—
120C22×C263#12011yescharacteristic
121C22×C263#12111yescharacteristic
122C22×C263#12711yescharacteristic
123C2×D263—44no—
124C2×D263—42no—
125C2×D263—82no—
126C2×D263—82no—
127C4×C263—41no—
128C4×C263—41no—
129C4×C263#12011yescharacteristic
130C4×C263#12011yescharacteristic
131C4×C263#12111yescharacteristic
132C4×C263#12111yescharacteristic
133Dic263—42no—
134Dic263—81no—
135C2×C263—21no—
136C2×C263—21no—
137C2×C263—21no—
138C2×C263—81no—
139C2×C263—81no—
140C2×C263#39211yescharacteristic
141D263—82no—
142C263#200811yescharacteristic, complemented, Sylow
143#2008—2631nomaximal, Sylow
144#575D26311yescharacteristic, complemented
145C2×AGL(1,ℤ/8)—2631no—
146#535—2631no—
147#421—2631no—
148#418—2631no—
149#410—2631no—
150#344—2631no—
151C2×#41C2×D26311yescharacteristic
152C2×#41C2×D26311yescharacteristic
153C22×D4—2631no—
154#137—21no—
155#137—21no—
156AGL(1,ℤ/8)—21no—
157AGL(1,ℤ/8)—21no—
158AGL(1,ℤ/8)—5262no—
159AGL(1,ℤ/8)—5262no—
160#135—22no—
161C2×SD16—5261no—
162C2×D8—5261no—
163C2×M16—2631no—
164C2×M16C2×D26311yescharacteristic
165#127—5261no—
166#124—5261no—
167#121—5262no—
168#120—5262no—
169#117—2631no—
170#117—2631no—
171#104—5262no—
172#102—5262no—
173#99—5262no—
174C24—5261no—
175#41—21no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—21no—
180#41—21no—
181#41—21no—
182#41—21no—
183C2×Q8C22⋊D26311yescharacteristic
184C2×Q8C22⋊D26311yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—2632no—
188C2×D4—5264no—
189C2×D4—5261no—
190C2×D4—5261no—
191C2×D4—5261no—
192C2×D4—5261no—
193C2×D4—5261no—
194C2×D4C22⋊D26311yescharacteristic
195C2×D4C22⋊D26311yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—21no—
198C22×C4C22×D26311yescharacteristic
199Q16—22no—
200SD16—22no—
201SD16—22no—
202SD16—5264no—
203D8—22no—
204D8—5264no—
205M16—21no—
206M16—21no—
207M16—2632no—
208M16—5261no—
209C2×C8—5261no—
210C2×C8C22⋊D26312yescomplemented
211C4⋊C4—5261no—
212C4⋊C4—5261no—
213C22⋊C4—2632no—
214C22⋊C4—5264no—
215C22⋊C4—5261no—
216C42—5261no—
217C42—5261no—
218C23—21no—
219C23—21no—
220C23—5262no—
221C23—10521no—
222C23—10521no—
223C23—21042no—
224C23D4×D26311yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—21no—
228Q8—21no—
229D4—21no—
230D4—21no—
231D4—21no—
232D4—21no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—41no—
237D4—5262no—
238D4—5262no—
239D4—10521no—
240D4—10521no—
241D4—21044no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—5262no—
249C2×C4—10521no—
250C2×C4D4×D26311yescharacteristic
251C2×C4D4×D26311yescharacteristic
252C2×C4C2×C22⋊D26311yescharacteristic
253C2×C4C2×C22⋊D26311yescharacteristic
254C2×C4C2×C22⋊D26311yescharacteristic
255C2×C4#1686237511yescharacteristic
256C8—22no—
257C8—5262no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22—41no—
262C22—81no—
263C22—10524no—
264C22—10522no—
265C22—21042no—
266C22—21042no—
267C22#2255443811yescharacteristic
268C22#2255444211yescharacteristic
269C22#2255446611yescharacteristic
270C4—41no—
271C4—41no—
272C4—10522no—
273C4—21041no—
274C4#2255443811yescharacteristic
275C4#2255443911yescharacteristic
276C4#2255444111yescharacteristic
277C4#2255444211yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—81no—
282C2—81no—
283C2—21042no—
284C2#3068184611yescharacteristic
subgroupG/H
centerC2#30681846
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#575×C263C2
socleC2×C263#392
hypercenter#575D263
hypocenterC263#2008
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C2×#22554495C2semidirect
2. #30682502C2semidirect
3. #30681955C2semidirect
4. #30681944C2semidirect
5. #30681912C2semidirect
6. #30681709C2semidirect
7. #575×C263C2semidirect
42. #16862360D4semidirect
60. C2×Q8×C263D4semidirect
64. C2×D4×C263D4semidirect
74. C2×C8×C263D4semidirect
142. C263#2008semidirect
144. #575D263semidirect
184. C2×Q8C22⋊D263semidirect
195. C2×D4C22⋊D263semidirect
210. C2×C8C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544952
#306825022
#306819552
#306819442
#306819122
#306817092
#575×C2632
#2008263