Finite Group Databasebeta

← #46783792

Subgroups — #46783792

Order 33664.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22554501C211yesmaximal, characteristic, complemented
2#30682516C211yesmaximal, characteristic
3C2×#22554397C211yesmaximal, characteristic, complemented
4C2×#22554396C211yesmaximal, characteristic, complemented
5#30681845C211yesmaximal, characteristic, complemented
6#30681706C211yesmaximal, characteristic, complemented
7C2×#137×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554501—22no—
10#22554501—22no—
11C2×#16862366—21no—
12C2×#16862363—21no—
13C2×#16862360C2211yescharacteristic
14#22554449—21no—
15#22554446—21no—
16#22554444—21no—
17#22554442—22no—
18#22554441—21no—
19C2×C4⋊Dic263C2211yescharacteristic
20C2×C4×Dic263C2211yescharacteristic
21#22554397—22no—
22#22554396—22no—
23C263⋊#95—22no—
24C2×#41×C263C2211yescharacteristic
25C22×Q8×C263C2211yescharacteristic
26#137×C263—22no—
27#137×C263—22no—
28C2×Q16×C263—21no—
29C2×SD16×C263—21no—
30C2×M16×C263C2211yescharacteristic
31#16862376—21no—
32#16862376—21no—
33#16862376—21no—
34#16862376—21no—
35C2×Dic526D411yescharacteristic
36C2×D1052D411yescharacteristic
37C2×C22⋊D263—22no—
38C2×C22⋊D263—21no—
39C22×Dic263—21no—
40C22×Dic263D412yes—
41C2×C4×D263—21no—
42#16862366—24no—
43#16862363—24no—
44#16862360—21no—
45#16862360D412yescomplemented
46C2×C263⋊C8—21no—
47C4⋊Dic263—21no—
48C4⋊Dic263—21no—
49Dic263⋊C4—22no—
50C22⋊Dic263—22no—
51(C2×D263)⋊C4—22no—
52C4×Dic263—21no—
53C4×Dic263—21no—
54#41×C263—21no—
55#41×C263—21no—
56#41×C263—21no—
57#41×C263—21no—
58C2×Q8×C263—21no—
59C2×Q8×C263—21no—
60C2×Q8×C263—21no—
61C2×Q8×C263—21no—
62C2×Q8×C263—21no—
63C2×Q8×C263D411yescharacteristic
64C2×Q8×C263D412yescomplemented
65C2×D4×C263—21no—
66C2×D4×C263D411yescharacteristic
67C22×C4×C263—21no—
68C22×C4×C263—21no—
69C22×C4×C263C2311yescharacteristic
70Q16×C263—24no—
71SD16×C263—24no—
72M16×C263—21no—
73M16×C263D412yescomplemented
74C2×C8×C263—21no—
75C22×D263—21no—
76Dic526—21no—
77Dic526—21no—
78D1052—21no—
79D1052—21no—
80C22⋊D263—41no—
81C22⋊D263—41no—
82C22⋊D263—82no—
83C2×Dic263—22no—
84C2×Dic263—22no—
85C2×Dic263—21no—
86C2×Dic263—41no—
87C2×Dic263—41no—
88C2×Dic263—42no—
89C4×D263—41no—
90C4×D263—41no—
91C263⋊C8—22no—
92C23×C263—21no—
93C23×C263C2×D411yescharacteristic
94Q8×C263—22no—
95Q8×C263—21no—
96Q8×C263—22no—
97Q8×C263—21no—
98Q8×C263—41no—
99Q8×C263—41no—
100D4×C263—21no—
101D4×C263—21no—
102D4×C263—41no—
103D4×C263—41no—
104C2×C4×C263—21no—
105C2×C4×C263—22no—
106C2×C4×C263—41no—
107C2×C4×C263—41no—
108C2×C4×C263—41no—
109C2×C4×C263—41no—
110C2×C4×C263C2×D411yescharacteristic
111C2×C4×C263C2×D411yescharacteristic
112C2×C4×C263C2×D411yescharacteristic
113C2×C4×C263C2×D411yescharacteristic
114C2×C4×C263C2×D411yescharacteristic
115C2×C4×C263#4111yescharacteristic
116C8×C263—22no—
117C22×C263—21no—
118C22×C263—21no—
119C22×C263—41no—
120C22×C263—41no—
121C22×C263—41no—
122C22×C263#12011yescharacteristic
123C22×C263#12111yescharacteristic
124C22×C263#12711yescharacteristic
125C2×D263—41no—
126C2×D263—41no—
127C2×D263—41no—
128C4×C263—41no—
129C4×C263—42no—
130C4×C263#12011yescharacteristic
131C4×C263#12011yescharacteristic
132C4×C263#12111yescharacteristic
133C4×C263#12111yescharacteristic
134Dic263—42no—
135Dic263—41no—
136Dic263—42no—
137C2×C263—21no—
138C2×C263—21no—
139C2×C263—81no—
140C2×C263#39211yescharacteristic
141C2×C263#45511yescharacteristic
142C2×C263#45611yescharacteristic
143D263—81no—
144C263#200711yescharacteristic, complemented, Sylow
145#2007—2631nomaximal, Sylow
146C2×#137—2631no—
147C2×#137D26311yescharacteristic, complemented
148#537—2631no—
149C2×#104—2631no—
150C2×#104—2631no—
151#391—2631no—
152#343—2631no—
153C2×#41—2631no—
154C2×#41C2×D26311yescharacteristic
155C22×Q8C2×D26311yescharacteristic
156#137—22no—
157#137—22no—
158#137—5262no—
159#137—5262no—
160C2×Q16—21no—
161C2×Q16—5261no—
162C2×SD16—21no—
163C2×SD16—5261no—
164C2×M16—2631no—
165C2×M16C2×D26311yescharacteristic
166C22⋊Q8—5261no—
167C22⋊Q8—5261no—
168#121—5261no—
169#121—5262no—
170#121—5261no—
171C2×C4⋊C4—2631no—
172C2×C42—2631no—
173#104—5262no—
174#104—5262no—
175#95—5262no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—21no—
180#41—5261no—
181#41—5261no—
182#41—5261no—
183#41—5261no—
184C2×Q8—21no—
185C2×Q8—21no—
186C2×Q8—21no—
187C2×Q8—21no—
188C2×Q8—21no—
189C2×Q8—2631no—
190C2×Q8C22⋊D26311yescharacteristic
191C2×Q8C22⋊D26312yescomplemented
192C2×D4—21no—
193C2×D4—2631no—
194C2×D4—5261no—
195C2×D4—5262no—
196C2×D4C22⋊D26311yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—2632no—
200C22×C4—5261no—
201C22×C4—5261no—
202C22×C4C22×D26311yescharacteristic
203Q16—24no—
204Q16—5264no—
205SD16—24no—
206SD16—5264no—
207M16—21no—
208M16—2632no—
209M16—5261no—
210M16C22⋊D26312yescomplemented
211C2×C8—21no—
212C2×C8—5261no—
213C4⋊C4—5262no—
214C4⋊C4—5261no—
215C4⋊C4—5261no—
216C22⋊C4—5262no—
217C22⋊C4—5262no—
218C42—5261no—
219C42—5261no—
220C23—21no—
221C23—5261no—
222C23D4×D26311yescharacteristic
223Q8—22no—
224Q8—22no—
225Q8—21no—
226Q8—21no—
227Q8—41no—
228Q8—41no—
229Q8—5261no—
230Q8—5261no—
231D4—21no—
232D4—21no—
233D4—41no—
234D4—41no—
235D4—5261no—
236D4—5261no—
237D4—10521no—
238D4—10521no—
239D4—21042no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—5262no—
247C2×C4—5262no—
248C2×C4—5261no—
249C2×C4—10521no—
250C2×C4—10521no—
251C2×C4—10521no—
252C2×C4—10521no—
253C2×C4—10522no—
254C2×C4D4×D26311yescharacteristic
255C2×C4D4×D26311yescharacteristic
256C2×C4C2×C22⋊D26311yescharacteristic
257C2×C4C2×C22⋊D26311yescharacteristic
258C2×C4C2×C22⋊D26311yescharacteristic
259C2×C4#1686237511yescharacteristic
260C8—22no—
261C8—5262no—
262C22—21no—
263C22—21no—
264C22—41no—
265C22—41no—
266C22—41no—
267C22—10521no—
268C22—10521no—
269C22—10521no—
270C22#2255443811yescharacteristic
271C22#2255444211yescharacteristic
272C22#2255446611yescharacteristic
273C4—41no—
274C4—42no—
275C4—10522no—
276C4—10522no—
277C4—10521no—
278C4#2255443811yescharacteristic
279C4#2255443911yescharacteristic
280C4#2255444111yescharacteristic
281C4#2255444211yescharacteristic
282C2—21no—
283C2—21no—
284C2—81no—
285C2—21041no—
286C2#3068184611yescharacteristic
287C2#3068211411yescharacteristic
288C2#3068211911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#137×C263C2
socleC22×C263#120
prime radical#30682516C2
hypercenterC2×#137D263
hypocenterC263#2007
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#22554501C2semidirect
3. C2×#22554397C2semidirect
4. C2×#22554396C2semidirect
5. #30681845C2semidirect
6. #30681706C2semidirect
7. C2×#137×C263C2semidirect
45. #16862360D4semidirect
64. C2×Q8×C263D4semidirect
73. M16×C263D4semidirect
144. C263#2007semidirect
147. C2×#137D263semidirect
191. C2×Q8C22⋊D263semidirect
210. M16C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225545012
#306825162
C2×#225543972
C2×#225543962
#306818452
#306817062
C2×#137×C2632
#2007263