Finite Group Databasebeta

← #15776455

Subgroups — #15776455

Order 3328.

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

normal subgroups only

This group has 362 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
1#13117091C211yesmaximal, characteristic, complemented
2#13116881C211yesmaximal, characteristic, complemented
3#13114206C211yesmaximal, characteristic, complemented
4#13112882C211yesmaximal, characteristic, complemented
5Q8⋊#6090C211yesmaximal, characteristic, complemented
6#13112797C211yesmaximal, characteristic, complemented
7C13×#3391C211yesmaximal, characteristic
8C13×#550—21no—
9C13×#493—21no—
10C13×#493C2211yescharacteristic
11C13×#459—22no—
12C13×#459—21no—
13C8×Q8×C13C2211yescharacteristic
14C4×C13×D8—21no—
15C4×C13×D8C2211yescharacteristic
16C2×#88067—22no—
17C2×#88067—21no—
18#11718681—21no—
19#11718360C2211yescharacteristic
20#11718084—21no—
21#11718074—21no—
22C4⋊#6090C2211yescharacteristic
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×#41—41no—
26C2×C13×D8—22no—
27C2×C13×D8—21no—
28C2×C13×D8D411yescharacteristic
29C2×C13×D8D412yes—
30C13×#127—22no—
31C13×#127—21no—
32C13×#121—42no—
33C13×#121—41no—
34C4×Q8×C13D411yescharacteristic
35C4×D4×C13—22no—
36C4×D4×C13—21no—
37C2×Dic52—21no—
38C2×Dic52—21no—
39#88123—21no—
40C13×#107D411yescharacteristic
41C13×C4⋊C8—21no—
42C13×C4⋊C8D411yescharacteristic
43C13×#102—22no—
44C13×#102—21no—
45C4×C8×C13—21no—
46C4×C8×C13C2311yescharacteristic
47#88075—41no—
48#88067—44no—
49#88067—42no—
50C2×#6090—21no—
51C2×#6090—21no—
52#88048—41no—
53C4⋊#1055—21no—
54#12332—131nomaximal, Sylow
55C13×#41—82no—
56C13×#41—82no—
57C2×Q8×C13D811yescharacteristic
58C2×D4×C13—21no—
59C2×D4×C13—22no—
60C2×D4×C13—42no—
61C2×D4×C13—42no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C22×C4×C13—42no—
65C22×C4×C13—41no—
66C2×Dic26—41no—
67C13×D8—21no—
68C13×D8—21no—
69C13×D8—42no—
70C13×D8—41no—
71C13×D8—41no—
72C13×D8—82no—
73C2×C8×C13—21no—
74C2×C8×C13C2×D411yescharacteristic
75C2×C8×C13C2×D411yescharacteristic
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4D811yescharacteristic
79C13×C22⋊C4—42no—
80C13×C22⋊C4—41no—
81C42×C13—21no—
82C42×C13C2×D411yescharacteristic
83C4⋊Dic13—41no—
84C4⋊Dic13—41no—
85C2×#1055—41no—
86Dic52—42no—
87Dic52—41no—
88Dic52—41no—
89#6090—22no—
90#6090—41no—
91#3391D1311yescharacteristic
92#2248—131no—
93#2208—131no—
94#1670—131no—
95#1361—131no—
96Q8⋊C16—131no—
97#1331—131no—
98C23×C13—42no—
99C23×C13—41no—
100Q8×C13—21no—
101Q8×C13SD3212yescomplemented
102D4×C13—41no—
103D4×C13—42no—
104D4×C13—42no—
105D4×C13—41no—
106D4×C13—84no—
107D4×C13—81no—
108D4×C13—81no—
109D4×C13—161no—
110D4×C13—162no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—41no—
114C2×C4×C13—84no—
115C2×C4×C13—81no—
116C2×C4×C13—81no—
117C2×C4×C13#12011yescharacteristic
118C2×C4×C13C2×D811yescharacteristic
119C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
120C2×Dic13—81no—
121Dic26—81no—
122Dic26—81no—
123C8×C13—21no—
124C8×C13—41no—
125C8×C13#13511yescharacteristic
126C8×C13AGL(1,ℤ/8)11yescharacteristic
127#1055—81no—
128#550—21no—
129C2×SD32—261no—
130C2×SD32—262no—
131#494—131no—
132#493—21no—
133#493C2×D1311yescharacteristic
134#475—261no—
135#459—22no—
136#459—21no—
137C8×Q8C2×D1311yescharacteristic
138C4×D8—21no—
139C4×D8C2×D1311yescharacteristic
140C4⋊C16—131no—
141#358—261no—
142C4×C16—131no—
143#335—131no—
144#332—261no—
145C22×C13—81no—
146C22×C13—82no—
147C22×C13—82no—
148C22×C13—81no—
149C22×C13—82no—
150C22×C13—81no—
151C22×C13#44711yescharacteristic
152C4×C13—22no—
153C4×C13—21no—
154C4×C13—41no—
155C4×C13—81no—
156C4×C13#44911yescharacteristic
157C4×C13#45311yescharacteristic
158C4×C13C2×SD3211yescharacteristic
159C4×C13#50911yescharacteristic
160Dic13—161no—
161C2×#41—41no—
162C2×Q16—261no—
163C2×Q16—261no—
164C2×D8—22no—
165C2×D8—21no—
166C2×D8C22⋊D1311yescharacteristic
167C2×D8C22⋊D1312yes—
168C4⋊Q8—261no—
169#127—22no—
170#127—21no—
171#121—42no—
172#121—41no—
173C4×Q8C22⋊D1311yescharacteristic
174C4×D4—22no—
175C4×D4—21no—
176SD32—524no—
177SD32—522no—
178C2×C16—261no—
179C2×C16—261no—
180#107C22⋊D1311yescharacteristic
181#106—521no—
182C4⋊C8—21no—
183C4⋊C8—261no—
184C4⋊C8C22⋊D1311yescharacteristic
185#103—521no—
186#102—22no—
187#102—21no—
188C4×C8—21no—
189C4×C8C22×D1311yescharacteristic
190C2×C13—161no—
191C2×C13—162no—
192C2×C13#162111yescharacteristic
193C2×C13#218711yescharacteristic
194C2×C13#219411yescharacteristic
195#41—82no—
196#41—82no—
197C2×Q8—521no—
198C2×Q8#610411yescharacteristic
199C2×D4—21no—
200C2×D4—22no—
201C2×D4—42no—
202C2×D4—42no—
203C2×D4—41no—
204C2×D4—41no—
205C22×C4—42no—
206C22×C4—41no—
207Q16—522no—
208Q16—521no—
209Q16—521no—
210D8—21no—
211D8—21no—
212D8—42no—
213D8—41no—
214D8—41no—
215D8—82no—
216C2×C8—21no—
217C2×C8—521no—
218C2×C8C2×C22⋊D1311yescharacteristic
219C2×C8C2×C22⋊D1311yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—521no—
223C4⋊C4—521no—
224C4⋊C4#610411yescharacteristic
225C22⋊C4—42no—
226C22⋊C4—41no—
227C42—21no—
228C42C2×C22⋊D1311yescharacteristic
229C16—262no—
230C16—521no—
231C13#1233211yescharacteristic, complemented, Sylow
232C23—42no—
233C23—41no—
234Q8—21no—
235Q8—1041no—
236Q8—1041no—
237Q8#8806712yescomplemented
238D4—41no—
239D4—42no—
240D4—42no—
241D4—41no—
242D4—84no—
243D4—81no—
244D4—81no—
245D4—161no—
246D4—162no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—84no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—1041no—
254C2×C4C2×#610411yescharacteristic
255C2×C4#8818611yescharacteristic
256C2×C4#8820711yescharacteristic
257C8—21no—
258C8—41no—
259C8—1041no—
260C8#8820311yescharacteristic
261C8#8820411yescharacteristic
262C22—81no—
263C22—82no—
264C22—82no—
265C22—81no—
266C22—82no—
267C22—81no—
268C22#1171887811yescharacteristic
269C4—22no—
270C4—21no—
271C4—41no—
272C4—81no—
273C4—2081no—
274C4#1171880811yescharacteristic
275C4C2×#8806711yescharacteristic
276C4#1171889911yescharacteristic
277C4#1171890211yescharacteristic
278C2—161no—
279C2—162no—
280C2#1311390111yescharacteristic
281C2#1311676511yescharacteristic
282C2#1311680711yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
Fitting, prime radicalC13×#3391C2
socleC22×C13#447
hypercenter#3391D13
hypocenterC13#12332
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3391

Complements

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

NH ≅ G/Ntype
1. #13117091C2semidirect
2. #13116881C2semidirect
3. #13114206C2semidirect
4. #13112882C2semidirect
5. Q8⋊#6090C2semidirect
6. #13112797C2semidirect
101. Q8×C13SD32semidirect
231. C13#12332semidirect
237. Q8#88067semidirect

Maximal subgroups

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

subgroupindex
#131170912
#131168812
#131142062
#131128822
Q8⋊#60902
#131127972
C13×#33912
#1233213