Finite Group Databasebeta

← #15776748

Subgroups — #15776748

Order 3328.

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

normal subgroups only

This group has 350 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#13117063C211yesmaximal, characteristic, complemented
2#13116983C211yesmaximal, characteristic, complemented
3#13114235C211yesmaximal, characteristic, complemented
4#13112885C211yesmaximal, characteristic, complemented
5#13112797C211yesmaximal, characteristic, complemented
6D4⋊#6090C211yesmaximal, characteristic, complemented
7C13×#3283C211yesmaximal, characteristic
8C2×C13×#135—21no—
9C13×#547—21no—
10C13×#494C2211yescharacteristic
11C13×#467—21no—
12C13×#461—21no—
13C13×#452—22no—
14C4×C13×D8C2211yescharacteristic
15C8×D4×C13C2211yescharacteristic
16#11718669—21no—
17#11718343C2211yescharacteristic
18#11718156—22no—
19#11718154—21no—
20#11718082—21no—
21#11718073—21no—
22C4⋊#6090C2211yescharacteristic
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×#41—22no—
26C13×#135—42no—
27C13×#135—42no—
28C2×C13×Q16—21no—
29C2×C13×Q16D412yes—
30C2×C13×SD16—22no—
31C2×C13×D8D411yescharacteristic
32C22×C8×C13—21no—
33C13×C4⋊Q8—21no—
34C13×#123—42no—
35C13×C22⋊Q8—22no—
36C13×#121—41no—
37C4×D4×C13—21no—
38C4×D4×C13D411yescharacteristic
39C2×C13×C4⋊C4—41no—
40#88123—21no—
41C13×#107D411yescharacteristic
42C13×C4⋊C8D411yescharacteristic
43C13×#103—22no—
44C13×#102—21no—
45C13×C22⋊C8—21no—
46C4×C8×C13C2311yescharacteristic
47#88072—41no—
48#88058—21no—
49#88058—21no—
50C2×#6090—21no—
51C2×#6090—21no—
52#88048—41no—
53C4⋊#1055—21no—
54#12375—131nomaximal, Sylow
55C13×#41—44no—
56C13×#41—82no—
57C2×Q8×C13—22no—
58C2×D4×C13—21no—
59C2×D4×C13—42no—
60C2×D4×C13D811yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13—42no—
63C22×C4×C13—41no—
64C2×Dic26—41no—
65C13×Q16—42no—
66C13×Q16—41no—
67C13×Q16—41no—
68C13×SD16—44no—
69C13×D8—21no—
70C13×D8SD1612yes—
71C2×C8×C13—21no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13C2×D411yescharacteristic
75C2×C8×C13C2×D411yescharacteristic
76C13×C4⋊C4—21no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4D811yescharacteristic
81C13×C22⋊C4—21no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—41no—
84C42×C13C2×D411yescharacteristic
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87C2×#1055—41no—
88#6090—41no—
89#6090—41no—
90#3283D1311yescharacteristic
91#2241—131no—
92#2226—131no—
93#1675—131no—
94#1362—131no—
95#1331—131no—
96D4⋊C16—131no—
97C23×C13—21no—
98C23×C13—41no—
99Q8×C13—42no—
100Q8×C13—42no—
101D4×C13—22no—
102D4×C13—21no—
103D4×C13—21no—
104D4×C13—41no—
105D4×C13—84no—
106C2×C4×C13—21no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—84no—
112C2×C4×C13—81no—
113C2×C4×C13—81no—
114C2×C4×C13#12011yescharacteristic
115C2×C4×C13C2×D811yescharacteristic
116C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
117C2×Dic13—81no—
118Dic26—161no—
119C8×C13—21no—
120C8×C13—41no—
121C8×C13C2×SD1611yescharacteristic
122C8×C13AGL(1,ℤ/8)11yescharacteristic
123#1055—81no—
124C2×#135—21no—
125#547—21no—
126#500—131no—
127#494C2×D1311yescharacteristic
128#476—261no—
129#467—21no—
130#461—21no—
131#452—22no—
132C4×D8C2×D1311yescharacteristic
133C8×D4C2×D1311yescharacteristic
134#367—261no—
135C4⋊C16—131no—
136#358—262no—
137#357—261no—
138C4×C16—131no—
139#335—131no—
140#333—261no—
141C22×C13—41no—
142C22×C13—42no—
143C22×C13—41no—
144C22×C13—41no—
145C22×C13—81no—
146C22×C13—81no—
147C22×C13#44711yescharacteristic
148C4×C13—21no—
149C4×C13—41no—
150C4×C13—82no—
151C4×C13—81no—
152C4×C13#45011yescharacteristic
153C4×C13#45511yescharacteristic
154C4×C13#50811yescharacteristic
155C4×C13#51011yescharacteristic
156Dic13—161no—
157C2×#41—22no—
158#135—42no—
159#135—42no—
160C2×Q16—21no—
161C2×Q16C22⋊D1312yes—
162C2×SD16—22no—
163C2×D8C22⋊D1311yescharacteristic
164C22×C8—21no—
165C4⋊Q8—21no—
166C4⋊Q8—261no—
167#123—42no—
168C22⋊Q8—22no—
169#121—41no—
170C4×D4—21no—
171C4×D4C22⋊D1311yescharacteristic
172C2×C4⋊C4—41no—
173C2×C16—261no—
174C2×C16—261no—
175#107—261no—
176#107—261no—
177#107C22⋊D1311yescharacteristic
178#106—521no—
179C4⋊C8—261no—
180C4⋊C8C22⋊D1311yescharacteristic
181#103—22no—
182#102—21no—
183#102—521no—
184C22⋊C8—21no—
185C4×C8C22×D1311yescharacteristic
186C2×C13—81no—
187C2×C13—82no—
188C2×C13#163911yescharacteristic
189C2×C13#218911yescharacteristic
190C2×C13#219311yescharacteristic
191#41—44no—
192#41—82no—
193C2×Q8—22no—
194C2×Q8—521no—
195C2×D4—21no—
196C2×D4—42no—
197C2×D4#610411yescharacteristic
198C22×C4—21no—
199C22×C4—42no—
200C22×C4—41no—
201Q16—42no—
202Q16—41no—
203Q16—41no—
204SD16—44no—
205D8—21no—
206D8#610512yes—
207C2×C8—21no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—521no—
211C2×C8C2×C22⋊D1311yescharacteristic
212C2×C8C2×C22⋊D1311yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—521no—
218C4⋊C4—521no—
219C4⋊C4#610411yescharacteristic
220C22⋊C4—21no—
221C22⋊C4—42no—
222C22⋊C4—41no—
223C42C2×C22⋊D1311yescharacteristic
224C16—521no—
225C16—521no—
226C13#1237511yescharacteristic, complemented, Sylow
227C23—21no—
228C23—41no—
229Q8—42no—
230Q8—42no—
231Q8—2081no—
232D4—21no—
233D4—21no—
234D4—22no—
235D4—41no—
236D4—84no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—84no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—1041no—
246C2×C4C2×#610411yescharacteristic
247C2×C4#8818611yescharacteristic
248C2×C4#8820711yescharacteristic
249C8—21no—
250C8—41no—
251C8—1041no—
252C8#8818611yescharacteristic
253C8C2×#610511yescharacteristic
254C22—41no—
255C22—41no—
256C22—41no—
257C22—42no—
258C22—81no—
259C22—81no—
260C22#1171887811yescharacteristic
261C4—21no—
262C4—41no—
263C4—81no—
264C4—82no—
265C4—2081no—
266C4#1171885511yescharacteristic
267C4#1171885611yescharacteristic
268C4#1171887911yescharacteristic
269C4#1171890311yescharacteristic
270C2—81no—
271C2—82no—
272C2#1311401511yescharacteristic
273C2#1311677611yescharacteristic
274C2#1311680011yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
Fitting, prime radicalC13×#3283C2
socleC22×C13#447
hypercenter#3283D13
hypocenterC13#12375
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. #13117063C2semidirect
2. #13116983C2semidirect
3. #13114235C2semidirect
4. #13112885C2semidirect
5. #13112797C2semidirect
6. D4⋊#6090C2semidirect
226. C13#12375semidirect

Maximal subgroups

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

subgroupindex
#131170632
#131169832
#131142352
#131128852
#131127972
D4⋊#60902
C13×#32832
#1237513