Finite Group Databasebeta

← #15776532

Subgroups — #15776532

Order 3328.

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

normal subgroups only

This group has 318 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
1#13117061C211yesmaximal, characteristic, complemented
2#13116871C211yesmaximal, characteristic, complemented
3#13114191C211yesmaximal, characteristic, complemented
4#13112894C211yesmaximal, characteristic, complemented
5#13112797C211yesmaximal, characteristic, complemented
6D4⋊#6090C211yesmaximal, characteristic, complemented
7C13×#3341C211yesmaximal, characteristic, complemented
8C13×#555—21no—
9C13×#500C2211yescharacteristic
10C13×#482—22no—
11C13×#476—21no—
12C13×#466—21no—
13C4×C13×D8C2211yescharacteristic
14C8×D4×C13C2211yescharacteristic
15C13×#427—21no—
16C2×#88066—21no—
17#11718676—21no—
18#11718356C2211yescharacteristic
19#11718083—22no—
20#11718083—21no—
21#11718077—21no—
22C4⋊#6090C2211yescharacteristic
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×D8D411yescharacteristic
26C22×C8×C13—21no—
27C13×C4⋊Q8—21no—
28C13×#124—42no—
29C13×#121—22no—
30C13×#121—41no—
31C4×D4×C13—21no—
32C4×D4×C13D411yescharacteristic
33C13×#117—22no—
34C13×#117—41no—
35C2×#6104—41no—
36C2×D104—21no—
37C2×D104—21no—
38#88128—21no—
39C13×#107—21no—
40C13×#107D411yescharacteristic
41C13×#107D412yes—
42C13×#106—22no—
43C13×C4⋊C8D411yescharacteristic
44C13×#102—22no—
45C13×#102—21no—
46C13×C22⋊C8—21no—
47C4×C8×C13C2311yescharacteristic
48#88066—42no—
49C2×#6090—21no—
50C2×#6090—21no—
51#88049—41no—
52C4⋊#1055—21no—
53#12343—131nomaximal, Sylow
54C2×Q8×C13—41no—
55C2×D4×C13—21no—
56C2×D4×C13—42no—
57C2×D4×C13D811yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—41no—
60C2×D52—41no—
61C2×D52—41no—
62C2×D52—41no—
63C13×D8—21no—
64C13×D8—21no—
65C2×C8×C13—21no—
66C2×C8×C13—41no—
67C2×C8×C13—41no—
68C2×C8×C13C2×D411yescharacteristic
69C2×C8×C13C2×D411yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4—22no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4D811yescharacteristic
74C13×C22⋊C4—21no—
75C13×C22⋊C4—42no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—41no—
78C42×C13—42no—
79C42×C13C2×D411yescharacteristic
80#6104—82no—
81C2×#1055—41no—
82D104—42no—
83D104—41no—
84D104—41no—
85#6090—41no—
86#6090—41no—
87#3341D1311yescharacteristic, complemented
88#2240—131no—
89#2206—131no—
90#1667—131no—
91#1365—131no—
92#1331—131no—
93D4⋊C16—131no—
94C23×C13—21no—
95C23×C13—41no—
96C22×D13—81no—
97Q8×C13—161no—
98D4×C13—21no—
99D4×C13—21no—
100D4×C13—41no—
101D4×C13—41no—
102D4×C13—162no—
103C2×C4×C13—21no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—81no—
109C2×C4×C13—81no—
110C2×C4×C13#12011yescharacteristic
111C2×C4×C13C2×D811yescharacteristic
112C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
113D52—81no—
114D52—81no—
115D52—81no—
116D52—81no—
117D52—161no—
118C8×C13—21no—
119C8×C13—41no—
120C8×C13#13511yescharacteristic
121C8×C13AGL(1,ℤ/8)11yescharacteristic
122#1055—81no—
123#555—21no—
124C2×D16—261no—
125#500C2×D1311yescharacteristic
126#493—131no—
127#482—22no—
128#476—21no—
129#466—21no—
130#459—261no—
131C4×D8C2×D1311yescharacteristic
132C8×D4C2×D1311yescharacteristic
133#427—21no—
134C4⋊C16—131no—
135#357—261no—
136#357—262no—
137C4×C16—131no—
138#335—131no—
139#331—261no—
140C22×C13—41no—
141C22×C13—41no—
142C22×C13—41no—
143C22×C13—81no—
144C22×C13—81no—
145C22×C13—81no—
146C22×C13#44711yescharacteristic
147C2×D13—161no—
148C2×D13—161no—
149C2×D13—161no—
150C4×C13—21no—
151C4×C13—41no—
152C4×C13—81no—
153C4×C13—82no—
154C4×C13#44911yescharacteristic
155C4×C13#45411yescharacteristic
156C4×C13#50811yescharacteristic
157C4×C13#50911yescharacteristic
158C2×D8—261no—
159C2×D8—261no—
160C2×D8—521no—
161C2×D8C22⋊D1311yescharacteristic
162C22×C8—21no—
163C4⋊Q8—21no—
164#127—261no—
165#124—42no—
166#121—22no—
167#121—41no—
168C4×D4—21no—
169C4×D4C22⋊D1311yescharacteristic
170#117—22no—
171#117—41no—
172D16—522no—
173C2×C16—261no—
174C2×C16—261no—
175#107—21no—
176#107C22⋊D1311yescharacteristic
177#107C22⋊D1312yes—
178#106—22no—
179C4⋊C8—261no—
180C4⋊C8C22⋊D1311yescharacteristic
181#102—22no—
182#102—21no—
183#102—521no—
184C22⋊C8—21no—
185C4×C8C22×D1311yescharacteristic
186C2×C13—81no—
187C2×C13—161no—
188C2×C13#162511yescharacteristic
189C2×C13#218611yescharacteristic
190C2×C13#219211yescharacteristic
191D13—321no—
192C2×Q8—41no—
193C2×D4—21no—
194C2×D4—42no—
195C2×D4—521no—
196C2×D4—521no—
197C2×D4—521no—
198C2×D4#610411yescharacteristic
199C22×C4—21no—
200C22×C4—41no—
201D8—21no—
202D8—21no—
203D8—522no—
204D8—521no—
205D8—521no—
206D8—1042no—
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—22no—
215C4⋊C4—41no—
216C4⋊C4#610411yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—42no—
219C22⋊C4—42no—
220C22⋊C4—41no—
221C42—42no—
222C42C2×C22⋊D1311yescharacteristic
223C16—521no—
224C16—521no—
225C13#1234311yescharacteristic, complemented, Sylow
226C23—21no—
227C23—41no—
228C23—1041no—
229Q8—161no—
230D4—21no—
231D4—21no—
232D4—41no—
233D4—41no—
234D4—162no—
235D4—1041no—
236D4—1041no—
237D4—1041no—
238D4—1041no—
239D4—2081no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4C2×#610411yescharacteristic
248C2×C4#8818611yescharacteristic
249C2×C4#8820711yescharacteristic
250C8—21no—
251C8—41no—
252C8—1041no—
253C8#8820311yescharacteristic
254C8#8820411yescharacteristic
255C22—41no—
256C22—41no—
257C22—41no—
258C22—81no—
259C22—81no—
260C22—81no—
261C22—2081no—
262C22—2081no—
263C22—2081no—
264C22#1171887811yescharacteristic
265C4—21no—
266C4—41no—
267C4—81no—
268C4—82no—
269C4#1171885411yescharacteristic
270C4#1171885511yescharacteristic
271C4#1171889911yescharacteristic
272C4#1171890611yescharacteristic
273C2—81no—
274C2—161no—
275C2—4161no—
276C2#1311392511yescharacteristic
277C2#1311675911yescharacteristic
278C2#1311679311yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#3341C2
socleC22×C13#447
hypercenter#3341D13
hypocenterC13#12343
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #3341

Complements

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

NH ≅ G/Ntype
1. #13117061C2semidirect
2. #13116871C2semidirect
3. #13114191C2semidirect
4. #13112894C2semidirect
5. #13112797C2semidirect
6. D4⋊#6090C2semidirect
7. C13×#3341C2semidirect
87. #3341D13semidirect
225. C13#12343semidirect

Maximal subgroups

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

subgroupindex
#131170612
#131168712
#131141912
#131128942
#131127972
D4⋊#60902
C13×#33412
#1234313