Finite Group Databasebeta

← #15776120

Subgroups — #15776120

Order 3328.

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

normal subgroups only

This group has 396 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#13117014C212yesmaximal, complemented
2#13116259C211yesmaximal, characteristic, complemented
3#13112845C212yesmaximal, complemented
4#13112760C211yesmaximal, characteristic, complemented
5C13×#3186C211yesmaximal, characteristic
6C2×C13×#121—21no—
7C13×#480—22no—
8C13×#466—21no—
9C13×#466C2212yes—
10C13×#447—22no—
11C2×C13×C22⋊C8C2211yescharacteristic
12#11718873—21no—
13C2×#88058C2211yescharacteristic, complemented
14#11718154—22no—
15#11718143—21no—
16#11718143C2211yescharacteristic, complemented
17C22⋊#6090C2212yescomplemented
18#11718081—22no—
19C22×D4×C13—21no—
20C22×D4×C13—41no—
21C23×C4×C13D411yescharacteristic
22C2×C13×D8—21no—
23C2×C13×D8D412yes—
24C22×C8×C13D411yescharacteristic
25C22×C8×C13C2311yescharacteristic
26C13×#121—22no—
27C13×#121—22no—
28C13×#121—41no—
29C13×#121—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C22⋊C4—41no—
32C2×C22⋊Dic13—41no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C13×#107—21no—
36C13×#107D412yes—
37C13×#102—22no—
38C13×#102—22no—
39C13×C22⋊C8—22no—
40#88071—41no—
41#88058—22no—
42C2×#6090—22no—
43#12278—131nomaximal, Sylow
44C24×C13—41no—
45C24×C13D811yescharacteristic
46C2×D4×C13—22no—
47C2×D4×C13—41no—
48C2×D4×C13—42no—
49C2×D4×C13—42no—
50C2×D4×C13—81no—
51C2×D4×C13—81no—
52C2×D4×C13—82no—
53C2×D4×C13—82no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—41no—
57C22×C4×C13—41no—
58C22×C4×C13—41no—
59C22×C4×C13D811yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×Dic13—41no—
62C22×Dic13—41no—
63C13×D8—42no—
64C13×D8—81no—
65C2×C8×C13—21no—
66C2×C8×C13—41no—
67C2×C8×C13—41no—
68C2×C8×C13C2×D412yes—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—41no—
71C13×C22⋊C4—42no—
72C13×C22⋊C4—42no—
73C22⋊Dic13—82no—
74C4⋊Dic13—41no—
75C4⋊Dic13—41no—
76C4⋊Dic13—41no—
77C4⋊Dic13—41no—
78#6090—42no—
79#3186D1311yescharacteristic
80#2232—132no—
81#2075—131no—
82#1347—132no—
83#1314—131no—
84C23×C13—21no—
85C23×C13—21no—
86C23×C13—41no—
87C23×C13—41no—
88C23×C13—42no—
89C23×C13—82no—
90C23×C13—82no—
91C23×C13—82no—
92C23×C13D1612yes—
93C23×C13C2×D811yescharacteristic
94D4×C13—42no—
95D4×C13—42no—
96D4×C13—82no—
97D4×C13—84no—
98D4×C13—82no—
99D4×C13—82no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—81no—
108C2×C4×C13—82no—
109C2×C4×C13#12011yescharacteristic
110C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
111C2×Dic13—81no—
112C2×Dic13—81no—
113C2×Dic13—81no—
114C2×Dic13—81no—
115C2×Dic13—81no—
116C2×Dic13—81no—
117C8×C13—22no—
118C8×C13—41no—
119C2×#121—21no—
120#480—22no—
121#466—21no—
122#466C2×D1312yes—
123#447—22no—
124C2×#107—131no—
125C2×C22⋊C8C2×D1311yescharacteristic
126#380—261no—
127#366—262no—
128#357—262no—
129C22⋊C16—132no—
130#340—131no—
131#340—261no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—22no—
135C22×C13—42no—
136C22×C13—41no—
137C22×C13—41no—
138C22×C13—81no—
139C22×C13—82no—
140C22×C13—82no—
141C22×C13—82no—
142C22×C13—164no—
143C22×C13#44711yescharacteristic
144C22×C13C2×D1611yescharacteristic
145C22×C13#50911yescharacteristic
146C4×C13—21no—
147C4×C13—41no—
148C4×C13—82no—
149C4×C13#45511yescharacteristic
150C4×C13#45811yescharacteristic
151Dic13—161no—
152Dic13—161no—
153C22×D4—21no—
154C22×D4—41no—
155C23×C4C22⋊D1311yescharacteristic
156C2×D8—21no—
157C2×D8C22⋊D1312yes—
158C22×C8C22⋊D1311yescharacteristic
159C22×C8C22×D1311yescharacteristic
160#121—22no—
161#121—22no—
162#121—41no—
163#121—41no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—261no—
166C2×C4⋊C4—261no—
167C2×C22⋊C4—41no—
168C2×C22⋊C4—521no—
169C2×C16—262no—
170#107—21no—
171#107—262no—
172#107C22⋊D1312yes—
173#102—22no—
174#102—22no—
175C22⋊C8—22no—
176#95—521no—
177C2×C13—21no—
178C2×C13—21no—
179C2×C13—42no—
180C2×C13—162no—
181C2×C13#160711yescharacteristic
182C2×C13#218411yescharacteristic
183C2×C13#219111yescharacteristic
184C24—41no—
185C24#610411yescharacteristic
186C2×D4—22no—
187C2×D4—41no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4—81no—
191C2×D4—81no—
192C2×D4—82no—
193C2×D4—82no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—521no—
200C22×C4—521no—
201C22×C4#610411yescharacteristic
202C22×C4C2×C22⋊D1311yescharacteristic
203D8—42no—
204D8—81no—
205C2×C8—21no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8C2×C22⋊D1312yes—
209C4⋊C4—22no—
210C4⋊C4—41no—
211C4⋊C4—521no—
212C4⋊C4—521no—
213C4⋊C4—521no—
214C4⋊C4—521no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C22⋊C4—1042no—
218C16—522no—
219C13#1227811yescharacteristic, complemented, Sylow
220C23—21no—
221C23—21no—
222C23—41no—
223C23—41no—
224C23—42no—
225C23—82no—
226C23—82no—
227C23—82no—
228C23#8806612yes—
229C23C2×#610411yescharacteristic
230D4—42no—
231D4—42no—
232D4—82no—
233D4—84no—
234D4—82no—
235D4—82no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—81no—
244C2×C4—82no—
245C2×C4—1041no—
246C2×C4—1041no—
247C2×C4—1041no—
248C2×C4—1041no—
249C2×C4—1041no—
250C2×C4—1041no—
251C2×C4#8818611yescharacteristic
252C2×C4#8820711yescharacteristic
253C8—22no—
254C8—41no—
255C22—21no—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—81no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—164no—
266C22C2×#8806611yescharacteristic
267C22#1171880811yescharacteristic
268C22#1171887811yescharacteristic
269C4—21no—
270C4—41no—
271C4—82no—
272C4—2081no—
273C4—2081no—
274C4#1171890311yescharacteristic
275C4#1171890411yescharacteristic
276C2—21no—
277C2—21no—
278C2—42no—
279C2—162no—
280C2#1311382211yescharacteristic
281C2#1311674811yescharacteristic
282C2#1311678711yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
Fitting, prime radicalC13×#3186C2
socleC22×C13#447
hypercenter#3186D13
hypocenterC13#12278
LCSG ▷ C22×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #3186

Complements

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

NH ≅ G/Ntype
1. #13117014C2semidirect
2. #13116259C2semidirect
3. #13112845C2semidirect
4. #13112760C2semidirect
13. C2×#88058C22semidirect
16. #11718143C22semidirect
17. C22⋊#6090C22semidirect
219. C13#12278semidirect

Maximal subgroups

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

subgroupindex
#131170142
#131162592
#131128452
#131127602
C13×#31862
#1227813