Finite Group Databasebeta

← #15757069

Subgroups — #15757069

Order 3328.

364 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 107 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#13123773C211yesmaximal, characteristic
2#13115557C211yesmaximal, characteristic
3#13113336C211yesmaximal, characteristic
4#13113238C211yesmaximal, characteristic
5#13112737C211yesmaximal, characteristic
6#13112680C211yesmaximal, characteristic
7C13×#1570C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#423C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12#11718783—21no—
13#11718780—21no—
14C2×#88054—21no—
15C4×C4⋊Dic13C2211yescharacteristic
16#11718586C2211yescharacteristic
17C2×#88043C2211yescharacteristic
18#11718489—22no—
19#11718489—22no—
20C13×#334—22no—
21#11718142—21no—
22#11718076—22no—
23#11718059C412yes—
24#11718059C412yes—
25C2×C13×M16—21no—
26C22×C8×C13—21no—
27C2×C42×C13C2311yescharacteristic
28#88180—21no—
29C2×C4⋊Dic13—21no—
30#88178—21no—
31#88178C2×C412yes—
32C2×C4×Dic13—21no—
33C22×#1055D411yescharacteristic
34C22×#1055D411yescharacteristic
35#88124—21no—
36#88123Q811yescharacteristic
37#88123Q811yescharacteristic
38C4×Dic26—21no—
39C4×Dic26D412yes—
40C13×C4⋊C8—21no—
41C13×C4⋊C8—21no—
42C13×C4⋊C8—21no—
43C13×C4⋊C8—21no—
44C13×C4⋊C8D412yes—
45C13×C22⋊C8C2×C412yes—
46C4×C8×C13—21no—
47#88071C2×C411yescharacteristic
48#88071C2×C411yescharacteristic
49C22⋊#1055—21no—
50#88055—22no—
51#88054—24no—
52#88054—42no—
53C8×Dic13—22no—
54C4⋊#1055—21no—
55#88043—21no—
56#88043—21no—
57C4×#1055—21no—
58#8881—131nomaximal, Sylow
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13#4111yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C2×Dic26—21no—
65C2×Dic26C4⋊C412yes—
66C13×M16—41no—
67C13×M16—41no—
68C2×C8×C13—22no—
69C2×C8×C13—22no—
70C2×C8×C13—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C42×C13C2×D411yescharacteristic
74C42×C13C2×D411yescharacteristic
75C42×C13C2×Q811yescharacteristic
76C42×C13#4111yescharacteristic
77C22⋊Dic13—22no—
78C4⋊Dic13—21no—
79C4⋊Dic13—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13—42no—
82C4⋊Dic13C4⋊C412yes—
83#6101—22no—
84#6101—22no—
85C4×Dic13—22no—
86C4×Dic13—41no—
87C4×Dic13—41no—
88C2×#1055—21no—
89C2×#1055—21no—
90C2×#1055—21no—
91C2×#1055—21no—
92C2×#1055—21no—
93C2×#1055—41no—
94C2×#1055SD1612yes—
95#2961—131no—
96#1940—131no—
97#1570D1311yescharacteristic
98#1503—131no—
99#1481—131no—
100#1303—131no—
101#1281—131no—
102C23×C13C4×D411yescharacteristic
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13C2×C4⋊C411yescharacteristic
106C2×C4×C13C4×D411yescharacteristic
107C2×C4×C13#12011yescharacteristic
108C2×C4×C13C22⋊Q811yescharacteristic
109C2×C4×C13C22⋊Q811yescharacteristic
110C2×C4×C13#12311yescharacteristic
111C2×C4×C13C2×SD1611yescharacteristic
112C2×C4×C13#13511yescharacteristic
113C2×C4×C13#13711yescharacteristic
114C2×C4×C13#13711yescharacteristic
115C2×Dic13—22no—
116C2×Dic13—22no—
117C2×Dic13—22no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123Dic26—42no—
124Dic26—81no—
125C8×C13—42no—
126C8×C13—42no—
127C8×C13—81no—
128#1055—22no—
129#1055—41no—
130#1055—81no—
131#533—131no—
132#446—262no—
133#446—262no—
134#431—131no—
135#431C2×D1311yescharacteristic
136#424—261no—
137#423C2×D1311yescharacteristic
138C2×C4⋊C8—261no—
139C2×C4⋊C8C2×D1311yescharacteristic
140#405—261no—
141C2×#97—131no—
142C4×C4⋊C4—131no—
143#336—261no—
144#334—22no—
145#328—132no—
146#328—132no—
147Q8⋊C8—262no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13#38511yescharacteristic
151C22×C13C4×SD1611yescharacteristic
152C22×C13#44111yescharacteristic
153C4×C13—21no—
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—21no—
157C4×C13#44811yescharacteristic
158C4×C13#45211yescharacteristic
159C4×C13#47511yescharacteristic
160C4×C13#47911yescharacteristic
161Dic13—42no—
162Dic13—42no—
163Dic13—42no—
164Dic13—81no—
165C2×M16—21no—
166C22×C8—21no—
167C22×C8—131no—
168C22×C8—131no—
169C4⋊Q8—131no—
170C4⋊Q8—131no—
171#125—261no—
172C22⋊Q8—132no—
173C22⋊Q8—261no—
174C4×Q8—132no—
175C4×Q8—261no—
176#117—261no—
177C2×C4⋊C4—261no—
178C2×C42—261no—
179C2×C42C22×D1311yescharacteristic
180C4⋊C8—21no—
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8—21no—
184C4⋊C8—264no—
185C4⋊C8—261no—
186C4⋊C8—522no—
187C4⋊C8C22⋊D1312yes—
188C22⋊C8—261no—
189C22⋊C8C4×D1312yes—
190#97—262no—
191#97—261no—
192#97—261no—
193C4×C8—21no—
194C4×C8—262no—
195C4×C8—261no—
196#95—131no—
197#95—131no—
198C2×C13—21no—
199C2×C13—21no—
200C2×C13#186111yescharacteristic
201C2×C13#186511yescharacteristic
202C2×C13#186811yescharacteristic
203C2×Q8—132no—
204C2×Q8—261no—
205C22×C4—261no—
206C22×C4—261no—
207C22×C4C2×C4×D1311yescharacteristic
208C22×C4D4×D1311yescharacteristic
209C22×C4#613111yescharacteristic
210M16—41no—
211M16—41no—
212C2×C8—22no—
213C2×C8—22no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—132no—
218C2×C8—261no—
219C2×C8—261no—
220C2×C8—261no—
221C2×C8—261no—
222C2×C8—261no—
223C2×C8—521no—
224C4⋊C4—132no—
225C4⋊C4—262no—
226C4⋊C4—261no—
227C4⋊C4—261no—
228C4⋊C4—262no—
229C4⋊C4—261no—
230C4⋊C4—522no—
231C22⋊C4—262no—
232C42—262no—
233C42—521no—
234C42—521no—
235C42#612711yescharacteristic
236C42D4×D1311yescharacteristic
237C42Q8×D1311yescharacteristic
238C42C2×C22⋊D1311yescharacteristic
239C13#888111yescharacteristic, complemented, Sylow
240C23#8814711yescharacteristic
241Q8—522no—
242Q8—1041no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—521no—
249C2×C4—521no—
250C2×C4—521no—
251C2×C4—521no—
252C2×C4—521no—
253C2×C4C4⋊C4×D1311yescharacteristic
254C2×C4#8814811yescharacteristic
255C2×C4#8815011yescharacteristic
256C2×C4SD16×D1311yescharacteristic
257C2×C4#8816911yescharacteristic
258C2×C4#8816911yescharacteristic
259C2×C4#8817011yescharacteristic
260C2×C4C4×C22⋊D1311yescharacteristic
261C2×C4#8819111yescharacteristic
262C2×C4#8820011yescharacteristic
263C8—42no—
264C8—42no—
265C8—81no—
266C8—262no—
267C8—521no—
268C8—1041no—
269C22—21no—
270C22—21no—
271C22#1171851311yescharacteristic
272C22#1171851411yescharacteristic
273C22#1171865011yescharacteristic
274C4—21no—
275C4—21no—
276C4—21no—
277C4—21no—
278C4—522no—
279C4—522no—
280C4—522no—
281C4—1041no—
282C4#1171851511yescharacteristic
283C4#1171851811yescharacteristic
284C4#1171883111yescharacteristic
285C4#1171883411yescharacteristic
286C2—21no—
287C2—21no—
288C2#1311507311yescharacteristic
289C2#1311510111yescharacteristic
290C2#1311512011yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1570C2
socleC22×C13#385
prime radicalC23×C13C4×D4
cosocleC2×C42×C13C23
hypercenter#1570D13
hypocenterC13#8881
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
239. C13#8881semidirect

Maximal subgroups

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

subgroupindex
#131237732
#131155572
#131133362
#131132382
#131127372
#131126802
C13×#15702
#888113