Finite Group Databasebeta

← #15767584

Subgroups — #15767584

Order 3328.

322 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 93 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#13115679C211yesmaximal, characteristic
2#13115609C211yesmaximal, characteristic
3#13113608C211yesmaximal, characteristic
4#13113586C211yesmaximal, characteristic
5#13113509C211yesmaximal, characteristic
6C2×#11718078C211yesmaximal, characteristic
7C13×#1292C211yesmaximal, characteristic
8C2×#88123C2211yescharacteristic
9C13×#423C2211yescharacteristic
10C13×#423C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88064—21no—
13C2×#88064—21no—
14C2×#88062—21no—
15#11718586C2211yescharacteristic
16C2×C4⋊#1055C2211yescharacteristic
17C4×#6099C2211yescharacteristic
18#11718150—21no—
19#11718078—22no—
20#11718074—21no—
21#11718074—21no—
22#11718072—22no—
23#11718072—21no—
24#11718071—21no—
25C22×Dic26—21no—
26C2×C13×M16—21no—
27C2×C13×M16—21no—
28C22×C8×C13—21no—
29C2×C42×C13C2311yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13Q812yes—
32C2×#6099D411yescharacteristic
33C2×#6099D411yescharacteristic
34C22×#1055—21no—
35#88123—21no—
36#88123—21no—
37#88123—21no—
38#88123—21no—
39C13×C4⋊C8—21no—
40C13×C4⋊C8—21no—
41C13×C4⋊C8—21no—
42C13×C4⋊C8—21no—
43C13×C4⋊C8—21no—
44C13×C4⋊C8—21no—
45C22⋊#1055—21no—
46#88064—42no—
47#88064—42no—
48#88062—42no—
49C4⋊#1055—21no—
50C4⋊#1055D411yescharacteristic
51C4⋊#1055D412yes—
52C4⋊#1055D411yescharacteristic
53#88043—21no—
54C4×#1055—21no—
55C4×#1055—21no—
56#10608—131nomaximal, Sylow
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×Q811yescharacteristic
59C22×C4×C13#4111yescharacteristic
60C22×Dic13—22no—
61C2×Dic26—41no—
62C2×Dic26—41no—
63C2×Dic26—41no—
64C2×Dic26—41no—
65C2×Dic26—41no—
66C2×Dic26—41no—
67C13×M16—41no—
68C13×M16—41no—
69C13×M16—41no—
70C13×M16—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13—81no—
75C42×C13C2×D411yescharacteristic
76C42×C13C2×D411yescharacteristic
77C42×C13#4111yescharacteristic
78C42×C13#4111yescharacteristic
79C4⋊Dic13—22no—
80C4⋊Dic13—22no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83#6099—21no—
84#6099—21no—
85#6099—21no—
86#6099SD1612yes—
87C2×#1055—21no—
88C2×#1055—21no—
89C2×#1055—21no—
90C2×#1055—22no—
91C2×#1055—21no—
92C2×#1055—41no—
93C2×#1055—41no—
94#1966—131no—
95#1950—131no—
96#1570—131no—
97#1565—131no—
98#1546—131no—
99C2×#332—131no—
100#1292D1311yescharacteristic
101C23×C13C22⋊Q811yescharacteristic
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—41no—
105C2×C4×C13#12111yescharacteristic
106C2×C4×C13#12111yescharacteristic
107C2×C4×C13#12111yescharacteristic
108C2×C4×C13C22⋊Q811yescharacteristic
109C2×C4×C13C22⋊Q811yescharacteristic
110C2×C4×C13#12611yescharacteristic
111C2×C4×C13C2×SD1611yescharacteristic
112C2×C4×C13#13511yescharacteristic
113C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118Dic26—81no—
119Dic26—81no—
120Dic26—81no—
121Dic26—81no—
122C8×C13—81no—
123C8×C13—81no—
124C8×C13—81no—
125#1055—22no—
126#1055—42no—
127#1055—41no—
128#1055—41no—
129#1055—41no—
130C2×C4⋊Q8—131no—
131#431—131no—
132C2×#108—261no—
133#423C2×D1311yescharacteristic
134#423C2×D1311yescharacteristic
135C2×C4⋊C8—131no—
136C2×C4⋊C8C2×D1311yescharacteristic
137C2×#101—261no—
138C2×#101—261no—
139C4×M16—131no—
140#341—261no—
141#335—261no—
142#334—261no—
143#334—262no—
144#332—262no—
145#332—261no—
146#332—261no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13#39611yescharacteristic
150C22×C13#47611yescharacteristic
151C22×C13#47811yescharacteristic
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—21no—
155C4×C13#46011yescharacteristic
156C4×C13#46311yescharacteristic
157C4×C13#46511yescharacteristic
158C4×C13#46911yescharacteristic
159C4×C13#47111yescharacteristic
160C4×C13#47311yescharacteristic
161Dic13—82no—
162C22×Q8—261no—
163C2×M16—21no—
164C2×M16—21no—
165C2×M16—131no—
166C2×M16—131no—
167C22×C8—21no—
168C22×C8—261no—
169C4⋊Q8—261no—
170C4⋊Q8—261no—
171C4⋊Q8—261no—
172C4⋊Q8—261no—
173C2×C4⋊C4—132no—
174C2×C4⋊C4—261no—
175C2×C42C22×D1311yescharacteristic
176#108—522no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—21no—
180C4⋊C8—21no—
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8—132no—
184C4⋊C8—131no—
185C4⋊C8—131no—
186C4⋊C8—261no—
187#101—522no—
188#101—522no—
189C22⋊C8—261no—
190#97—261no—
191C4×C8—261no—
192C4×C8—261no—
193C2×C13—21no—
194C2×C13—21no—
195C2×C13#206411yescharacteristic
196C2×C13#206511yescharacteristic
197C2×C13#207011yescharacteristic
198C2×Q8—521no—
199C2×Q8—521no—
200C2×Q8—521no—
201C2×Q8—521no—
202C2×Q8—521no—
203C2×Q8—521no—
204C22×C4—262no—
205C22×C4#612711yescharacteristic
206C22×C4D4×D1311yescharacteristic
207C22×C4Q8×D1311yescharacteristic
208M16—41no—
209M16—41no—
210M16—41no—
211M16—41no—
212M16—132no—
213M16—261no—
214M16—261no—
215M16—261no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—81no—
220C2×C8—261no—
221C2×C8—261no—
222C2×C8—261no—
223C2×C8—261no—
224C2×C8—262no—
225C2×C8—521no—
226C2×C8—521no—
227C4⋊C4—262no—
228C4⋊C4—262no—
229C4⋊C4—521no—
230C4⋊C4—521no—
231C42#612711yescharacteristic
232C42#612711yescharacteristic
233C42D4×D1311yescharacteristic
234C42D4×D1311yescharacteristic
235C13#1060811yescharacteristic, complemented, Sylow
236C23#8815011yescharacteristic
237Q8—1041no—
238Q8—1041no—
239Q8—1041no—
240Q8—1041no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—522no—
245C2×C4—522no—
246C2×C4—522no—
247C2×C4#8813011yescharacteristic
248C2×C4#8813811yescharacteristic
249C2×C4#8813811yescharacteristic
250C2×C4#8813811yescharacteristic
251C2×C4#8815011yescharacteristic
252C2×C4#8815011yescharacteristic
253C2×C4#8816511yescharacteristic
254C2×C4SD16×D1311yescharacteristic
255C2×C4#8816811yescharacteristic
256C2×C4#8817311yescharacteristic
257C8—81no—
258C8—81no—
259C8—81no—
260C8—262no—
261C8—521no—
262C8—521no—
263C8—521no—
264C8—522no—
265C22—21no—
266C22—21no—
267C22#1171833711yescharacteristic
268C22#1171853111yescharacteristic
269C22#1171855211yescharacteristic
270C4—21no—
271C4—21no—
272C4—21no—
273C4—1042no—
274C4#1171840911yescharacteristic
275C4#1171841611yescharacteristic
276C4#1171842311yescharacteristic
277C4#1171844311yescharacteristic
278C4#1171846811yescharacteristic
279C4#1171848011yescharacteristic
280C2—21no—
281C2—21no—
282C2#1311620411yescharacteristic
283C2#1311621111yescharacteristic
284C2#1311623811yescharacteristic
subgroupG/H
centerC22#11718337
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1292C2
socleC22×C13#396
prime radicalC23×C13C22⋊Q8
hypercenter#1292D13
hypocenterC13#10608
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
235. C13#10608semidirect

Maximal subgroups

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

subgroupindex
#131156792
#131156092
#131136082
#131135862
#131135092
C2×#117180782
C13×#12922
#1060813