Finite Group Databasebeta

← #15765641

Subgroups — #15765641

Order 3328.

504 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 109 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#13125984C211yesmaximal, characteristic
2#13123213C211yesmaximal, characteristic
3#13115814C211yesmaximal, characteristic
4#13113521C211yesmaximal, characteristic
5#13113520C211yesmaximal, characteristic
6#13112668C211yesmaximal, characteristic
7C13×#3230C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C13×#500—21no—
12C13×#487—21no—
13C13×#484—22no—
14C13×#477—22no—
15C13×#431C2211yescharacteristic
16#11718891—22no—
17#11718742—21no—
18#11718739—21no—
19#11718705—22no—
20#11718682—22no—
21#11718638—22no—
22#11718635—22no—
23C42×Dic13C2211yescharacteristic
24#11718586C2211yescharacteristic
25#11718585C2211yescharacteristic
26#11718139—22no—
27#11718124—22no—
28#11718074—22no—
29C22×Q8×C13—21no—
30C22×Dic26—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8D411yescharacteristic
36C13×C4⋊Q8D411yescharacteristic
37C13×#125—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C13×#117—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4D412yes—
45C2×C42×C13C2311yescharacteristic
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13D412yes—
48C2×C4×Dic13—21no—
49C2×C4×Dic13—21no—
50C2×C4×Dic13D412yes—
51C2×#6099—21no—
52#88123—21no—
53#88123—21no—
54#88123—21no—
55#88123—21no—
56C13×#107—24no—
57C13×C4⋊C8D412yes—
58C13×#103—24no—
59C13×C22⋊C8—21no—
60C4×C8×C13—21no—
61#88075—24no—
62#88071—28no—
63C22⋊#1055—21no—
64#88047—24no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055D412yes—
68C4×#1055—21no—
69#10295—131nomaximal, Sylow
70C2×Q8×C13—21no—
71C2×Q8×C13—21no—
72C2×Q8×C13—44no—
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C22×C4×C13—22no—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—22no—
80C22×Dic13—22no—
81C2×Dic26—44no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C2×C8×C13—22no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C22⋊C4—41no—
96C42×C13—41no—
97C42×C13C2×D411yescharacteristic
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13#4111yescharacteristic
101C4⋊Dic13—22no—
102C4⋊Dic13—22no—
103C4⋊Dic13—41no—
104C4⋊Dic13—41no—
105C4×Dic13—22no—
106C4×Dic13—42no—
107C4×Dic13—42no—
108C4×Dic13Q1614yes—
109#6099—42no—
110C2×#1055—22no—
111C2×#1055—41no—
112#3230—131no—
113#3230D1311yescharacteristic
114#2862—131no—
115#1994—131no—
116#1549—131no—
117#1549—131no—
118#1276—131no—
119C23×C13#12011yescharacteristic
120Q8×C13—42no—
121Q8×C13—42no—
122Q8×C13—82no—
123Q8×C13—82no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—44no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12011yescharacteristic
132C2×C4×C13#12111yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12711yescharacteristic
136C2×C4×C13C2×Q1612yes—
137C2×C4×C13#13712yes—
138C2×Dic13—24no—
139C2×Dic13—42no—
140C2×Dic13—42no—
141C2×Dic13—44no—
142C2×Dic13—42no—
143Dic26—82no—
144Dic26—82no—
145C8×C13—42no—
146#1055—42no—
147#1055—81no—
148#533C2×D1311yescharacteristic
149C2×C4⋊Q8—131no—
150C2×C4⋊Q8C2×D1311yescharacteristic
151#500—21no—
152#500—261no—
153#487—21no—
154#487—261no—
155#484—22no—
156#484—262no—
157#477—22no—
158#477—262no—
159#431—131no—
160#431C2×D1311yescharacteristic
161#423—131no—
162#391—262no—
163#391—262no—
164#382—262no—
165C43—131no—
166#339—262no—
167#332—262no—
168#332—262no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13#39211yescharacteristic
172C22×C13#45112yes—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—82no—
176C4×C13—81no—
177C4×C13—81no—
178C4×C13#45412yes—
179C4×C13#45412yes—
180C4×C13#46212yes—
181C4×C13#49411yescharacteristic
182C4×C13#49711yescharacteristic
183Dic13—44no—
184Dic13—82no—
185C22×Q8—21no—
186C22×Q8—261no—
187C2×M16—261no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—261no—
193C4⋊Q8—261no—
194C4⋊Q8—261no—
195C4⋊Q8—261no—
196C4⋊Q8C22⋊D1311yescharacteristic
197C4⋊Q8C22⋊D1311yescharacteristic
198#125—21no—
199C22⋊Q8—21no—
200C22⋊Q8—21no—
201C4×Q8—21no—
202C4×Q8—21no—
203#117—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—132no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4C22⋊D1312yes—
208C2×C42—132no—
209C2×C42—261no—
210C2×C42—261no—
211C2×C42C22×D1311yescharacteristic
212#107—24no—
213#107—264no—
214C4⋊C8—132no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217C4⋊C8C22⋊D1312yes—
218#103—24no—
219#103—264no—
220C22⋊C8—21no—
221C22⋊C8—261no—
222C4×C8—21no—
223C4×C8—261no—
224#95—268no—
225C2×C13—22no—
226C2×C13#200311yescharacteristic
227C2×C13#200311yescharacteristic
228C2×C13#201611yescharacteristic
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—44no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—524no—
235C2×Q8—521no—
236C2×Q8—521no—
237C22×C4—22no—
238C22×C4—262no—
239C22×C4—262no—
240C22×C4D4×D1311yescharacteristic
241C22×C4D4×D1311yescharacteristic
242C22×C4C2×C22⋊D1311yescharacteristic
243M16—522no—
244C2×C8—22no—
245C2×C8—262no—
246C2×C8—521no—
247C4⋊C4—21no—
248C4⋊C4—22no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—22no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—262no—
258C4⋊C4—262no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C22⋊C4—41no—
262C42—41no—
263C42—134no—
264C42—262no—
265C42—522no—
266C42—522no—
267C42D4×D1311yescharacteristic
268C42#612911yescharacteristic
269C42C2×C22⋊D1311yescharacteristic
270C42C2×C22⋊D1311yescharacteristic
271C13#1029511yescharacteristic, complemented, Sylow
272C23#8819111yescharacteristic
273Q8—42no—
274Q8—42no—
275Q8—82no—
276Q8—82no—
277Q8—1042no—
278Q8—1042no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—44no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—264no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—524no—
289C2×C4—522no—
290C2×C4Q16×D1312yes—
291C2×C4#8817212yes—
292C2×C4#8819111yescharacteristic
293C2×C4#8819211yescharacteristic
294C2×C4#8819311yescharacteristic
295C2×C4#8819311yescharacteristic
296C2×C4#8819411yescharacteristic
297C2×C4#8820711yescharacteristic
298C8—42no—
299C8—522no—
300C8—1041no—
301C22—21no—
302C22—21no—
303C22#1171884712yes—
304C22#1171888411yescharacteristic
305C4—21no—
306C4—21no—
307C4—82no—
308C4—81no—
309C4—81no—
310C4—524no—
311C4—1042no—
312C4#1171884211yescharacteristic
313C4#1171884312yes—
314C4#1171885111yescharacteristic
315C4#1171886212yes—
316C4#1171890612yes—
317C2—22no—
318C2#1311585511yescharacteristic
319C2#1311585611yescharacteristic
320C2#1311593411yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3230C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#3230D13
hypocenterC13#10295
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
271. C13#10295semidirect

Maximal subgroups

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

subgroupindex
#131259842
#131232132
#131158142
#131135212
#131135202
#131126682
C13×#32302
#1029513