Finite Group Databasebeta

← #15764727

Subgroups — #15764727

Order 3328.

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

normal subgroups only

This group has 552 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#13125784C211yesmaximal, characteristic
2#13125378C211yesmaximal, characteristic
3#13115826C211yesmaximal, characteristic
4#13113521C211yesmaximal, characteristic
5#13113292C211yesmaximal, characteristic
6#13112673C211yesmaximal, characteristic
7C2×C13×#494C211yesmaximal, characteristic
8C22×C13×Q16—22no—
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11#11719175C2211yescharacteristic
12C13×#494—22no—
13C13×#494—22no—
14C2×C4×C8×C13C2211yescharacteristic
15#11718889—22no—
16#11718753—21no—
17#11718751—22no—
18#11718742—21no—
19#11718741—22no—
20#11718740—21no—
21#11718739—21no—
22#11718625—22no—
23#11718586C2211yescharacteristic
24#11718585C2211yescharacteristic
25C4×#6099C2211yescharacteristic
26#11718139—22no—
27#11718122—22no—
28#11718048—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13D412yes—
31C2×C13×Q16—28no—
32C2×C13×Q16—48no—
33C22×C8×C13—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8D412yes—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C42×C13C2311yescharacteristic
47C2×#6107—24no—
48#88180—21no—
49#88178—21no—
50#88178—21no—
51C2×#6099—21no—
52C2×#6099D412yes—
53#88124—21no—
54#88123D411yescharacteristic
55#88123D411yescharacteristic
56C4×Dic26—21no—
57C4×Dic26—21no—
58C4×C8×C13—21no—
59C4×C8×C13D412yes—
60#88075—24no—
61C22⋊#1055—21no—
62#88048—24no—
63#88047—24no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055D412yes—
67#88043—21no—
68C4×#1055—21no—
69C4×#1055—21no—
70#10155—131nomaximal, Sylow
71C2×Q8×C13—22no—
72C2×Q8×C13—22no—
73C2×Q8×C13—22no—
74C2×Q8×C13—44no—
75C2×Q8×C13—44no—
76C2×Q8×C13—41no—
77C22×C4×C13—22no—
78C22×C4×C13—41no—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C2×Dic26—21no—
83C2×Dic26—21no—
84C13×Q16—416no—
85C2×C8×C13—24no—
86C2×C8×C13—22no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13C2×D411yescharacteristic
99C22⋊Dic13—41no—
100#6107—84no—
101C4⋊Dic13—21no—
102C4⋊Dic13—21no—
103C4⋊Dic13—21no—
104C4⋊Dic13—21no—
105#6101—41no—
106#6101—41no—
107C4×Dic13—41no—
108#6099—22no—
109#6099—42no—
110#6099Q1614yescomplemented
111C2×#1055—22no—
112C2×#1055—22no—
113C2×#1055—41no—
114#3209—131no—
115#3165—131no—
116C2×#494D1311yescharacteristic
117#1997—131no—
118#1549—131no—
119#1493—131no—
120#1278—131no—
121C23×C13#12111yescharacteristic
122Q8×C13—44no—
123Q8×C13—44no—
124Q8×C13—44no—
125Q8×C13—82no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—82no—
131C2×C4×C13—82no—
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12011yescharacteristic
134C2×C4×C13#12011yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12711yescharacteristic
138C2×C4×C13C2×Q1612yes—
139C2×C4×C13#13712yes—
140C2×Dic13—41no—
141C2×Dic13—41no—
142Dic26—42no—
143Dic26—42no—
144C8×C13—24no—
145#1055—24no—
146#1055—42no—
147#1055—81no—
148C22×Q16—22no—
149#533—131no—
150C2×C4⋊Q8C2×D1311yescharacteristic
151C2×C4⋊Q8C2×D1311yescharacteristic
152#501—262no—
153#500—261no—
154#498—261no—
155#494—22no—
156#494—22no—
157#494—261no—
158#487—261no—
159#462—262no—
160#451—262no—
161#431—131no—
162#428—262no—
163#423—131no—
164C4×M16—131no—
165C2×C4×C8C2×D1311yescharacteristic
166#343—262no—
167#332—262no—
168Q8⋊C8—262no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13#39211yescharacteristic
172C22×C13#46212yes—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—82no—
176C4×C13—82no—
177C4×C13#45112yes—
178C4×C13#45312yes—
179C4×C13#47312yes—
180C4×C13#49411yescharacteristic
181C4×C13#49711yescharacteristic
182Dic13—81no—
183Dic13—81no—
184C22×Q8—21no—
185C22×Q8C22⋊D1312yes—
186C2×Q16—28no—
187C2×Q16—48no—
188C2×Q16—264no—
189C2×M16—132no—
190C2×M16—261no—
191C22×C8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—131no—
200C4⋊Q8—131no—
201C4⋊Q8C22⋊D1312yes—
202#125—261no—
203C22⋊Q8—261no—
204C22⋊Q8—261no—
205C4×Q8—261no—
206C4×Q8—261no—
207#117—261no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C42C22×D1311yescharacteristic
213#107—264no—
214#106—264no—
215C4⋊C8—132no—
216C4⋊C8—261no—
217C4⋊C8—261no—
218#103—264no—
219C22⋊C8—261no—
220#97—261no—
221C4×C8—21no—
222C4×C8—261no—
223C4×C8—261no—
224C4×C8C22⋊D1312yes—
225C2×C13—22no—
226C2×C13#200211yescharacteristic
227C2×C13#201611yescharacteristic
228C2×C13#202011yescharacteristic
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—22no—
232C2×Q8—44no—
233C2×Q8—44no—
234C2×Q8—41no—
235C2×Q8—261no—
236C2×Q8—261no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4D4×D1311yescharacteristic
240C22×C4#612911yescharacteristic
241C22×C4C2×C22⋊D1311yescharacteristic
242Q16—416no—
243Q16—1044no—
244M16—134no—
245M16—262no—
246M16—522no—
247C2×C8—24no—
248C2×C8—22no—
249C2×C8—262no—
250C2×C8—262no—
251C2×C8—521no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C22⋊C4—521no—
267C42—521no—
268C42D4×D1311yescharacteristic
269C42D4×D1311yescharacteristic
270C42C2×C22⋊D1311yescharacteristic
271C42C2×C22⋊D1311yescharacteristic
272C13#1015511yescharacteristic, complemented, Sylow
273C23#8819311yescharacteristic
274Q8—44no—
275Q8—44no—
276Q8—44no—
277Q8—82no—
278Q8—522no—
279Q8—522no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4Q16×D1312yes—
289C2×C4#8817212yes—
290C2×C4#8819111yescharacteristic
291C2×C4#8819111yescharacteristic
292C2×C4#8819211yescharacteristic
293C2×C4#8819311yescharacteristic
294C2×C4#8819411yescharacteristic
295C2×C4#8820711yescharacteristic
296C8—24no—
297C8—264no—
298C8—522no—
299C8—1041no—
300C22—21no—
301C22—21no—
302C22#1171884312yes—
303C22#1171888411yescharacteristic
304C4—21no—
305C4—21no—
306C4—82no—
307C4—82no—
308C4—1041no—
309C4—1041no—
310C4#1171873812yes—
311C4#1171884211yescharacteristic
312C4#1171884712yes—
313C4#1171885111yescharacteristic
314C4#1171885312yes—
315C2—22no—
316C2#1311585111yescharacteristic
317C2#1311593411yescharacteristic
318C2#1311595511yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#494C2
socleC22×C13#392
prime radicalC23×C13#121
hypercenterC2×#494D13
hypocenterC13#10155
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
110. #6099Q16semidirect
272. C13#10155semidirect

Maximal subgroups

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

subgroupindex
#131257842
#131253782
#131158262
#131135212
#131132922
#131126732
C2×C13×#4942
#1015513