Finite Group Databasebeta

← #15764797

Subgroups — #15764797

Order 3328.

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

normal subgroups only

This group has 476 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#13125987C211yesmaximal, characteristic
2#13125378C211yesmaximal, characteristic
3#13115826C211yesmaximal, characteristic
4#13113517C211yesmaximal, characteristic
5#13113292C211yesmaximal, characteristic
6#13112673C211yesmaximal, characteristic
7C2×C13×#500C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10#11719175C2211yescharacteristic
11C13×#500—22no—
12C13×#500—22no—
13C2×C13×#107—22no—
14C2×C4×C8×C13C2211yescharacteristic
15#11718754—21no—
16#11718752—22no—
17#11718741—22no—
18#11718740—21no—
19#11718739—21no—
20#11718739—21no—
21#11718631—22no—
22#11718625—22no—
23#11718586C2211yescharacteristic
24#11718585C2211yescharacteristic
25C4×#6099C2211yescharacteristic
26#11718138—22no—
27#11718122—22no—
28#11718048—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13—21no—
31C22×C8×C13—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8D412yes—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4D412yes—
44C2×C42×C13C2311yescharacteristic
45#88180—21no—
46#88178—21no—
47#88178—21no—
48C2×#6099—21no—
49C2×#6099D412yes—
50#88124—21no—
51#88123D411yescharacteristic
52#88123D411yescharacteristic
53C4×Dic26—21no—
54C4×Dic26—21no—
55C13×#107—28no—
56C4×C8×C13—21no—
57C4×C8×C13D412yes—
58C22⋊#1055—21no—
59#88050—24no—
60#88048—24no—
61#88047—24no—
62#88047—24no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055D412yes—
66#88043—21no—
67C4×#1055—21no—
68C4×#1055—21no—
69#10165—131nomaximal, Sylow
70C2×Q8×C13—22no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C2×Q8×C13—82no—
75C2×Q8×C13—82no—
76C22×C4×C13—22no—
77C22×C4×C13—41no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C2×Dic26—21no—
82C2×Dic26—21no—
83C2×C8×C13—24no—
84C2×C8×C13—22no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—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—
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C22⋊Dic13—41no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102#6101—41no—
103#6101—41no—
104C4×Dic13—41no—
105#6099—22no—
106#6099—42no—
107#6099Q1614yes—
108C2×#1055—22no—
109C2×#1055—22no—
110C2×#1055—41no—
111#3230—131no—
112#3165—131no—
113C2×#500D1311yescharacteristic
114#1997—131no—
115#1548—131no—
116#1493—131no—
117#1278—131no—
118C23×C13#12111yescharacteristic
119Q8×C13—82no—
120Q8×C13—82no—
121Q8×C13—82no—
122Q8×C13—82no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—82no—
128C2×C4×C13—82no—
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12011yescharacteristic
132C2×C4×C13#12111yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12711yescharacteristic
135C2×C4×C13C2×Q1612yes—
136C2×C4×C13#13712yes—
137C2×Dic13—41no—
138C2×Dic13—41no—
139Dic26—42no—
140Dic26—42no—
141C8×C13—24no—
142#1055—24no—
143#1055—42no—
144#1055—81no—
145#533—131no—
146C2×C4⋊Q8C2×D1311yescharacteristic
147C2×C4⋊Q8C2×D1311yescharacteristic
148#501—262no—
149#500—22no—
150#500—22no—
151#500—261no—
152#500—261no—
153#498—261no—
154#487—261no—
155#484—262no—
156#477—262no—
157#431—131no—
158#428—262no—
159C2×#107—22no—
160#423—131no—
161C4×M16—131no—
162C2×C4×C8C2×D1311yescharacteristic
163#343—262no—
164#333—262no—
165Q8⋊C8—262no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13#39211yescharacteristic
169C22×C13#46212yes—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—82no—
173C4×C13—82no—
174C4×C13#45112yes—
175C4×C13#45612yes—
176C4×C13#47212yes—
177C4×C13#49411yescharacteristic
178C4×C13#49711yescharacteristic
179Dic13—81no—
180Dic13—81no—
181C22×Q8—21no—
182C22×Q8—21no—
183C2×M16—132no—
184C2×M16—261no—
185C22×C8—21no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—131no—
194C4⋊Q8—131no—
195C4⋊Q8C22⋊D1312yes—
196#125—261no—
197C22⋊Q8—261no—
198C22⋊Q8—261no—
199C4×Q8—261no—
200C4×Q8—261no—
201#117—261no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C22⋊D1312yes—
206C2×C42C22×D1311yescharacteristic
207#107—28no—
208#107—264no—
209#107—264no—
210#106—264no—
211C4⋊C8—132no—
212C4⋊C8—261no—
213C4⋊C8—261no—
214#103—264no—
215C22⋊C8—261no—
216#97—261no—
217C4×C8—21no—
218C4×C8—261no—
219C4×C8—261no—
220C4×C8C22⋊D1312yes—
221C2×C13—22no—
222C2×C13#200511yescharacteristic
223C2×C13#201611yescharacteristic
224C2×C13#201811yescharacteristic
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—82no—
230C2×Q8—82no—
231C2×Q8—261no—
232C2×Q8—261no—
233C22×C4—22no—
234C22×C4—41no—
235C22×C4D4×D1311yescharacteristic
236C22×C4#612911yescharacteristic
237C22×C4C2×C22⋊D1311yescharacteristic
238M16—134no—
239M16—262no—
240M16—522no—
241C2×C8—24no—
242C2×C8—22no—
243C2×C8—262no—
244C2×C8—262no—
245C2×C8—521no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C22⋊C4—521no—
261C42—521no—
262C42D4×D1311yescharacteristic
263C42D4×D1311yescharacteristic
264C42C2×C22⋊D1311yescharacteristic
265C42C2×C22⋊D1311yescharacteristic
266C13#1016511yescharacteristic, complemented, Sylow
267C23#8819311yescharacteristic
268Q8—82no—
269Q8—82no—
270Q8—82no—
271Q8—82no—
272Q8—522no—
273Q8—522no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4Q16×D1312yes—
283C2×C4#8817212yes—
284C2×C4#8819111yescharacteristic
285C2×C4#8819111yescharacteristic
286C2×C4#8819211yescharacteristic
287C2×C4#8819311yescharacteristic
288C2×C4#8819411yescharacteristic
289C2×C4#8820711yescharacteristic
290C8—24no—
291C8—264no—
292C8—522no—
293C8—1041no—
294C22—21no—
295C22—21no—
296C22#1171884312yes—
297C22#1171888411yescharacteristic
298C4—21no—
299C4—21no—
300C4—82no—
301C4—82no—
302C4—1041no—
303C4—1041no—
304C4#1171875612yes—
305C4#1171882112yes—
306C4#1171884211yescharacteristic
307C4#1171884712yes—
308C4#1171885111yescharacteristic
309C2—22no—
310C2#1311587211yescharacteristic
311C2#1311593411yescharacteristic
312C2#1311594311yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#500C2
socleC22×C13#392
prime radicalC23×C13#121
hypercenterC2×#500D13
hypocenterC13#10165
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
266. C13#10165semidirect

Maximal subgroups

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

subgroupindex
#131259872
#131253782
#131158262
#131135172
#131132922
#131126732
C2×C13×#5002
#1016513