Finite Group Databasebeta

← #15764366

Subgroups — #15764366

Order 3328.

458 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 85 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#13126042C211yesmaximal, characteristic
2#13125378C211yesmaximal, characteristic
3#13113553C211yesmaximal, characteristic
4#13113438C211yesmaximal, characteristic
5#13113347C211yesmaximal, characteristic
6#13112729C211yesmaximal, characteristic
7C13×#2642C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×#125C2211yescharacteristic
10#11719175C2211yescharacteristic
11C13×#400—22no—
12C13×#400—22no—
13C13×#391—21no—
14C13×#391—21no—
15C13×#376C2211yescharacteristic
16#11718741—22no—
17#11718740—21no—
18#11718739—21no—
19#11718730—21no—
20#11718726—21no—
21#11718724—22no—
22#11718632—21no—
23#11718631—21no—
24#11718625—22no—
25#11718587C2211yescharacteristic
26#11718587C2211yescharacteristic
27C4×#6099C2211yescharacteristic
28#11718139—22no—
29#11718135—22no—
30#11718044—22no—
31C22×Q8×C13—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×#125—21no—
37C13×#125—21no—
38C13×#125—21no—
39C13×#125—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4D411yescharacteristic
44C2×C13×C4⋊C4D411yescharacteristic
45C2×C13×C4⋊C4D412yes—
46C2×C42×C13—21no—
47C2×C42×C13C2311yescharacteristic
48#88180—21no—
49#88178—21no—
50#88178—21no—
51C2×#6099—21no—
52#88124—21no—
53#88123D411yescharacteristic
54#88123D411yescharacteristic
55C4×Dic26—21no—
56C4×Dic26—21no—
57C13×#95—24no—
58C13×#95—24no—
59C13×#95—21no—
60C13×#95D412yes—
61C22⋊#1055—21no—
62C22⋊#1055—21no—
63#88050—22no—
64#88050—22no—
65#88048—22no—
66#88048—24no—
67#88047—22no—
68#88047—24no—
69C4⋊#1055—21no—
70C4⋊#1055D412yes—
71#88043—21no—
72#88043—21no—
73#88043D412yes—
74C4×#1055—21no—
75#10103—131nomaximal, Sylow
76C2×Q8×C13—44no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C22×C4×C13—22no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—22no—
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C2×Dic26—21no—
87C2×Dic26—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C42×C13—42no—
101C42×C13C2×D411yescharacteristic
102C42×C13C2×D411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13#4111yescharacteristic
105C22⋊Dic13—41no—
106C4⋊Dic13—21no—
107C4⋊Dic13—21no—
108C4⋊Dic13—21no—
109C4⋊Dic13—21no—
110#6101—41no—
111#6101—41no—
112C4×Dic13—41no—
113#6099—24no—
114C2×#1055—22no—
115C2×#1055—22no—
116C2×#1055—41no—
117#3236—131no—
118#3165—131no—
119#2642D1311yescharacteristic
120#1556—131no—
121#1528—131no—
122#1506—131no—
123#1300—131no—
124C23×C13#12011yescharacteristic
125Q8×C13—82no—
126Q8×C13—82no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—44no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13#12011yescharacteristic
140C2×C4×C13#12011yescharacteristic
141C2×C4×C13#12111yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13#12711yescharacteristic
145C2×Dic13—41no—
146C2×Dic13—41no—
147Dic26—42no—
148Dic26—81no—
149#1055—24no—
150#1055—42no—
151#1055—81no—
152#533—131no—
153C2×C4⋊Q8C2×D1311yescharacteristic
154C2×#125C2×D1311yescharacteristic
155#501—262no—
156#501—261no—
157#500—261no—
158#498—261no—
159#491—261no—
160#484—261no—
161#483—261no—
162#479—262no—
163#432—131no—
164#432—131no—
165#428—262no—
166C4×M16—131no—
167#400—22no—
168#400—22no—
169#391—21no—
170#391—21no—
171#376C2×D1311yescharacteristic
172#332—262no—
173#330—262no—
174#328—262no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13#39211yescharacteristic
178C22×C13#45612yes—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—82no—
185C4×C13—82no—
186C4×C13—81no—
187C4×C13—81no—
188C4×C13#45412yes—
189Dic13—81no—
190Dic13—81no—
191C22×Q8—21no—
192C2×M16—261no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—131no—
198C4⋊Q8—131no—
199#125—21no—
200#125—21no—
201#125—21no—
202#125—21no—
203#125—261no—
204C22⋊Q8—261no—
205C22⋊Q8—261no—
206C4×Q8—261no—
207C4×Q8—261no—
208#117—261no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C22⋊D1311yescharacteristic
213C2×C4⋊C4C22⋊D1311yescharacteristic
214C2×C4⋊C4C22⋊D1312yes—
215C2×C42—21no—
216C2×C42C22×D1311yescharacteristic
217#107—264no—
218#107—262no—
219#106—264no—
220#106—262no—
221C4⋊C8—132no—
222C4⋊C8—261no—
223#103—262no—
224#103—262no—
225C22⋊C8—261no—
226C22⋊C8—261no—
227#97—132no—
228#97—261no—
229#97—261no—
230C4×C8—261no—
231#95—24no—
232#95—24no—
233#95—21no—
234#95C22⋊D1312yes—
235C2×C13—22no—
236C2×C13#200311yescharacteristic
237C2×C13#200511yescharacteristic
238C2×C13#200911yescharacteristic
239C2×Q8—44no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—261no—
243C2×Q8—261no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4C2×C22⋊D1311yescharacteristic
249C22×C4C2×C22⋊D1311yescharacteristic
250C22×C4C2×C22⋊D1311yescharacteristic
251M16—264no—
252C2×C8—262no—
253C2×C8—262no—
254C2×C8—521no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—22no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—521no—
272C4⋊C4—521no—
273C22⋊C4—521no—
274C42—42no—
275C42—521no—
276C42D4×D1311yescharacteristic
277C42D4×D1311yescharacteristic
278C42D4×D1311yescharacteristic
279C42#612911yescharacteristic
280C13#1010311yescharacteristic, complemented, Sylow
281C23#8820711yescharacteristic
282Q8—82no—
283Q8—82no—
284Q8—522no—
285Q8—1041no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4#8819111yescharacteristic
301C2×C4#8819111yescharacteristic
302C2×C4#8819211yescharacteristic
303C2×C4#8819311yescharacteristic
304C2×C4#8819311yescharacteristic
305C2×C4#8819411yescharacteristic
306C8—264no—
307C8—522no—
308C8—1041no—
309C22—21no—
310C22—21no—
311C22#1171888411yescharacteristic
312C22#1171890712yes—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—82no—
319C4—82no—
320C4—81no—
321C4—81no—
322C4—1041no—
323C4—1041no—
324C4#1171872312yes—
325C2—22no—
326C2#1311585811yescharacteristic
327C2#1311587011yescharacteristic
328C2#1311589611yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2642C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#2642D13
hypocenterC13#10103
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2642

Complements

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

NH ≅ G/Ntype
280. C13#10103semidirect

Maximal subgroups

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

subgroupindex
#131260422
#131253782
#131135532
#131134382
#131133472
#131127292
C13×#26422
#1010313