Finite Group Databasebeta

← #15765647

Subgroups — #15765647

Order 3328.

504 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 105 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#13125977C211yesmaximal, characteristic
2#13123213C211yesmaximal, characteristic
3#13115814C211yesmaximal, characteristic
4#13113521C211yesmaximal, characteristic
5#13113507C211yesmaximal, 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#11718740—21no—
19#11718704—22no—
20#11718681—22no—
21#11718638—22no—
22#11718635—22no—
23C42×Dic13C2211yescharacteristic
24#11718586C2211yescharacteristic
25#11718585C2211yescharacteristic
26#11718139—22no—
27#11718124—22no—
28#11718078—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#88048—24no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055D412yes—
68C4×#1055—21no—
69#10296—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—41no—
82C2×Dic26—41no—
83C2×Dic26—42no—
84C2×Dic26—42no—
85C2×C8×C13—22no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C22⋊C4—41no—
97C42×C13—41no—
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13#4111yescharacteristic
102C4⋊Dic13—22no—
103C4⋊Dic13—22no—
104C4⋊Dic13—41no—
105C4⋊Dic13—41no—
106C4×Dic13—24no—
107C4×Dic13—22no—
108C4×Dic13—22no—
109C4×Dic13—42no—
110#6099—42no—
111C2×#1055—22no—
112C2×#1055—41no—
113#3230D1311yescharacteristic
114#3229—131no—
115#2862—131no—
116#1994—131no—
117#1549—131no—
118#1546—131no—
119#1276—131no—
120C23×C13#12011yescharacteristic
121Q8×C13—42no—
122Q8×C13—42no—
123Q8×C13—82no—
124Q8×C13—82no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—44no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13#12011yescharacteristic
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12711yescharacteristic
137C2×C4×C13#13512yes—
138C2×C4×C13#13712yes—
139C2×Dic13—24no—
140C2×Dic13—42no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—44no—
144Dic26—82no—
145Dic26—81no—
146Dic26—81no—
147C8×C13—42no—
148#1055—42no—
149#1055—81no—
150#533C2×D1311yescharacteristic
151C2×C4⋊Q8—131no—
152C2×C4⋊Q8C2×D1311yescharacteristic
153#500—21no—
154#498—261no—
155#487—21no—
156#487—261no—
157#484—22no—
158#483—262no—
159#477—22no—
160#475—262no—
161#431—131no—
162#431C2×D1311yescharacteristic
163#423—131no—
164#391—262no—
165#391—262no—
166#382—262no—
167C43—131no—
168#339—262no—
169#332—262no—
170#332—262no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13#39211yescharacteristic
174C22×C13#45212yes—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—82no—
178C4×C13—81no—
179C4×C13—81no—
180C4×C13#45412yes—
181C4×C13#45612yes—
182C4×C13#46412yes—
183C4×C13#49511yescharacteristic
184C4×C13#49711yescharacteristic
185Dic13—44no—
186Dic13—82no—
187C22×Q8—21no—
188C22×Q8—261no—
189C2×M16—261no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—261no—
195C4⋊Q8—261no—
196C4⋊Q8—261no—
197C4⋊Q8—261no—
198C4⋊Q8C22⋊D1311yescharacteristic
199C4⋊Q8C22⋊D1311yescharacteristic
200#125—21no—
201C22⋊Q8—21no—
202C22⋊Q8—21no—
203C4×Q8—21no—
204C4×Q8—21no—
205#117—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—132no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4C22⋊D1312yes—
210C2×C42—132no—
211C2×C42—261no—
212C2×C42—261no—
213C2×C42C22×D1311yescharacteristic
214#107—24no—
215#106—264no—
216C4⋊C8—132no—
217C4⋊C8—261no—
218C4⋊C8—261no—
219C4⋊C8C22⋊D1312yes—
220#103—24no—
221#103—264no—
222C22⋊C8—21no—
223C22⋊C8—261no—
224C4×C8—21no—
225C4×C8—261no—
226#95—268no—
227C2×C13—22no—
228C2×C13#200311yescharacteristic
229C2×C13#200511yescharacteristic
230C2×C13#201511yescharacteristic
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—44no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—522no—
237C2×Q8—522no—
238C2×Q8—521no—
239C2×Q8—521no—
240C22×C4—22no—
241C22×C4—262no—
242C22×C4—262no—
243C22×C4D4×D1311yescharacteristic
244C22×C4D4×D1311yescharacteristic
245C22×C4C2×C22⋊D1311yescharacteristic
246M16—522no—
247C2×C8—22no—
248C2×C8—262no—
249C2×C8—521no—
250C4⋊C4—21no—
251C4⋊C4—22no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—22no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—262no—
261C4⋊C4—262no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C22⋊C4—41no—
265C42—41no—
266C42—264no—
267C42—262no—
268C42—262no—
269C42—522no—
270C42D4×D1311yescharacteristic
271C42#612911yescharacteristic
272C42C2×C22⋊D1311yescharacteristic
273C42C2×C22⋊D1311yescharacteristic
274C13#1029611yescharacteristic, complemented, Sylow
275C23#8819111yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—82no—
279Q8—82no—
280Q8—1042no—
281Q8—1041no—
282Q8—1041no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—44no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—264no—
290C2×C4—522no—
291C2×C4—522no—
292C2×C4—524no—
293C2×C4—522no—
294C2×C4#8817212yes—
295C2×C4#8817312yes—
296C2×C4#8819111yescharacteristic
297C2×C4#8819211yescharacteristic
298C2×C4#8819311yescharacteristic
299C2×C4#8819311yescharacteristic
300C2×C4#8819411yescharacteristic
301C2×C4#8820711yescharacteristic
302C8—42no—
303C8—522no—
304C8—1041no—
305C22—21no—
306C22—21no—
307C22#1171884812yes—
308C22#1171888411yescharacteristic
309C4—21no—
310C4—21no—
311C4—82no—
312C4—81no—
313C4—81no—
314C4—524no—
315C4—1042no—
316C4#1171884612yes—
317C4#1171885111yescharacteristic
318C4#1171885211yescharacteristic
319C4#1171886212yes—
320C4#1171890712yes—
321C2—22no—
322C2#1311585511yescharacteristic
323C2#1311587011yescharacteristic
324C2#1311592711yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3230C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#3230D13
hypocenterC13#10296
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
274. C13#10296semidirect

Maximal subgroups

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

subgroupindex
#131259772
#131232132
#131158142
#131135212
#131135072
#131126682
C13×#32302
#1029613