Finite Group Databasebeta

← #15835413

Subgroups — #15835413

Order 3328.

930 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 183 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#13124780C212yesmaximal
2#13119123C211yesmaximal, characteristic
3#13113878C214yesmaximal, complemented
4#13113844C214yesmaximal, complemented
5#13113369C212yesmaximal
6#13113166C211yesmaximal, characteristic
7C2×C13×#544C211yesmaximal, characteristic
8C13×#544—24no—
9C13×#544—22no—
10C13×#544C2214yes—
11C2×C13×C4⋊Q8—22no—
12C2×C13×#125—22no—
13C2×C13×C22⋊Q8—21no—
14C2×C13×C22⋊Q8C2212yes—
15C2×C13×#117—21no—
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18#11718886—22no—
19#11718872—21no—
20#11718872C2211yescharacteristic
21#11718871—21no—
22#11718868C2212yes—
23#11718706—24no—
24#11718705C2214yes—
25#11718704C2214yes—
26#11718647C2212yes—
27#11718644C2212yes—
28#11718639—22no—
29#11718625—22no—
30#11718130C2218yes—
31#11718120C2214yes—
32C22×Q8×C13—21no—
33C22×Q8×C13D412yes—
34C23×C4×C13D411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C13×C4⋊Q8—28no—
38C13×C4⋊Q8—28no—
39C13×#125—28no—
40C13×#125—28no—
41C13×C22⋊Q8—24no—
42C13×C22⋊Q8—24no—
43C13×C22⋊Q8—22no—
44C13×C22⋊Q8—22no—
45C13×C22⋊Q8D414yes—
46C13×C22⋊Q8C2314yes—
47C13×#117—24no—
48C13×#117—24no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4D412yes—
57C2×C13×C4⋊C4D412yes—
58C2×C13×C4⋊C4C2312yes—
59C2×C13×C22⋊C4—22no—
60C2×C42×C13—22no—
61C2×C22⋊Dic13—21no—
62C2×C22⋊Dic13—21no—
63#88180—22no—
64#88180—22no—
65C2×C4⋊Dic13C2311yescharacteristic
66C2×C4⋊Dic13C2311yescharacteristic
67C2×#6101—22no—
68C2×C4×Dic13—21no—
69C2×#6099—22no—
70#88075—24no—
71#88075—24no—
72#88071—22no—
73#88071—22no—
74#88071—22no—
75#88071—21no—
76#88071C2312yes—
77C22⋊#1055—22no—
78C22⋊#1055C2314yes—
79#88048—24no—
80#88047—24no—
81#18148—131nomaximal, Sylow
82C24×C13C2×D411yescharacteristic
83C2×Q8×C13—24no—
84C2×Q8×C13—22no—
85C2×Q8×C13—44no—
86C2×Q8×C13—82no—
87C2×Q8×C13C2×D414yes—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—24no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—42no—
96C22×C4×C13—42no—
97C22×C4×C13C2×D412yes—
98C22×C4×C13C2×D412yes—
99C22×C4×C13C2×D412yes—
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D412yes—
102C22×C4×C13C2411yescharacteristic
103C22×Dic13—22no—
104C22×Dic13—21no—
105C22×Dic13—21no—
106C13×C4⋊C4—24no—
107C13×C4⋊C4—24no—
108C13×C4⋊C4—24no—
109C13×C4⋊C4—28no—
110C13×C4⋊C4—24no—
111C13×C4⋊C4—24no—
112C13×C4⋊C4—22no—
113C13×C4⋊C4—24no—
114C13×C4⋊C4—24no—
115C13×C4⋊C4C2×D414yes—
116C13×C22⋊C4—24no—
117C13×C22⋊C4—24no—
118C42×C13—28no—
119C22⋊Dic13—42no—
120C22⋊Dic13—41no—
121C22⋊Dic13—41no—
122C4⋊Dic13—22no—
123C4⋊Dic13—22no—
124#6101—44no—
125C4×Dic13—42no—
126#6099—44no—
127C2×#1055—24no—
128C2×#544D1311yescharacteristic
129#3095—132no—
130#2484—131no—
131#1617—134no—
132#1611—134no—
133#1511—132no—
134#1463—131no—
135C23×C13—22no—
136C23×C13—22no—
137C23×C13—41no—
138C23×C13#12011yescharacteristic
139C23×C13#12011yescharacteristic
140C23×C13C22×D411yescharacteristic
141Q8×C13—44no—
142Q8×C13—82no—
143Q8×C13—84no—
144C2×C4×C13—24no—
145C2×C4×C13—24no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—24no—
149C2×C4×C13—24no—
150C2×C4×C13—24no—
151C2×C4×C13—22no—
152C2×C4×C13—42no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—44no—
156C2×C4×C13—42no—
157C2×C4×C13—44no—
158C2×C4×C13—42no—
159C2×C4×C13—81no—
160C2×C4×C13#12012yes—
161C2×C4×C13#13714yes—
162C2×C4×C13C22×D412yes—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13—42no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—42no—
169C2×Dic13—42no—
170#1055—44no—
171#544—24no—
172#544—22no—
173#544C2×D1314yes—
174C2×C4⋊Q8—22no—
175C2×#125—22no—
176C2×C22⋊Q8—21no—
177C2×C22⋊Q8C2×D1312yes—
178C2×#117—21no—
179C2×#117—131no—
180C22×C4⋊C4C2×D1311yescharacteristic
181#485—264no—
182#484—134no—
183#483—134no—
184#428—262no—
185#419—262no—
186#407—132no—
187#400—132no—
188#398—132no—
189#387—262no—
190#385—261no—
191#381—131no—
192#381—261no—
193#328—138no—
194#324—134no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—44no—
203C22×C13#45812yes—
204C22×C13C2×#12011yescharacteristic
205C22×C13C2×#13712yes—
206C4×C13—24no—
207C4×C13—22no—
208C4×C13—22no—
209C4×C13—44no—
210C4×C13—42no—
211C4×C13—44no—
212Dic13—82no—
213Dic13—81no—
214Dic13—81no—
215C22×Q8—21no—
216C22×Q8C22⋊D1312yes—
217C23×C4C22⋊D1311yescharacteristic
218C23×C4C22⋊D1311yescharacteristic
219C23×C4C22×D1311yescharacteristic
220C2×M16—262no—
221C4⋊Q8—28no—
222C4⋊Q8—28no—
223#125—28no—
224#125—28no—
225C22⋊Q8—24no—
226C22⋊Q8—24no—
227C22⋊Q8—22no—
228C22⋊Q8—22no—
229C22⋊Q8C22⋊D1314yes—
230C22⋊Q8C22×D1314yes—
231#117—24no—
232#117—24no—
233#117—262no—
234#117—262no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—131no—
243C2×C4⋊C4—131no—
244C2×C4⋊C4—262no—
245C2×C4⋊C4C22⋊D1312yes—
246C2×C4⋊C4C22⋊D1312yes—
247C2×C4⋊C4C22×D1312yes—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—261no—
250C2×C22⋊C4—261no—
251C2×C42—22no—
252C2×C42—261no—
253#107—264no—
254#106—264no—
255#103—264no—
256#103—264no—
257C22⋊C8—134no—
258C22⋊C8—262no—
259#95—132no—
260#95—261no—
261#95—262no—
262#95—262no—
263#95—262no—
264C2×C13—22no—
265C2×C13—22no—
266C2×C13—41no—
267C2×C13#300411yescharacteristic
268C2×C13#302011yescharacteristic
269C2×C13C2×#45811yescharacteristic
270C24C2×C22⋊D1311yescharacteristic
271C2×Q8—24no—
272C2×Q8—22no—
273C2×Q8—44no—
274C2×Q8—82no—
275C2×Q8C2×C22⋊D1314yes—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—262no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4C2×C22⋊D1312yes—
289C22×C4C2×C22⋊D1312yes—
290C22×C4C2×C22⋊D1312yes—
291C22×C4C2×C22⋊D1311yescharacteristic
292C22×C4C2×C22⋊D1312yes—
293C22×C4C23×D1311yescharacteristic
294M16—524no—
295C2×C8—264no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—28no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—22no—
303C4⋊C4—24no—
304C4⋊C4—24no—
305C4⋊C4—262no—
306C4⋊C4—262no—
307C4⋊C4—524no—
308C4⋊C4C2×C22⋊D1314yes—
309C22⋊C4—24no—
310C22⋊C4—24no—
311C22⋊C4—522no—
312C22⋊C4—521no—
313C22⋊C4—521no—
314C42—28no—
315C42—522no—
316C13#1814811yescharacteristic, complemented, Sylow
317C23—22no—
318C23—22no—
319C23—41no—
320C23#8820711yescharacteristic
321C23#8820711yescharacteristic
322C23C22×C22⋊D1311yescharacteristic
323Q8—44no—
324Q8—82no—
325Q8—84no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—522no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4—522no—
347C2×C4—521no—
348C2×C4—521no—
349C2×C4#8819614yes—
350C2×C4#8820712yes—
351C2×C4C22×C22⋊D1312yes—
352C8—524no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22#1171890412yes—
362C22C2×#8819612yes—
363C22C2×#8820711yescharacteristic
364C4—22no—
365C4—22no—
366C4—24no—
367C4—44no—
368C4—42no—
369C4—44no—
370C4—1042no—
371C4—1041no—
372C4—1041no—
373C2—22no—
374C2—22no—
375C2—41no—
376C2#1312407011yescharacteristic
377C2#1312420011yescharacteristic
378C2C2×#1171890411yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#544C2
socleC22×C13C2×#120
prime radicalC24×C13C2×D4
hypercenterC2×#544D13
hypocenterC13#18148
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13113878C2semidirect
4. #13113844C2semidirect
316. C13#18148semidirect

Maximal subgroups

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

subgroupindex
#131247802
#131191232
#131138782
#131138442
#131133692
#131131662
C2×C13×#5442
#1814813