Finite Group Databasebeta

← #15837819

Subgroups — #15837819

Order 3328.

906 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 906 conjugacy classes of subgroups — too many to draw. Only its 207 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#13125977C212yesmaximal
2#13119821C211yesmaximal, characteristic
3#13113844C218yesmaximal
4#13113335C212yesmaximal
5#13113160C211yesmaximal, characteristic
6C13×#3502C211yesmaximal, characteristic
7Q82×C13—22no—
8C13×#557—22no—
9C13×#557—24no—
10C13×#544—21no—
11C13×#544C2214yes—
12C13×#533—22no—
13C13×#533C2212yes—
14C13×#519—21no—
15C2×C4×Q8×C13C2211yescharacteristic
16C2×#88198—21no—
17C2×#88123C2211yescharacteristic
18#11718742—22no—
19#11718740—22no—
20#11718704C2218yes—
21#11718681—24no—
22#11718644C2214yes—
23#11718635—21no—
24C4×C4⋊Dic13C2211yescharacteristic
25#11718589—22no—
26#11718586C2212yes—
27#11718130C2218yes—
28#11718120C2214yes—
29C22×Q8×C13D411yescharacteristic
30C22×Dic26—21no—
31C13×C4⋊Q8—22no—
32C13×C4⋊Q8—22no—
33C13×C4⋊Q8—24no—
34C13×C4⋊Q8—28no—
35C13×C4⋊Q8D412yes—
36C13×C4⋊Q8D412yes—
37C13×#125—24no—
38C13×#125—24no—
39C13×#125—28no—
40C13×#125—22no—
41C13×C22⋊Q8—22no—
42C13×C22⋊Q8—24no—
43C13×C22⋊Q8C2314yes—
44C4×Q8×C13—24no—
45C4×Q8×C13—24no—
46C4×Q8×C13—24no—
47C4×Q8×C13—24no—
48C4×Q8×C13—22no—
49C4×Q8×C13—22no—
50C4×Q8×C13—22no—
51C4×Q8×C13D414yes—
52C13×#117—24no—
53C13×#117—22no—
54C2×C13×C4⋊C4D411yescharacteristic
55C2×C13×C4⋊C4C2312yes—
56C2×C42×C13D412yes—
57C2×C42×C13C2311yescharacteristic
58#88198—44no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13C2312yes—
62C2×#6101—24no—
63C2×C4×Dic13—21no—
64#88123—22no—
65#88123—22no—
66#88075—28no—
67#88071—24no—
68#88071C2312yes—
69C22⋊#1055C2314yes—
70#88048—28no—
71C4⋊#1055—22no—
72C4×#1055—22no—
73#18410—131nomaximal, Sylow
74C2×Q8×C13—24no—
75C2×Q8×C13—22no—
76C2×Q8×C13—22no—
77C2×Q8×C13—22no—
78C2×Q8×C13SD1614yes—
79C2×Q8×C13C2×D414yes—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D412yes—
82C22×C4×C13C2×D412yes—
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2411yescharacteristic
85C22×Dic13—22no—
86C22×Dic13—22no—
87C2×Dic26—42no—
88C2×Dic26—42no—
89C2×Dic26—42no—
90C13×C4⋊C4—24no—
91C13×C4⋊C4—24no—
92C13×C4⋊C4—24no—
93C13×C4⋊C4—28no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—24no—
99C13×C4⋊C4—24no—
100C13×C4⋊C4—24no—
101C13×C4⋊C4C2×D414yes—
102C13×C22⋊C4—24no—
103C42×C13—28no—
104C42×C13—22no—
105C42×C13—22no—
106C42×C13—24no—
107C42×C13C2×D412yes—
108C42×C13C2×D412yes—
109C4⋊Dic13—24no—
110C4⋊Dic13—24no—
111C4⋊Dic13—41no—
112C4⋊Dic13—41no—
113#6101—48no—
114C4×Dic13—42no—
115C2×#1055—24no—
116#3502D1311yescharacteristic
117#3229—132no—
118#2546—131no—
119#1611—138no—
120#1503—132no—
121#1461—131no—
122C23×C13C22×D411yescharacteristic
123Q8×C13—28no—
124Q8×C13—44no—
125Q8×C13—44no—
126Q8×C13—84no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—24no—
131C2×C4×C13—24no—
132C2×C4×C13—22no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13#12011yescharacteristic
136C2×C4×C13#12012yes—
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13C2×SD1614yes—
139C2×C4×C13C2×SD1612yes—
140C2×C4×C13#13712yes—
141C2×C4×C13C22×D412yes—
142C2×Dic13—24no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C2×Dic13—42no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148Dic26—84no—
149#1055—44no—
150Q82—22no—
151#557—22no—
152#557—24no—
153#544—21no—
154#544C2×D1314yes—
155#533—22no—
156#533C2×D1312yes—
157C2×C4⋊Q8—131no—
158C2×C4⋊Q8—261no—
159#519—21no—
160C2×C4×Q8C2×D1311yescharacteristic
161#498—262no—
162#487—262no—
163#483—138no—
164#475—264no—
165#431—132no—
166#398—134no—
167#391—261no—
168#389—262no—
169C4×C4⋊C4—131no—
170#328—138no—
171#324—134no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13C2×#12011yescharacteristic
175C22×C13C22×SD1611yescharacteristic
176C22×C13C2×#13711yescharacteristic
177C4×C13—24no—
178C4×C13—21no—
179C4×C13—22no—
180C4×C13—44no—
181C4×C13—42no—
182C4×C13—44no—
183C4×C13#44814yes—
184C4×C13#45612yes—
185Dic13—44no—
186Dic13—82no—
187C22×Q8—261no—
188C22×Q8C22⋊D1311yescharacteristic
189C4⋊Q8—22no—
190C4⋊Q8—22no—
191C4⋊Q8—24no—
192C4⋊Q8—28no—
193C4⋊Q8—262no—
194C4⋊Q8—262no—
195C4⋊Q8—524no—
196C4⋊Q8C22⋊D1312yes—
197C4⋊Q8C22⋊D1312yes—
198#125—24no—
199#125—24no—
200#125—28no—
201#125—22no—
202C22⋊Q8—22no—
203C22⋊Q8—24no—
204C22⋊Q8C22×D1314yes—
205C4×Q8—24no—
206C4×Q8—24no—
207C4×Q8—24no—
208C4×Q8—24no—
209C4×Q8—22no—
210C4×Q8—22no—
211C4×Q8—22no—
212C4×Q8C22⋊D1314yes—
213#117—24no—
214#117—22no—
215C2×C4⋊C4—132no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—264no—
219C2×C4⋊C4C22⋊D1311yescharacteristic
220C2×C4⋊C4C22×D1312yes—
221C2×C42—261no—
222C2×C42C22⋊D1312yes—
223C2×C42C22×D1311yescharacteristic
224#106—268no—
225C4⋊C8—262no—
226#103—268no—
227C22⋊C8—134no—
228C4×C8—262no—
229#95—132no—
230#95—264no—
231C2×C13—21no—
232C2×C13—21no—
233C2×C13C2×#44811yescharacteristic
234C2×C13C2×#45611yescharacteristic
235C2×C13#302811yescharacteristic
236C2×Q8—24no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—522no—
241C2×Q8—522no—
242C2×Q8—522no—
243C2×Q8#610614yes—
244C2×Q8C2×C22⋊D1314yes—
245C22×C4—262no—
246C22×C4—262no—
247C22×C4C2×C22⋊D1312yes—
248C22×C4C2×C22⋊D1311yescharacteristic
249C22×C4C2×C22⋊D1312yes—
250C22×C4C2×C22⋊D1311yescharacteristic
251C22×C4C23×D1311yescharacteristic
252C2×C8—264no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—28no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—24no—
262C4⋊C4—24no—
263C4⋊C4—24no—
264C4⋊C4—264no—
265C4⋊C4—264no—
266C4⋊C4—528no—
267C4⋊C4—521no—
268C4⋊C4—521no—
269C4⋊C4C2×C22⋊D1314yes—
270C22⋊C4—24no—
271C42—28no—
272C42—22no—
273C42—22no—
274C42—24no—
275C42—522no—
276C42C2×C22⋊D1312yes—
277C42C2×C22⋊D1312yes—
278C13#1841011yescharacteristic, complemented, Sylow
279C23C22×C22⋊D1311yescharacteristic
280Q8—28no—
281Q8—44no—
282Q8—44no—
283Q8—84no—
284Q8—1044no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—264no—
294C2×C4—522no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4C2×#610614yes—
300C2×C4C2×#610612yes—
301C2×C4#8819612yes—
302C2×C4#8820711yescharacteristic
303C2×C4#8820712yes—
304C2×C4#8820711yescharacteristic
305C2×C4C22×C22⋊D1312yes—
306C8—524no—
307C22—21no—
308C22—21no—
309C22C22×#610611yescharacteristic
310C22C2×#8819611yescharacteristic
311C22C2×#8820711yescharacteristic
312C4—21no—
313C4—22no—
314C4—24no—
315C4—44no—
316C4—42no—
317C4—44no—
318C4—524no—
319C4—1042no—
320C4#1171888814yes—
321C4#1171890712yes—
322C2—21no—
323C2—21no—
324C2C2×#1171888811yescharacteristic
325C2C2×#1171890711yescharacteristic
326C2#1312424211yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#3502C2
socleC22×C13C2×#120
prime radicalC23×C13C22×D4
hypercenter#3502D13
hypocenterC13#18410
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
278. C13#18410semidirect

Maximal subgroups

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

subgroupindex
#131259772
#131198212
#131138442
#131133352
#131131602
C13×#35022
#1841013