Finite Group Databasebeta

← #15760583

Subgroups — #15760583

Order 3328.

486 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 103 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#13119812C211yesmaximal, characteristic
2#13113459C212yesmaximal
3#13113180C211yesmaximal, characteristic, complemented
4#13112691C212yesmaximal, complemented
5C13×#2983C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88201C411yescharacteristic
8C2×#88198C411yescharacteristic
9C2×#88129C2211yescharacteristic
10C13×#446—24no—
11C13×#432—21no—
12C13×#432C2212yes—
13C13×#431—21no—
14#11718655—21no—
15#11718655—21no—
16#11718649C411yescharacteristic
17#11718635C411yescharacteristic
18#11718601—21no—
19#11718601—21no—
20C4×C4⋊Dic13C2211yescharacteristic
21#11718587C2212yes—
22#11718120—21no—
23#11718120—21no—
24#11718056—24no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D52C2×C411yescharacteristic
27C22×Dic26C2×C411yescharacteristic
28C4×Q8×C13—22no—
29C4×Q8×C13—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36#88201—42no—
37#88198—42no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×#6103—21no—
43C2×#6103—21no—
44C2×C4⋊Dic13—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×C4×Dic13C2×C411yescharacteristic
48C2×C4×Dic13C2×C411yescharacteristic
49#88129—22no—
50#88129—22no—
51C13×C4⋊C8—22no—
52C13×C4⋊C8—22no—
53C13×C4⋊C8—22no—
54C13×C22⋊C8—22no—
55C13×#97—22no—
56C13×#97D414yes—
57C4×C8×C13—22no—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61C22⋊#1055—22no—
62C4⋊#1055—22no—
63#88043—22no—
64#9448—131nomaximal, Sylow
65C23×D13—21no—
66C2×Q8×C13—22no—
67C2×Q8×C13—22no—
68C2×Q8×C13—41no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C2×D52—22no—
80C2×D52—41no—
81C2×D52—41no—
82C2×Dic26—22no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C2×C8×C13—24no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—21no—
93C42×C13C2×D412yes—
94C42×C13#4112yes—
95#6103—42no—
96#6103—42no—
97#6103—42no—
98#6103—42no—
99#6103—41no—
100#6103—42no—
101#6103—41no—
102C4⋊Dic13—42no—
103#6101—42no—
104#6101—42no—
105C4×Dic13—41no—
106C4×Dic13—41no—
107C2×#1055—42no—
108#2983D1311yescharacteristic, complemented
109#2545—131no—
110#1533—132no—
111#1467—131no—
112#1285—132no—
113C23×C13C2×C22⋊C411yescharacteristic
114C22×D13—41no—
115C22×D13—41no—
116C22×D13—41no—
117C22×D13—41no—
118C22×D13—41no—
119C22×D13—41no—
120C22×D13—41no—
121Q8×C13—44no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13#10012yes—
136C2×C4×C13C4×D412yes—
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12112yes—
139C2×C4×C13#12311yescharacteristic
140C2×Dic13—22no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149D52—82no—
150Dic26—82no—
151C8×C13—44no—
152#1055—82no—
153C2×C4⋊Q8—131no—
154C2×#124—131no—
155C2×#124—131no—
156C2×C4×Q8C2×D1311yescharacteristic
157#446—24no—
158#432—21no—
159#432—132no—
160#432C2×D1312yes—
161#431—21no—
162#396—261no—
163#396—261no—
164#391—131no—
165#390—131no—
166#388—261no—
167#388—261no—
168C4×C4⋊C4—131no—
169#329—264no—
170#324—261no—
171#324—261no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13#38611yescharacteristic
175C22×C13C2×#10011yescharacteristic
176C22×C13#41311yescharacteristic
177C2×D13—81no—
178C2×D13—81no—
179C2×D13—81no—
180C2×D13—81no—
181C2×D13—81no—
182C2×D13—81no—
183C2×D13—81no—
184C4×C13—22no—
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192Dic13—42no—
193Dic13—81no—
194Dic13—81no—
195C22×Q8—131no—
196C22×Q8C4×D1311yescharacteristic
197C22×D4—131no—
198C4⋊Q8—522no—
199#124—262no—
200#124—262no—
201#124—522no—
202C4×Q8—22no—
203C4×Q8—22no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4C4×D1311yescharacteristic
208C2×C4⋊C4D5211yescharacteristic
209C2×C4⋊C4D5211yescharacteristic
210C2×C22⋊C4—261no—
211C2×C22⋊C4—261no—
212C2×C22⋊C4—261no—
213C2×C22⋊C4—261no—
214C2×C22⋊C4—261no—
215C2×C22⋊C4—261no—
216C2×C42—131no—
217C2×C42—131no—
218C2×C42C22⋊D1311yescharacteristic
219C2×C42C22⋊D1311yescharacteristic
220C2×C42C22×D1311yescharacteristic
221C4⋊C8—22no—
222C4⋊C8—22no—
223C4⋊C8—22no—
224C4⋊C8—262no—
225C22⋊C8—22no—
226C22⋊C8—262no—
227#97—22no—
228#97—262no—
229#97C22⋊D1314yes—
230C4×C8—22no—
231#95—261no—
232#95—261no—
233#95—261no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13#188411yescharacteristic
237C2×C13#190011yescharacteristic
238C2×C13#191211yescharacteristic
239D13—161no—
240C24—261no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—262no—
245C2×Q8—521no—
246C2×Q8—521no—
247C2×D4—262no—
248C2×D4—521no—
249C2×D4—521no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4#610311yescharacteristic
254C22×C4#610311yescharacteristic
255C22×C4#610311yescharacteristic
256C22×C4#610311yescharacteristic
257C22×C4C2×C4×D1311yescharacteristic
258C22×C4C2×D5211yescharacteristic
259C22×C4C2×C22⋊D1311yescharacteristic
260C2×C8—24no—
261C2×C8—522no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—522no—
266C4⋊C4—522no—
267C4⋊C4—522no—
268C22⋊C4—522no—
269C22⋊C4—522no—
270C22⋊C4—522no—
271C22⋊C4—521no—
272C22⋊C4—522no—
273C22⋊C4—521no—
274C22⋊C4—522no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—521no—
280C42—521no—
281C42#612712yes—
282C42C2×C22⋊D1312yes—
283C13#944811yescharacteristic, complemented, Sylow
284C23—521no—
285C23—521no—
286C23—521no—
287C23—521no—
288C23—521no—
289C23—521no—
290C23—521no—
291C23C2×#610311yescharacteristic
292Q8—44no—
293Q8—1042no—
294D4—1042no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—262no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4#8806312yes—
318C2×C4C4×C22⋊D1312yes—
319C2×C4#8818311yescharacteristic
320C2×C4#8818412yes—
321C2×C4#8820711yescharacteristic
322C8—44no—
323C8—1042no—
324C22—21no—
325C22—21no—
326C22—1041no—
327C22—1041no—
328C22—1041no—
329C22—1041no—
330C22—1041no—
331C22—1041no—
332C22—1041no—
333C22C2×#8806311yescharacteristic
334C22#1171879311yescharacteristic
335C22#1171887411yescharacteristic
336C4—22no—
337C4—22no—
338C4—22no—
339C4—21no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—522no—
345C4—1041no—
346C4—1041no—
347C2—21no—
348C2—21no—
349C2—2081no—
350C2#1311521911yescharacteristic
351C2#1311529911yescharacteristic
352C2#1311537311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2983C2
socleC22×C13#386
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#2983D13
hypocenterC13#9448
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
3. #13113180C2semidirect
4. #13112691C2semidirect
5. C13×#2983C2semidirect
108. #2983D13semidirect
283. C13#9448semidirect

Maximal subgroups

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

subgroupindex
#131198122
#131134592
#131131802
#131126912
C13×#29832
#944813