Finite Group Databasebeta

← #15752227

Subgroups — #15752227

Order 3328.

350 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 81 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#13122821C211yesmaximal, characteristic
2#13116398C211yesmaximal, characteristic
3#13116375C211yesmaximal, characteristic
4#13112661C211yesmaximal, characteristic
5#13112660C211yesmaximal, characteristic
6#13112659C211yesmaximal, characteristic
7C13×#2100C211yesmaximal, characteristic
8C13×#389C2211yescharacteristic
9C13×#384C2211yescharacteristic
10#11718644—21no—
11#11718642—21no—
12#11718641—21no—
13#11718639—21no—
14C2×#88050—21no—
15C2×#88047—21no—
16#11718590C2211yescharacteristic
17#11718589C2211yescharacteristic
18#11718321—21no—
19#11718307—21no—
20C13×#340—21no—
21C13×#340—21no—
22C13×#336C2211yescharacteristic
23#11718121—21no—
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Dic26D411yescharacteristic
28C22×C8×C13—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C2×C4⋊Dic13D411yescharacteristic
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D411yescharacteristic
39C2×#6101—21no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C22×#1055—21no—
44C22×#1055—21no—
45C13×#95—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88050—42no—
55#88047—42no—
56#7831—131nomaximal, Sylow
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—41no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C2×Dic26—21no—
68C2×Dic26—41no—
69C2×Dic26—41no—
70C2×Dic26Q1612yes—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C42×C13—41no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88#6101—41no—
89#6101—41no—
90#6101—81no—
91#6101—81no—
92C4×Dic13—81no—
93C2×#1055—22no—
94C2×#1055—41no—
95C2×#1055—41no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99#2809—131no—
100#2100—131no—
101#2100D1311yescharacteristic
102#2095—131no—
103#1272—131no—
104#1271—131no—
105#1271—131no—
106C23×C13#12011yescharacteristic
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—81no—
120C2×C4×C13—81no—
121C2×C4×C13—81no—
122C2×C4×C13C2×Q1611yescharacteristic
123C2×C4×C13#13511yescharacteristic
124C2×C4×C13#13511yescharacteristic
125C2×C4×C13#13711yescharacteristic
126C2×C4×C13#13711yescharacteristic
127C2×C4×C13#13711yescharacteristic
128C2×Dic13—22no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140Dic26—42no—
141Dic26—81no—
142C8×C13—81no—
143#1055—42no—
144#1055—81no—
145C2×#107—261no—
146C2×#103—261no—
147#400—261no—
148#398—261no—
149#398—261no—
150#391—131no—
151#391—261no—
152#389—131no—
153#389C2×D1311yescharacteristic
154#387—261no—
155#387—261no—
156#384C2×D1311yescharacteristic
157#340—21no—
158#340—21no—
159#340—261no—
160#340—261no—
161#336—131no—
162#336—131no—
163#336C2×D1311yescharacteristic
164C22×C13#45111yescharacteristic
165C22×C13#45211yescharacteristic
166C22×C13#45211yescharacteristic
167C22×C13#45311yescharacteristic
168C22×C13#45411yescharacteristic
169C22×C13#45411yescharacteristic
170C22×C13#45811yescharacteristic
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—81no—
178C4×C13—81no—
179C4×C13—161no—
180Dic13—42no—
181Dic13—81no—
182Dic13—81no—
183Dic13—81no—
184C22×Q8—131no—
185C22×C8—21no—
186C22×C8—261no—
187C22×C8—261no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—131no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4C22⋊D1311yescharacteristic
199C2×C4⋊C4C22⋊D1311yescharacteristic
200C2×C42—261no—
201C2×C42C22×D1311yescharacteristic
202#107—522no—
203#103—522no—
204#95—21no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—261no—
209#95—261no—
210#95—261no—
211#95—261no—
212#95—261no—
213C2×C13#161411yescharacteristic
214C2×C13#161511yescharacteristic
215C2×C13#161511yescharacteristic
216C2×C13#163411yescharacteristic
217C2×C13#163611yescharacteristic
218C2×C13#163611yescharacteristic
219C2×C13#165711yescharacteristic
220C2×Q8—132no—
221C2×Q8—261no—
222C2×Q8—521no—
223C2×Q8—521no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4—261no—
231C22×C4D4×D1311yescharacteristic
232C22×C4D4×D1311yescharacteristic
233C22×C4C2×C22⋊D1311yescharacteristic
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—262no—
238C2×C8—521no—
239C2×C8—521no—
240C2×C8—521no—
241C2×C8—521no—
242C2×C8—521no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—521no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—1041no—
259C4⋊C4—1041no—
260C42—41no—
261C42—1041no—
262C13#783111yescharacteristic, complemented, Sylow
263C23#8819111yescharacteristic
264Q8—522no—
265Q8—1041no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—262no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4#8816911yescharacteristic
294C2×C4#8817011yescharacteristic
295C2×C4Q16×D1311yescharacteristic
296C2×C4#8817211yescharacteristic
297C2×C4#8819611yescharacteristic
298C2×C4#8820411yescharacteristic
299C8—81no—
300C8—522no—
301C8—1041no—
302C22#1171870811yescharacteristic
303C22#1171871411yescharacteristic
304C22#1171872311yescharacteristic
305C22#1171883411yescharacteristic
306C22#1171884711yescharacteristic
307C22#1171885911yescharacteristic
308C22#1171886211yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—81no—
316C4—81no—
317C4—161no—
318C4—522no—
319C4—1041no—
320C4—1041no—
321C4—1041no—
322C2#1311385911yescharacteristic
323C2#1311386411yescharacteristic
324C2#1311386511yescharacteristic
325C2#1311398011yescharacteristic
326C2#1311399111yescharacteristic
327C2#1311399211yescharacteristic
328C2#1311413311yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2100C2
socle, prime radicalC23×C13#120
hypercenter#2100D13
hypocenterC13#7831
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
262. C13#7831semidirect

Maximal subgroups

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

subgroupindex
#131228212
#131163982
#131163752
#131126612
#131126602
#131126592
C13×#21002
#783113