Finite Group Databasebeta

← #15752230

Subgroups — #15752230

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#13116400C211yesmaximal, characteristic
3#13116399C211yesmaximal, characteristic
4#13116373C211yesmaximal, characteristic
5#13112661C211yesmaximal, characteristic
6#13112658C211yesmaximal, characteristic
7C13×#1271C211yesmaximal, characteristic
8C13×#389C2211yescharacteristic
9C2×#88058—21no—
10C2×#88056—21no—
11#11718644—21no—
12#11718642—21no—
13#11718641—21no—
14#11718639—21no—
15#11718596C2211yescharacteristic
16#11718590C2211yescharacteristic
17#11718589C2211yescharacteristic
18#11718321—21no—
19#11718307—21no—
20C13×#336C2211yescharacteristic
21C13×#336C2211yescharacteristic
22#11718143—21no—
23#11718143—21no—
24#11718121—21no—
25#11718121—21no—
26#11718116C2211yescharacteristic
27C22×Dic26D411yescharacteristic
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4⋊Dic13D411yescharacteristic
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13—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#88058—42no—
55#88056—42no—
56#7831—131nomaximal, Sylow
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—41no—
67C2×Dic26—21no—
68C2×Dic26—41no—
69C2×Dic26—41no—
70C2×Dic26Q1612yes—
71C2×C8×C13—22no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C42×C13—41no—
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87C4⋊Dic13—42no—
88C4⋊Dic13—42no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91#6101—41no—
92#6101—41no—
93#6101—81no—
94#6101—81no—
95C4×Dic13—81no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99#2809—131no—
100#2100—131no—
101#2100—131no—
102#2095—131no—
103#1272—131no—
104#1271—131no—
105#1271D1311yescharacteristic
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×C13C2×Q1611yescharacteristic
120C2×C4×C13#13511yescharacteristic
121C2×C4×C13#13511yescharacteristic
122C2×C4×C13#13711yescharacteristic
123C2×C4×C13#13711yescharacteristic
124C2×C4×C13#13711yescharacteristic
125C2×Dic13—22no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
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—81no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140Dic26—42no—
141Dic26—81no—
142C8×C13—42no—
143C8×C13—81no—
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#384—131no—
157#340—261no—
158#340—261no—
159#340—261no—
160#340—261no—
161#336—131no—
162#336C2×D1311yescharacteristic
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—
179Dic13—42no—
180Dic13—81no—
181Dic13—81no—
182Dic13—81no—
183Dic13—161no—
184C22×Q8—131no—
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—261no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—131no—
190C2×C4⋊C4—131no—
191C2×C4⋊C4—131no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4D5211yescharacteristic
199C2×C4⋊C4D5211yescharacteristic
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—261no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4—521no—
231C22×C4C2×D5211yescharacteristic
232C22×C4D4×D1311yescharacteristic
233C22×C4D4×D1311yescharacteristic
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
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—261no—
249C4⋊C4—261no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C4⋊C4—521no—
253C4⋊C4—521no—
254C4⋊C4—522no—
255C4⋊C4—522no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—1041no—
259C4⋊C4—1041no—
260C42—41no—
261C42—1041no—
262C13#783111yescharacteristic, complemented, Sylow
263C23#8813611yescharacteristic
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—262no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—521no—
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—1041no—
291C2×C4—1041no—
292C2×C4—1041no—
293C2×C4#8815811yescharacteristic
294C2×C4#8816311yescharacteristic
295C2×C4#8816611yescharacteristic
296C2×C4#8816911yescharacteristic
297C2×C4#8816911yescharacteristic
298C2×C4Q16×D1311yescharacteristic
299C8—42no—
300C8—81no—
301C8—1041no—
302C22#1171839411yescharacteristic
303C22#1171840311yescharacteristic
304C22#1171841411yescharacteristic
305C22#1171844411yescharacteristic
306C22#1171846911yescharacteristic
307C22#1171848311yescharacteristic
308C22#1171848811yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—81no—
316C4—81no—
317C4—522no—
318C4—1041no—
319C4—1041no—
320C4—1041no—
321C4—2081no—
322C2#1311386211yescharacteristic
323C2#1311386811yescharacteristic
324C2#1311386911yescharacteristic
325C2#1311398311yescharacteristic
326C2#1311399511yescharacteristic
327C2#1311399611yescharacteristic
328C2#1311413611yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1271C2
socle, prime radicalC23×C13#120
hypercenter#1271D13
hypocenterC13#7831
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

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
#131164002
#131163992
#131163732
#131126612
#131126582
C13×#12712
#783113