Finite Group Databasebeta

← #15751327

Subgroups — #15751327

Order 3328.

468 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 97 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#13123145C211yesmaximal, characteristic
2#13114903C211yesmaximal, characteristic
3#13114593C211yesmaximal, characteristic
4#13112660C211yesmaximal, characteristic, complemented
5#13112659C211yesmaximal, characteristic, complemented
6#13112658C211yesmaximal, characteristic, complemented
7C13×#1271C211yesmaximal, characteristic, complemented
8C2×#88144C411yescharacteristic
9C2×C42×D13C2211yescharacteristic
10C13×#389C2211yescharacteristic
11C2×#88060—21no—
12C2×#88060—21no—
13C2×C8×Dic13—21no—
14#11718650—21no—
15#11718648C411yescharacteristic
16#11718648C411yescharacteristic
17#11718642—21no—
18#11718638C411yescharacteristic
19#11718589C2211yescharacteristic
20#11718329—21no—
21#11718313—21no—
22C13×#336C2211yescharacteristic
23C13×#336C2211yescharacteristic
24#11718142—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×C4×D13C2×C411yescharacteristic
28C22×C4×D13D411yescharacteristic
29C22×C4×D13D411yescharacteristic
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C2×#6103—21no—
37C2×#6103—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C22×#1055—21no—
47C22×#1055—21no—
48#88144—42no—
49C42×D13—42no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88060—24no—
57#88060—42no—
58C8×Dic13—42no—
59#7671—131nomaximal, Sylow
60C23×D13C22⋊C411yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C22⋊C411yescharacteristic
71C2×C4×D13—22no—
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13—22no—
79C2×C4×D13—22no—
80C2×C4×D13—41no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C8×C13—22no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C42×C13—41no—
95#6103—42no—
96#6103—42no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13—42no—
100C4⋊Dic13—41no—
101#6101—42no—
102#6101—41no—
103#6101—41no—
104C4×Dic13—22no—
105C4×Dic13—22no—
106C4×Dic13—41no—
107C2×#1055—22no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112C2×#1055—41no—
113#2851—131no—
114#1817—131no—
115C4×C22⋊C8—131no—
116#1271—131no—
117#1271—131no—
118#1271—131no—
119#1271D1311yescharacteristic, complemented
120C23×C13C2×C22⋊C411yescharacteristic
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
125C22×D13—21no—
126C22×D13—21no—
127C22×D13#10412yes—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13#13111yescharacteristic
141C2×C4×C13#13111yescharacteristic
142C2×C4×C13#13511yescharacteristic
143C2×C4×C13#13511yescharacteristic
144C2×C4×C13#13511yescharacteristic
145C2×C4×C13#13511yescharacteristic
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13#9912yes—
160C2×Dic13#10112yes—
161C4×D13—42no—
162C4×D13—42no—
163C4×D13—42no—
164C4×D13—42no—
165C4×D13—42no—
166C4×D13—42no—
167C8×C13—42no—
168C8×C13—81no—
169#1055—42no—
170#1055—81no—
171C2×#125—131no—
172C22×C42—131no—
173C2×C22⋊C8—261no—
174C2×C22⋊C8—261no—
175C2×C4×C8—261no—
176#389—131no—
177#389C2×D1311yescharacteristic
178#387—261no—
179#387—261no—
180#385—261no—
181#385—261no—
182#382—131no—
183#380—131no—
184#380—131no—
185#336—131no—
186#336—131no—
187#336—261no—
188#336C2×D1311yescharacteristic
189#336C2×D1311yescharacteristic
190C22×C13#40811yescharacteristic
191C22×C13C2×#9911yescharacteristic
192C22×C13C2×#10111yescharacteristic
193C22×C13#41611yescharacteristic
194C22×C13#41611yescharacteristic
195C22×C13C2×#10411yescharacteristic
196C22×C13#42111yescharacteristic
197C2×D13—22no—
198C2×D13—22no—
199C2×D13—22no—
200C2×D13—41no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—41no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—81no—
211C4×C13—81no—
212Dic13—22no—
213Dic13—22no—
214Dic13—41no—
215Dic13—81no—
216Dic13—81no—
217C23×C4—131no—
218C23×C4—131no—
219C23×C4—131no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—261no—
223C22×C8—261no—
224#125—522no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4—131no—
228C2×C4⋊C4—261no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4C4×D1311yescharacteristic
232C2×C4⋊C4C4×D1311yescharacteristic
233C2×C22⋊C4—261no—
234C2×C22⋊C4—261no—
235C2×C42—131no—
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—522no—
239C2×C42C22×D1311yescharacteristic
240C22⋊C8—264no—
241C22⋊C8—522no—
242C4×C8—522no—
243#95—21no—
244#95—261no—
245#95—261no—
246#95—261no—
247#95—261no—
248#95—261no—
249C2×C13#147211yescharacteristic
250C2×C13#148211yescharacteristic
251C2×C13#149411yescharacteristic
252C2×C13#150111yescharacteristic
253C2×C13#151611yescharacteristic
254C2×C13#152811yescharacteristic
255C2×C13#154411yescharacteristic
256D13—42no—
257C24—131no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—131no—
261C22×C4—131no—
262C22×C4—131no—
263C22×C4—262no—
264C22×C4—262no—
265C22×C4—262no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4—261no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4—521no—
275C22×C4—521no—
276C22×C4—521no—
277C22×C4C2×C4×D1311yescharacteristic
278C22×C4D4×D1311yescharacteristic
279C22×C4D4×D1311yescharacteristic
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—262no—
287C2×C8—521no—
288C2×C8—521no—
289C2×C8—521no—
290C2×C8—521no—
291C2×C8—521no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—261no—
298C4⋊C4—261no—
299C4⋊C4—521no—
300C4⋊C4—522no—
301C4⋊C4—522no—
302C4⋊C4—521no—
303C4⋊C4—521no—
304C22⋊C4—522no—
305C22⋊C4—522no—
306C42—41no—
307C42—262no—
308C42—262no—
309C42—521no—
310C13#767111yescharacteristic, complemented, Sylow
311C23—132no—
312C23—261no—
313C23—261no—
314C23—261no—
315C23—261no—
316C23—261no—
317C23—261no—
318C23C22⋊C4×D1311yescharacteristic
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—132no—
332C2×C4—132no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—522no—
341C2×C4—522no—
342C2×C4—522no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4—521no—
347C2×C4—521no—
348C2×C4—521no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4—521no—
352C2×C4#8815511yescharacteristic
353C2×C4#8816111yescharacteristic
354C2×C4#8816611yescharacteristic
355C2×C4#8817011yescharacteristic
356C2×C4#8817011yescharacteristic
357C2×C4#8817311yescharacteristic
358C8—42no—
359C8—81no—
360C8—522no—
361C8—1041no—
362C22—262no—
363C22—262no—
364C22—262no—
365C22—521no—
366C22—521no—
367C22—521no—
368C22—521no—
369C22#1171838811yescharacteristic
370C22D13×#9911yescharacteristic
371C22D13×#10111yescharacteristic
372C22#1171843311yescharacteristic
373C22#1171846511yescharacteristic
374C22D13×#10411yescharacteristic
375C22#1171848211yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—81no—
383C4—81no—
384C4—262no—
385C4—262no—
386C4—521no—
387C4—1041no—
388C4—1041no—
389C2—522no—
390C2#1311319811yescharacteristic
391C2#1311324111yescharacteristic
392C2#1311329511yescharacteristic
393C2#1311332411yescharacteristic
394C2#1311339111yescharacteristic
395C2#1311343611yescharacteristic
396C2#1311349911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1271C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1271D13
hypocenterC13#7671
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #13112660C2semidirect
5. #13112659C2semidirect
6. #13112658C2semidirect
7. C13×#1271C2semidirect
119. #1271D13semidirect
310. C13#7671semidirect

Maximal subgroups

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

subgroupindex
#131231452
#131149032
#131145932
#131126602
#131126592
#131126582
C13×#12712
#767113