Finite Group Databasebeta

← #15751003

Subgroups — #15751003

Order 3328.

482 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 109 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#13117294C211yesmaximal, characteristic
2#13114978C211yesmaximal, characteristic, complemented
3#13114951C211yesmaximal, characteristic, complemented
4#13112659C211yesmaximal, characteristic, complemented
5#13112656C211yesmaximal, characteristic
6#13112656C211yesmaximal, characteristic
7C13×#1271C211yesmaximal, characteristic, complemented
8C2×#88147C411yescharacteristic
9C2×#88146—21no—
10C13×#389C2211yescharacteristic
11C2×#88054—21no—
12#11718651—21no—
13#11718649C411yescharacteristic
14#11718646C411yescharacteristic
15C4⋊C4×Dic13C411yescharacteristic
16#11718600C2211yescharacteristic
17C42×Dic13C2211yescharacteristic
18#11718331—21no—
19#11718327—21no—
20C13×#336C2211yescharacteristic
21C13×#336C2211yescharacteristic
22#11718142—21no—
23#11718142—21no—
24#11718142—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×D52C2×C411yescharacteristic
28C22×C4×D13—21no—
29C22×C8×C13—21no—
30C22×C8×C13—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×#6103—21no—
36C2×#6103—21no—
37C2×#6103—21no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×C4×Dic13—21no—
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C22×#1055—21no—
50C22×#1055—21no—
51#88147—22no—
52#88147C814yescomplemented
53#88146—42no—
54#88146—42no—
55C13×#95—21no—
56#88071—21no—
57#88071—21no—
58#88054—42no—
59#7594—131nomaximal, Sylow
60C23×D13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—21no—
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C22⋊C411yescharacteristic
71C2×D52—21no—
72C2×D52—41no—
73C2×D52—41no—
74C2×D52C2×C812yes—
75C2×C4×D13—24no—
76C2×C4×D13—42no—
77C2×C4×D13—42no—
78C2×C8×C13—41no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4C2×C812yes—
89C42×C13—41no—
90#6103—24no—
91#6103—42no—
92#6103—42no—
93#6103—41no—
94#6103—41no—
95#6103—41no—
96#6103—41no—
97C4⋊Dic13—42no—
98C4⋊Dic13—41no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—41no—
104C4×Dic13—41no—
105C4×Dic13—41no—
106C4×Dic13—42no—
107C4×Dic13C2×C812yes—
108C4×Dic13M1612yes—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112C2×#1055—41no—
113C2×#1055—41no—
114C2×#1055—41no—
115#2293—131no—
116#1839—131no—
117#1831—131no—
118#1271—131no—
119#1271D1311yescharacteristic, complemented
120#1270—131no—
121#1270—131no—
122C23×C13C2×C22⋊C411yescharacteristic
123C22×D13—22no—
124C22×D13—41no—
125C22×D13—41no—
126C22×D13—41no—
127C22×D13—41no—
128C22×D13—41no—
129C22×D13—41no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—22no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13C22×C811yescharacteristic
143C2×C4×C13C2×M1611yescharacteristic
144C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C13#13711yescharacteristic
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13C22⋊C812yes—
162C2×Dic13C22⋊C812yes—
163D52—42no—
164D52—42no—
165C4×D13—48no—
166C8×C13—81no—
167C8×C13—81no—
168#1055—81no—
169#1055—81no—
170C2×C4×D4—131no—
171C2×#117—261no—
172C2×C4⋊C8—261no—
173#390—131no—
174#390—131no—
175#389—131no—
176#389C2×D1311yescharacteristic
177#388—261no—
178#388—261no—
179C4×C4⋊C4—131no—
180C4×C22⋊C4—261no—
181C43—131no—
182#336—131no—
183#336—131no—
184#336—261no—
185#336—261no—
186#336—261no—
187#336C2×D1311yescharacteristic
188#336C2×D1311yescharacteristic
189C22×C13C2×C22⋊C811yescharacteristic
190C22×C13#41011yescharacteristic
191C22×C13#41311yescharacteristic
192C22×C13#41711yescharacteristic
193C22×C13#41811yescharacteristic
194C22×C13#42111yescharacteristic
195C22×C13#42111yescharacteristic
196C2×D13—42no—
197C2×D13—42no—
198C2×D13—42no—
199C2×D13—81no—
200C2×D13—81no—
201C2×D13—81no—
202C2×D13—81no—
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—42no—
210C4×C13—81no—
211Dic13—22no—
212Dic13—22no—
213Dic13—41no—
214Dic13—41no—
215Dic13—81no—
216C22×D4—131no—
217C23×C4—261no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—261no—
221C22×C8—261no—
222C4×D4—134no—
223C4×D4—262no—
224#117—522no—
225#117—522no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—131no—
228C2×C4⋊C4—261no—
229C2×C4⋊C4C4×D1311yescharacteristic
230C2×C4⋊C4C4×D1311yescharacteristic
231C2×C22⋊C4—261no—
232C2×C22⋊C4—261no—
233C2×C22⋊C4—261no—
234C2×C22⋊C4—261no—
235C2×C22⋊C4—261no—
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—261no—
243C2×C42C22×D1311yescharacteristic
244C4⋊C8—522no—
245#95—21no—
246#95—261no—
247#95—261no—
248C2×C13#145811yescharacteristic
249C2×C13#147711yescharacteristic
250C2×C13#147811yescharacteristic
251C2×C13#151211yescharacteristic
252C2×C13#151411yescharacteristic
253C2×C13#153511yescharacteristic
254C2×C13#155711yescharacteristic
255D13—82no—
256C24—261no—
257C2×D4—132no—
258C2×D4—261no—
259C2×D4—521no—
260C2×D4—521no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—131no—
264C22×C4—131no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—264no—
268C22×C4—261no—
269C22×C4—522no—
270C22×C4—522no—
271C22×C4C2×C4×D1311yescharacteristic
272C22×C4D4×D1311yescharacteristic
273C22×C4D4×D1311yescharacteristic
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—521no—
281C2×C8—521no—
282C2×C8—521no—
283C2×C8—521no—
284C2×C8—521no—
285C2×C8—521no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—521no—
291C4⋊C4—522no—
292C4⋊C4C8×D1312yes—
293C22⋊C4—264no—
294C22⋊C4—522no—
295C22⋊C4—522no—
296C22⋊C4—521no—
297C22⋊C4—521no—
298C22⋊C4—521no—
299C22⋊C4—521no—
300C42—41no—
301C42—132no—
302C42—132no—
303C42—261no—
304C42—261no—
305C42—261no—
306C42—261no—
307C42—521no—
308C42—521no—
309C42—521no—
310C42—522no—
311C13#759411yescharacteristic, complemented, Sylow
312C23—262no—
313C23—521no—
314C23—521no—
315C23—521no—
316C23—521no—
317C23—521no—
318C23—521no—
319C23C22⋊C4×D1311yescharacteristic
320D4—522no—
321D4—522no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—132no—
335C2×C4—132no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—528no—
347C2×C4—521no—
348C2×C4—521no—
349C2×C4—521no—
350C2×C4C2×C8×D1311yescharacteristic
351C2×C4M16×D1311yescharacteristic
352C2×C4#8816511yescharacteristic
353C2×C4#8816811yescharacteristic
354C2×C4#8816811yescharacteristic
355C2×C4#8817211yescharacteristic
356C8—81no—
357C8—81no—
358C8—1041no—
359C8—1041no—
360C22—522no—
361C22—522no—
362C22—522no—
363C22—1041no—
364C22—1041no—
365C22—1041no—
366C22—1041no—
367C22D13×C22⋊C811yescharacteristic
368C22#1171840111yescharacteristic
369C22#1171841211yescharacteristic
370C22#1171843111yescharacteristic
371C22#1171846411yescharacteristic
372C22#1171848211yescharacteristic
373C22#1171848211yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—42no—
381C4—81no—
382C4—262no—
383C4—262no—
384C4—521no—
385C4—521no—
386C4—1041no—
387C2—1042no—
388C2#1311314911yescharacteristic
389C2#1311322211yescharacteristic
390C2#1311322511yescharacteristic
391C2#1311337311yescharacteristic
392C2#1311338111yescharacteristic
393C2#1311346611yescharacteristic
394C2#1311355711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1271C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1271D13
hypocenterC13#7594
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
2. #13114978C2semidirect
3. #13114951C2semidirect
4. #13112659C2semidirect
7. C13×#1271C2semidirect
52. #88147C8semidirect
119. #1271D13semidirect
311. C13#7594semidirect

Maximal subgroups

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

subgroupindex
#131172942
#131149782
#131149512
#131126592
#131126562
C13×#12712
#759413