Finite Group Databasebeta

← #15752213

Subgroups — #15752213

Order 3328.

404 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 87 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#13116399C211yesmaximal, characteristic, complemented
2#13116399C211yesmaximal, characteristic, complemented
3#13116369C211yesmaximal, characteristic
4#13112659C211yesmaximal, characteristic, complemented
5#13112659C211yesmaximal, characteristic, complemented
6#13112657C211yesmaximal, characteristic
7C13×#2727C211yesmaximal, characteristic
8C2×C13×#126—21no—
9C13×#399—21no—
10C13×#396—21no—
11C13×#394—21no—
12C13×#390C2211yescharacteristic
13C13×#389—21no—
14C13×#389C2211yescharacteristic
15C13×#389C2211yescharacteristic
16C13×#388—21no—
17C2×#88072—21no—
18C2×#88048—21no—
19#11718596C2211yescharacteristic
20#11718121—21no—
21#11718121—21no—
22#11718121—21no—
23#11718121—21no—
24#11718116C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×D4×C13D411yescharacteristic
28C13×#126—42no—
29C13×#126—42no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C42×C13—21no—
46C2×C42×C13C2311yescharacteristic
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13—21no—
50C22×#1055—21no—
51C22×#1055—21no—
52C22×#1055—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56#88072—42no—
57#88048—42no—
58#7828—131nomaximal, Sylow
59C24×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—41no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—81no—
85C13×C4⋊C4SD1612yes—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—81no—
93C13×C22⋊C4—81no—
94C42×C13—41no—
95C42×C13—42no—
96C4⋊Dic13—41no—
97C4⋊Dic13—42no—
98C4⋊Dic13—42no—
99C4⋊Dic13—41no—
100C2×#1055—22no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#1055—41no—
108C2×#1055—41no—
109#2727D1311yescharacteristic
110#2100—131no—
111#2100—131no—
112#2094—131no—
113#1271—131no—
114#1271—131no—
115#1270—131no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13#12011yescharacteristic
124D4×C13—42no—
125D4×C13—81no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—22no—
133C2×C4×C13—41no—
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—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13C2×SD1611yescharacteristic
148C2×C4×C13#13511yescharacteristic
149C2×C4×C13#13511yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C13#13711yescharacteristic
152C2×C4×C13#13711yescharacteristic
153C2×Dic13—81no—
154C2×Dic13—81no—
155C2×Dic13—81no—
156#1055—42no—
157#1055—81no—
158#1055—81no—
159C2×#126—21no—
160C2×#106—261no—
161C2×#102—261no—
162#399—21no—
163#396—21no—
164#394—21no—
165#390C2×D1311yescharacteristic
166#389—21no—
167#389C2×D1311yescharacteristic
168#389C2×D1311yescharacteristic
169#388—21no—
170#384—131no—
171#340—261no—
172#340—261no—
173#340—261no—
174#340—261no—
175#336—131no—
176#336—131no—
177#336—131no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13#45011yescharacteristic
186C22×C13#45211yescharacteristic
187C22×C13#45211yescharacteristic
188C22×C13#45311yescharacteristic
189C22×C13#45411yescharacteristic
190C22×C13#45411yescharacteristic
191C22×C13#45811yescharacteristic
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—42no—
199C4×C13—81no—
200C4×C13—81no—
201C4×C13—81no—
202C4×C13—81no—
203Dic13—161no—
204C22×D4C22⋊D1311yescharacteristic
205C22×C8—261no—
206C22×C8—261no—
207C22×C8—261no—
208#126—42no—
209#126—42no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4C22⋊D1311yescharacteristic
218C2×C4⋊C4C22⋊D1311yescharacteristic
219C2×C4⋊C4C22⋊D1311yescharacteristic
220C2×C4⋊C4C22⋊D1311yescharacteristic
221C2×C4⋊C4C22⋊D1311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C42—21no—
229C2×C42C22×D1311yescharacteristic
230#106—522no—
231#102—522no—
232#95—21no—
233#95—21no—
234#95—21no—
235C2×C13—161no—
236C2×C13#161511yescharacteristic
237C2×C13#161611yescharacteristic
238C2×C13#161811yescharacteristic
239C2×C13#163111yescharacteristic
240C2×C13#163511yescharacteristic
241C2×C13#163811yescharacteristic
242C2×C13#165711yescharacteristic
243C24—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C2×D4—41no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—521no—
254C22×C4C2×C22⋊D1311yescharacteristic
255C22×C4C2×C22⋊D1311yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257C2×C8—262no—
258C2×C8—521no—
259C2×C8—521no—
260C2×C8—521no—
261C2×C8—521no—
262C2×C8—521no—
263C2×C8—521no—
264C2×C8—521no—
265C2×C8—521no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—81no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C4⋊C4—522no—
281C4⋊C4—522no—
282C4⋊C4#610512yes—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—81no—
290C22⋊C4—81no—
291C42—41no—
292C42—42no—
293C13#782811yescharacteristic, complemented, Sylow
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23#8820711yescharacteristic
302D4—42no—
303D4—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—1041no—
326C2×C4—1041no—
327C2×C4—1041no—
328C2×C4#8818611yescharacteristic
329C2×C4C2×#610511yescharacteristic
330C2×C4#8820411yescharacteristic
331C2×C4#8820411yescharacteristic
332C2×C4#8820511yescharacteristic
333C2×C4#8820511yescharacteristic
334C8—522no—
335C8—1041no—
336C8—1041no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22#1171887911yescharacteristic
345C22#1171890011yescharacteristic
346C22#1171890011yescharacteristic
347C22#1171890211yescharacteristic
348C22#1171890411yescharacteristic
349C22#1171890611yescharacteristic
350C22#1171890611yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—42no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—81no—
362C4—2081no—
363C2—161no—
364C2#1311386711yescharacteristic
365C2#1311387311yescharacteristic
366C2#1311388411yescharacteristic
367C2#1311396311yescharacteristic
368C2#1311398711yescharacteristic
369C2#1311400811yescharacteristic
370C2#1311413411yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2727C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2727D13
hypocenterC13#7828
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2727

Complements

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

NH ≅ G/Ntype
1. #13116399C2semidirect
2. #13116399C2semidirect
4. #13112659C2semidirect
5. #13112659C2semidirect
293. C13#7828semidirect

Maximal subgroups

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

subgroupindex
#131163992
#131163692
#131126592
#131126572
C13×#27272
#782813