Finite Group Databasebeta

← #15751955

Subgroups — #15751955

Order 3328.

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

normal subgroups only

This group has 418 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#13116394C211yesmaximal, characteristic, complemented
2#13116307C211yesmaximal, characteristic, complemented
3#13116239C211yesmaximal, characteristic
4#13112659C211yesmaximal, characteristic, complemented
5#13112659C211yesmaximal, characteristic, complemented
6#13112657C211yesmaximal, characteristic
7C13×#2724C211yesmaximal, characteristic
8C2×C13×#123—21no—
9C13×#398—21no—
10C13×#397—21no—
11C13×#397—21no—
12C13×#390C2211yescharacteristic
13C13×#389C2211yescharacteristic
14C13×#389C2211yescharacteristic
15C13×#385—21no—
16C13×#385—21no—
17C2×#88072—21no—
18C2×#88047—21no—
19#11718596C2211yescharacteristic
20#11718121—21no—
21#11718121—21no—
22#11718121—21no—
23#11718121—21no—
24#11718116C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×D4×C13D411yescharacteristic
28C23×C4×C13—21no—
29C13×#123—42no—
30C13×#123—42no—
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×C42×C13C2311yescharacteristic
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13—21no—
48C22×#1055—21no—
49C22×#1055—21no—
50C22×#1055—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56#88072—42no—
57#88047—42no—
58#7788—131nomaximal, Sylow
59C24×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13D812yes—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—42no—
70C22×C4×C13—81no—
71C22×C4×C13—81no—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—41no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—81no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C42×C13—41no—
96C4⋊Dic13—42no—
97C4⋊Dic13—41no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101C2×#1055—22no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#1055—41no—
108C2×#1055—41no—
109C2×#1055—41no—
110#2724D1311yescharacteristic
111#2099—131no—
112#2083—131no—
113#2071—131no—
114#1271—131no—
115#1271—131no—
116#1270—131no—
117C23×C13—22no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13#12011yescharacteristic
125D4×C13—42no—
126D4×C13—81no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
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×C13—41no—
148C2×C4×C13—84no—
149C2×C4×C13C2×D811yescharacteristic
150C2×C4×C13#13511yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C13#13711yescharacteristic
155C2×Dic13—81no—
156C2×Dic13—81no—
157C2×Dic13—81no—
158#1055—42no—
159#1055—81no—
160#1055—81no—
161C2×#123—21no—
162C2×#107—261no—
163C2×#102—261no—
164#398—21no—
165#397—21no—
166#397—21no—
167#390C2×D1311yescharacteristic
168#389C2×D1311yescharacteristic
169#389C2×D1311yescharacteristic
170#385—21no—
171#385—21no—
172#384—131no—
173#340—261no—
174#340—261no—
175#340—261no—
176#340—261no—
177#336—131no—
178#336—131no—
179#336—131no—
180C22×C13—42no—
181C22×C13—42no—
182C22×C13—42no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13#44711yescharacteristic
188C22×C13#44911yescharacteristic
189C22×C13#45211yescharacteristic
190C22×C13#45411yescharacteristic
191C22×C13#45511yescharacteristic
192C22×C13#45611yescharacteristic
193C22×C13#45811yescharacteristic
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—81no—
201C4×C13—81no—
202C4×C13—81no—
203C4×C13—81no—
204C4×C13—81no—
205Dic13—161no—
206C22×D4C22⋊D1311yescharacteristic
207C23×C4—21no—
208C22×C8—261no—
209C22×C8—261no—
210C22×C8—261no—
211#123—42no—
212#123—42no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4C22⋊D1311yescharacteristic
220C2×C4⋊C4C22⋊D1311yescharacteristic
221C2×C4⋊C4C22⋊D1311yescharacteristic
222C2×C4⋊C4C22⋊D1311yescharacteristic
223C2×C4⋊C4C22⋊D1311yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C42C22×D1311yescharacteristic
230#107—522no—
231#102—522no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237C2×C13—82no—
238C2×C13#160711yescharacteristic
239C2×C13#160911yescharacteristic
240C2×C13#161511yescharacteristic
241C2×C13#162511yescharacteristic
242C2×C13#164011yescharacteristic
243C2×C13#164711yescharacteristic
244C2×C13#166411yescharacteristic
245C24—21no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4#610412yes—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—521no—
259C22×C4C2×C22⋊D1311yescharacteristic
260C22×C4C2×C22⋊D1311yescharacteristic
261C22×C4C2×C22⋊D1311yescharacteristic
262C2×C8—262no—
263C2×C8—521no—
264C2×C8—521no—
265C2×C8—521no—
266C2×C8—521no—
267C2×C8—521no—
268C2×C8—521no—
269C2×C8—521no—
270C2×C8—521no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—522no—
284C4⋊C4—521no—
285C4⋊C4—521no—
286C4⋊C4—521no—
287C4⋊C4—521no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C42—41no—
296C13#778811yescharacteristic, complemented, Sylow
297C23—22no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23#8820711yescharacteristic
305D4—42no—
306D4—81no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
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—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—84no—
329C2×C4—1041no—
330C2×C4—1041no—
331C2×C4—1041no—
332C2×C4C2×#610411yescharacteristic
333C2×C4#8818611yescharacteristic
334C2×C4#8820311yescharacteristic
335C2×C4#8820411yescharacteristic
336C2×C4#8820411yescharacteristic
337C2×C4#8820511yescharacteristic
338C8—522no—
339C8—1041no—
340C8—1041no—
341C22—42no—
342C22—42no—
343C22—42no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22#1171887811yescharacteristic
349C22#1171889911yescharacteristic
350C22#1171890011yescharacteristic
351C22#1171890311yescharacteristic
352C22#1171890411yescharacteristic
353C22#1171890611yescharacteristic
354C22#1171890711yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—81no—
365C4—81no—
366C4—2081no—
367C2—82no—
368C2#1311382211yescharacteristic
369C2#1311383311yescharacteristic
370C2#1311386711yescharacteristic
371C2#1311392511yescharacteristic
372C2#1311402211yescharacteristic
373C2#1311407111yescharacteristic
374C2#1311417011yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2724C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2724D13
hypocenterC13#7788
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2724

Complements

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

NH ≅ G/Ntype
1. #13116394C2semidirect
2. #13116307C2semidirect
4. #13112659C2semidirect
5. #13112659C2semidirect
296. C13#7788semidirect

Maximal subgroups

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

subgroupindex
#131163942
#131163072
#131162392
#131126592
#131126572
C13×#27242
#778813