Finite Group Databasebeta

← #15751872

Subgroups — #15751872

Order 3328.

446 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 446 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#13121795C211yesmaximal, characteristic
2#13116166C211yesmaximal, characteristic, complemented
3#13116079C211yesmaximal, characteristic, complemented
4#13112660C211yesmaximal, characteristic, complemented
5#13112658C211yesmaximal, characteristic, complemented
6#13112657C211yesmaximal, characteristic
7C13×#2023C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88133—21no—
10C2×C13×#102—21no—
11C13×#390C2211yescharacteristic
12C2×#88075—21no—
13C2×#88075—21no—
14#11718883—21no—
15#11718633—21no—
16C2×#88048—21no—
17#11718612—21no—
18#11718610—21no—
19#11718609—21no—
20#11718589C2211yescharacteristic
21#11718589C2211yescharacteristic
22C13×#340—21no—
23C13×#336C2211yescharacteristic
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13—21no—
28C22×D4×C13D411yescharacteristic
29C22×C8×C13—21no—
30C13×C4⋊Q8—42no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C42×C13C2311yescharacteristic
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—21no—
41C2×C4⋊Dic13D411yescharacteristic
42C2×C4⋊Dic13D411yescharacteristic
43C2×C4⋊Dic13D411yescharacteristic
44C2×C4⋊Dic13D411yescharacteristic
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×#6101—21no—
49C2×C4×Dic13—21no—
50C22×#1055—21no—
51C22×#1055—21no—
52#88133—42no—
53#88133—42no—
54C13×#102—42no—
55#88075—42no—
56#88075—42no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88048—42no—
61#7776—131nomaximal, Sylow
62C24×C13—21no—
63C2×Q8×C13—22no—
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C2×Q8×C13—41no—
69C2×D4×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C22×C4×C13—21no—
74C22×C4×C13—41no—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C42×C13—41no—
95C22⋊Dic13—42no—
96C22⋊Dic13—42no—
97C22⋊Dic13—81no—
98C22⋊Dic13—81no—
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13—41no—
103C4⋊Dic13—41no—
104C4⋊Dic13SD1612yes—
105#6101—42no—
106#6101—41no—
107#6101—41no—
108#6101—41no—
109#6101—41no—
110#6101—81no—
111C4×Dic13—42no—
112C2×#1055—22no—
113C2×#1055—41no—
114C2×#1055—41no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118#2727—131no—
119#2058—131no—
120#2043—131no—
121#2023D1311yescharacteristic
122#1271—131no—
123#1271—131no—
124#1270—131no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13#12011yescharacteristic
133Q8×C13—42no—
134Q8×C13—42no—
135Q8×C13—81no—
136Q8×C13—81no—
137D4×C13—42no—
138D4×C13—81no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—42no—
149C2×C4×C13—81no—
150C2×C4×C13—81no—
151C2×C4×C13C2×SD1611yescharacteristic
152C2×C4×C13#13511yescharacteristic
153C2×C4×C13#13511yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C13#13711yescharacteristic
157C2×Dic13—22no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C8×C13—81no—
170#1055—42no—
171#1055—81no—
172C2×C4⋊Q8C2×D1311yescharacteristic
173C2×#126—261no—
174C2×#106—261no—
175C2×#103—261no—
176C2×#103—261no—
177C2×#102—21no—
178#399—261no—
179#396—261no—
180#394—261no—
181#390C2×D1311yescharacteristic
182#389—131no—
183#389—131no—
184#389—261no—
185#388—261no—
186#340—21no—
187#340—261no—
188#336—131no—
189#336—131no—
190#336C2×D1311yescharacteristic
191C22×C13—81no—
192C22×C13—81no—
193C22×C13—81no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13#44911yescharacteristic
199C22×C13#45011yescharacteristic
200C22×C13#45211yescharacteristic
201C22×C13#45411yescharacteristic
202C22×C13#45511yescharacteristic
203C22×C13#45611yescharacteristic
204C22×C13B(4,𝔽2)11yescharacteristic
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—82no—
212C4×C13—81no—
213Dic13—42no—
214Dic13—81no—
215Dic13—81no—
216Dic13—81no—
217C22×Q8—21no—
218C22×D4C22⋊D1311yescharacteristic
219C22×C8—21no—
220C22×C8—261no—
221C22×C8—261no—
222C4⋊Q8—42no—
223#126—522no—
224#126—522no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—131no—
228C2×C4⋊C4—131no—
229C2×C4⋊C4—131no—
230C2×C4⋊C4—131no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—261no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4—261no—
235C2×C4⋊C4C22⋊D1311yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—261no—
239C2×C22⋊C4—261no—
240C2×C22⋊C4—261no—
241C2×C22⋊C4—261no—
242C2×C42—261no—
243C2×C42C22×D1311yescharacteristic
244#106—522no—
245#103—522no—
246#103—522no—
247#102—42no—
248#95—261no—
249#95—261no—
250#95—261no—
251C2×C13—161no—
252C2×C13#159711yescharacteristic
253C2×C13#160411yescharacteristic
254C2×C13#160611yescharacteristic
255C2×C13#163511yescharacteristic
256C2×C13#164211yescharacteristic
257C2×C13#165211yescharacteristic
258C2×C13#166411yescharacteristic
259C24—21no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4—261no—
276C22×C4D4×D1311yescharacteristic
277C22×C4D4×D1311yescharacteristic
278C22×C4C2×C22⋊D1311yescharacteristic
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—262no—
283C2×C8—521no—
284C2×C8—521no—
285C2×C8—521no—
286C2×C8—521no—
287C2×C8—521no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—132no—
294C4⋊C4—261no—
295C4⋊C4—261no—
296C4⋊C4—261no—
297C4⋊C4—521no—
298C4⋊C4—521no—
299C4⋊C4—522no—
300C4⋊C4—521no—
301C4⋊C4—521no—
302C4⋊C4—521no—
303C4⋊C4—521no—
304C4⋊C4—1041no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—522no—
310C22⋊C4—522no—
311C22⋊C4—1041no—
312C22⋊C4—1041no—
313C42—41no—
314C42—522no—
315C13#777611yescharacteristic, complemented, Sylow
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23#8819111yescharacteristic
324Q8—42no—
325Q8—42no—
326Q8—81no—
327Q8—81no—
328D4—42no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—262no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—521no—
346C2×C4—521no—
347C2×C4—521no—
348C2×C4—521no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4#8816511yescharacteristic
355C2×C4#8816611yescharacteristic
356C2×C4SD16×D1311yescharacteristic
357C2×C4#8816811yescharacteristic
358C2×C4#8819611yescharacteristic
359C2×C4#8820411yescharacteristic
360C8—81no—
361C8—522no—
362C8—1041no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22#1171869311yescharacteristic
371C22#1171870811yescharacteristic
372C22#1171872211yescharacteristic
373C22#1171881911yescharacteristic
374C22#1171883011yescharacteristic
375C22#1171886211yescharacteristic
376C22#1171886611yescharacteristic
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—82no—
384C4—81no—
385C4—522no—
386C4—1041no—
387C4—1041no—
388C4—1041no—
389C2—161no—
390C2#1311376211yescharacteristic
391C2#1311380311yescharacteristic
392C2#1311381411yescharacteristic
393C2#1311398611yescharacteristic
394C2#1311403311yescharacteristic
395C2#1311410511yescharacteristic
396C2#1311416911yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2023C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2023D13
hypocenterC13#7776
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
2. #13116166C2semidirect
3. #13116079C2semidirect
4. #13112660C2semidirect
5. #13112658C2semidirect
315. C13#7776semidirect

Maximal subgroups

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

subgroupindex
#131217952
#131161662
#131160792
#131126602
#131126582
#131126572
C13×#20232
#777613