Finite Group Databasebeta

← #15751815

Subgroups — #15751815

Order 3328.

416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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#13121788C211yesmaximal, characteristic
2#13116166C211yesmaximal, characteristic
3#13116079C211yesmaximal, characteristic
4#13112660C211yesmaximal, characteristic
5#13112660C211yesmaximal, characteristic
6#13112659C211yesmaximal, characteristic
7C13×#2058C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88143—21no—
10C2×C13×#106—21no—
11C13×#389C2211yescharacteristic
12C2×#88075—21no—
13C2×#88075—21no—
14#11718646—21no—
15#11718644—21no—
16#11718644—21no—
17C2×#88048—21no—
18#11718589C2211yescharacteristic
19#11718589C2211yescharacteristic
20#11718322—21no—
21#11718314—21no—
22C13×#340—21no—
23C13×#336C2211yescharacteristic
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13—21no—
28C22×C8×C13—21no—
29C13×C4⋊Q8—42no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4⋊Dic13D411yescharacteristic
40C2×C4⋊Dic13D411yescharacteristic
41C2×C4⋊Dic13D411yescharacteristic
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×C4×Dic13—21no—
47C22×#1055—21no—
48C22×#1055—21no—
49#88143—42no—
50#88143—42no—
51C13×#106—42no—
52C13×#95—21no—
53#88075—42no—
54#88075—42no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88048—42no—
61#7768—131nomaximal, Sylow
62C2×Q8×C13—22no—
63C2×Q8×C13—41no—
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—41no—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C2×C8×C13—22no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4SD1612yes—
90C42×C13—41no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—42no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97C4⋊Dic13—81no—
98C4⋊Dic13SD1612yes—
99#6101—42no—
100#6101—42no—
101#6101—41no—
102#6101—41no—
103#6101—41no—
104#6101—41no—
105C4×Dic13—42no—
106C2×#1055—22no—
107C2×#1055—41no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112#2726—131no—
113#2058—131no—
114#2058D1311yescharacteristic
115#2043—131no—
116#1271—131no—
117#1271—131no—
118#1271—131no—
119C23×C13#12011yescharacteristic
120Q8×C13—42no—
121Q8×C13—42no—
122Q8×C13—81no—
123Q8×C13—81no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—22no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—42no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13C2×SD1611yescharacteristic
140C2×C4×C13C2×SD1611yescharacteristic
141C2×C4×C13#13511yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C2×C4×C13#13711yescharacteristic
145C2×Dic13—22no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C8×C13—42no—
158#1055—42no—
159#1055—81no—
160C2×C4⋊Q8C2×D1311yescharacteristic
161C2×#125—261no—
162C2×#106—21no—
163C2×#106—261no—
164C2×#103—261no—
165C2×#103—261no—
166#398—261no—
167#398—261no—
168#398—261no—
169#389—131no—
170#389—131no—
171#389—261no—
172#389C2×D1311yescharacteristic
173#387—261no—
174#340—21no—
175#340—261no—
176#336—131no—
177#336—131no—
178#336C2×D1311yescharacteristic
179C22×C13#44811yescharacteristic
180C22×C13#45011yescharacteristic
181C22×C13#45211yescharacteristic
182C22×C13#45411yescharacteristic
183C22×C13#45611yescharacteristic
184C22×C13#45611yescharacteristic
185C22×C13B(4,𝔽2)11yescharacteristic
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—42no—
193C4×C13—82no—
194C4×C13—81no—
195Dic13—42no—
196Dic13—81no—
197Dic13—81no—
198Dic13—81no—
199C22×Q8—21no—
200C22×C8—21no—
201C22×C8—261no—
202C22×C8—261no—
203C4⋊Q8—42no—
204#125—522no—
205#125—522no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4C22⋊D1311yescharacteristic
220C2×C4⋊C4C22⋊D1311yescharacteristic
221C2×C42—261no—
222C2×C42C22×D1311yescharacteristic
223#106—42no—
224#106—522no—
225#103—522no—
226#103—522no—
227#95—21no—
228#95—261no—
229#95—261no—
230#95—261no—
231#95—261no—
232#95—261no—
233C2×C13#159911yescharacteristic
234C2×C13#160311yescharacteristic
235C2×C13#160411yescharacteristic
236C2×C13#163511yescharacteristic
237C2×C13#165111yescharacteristic
238C2×C13#165311yescharacteristic
239C2×C13#166311yescharacteristic
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4D4×D1311yescharacteristic
254C22×C4D4×D1311yescharacteristic
255C22×C4C2×C22⋊D1311yescharacteristic
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—262no—
260C2×C8—521no—
261C2×C8—521no—
262C2×C8—521no—
263C2×C8—521no—
264C2×C8—521no—
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—132no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—521no—
278C4⋊C4—521no—
279C4⋊C4—522no—
280C4⋊C4—522no—
281C4⋊C4—522no—
282C4⋊C4—521no—
283C4⋊C4—521no—
284C4⋊C4—521no—
285C4⋊C4—521no—
286C4⋊C4—1041no—
287C4⋊C4#610612yes—
288C42—41no—
289C42—522no—
290C13#776811yescharacteristic, complemented, Sylow
291C23#8819111yescharacteristic
292Q8—42no—
293Q8—42no—
294Q8—81no—
295Q8—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—262no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4SD16×D1311yescharacteristic
324C2×C4#8816911yescharacteristic
325C2×C4#8816911yescharacteristic
326C2×C4#8817011yescharacteristic
327C2×C4C2×#610611yescharacteristic
328C2×C4#8820311yescharacteristic
329C8—42no—
330C8—522no—
331C8—1041no—
332C22#1171869311yescharacteristic
333C22#1171870711yescharacteristic
334C22#1171875611yescharacteristic
335C22#1171883111yescharacteristic
336C22#1171883411yescharacteristic
337C22#1171886211yescharacteristic
338C22#1171886611yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—42no—
346C4—82no—
347C4—81no—
348C4—522no—
349C4—1041no—
350C4—1041no—
351C4—1041no—
352C2#1311377411yescharacteristic
353C2#1311379611yescharacteristic
354C2#1311380411yescharacteristic
355C2#1311398511yescharacteristic
356C2#1311409811yescharacteristic
357C2#1311411011yescharacteristic
358C2#1311416311yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2058C2
socle, prime radicalC23×C13#120
hypercenter#2058D13
hypocenterC13#7768
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2058

Complements

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

NH ≅ G/Ntype
290. C13#7768semidirect

Maximal subgroups

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

subgroupindex
#131217882
#131161662
#131160792
#131126602
#131126592
C13×#20582
#776813