Finite Group Databasebeta

← #15751808

Subgroups — #15751808

Order 3328.

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

normal subgroups only

This group has 392 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#13122786C211yesmaximal, characteristic
2#13116079C211yesmaximal, characteristic
3#13115974C211yesmaximal, characteristic
4#13112661C211yesmaximal, characteristic
5#13112660C211yesmaximal, characteristic
6#13112659C211yesmaximal, characteristic
7C13×#2058C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×#106—21no—
10C13×#389C2211yescharacteristic
11C2×#88075—21no—
12C2×#88075—21no—
13#11718643—21no—
14#11718642—21no—
15#11718640—21no—
16#11718633—21no—
17C2×#88050—21no—
18#11718590C2211yescharacteristic
19#11718589C2211yescharacteristic
20#11718321—21no—
21#11718314—21no—
22C13×#340—21no—
23C13×#336C2211yescharacteristic
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13—21no—
28C22×Dic26D411yescharacteristic
29C22×C8×C13—21no—
30C13×C4⋊Q8—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×C42×C13C2311yescharacteristic
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4⋊Dic13D411yescharacteristic
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13—21no—
44C22×#1055—21no—
45C22×#1055—21no—
46C13×#106—42no—
47C13×#95—21no—
48#88075—42no—
49#88075—42no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88050—42no—
59#7767—131nomaximal, Sylow
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×Q8×C13—41no—
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—41no—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C2×Dic26—21no—
77C2×Dic26—21no—
78C2×Dic26—41no—
79C2×Dic26—41no—
80C2×C8×C13—22no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C42×C13—41no—
93C4⋊Dic13—21no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C4⋊Dic13SD1612yes—
97#6101—41no—
98#6101—41no—
99#6101—81no—
100#6101—81no—
101C4×Dic13—81no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#1055—41no—
108#2805—131no—
109#2058D1311yescharacteristic
110#2043—131no—
111#2024—131no—
112#1272—131no—
113#1271—131no—
114#1271—131no—
115C23×C13#12011yescharacteristic
116Q8×C13—42no—
117Q8×C13—42no—
118Q8×C13—81no—
119Q8×C13—81no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13C2×SD1611yescharacteristic
136C2×C4×C13#13511yescharacteristic
137C2×C4×C13#13511yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C2×C4×C13#13711yescharacteristic
140C2×C4×C13#13711yescharacteristic
141C2×Dic13—22no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153Dic26—42no—
154Dic26—81no—
155C8×C13—42no—
156#1055—81no—
157#1055—81no—
158C2×C4⋊Q8C2×D1311yescharacteristic
159C2×#106—21no—
160C2×#103—261no—
161C2×#103—261no—
162C2×#103—261no—
163#400—261no—
164#400—261no—
165#395—261no—
166#391—131no—
167#389—131no—
168#389—261no—
169#389C2×D1311yescharacteristic
170#387—261no—
171#387—261no—
172#340—21no—
173#340—261no—
174#336—131no—
175#336—131no—
176#336C2×D1311yescharacteristic
177C22×C13#44811yescharacteristic
178C22×C13#45211yescharacteristic
179C22×C13#45211yescharacteristic
180C22×C13#45411yescharacteristic
181C22×C13#45511yescharacteristic
182C22×C13#45611yescharacteristic
183C22×C13B(4,𝔽2)11yescharacteristic
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—82no—
191C4×C13—81no—
192C4×C13—81no—
193Dic13—42no—
194Dic13—81no—
195Dic13—81no—
196Dic13—81no—
197C22×Q8—21no—
198C22×Q8—131no—
199C22×C8—21no—
200C22×C8—261no—
201C22×C8—261no—
202C4⋊Q8—42no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4C22⋊D1311yescharacteristic
213C2×C4⋊C4C22⋊D1311yescharacteristic
214C2×C42—261no—
215C2×C42C22×D1311yescharacteristic
216#106—42no—
217#103—522no—
218#103—522no—
219#103—522no—
220#95—21no—
221#95—261no—
222#95—261no—
223#95—261no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228#95—261no—
229C2×C13#159911yescharacteristic
230C2×C13#160311yescharacteristic
231C2×C13#160611yescharacteristic
232C2×C13#163811yescharacteristic
233C2×C13#164311yescharacteristic
234C2×C13#165311yescharacteristic
235C2×C13#166411yescharacteristic
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—261no—
243C2×Q8—261no—
244C2×Q8—521no—
245C2×Q8—521no—
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—521no—
260C2×C8—521no—
261C2×C8—521no—
262C2×C8—521no—
263C2×C8—521no—
264C2×C8—521no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—132no—
275C4⋊C4—261no—
276C4⋊C4—521no—
277C4⋊C4—521no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C4⋊C4—1041no—
281C4⋊C4—1041no—
282C42—41no—
283C42—1041no—
284C13#776711yescharacteristic, complemented, Sylow
285C23#8819111yescharacteristic
286Q8—42no—
287Q8—42no—
288Q8—81no—
289Q8—81no—
290Q8—522no—
291Q8—1041no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—262no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4SD16×D1311yescharacteristic
320C2×C4#8816911yescharacteristic
321C2×C4#8816911yescharacteristic
322C2×C4#8817011yescharacteristic
323C2×C4#8819611yescharacteristic
324C2×C4#8820411yescharacteristic
325C8—42no—
326C8—1041no—
327C8—1041no—
328C22#1171869311yescharacteristic
329C22#1171870811yescharacteristic
330C22#1171875611yescharacteristic
331C22#1171883111yescharacteristic
332C22#1171883411yescharacteristic
333C22#1171886211yescharacteristic
334C22#1171886311yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—81no—
342C4—82no—
343C4—81no—
344C4—522no—
345C4—1041no—
346C4—1041no—
347C4—1041no—
348C2#1311377411yescharacteristic
349C2#1311379711yescharacteristic
350C2#1311381311yescharacteristic
351C2#1311400611yescharacteristic
352C2#1311404211yescharacteristic
353C2#1311411011yescharacteristic
354C2#1311416811yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2058C2
socle, prime radicalC23×C13#120
hypercenter#2058D13
hypocenterC13#7767
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
284. C13#7767semidirect

Maximal subgroups

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

subgroupindex
#131227862
#131160792
#131159742
#131126612
#131126602
#131126592
C13×#20582
#776713