Finite Group Databasebeta

← #15767422

Subgroups — #15767422

Order 3328.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#13123108C211yesmaximal, characteristic
2#13115004C211yesmaximal, characteristic
3#13114970C211yesmaximal, characteristic
4#13114969C211yesmaximal, characteristic
5#13112718C211yesmaximal, characteristic
6#13112718C211yesmaximal, characteristic
7C13×#1295C211yesmaximal, characteristic
8C2×C13×#97C2211yescharacteristic
9C2×C13×#97C2211yescharacteristic
10C13×#382C2211yescharacteristic
11C2×#88058—21no—
12C2×#88057—21no—
13#11718647—21no—
14#11718640—21no—
15#11718597C2211yescharacteristic
16#11718597C2211yescharacteristic
17#11718596C2211yescharacteristic
18C2×#88043C2211yescharacteristic
19#11718321—21no—
20#11718321—21no—
21#11718317—21no—
22#11718317—21no—
23#11718143—21no—
24#11718143—21no—
25#11718121—21no—
26#11718121—21no—
27C22×Dic26—21no—
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4⋊Dic13D411yescharacteristic
40C2×C4⋊Dic13D411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C22×#1055—21no—
44C13×#97—21no—
45C13×#97—21no—
46C13×#97Q812yescomplemented
47C13×#97Q812yescomplemented
48C13×#95—21no—
49C13×#95—21no—
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#88058—42no—
59#88057—42no—
60#88043—21no—
61#88043Q812yescomplemented
62#10584—131nomaximal, Sylow
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—41no—
73C2×Dic26—81no—
74C2×Dic26—81no—
75C2×Dic26—81no—
76C2×C8×C13—22no—
77C2×C8×C13—22no—
78C2×C8×C13—22no—
79C2×C8×C13—22no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C42×C13C2×Q811yescharacteristic
85C42×C13C2×Q811yescharacteristic
86C42×C13C2×Q811yescharacteristic
87C42×C13#4111yescharacteristic
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13—42no—
93C4⋊Dic13—42no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C4⋊Dic13—81no—
97#6101—81no—
98#6101—81no—
99C2×#1055—22no—
100C2×#1055—41no—
101C2×#1055—41no—
102#2844—131no—
103#1847—131no—
104#1836—131no—
105#1836—131no—
106#1295—131no—
107#1295—131no—
108#1295D1311yescharacteristic
109C23×C13#12011yescharacteristic
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13C22⋊Q811yescharacteristic
123C2×C4×C13C22⋊Q811yescharacteristic
124C2×C4×C13C22⋊Q811yescharacteristic
125C2×C4×C13C4⋊Q811yescharacteristic
126C2×C4×C13C4⋊Q811yescharacteristic
127C2×C4×C13C4⋊Q811yescharacteristic
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—81no—
141C2×Dic13—81no—
142C2×Dic13—81no—
143Dic26—84no—
144C8×C13—24no—
145C8×C13—42no—
146#1055—42no—
147C2×#107—261no—
148C2×#106—261no—
149C2×#97—131no—
150C2×#97C2×D1311yescharacteristic
151C2×#97C2×D1311yescharacteristic
152#400—261no—
153#400—261no—
154#400—261no—
155#395—261no—
156#395—261no—
157#395—261no—
158#384—131no—
159#382—131no—
160#382—131no—
161#382C2×D1311yescharacteristic
162#340—261no—
163#340—261no—
164#340—261no—
165#340—261no—
166C22×C13#39511yescharacteristic
167C22×C13#45311yescharacteristic
168C22×C13#45411yescharacteristic
169C22×C13#45411yescharacteristic
170C22×C13#45511yescharacteristic
171C22×C13#45511yescharacteristic
172C22×C13#45611yescharacteristic
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—81no—
180C4×C13—81no—
181Dic13—81no—
182Dic13—81no—
183Dic13—81no—
184Dic13—81no—
185Dic13—161no—
186C22×Q8—261no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—261no—
190C2×C4⋊C4—131no—
191C2×C4⋊C4—131no—
192C2×C4⋊C4—131no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4D5211yescharacteristic
201C2×C4⋊C4D5211yescharacteristic
202C2×C42C22×D1311yescharacteristic
203#107—522no—
204#106—522no—
205#97—21no—
206#97—21no—
207#97—132no—
208#97—261no—
209#97Dic2612yescomplemented
210#97Dic2612yescomplemented
211#95—21no—
212#95—21no—
213#95—261no—
214#95—261no—
215#95—261no—
216#95—261no—
217#95—261no—
218#95—261no—
219#95—261no—
220#95—261no—
221C2×C13#165711yescharacteristic
222C2×C13#165911yescharacteristic
223C2×C13#166411yescharacteristic
224C2×C13#166411yescharacteristic
225C2×C13#206011yescharacteristic
226C2×C13#206111yescharacteristic
227C2×C13#206111yescharacteristic
228C2×Q8—1041no—
229C2×Q8—1041no—
230C2×Q8—1041no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—521no—
238C22×C4C2×D5211yescharacteristic
239C22×C4D4×D1311yescharacteristic
240C22×C4D4×D1311yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—262no—
248C2×C8—521no—
249C2×C8—521no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—521no—
253C4⋊C4—521no—
254C4⋊C4—521no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—522no—
259C4⋊C4—522no—
260C4⋊C4—1041no—
261C4⋊C4—1041no—
262C4⋊C4—1041no—
263C42C2×Dic2611yescharacteristic
264C42C2×Dic2611yescharacteristic
265C42#612911yescharacteristic
266C42Q8×D1311yescharacteristic
267C13#1058411yescharacteristic, complemented, Sylow
268C23#8813611yescharacteristic
269Q8—1044no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—1041no—
295C2×C4—1041no—
296C2×C4—1041no—
297C2×C4#8812311yescharacteristic
298C2×C4#8813211yescharacteristic
299C2×C4#8813211yescharacteristic
300C2×C4#8814211yescharacteristic
301C2×C4#8814211yescharacteristic
302C2×C4#8815111yescharacteristic
303C8—24no—
304C8—42no—
305C8—522no—
306C22#1171831711yescharacteristic
307C22#1171840711yescharacteristic
308C22#1171841411yescharacteristic
309C22#1171848311yescharacteristic
310C22#1171848611yescharacteristic
311C22#1171848711yescharacteristic
312C22#1171848811yescharacteristic
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—81no—
320C4—81no—
321C4—1041no—
322C4—1041no—
323C4—1041no—
324C4—1041no—
325C4—2081no—
326C2#1311413611yescharacteristic
327C2#1311414411yescharacteristic
328C2#1311417111yescharacteristic
329C2#1311417311yescharacteristic
330C2#1311618011yescharacteristic
331C2#1311618511yescharacteristic
332C2#1311618711yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1295C2
socle, prime radicalC23×C13#120
hypercenter#1295D13
hypocenterC13#10584
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
46. C13×#97Q8semidirect
47. C13×#97Q8semidirect
61. #88043Q8semidirect
209. #97Dic26semidirect
210. #97Dic26semidirect
267. C13#10584semidirect

Maximal subgroups

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

subgroupindex
#131231082
#131150042
#131149702
#131149692
#131127182
C13×#12952
#1058413