Finite Group Databasebeta

← #15764872

Subgroups — #15764872

Order 3328.

492 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 103 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#13125977C211yesmaximal, characteristic
2C2×#11718343C211yesmaximal, characteristic
3#13125218C211yesmaximal, characteristic
4#13115679C211yesmaximal, characteristic
5#13113509C211yesmaximal, characteristic
6#13112673C211yesmaximal, characteristic
7C13×#1493C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C2×#88064—22no—
14C2×#88058—22no—
15#11718754—21no—
16#11718754—21no—
17#11718742—21no—
18#11718740—21no—
19#11718730—22no—
20#11718704—22no—
21#11718681—22no—
22#11718665—22no—
23#11718586C2211yescharacteristic
24C4×#6099C2211yescharacteristic
25#11718343—22no—
26#11718343—22no—
27C13×Q8⋊C8—22no—
28#11718074—22no—
29C22×Dic26—21no—
30C22×Dic26—21no—
31C2×C13×M16—21no—
32C22×C8×C13—21no—
33C13×C4⋊Q8D411yescharacteristic
34C13×C4⋊Q8D411yescharacteristic
35C13×#125—21no—
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8—21no—
38C4×Q8×C13—21no—
39C4×Q8×C13—21no—
40C13×#117—21no—
41C2×C42×C13C2311yescharacteristic
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13D412yes—
46C2×#6099D412yes—
47#88123—21no—
48#88123—21no—
49#88123—21no—
50#88123—21no—
51#88123—21no—
52#88123—21no—
53#88123—21no—
54#88123D412yes—
55C13×C4⋊C8—21no—
56C13×C4⋊C8—21no—
57C4×C8×C13—21no—
58C4×C8×C13D412yes—
59#88075—24no—
60C22⋊#1055—21no—
61#88064—44no—
62#88058—28no—
63#88050—24no—
64#88050—24no—
65#88048—24no—
66C4⋊#1055D412yes—
67#88043—21no—
68C4×#1055—21no—
69C4×#1055—21no—
70#10175—131nomaximal, Sylow
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13#4111yescharacteristic
76C22×Dic13—22no—
77C22×Dic13—41no—
78C2×Dic26—22no—
79C2×Dic26—42no—
80C2×Dic26—42no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C2×Dic26—42no—
85C2×Dic26—42no—
86C13×M16—42no—
87C2×C8×C13—24no—
88C2×C8×C13—22no—
89C2×C8×C13—41no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C22⋊C4—41no—
97C42×C13—41no—
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C4⋊Dic13—22no—
103C4⋊Dic13—22no—
104C4⋊Dic13—22no—
105C4⋊Dic13—22no—
106C4⋊Dic13—41no—
107C4⋊Dic13—41no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110#6099—22no—
111#6099—22no—
112C2×#1055—22no—
113C2×#1055—22no—
114#3229—131no—
115C2×#500—131no—
116#3139—131no—
117#1966—131no—
118#1546—131no—
119#1493D1311yescharacteristic
120#1278—131no—
121C23×C13#12111yescharacteristic
122Q8×C13—42no—
123Q8×C13—42no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12111yescharacteristic
132C2×C4×C13#12111yescharacteristic
133C2×C4×C13#12711yescharacteristic
134C2×C4×C13#13512yes—
135C2×C4×C13AGL(1,ℤ/8)12yes—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—44no—
139C2×Dic13—82no—
140Dic26—44no—
141Dic26—82no—
142Dic26—81no—
143Dic26—81no—
144Dic26—81no—
145Dic26—81no—
146C8×C13—24no—
147C8×C13—81no—
148#1055—42no—
149#1055—42no—
150#533C2×D1311yescharacteristic
151C2×C4⋊Q8—131no—
152C2×C4⋊Q8—131no—
153#500—262no—
154#500—262no—
155#498—261no—
156#491—262no—
157#487—261no—
158#487—261no—
159#487—261no—
160#483—262no—
161#475—262no—
162#431—131no—
163C2×#107—262no—
164#423C2×D1311yescharacteristic
165#419—262no—
166C2×#101—262no—
167C4×M16—131no—
168C2×C4×C8C2×D1311yescharacteristic
169#332—262no—
170Q8⋊C8—22no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13#39211yescharacteristic
174C22×C13#46312yes—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—81no—
178C4×C13—81no—
179C4×C13#44912yes—
180C4×C13#45612yes—
181C4×C13#47312yes—
182C4×C13#49511yescharacteristic
183C4×C13#49611yescharacteristic
184Dic13—82no—
185Dic13—82no—
186C22×Q8—261no—
187C22×Q8—261no—
188C2×M16—21no—
189C2×M16—132no—
190C22×C8—21no—
191C4⋊Q8—132no—
192C4⋊Q8—261no—
193C4⋊Q8—261no—
194C4⋊Q8—261no—
195C4⋊Q8—261no—
196C4⋊Q8—261no—
197C4⋊Q8—261no—
198C4⋊Q8—261no—
199C4⋊Q8D5211yescharacteristic
200C4⋊Q8D5211yescharacteristic
201#125—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206#117—21no—
207C2×C4⋊C4—132no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4—261no—
211C2×C42C22×D1311yescharacteristic
212#107—268no—
213#106—264no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—132no—
217#103—264no—
218#103—264no—
219#103—264no—
220#101—524no—
221C22⋊C8—261no—
222#97—261no—
223C4×C8—21no—
224C4×C8—261no—
225C4×C8—261no—
226C4×C8C22⋊D1312yes—
227C2×C13—22no—
228C2×C13#200511yescharacteristic
229C2×C13#201211yescharacteristic
230C2×C13#202011yescharacteristic
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—262no—
234C2×Q8—521no—
235C2×Q8—522no—
236C2×Q8—522no—
237C2×Q8—521no—
238C2×Q8—521no—
239C2×Q8—522no—
240C2×Q8—522no—
241C22×C4—262no—
242C22×C4—521no—
243C22×C4#612711yescharacteristic
244C22×C4D4×D1311yescharacteristic
245C22×C4D4×D1311yescharacteristic
246M16—42no—
247M16—262no—
248M16—262no—
249C2×C8—24no—
250C2×C8—22no—
251C2×C8—41no—
252C2×C8—262no—
253C2×C8—262no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—262no—
261C4⋊C4—262no—
262C4⋊C4—262no—
263C4⋊C4—262no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C22⋊C4—41no—
269C42—41no—
270C42C2×D5211yescharacteristic
271C42D4×D1311yescharacteristic
272C42D4×D1311yescharacteristic
273C42C2×C22⋊D1311yescharacteristic
274C13#1017511yescharacteristic, complemented, Sylow
275C23#8813811yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—524no—
279Q8—1042no—
280Q8—1041no—
281Q8—1041no—
282Q8—1041no—
283Q8—1041no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—524no—
289C2×C4—522no—
290C2×C4—522no—
291C2×C4—1042no—
292C2×C4#8813611yescharacteristic
293C2×C4#8813611yescharacteristic
294C2×C4#8813811yescharacteristic
295C2×C4#8816812yes—
296C2×C4#8817312yes—
297C2×C4#8818411yescharacteristic
298C2×C4#8819111yescharacteristic
299C2×C4#8819411yescharacteristic
300C8—24no—
301C8—81no—
302C8—522no—
303C8—522no—
304C22—21no—
305C22—21no—
306C22#1171848012yes—
307C22#1171862111yescharacteristic
308C4—21no—
309C4—21no—
310C4—81no—
311C4—81no—
312C4—1042no—
313C4—1042no—
314C4#1171847212yes—
315C4#1171848712yes—
316C4#1171880412yes—
317C4#1171883711yescharacteristic
318C4#1171885211yescharacteristic
319C2—22no—
320C2#1311587111yescharacteristic
321C2#1311591411yescharacteristic
322C2#1311595711yescharacteristic
subgroupG/H
centerC22#11718621
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1493C2
socleC22×C13#392
prime radicalC23×C13#121
hypercenter#1493D13
hypocenterC13#10175
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
274. C13#10175semidirect

Maximal subgroups

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

subgroupindex
#131259772
C2×#117183432
#131252182
#131156792
#131135092
#131126732
C13×#14932
#1017513