Finite Group Databasebeta

← #15764841

Subgroups — #15764841

Order 3328.

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

normal subgroups only

This group has 488 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#13125786C211yesmaximal, characteristic
2#13125216C211yesmaximal, characteristic
3C2×#11718754C211yesmaximal, characteristic
4#13115824C211yesmaximal, characteristic
5#13113290C211yesmaximal, characteristic
6#13112672C211yesmaximal, characteristic
7C13×#1546C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9#11719175C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#423C2211yescharacteristic
13#11718886—22no—
14#11718754—22no—
15#11718754—22no—
16#11718743—22no—
17#11718742—21no—
18#11718742—21no—
19C2×#88050—22no—
20C4×#6099C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718510—22no—
23#11718400—22no—
24#11718360—21no—
25#11718342—21no—
26C13×#332—22no—
27#11718146—22no—
28#11718076—22no—
29C22×Q8×C13—21no—
30C22×Dic26D412yes—
31C2×C13×M16—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8D412yes—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C42×C13C2311yescharacteristic
39#88180—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42#88178—21no—
43#88178—21no—
44C2×#6099D412yes—
45C22×#1055—21no—
46C2×Dic52—24no—
47#88124—21no—
48#88123—21no—
49#88123—21no—
50#88123—21no—
51#88123—21no—
52#88123D411yescharacteristic
53#88123D411yescharacteristic
54C4×Dic26—21no—
55C4×Dic26—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8D412yes—
59C13×C22⋊C8—21no—
60C4×C8×C13—21no—
61#88075—24no—
62#88075—24no—
63#88056—24no—
64#88050—28no—
65#88043—21no—
66C4×#1055—21no—
67C4×#1055—21no—
68C4×#1055D412yes—
69#10171—131nomaximal, Sylow
70C2×Q8×C13—22no—
71C2×Q8×C13—41no—
72C2×Q8×C13—42no—
73C2×Q8×C13—42no—
74C22×C4×C13—41no—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13#4111yescharacteristic
78C22×Dic13—22no—
79C2×Dic26—21no—
80C2×Dic26—22no—
81C2×Dic26—22no—
82C2×Dic26—21no—
83C2×Dic26—44no—
84C13×M16—42no—
85C2×C8×C13—22no—
86C2×C8×C13—41no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C42×C13C2×D411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C22⋊Dic13—41no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102C4⋊Dic13—41no—
103C4⋊Dic13—41no—
104#6101—41no—
105#6101—41no—
106C4×Dic13—41no—
107#6099—22no—
108#6099—22no—
109C2×#1055—22no—
110C2×#1055—22no—
111C2×#1055—42no—
112Dic52—84no—
113#3209—131no—
114#3139—131no—
115C2×#487—131no—
116#1997—131no—
117#1546D1311yescharacteristic
118#1493—131no—
119#1278—131no—
120C23×C13#12111yescharacteristic
121Q8×C13—44no—
122Q8×C13—81no—
123Q8×C13—81no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—42no—
127C2×C4×C13—82no—
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×C13#13712yes—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—42no—
139C2×Dic13—82no—
140Dic26—44no—
141Dic26—42no—
142Dic26—44no—
143Dic26—42no—
144C8×C13—42no—
145C8×C13—81no—
146#1055—42no—
147#1055—42no—
148#533—131no—
149C2×C4⋊Q8—131no—
150C2×C4⋊Q8C2×D1311yescharacteristic
151#494—261no—
152#491—262no—
153#487—261no—
154#487—262no—
155#487—261no—
156#487—261no—
157#487—262no—
158#462—262no—
159#451—262no—
160#431C2×D1311yescharacteristic
161#423C2×D1311yescharacteristic
162#419—262no—
163C2×#103—262no—
164C4×M16—131no—
165C2×C4×C8—131no—
166#343—262no—
167#332—22no—
168Q8⋊C8—262no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13#39211yescharacteristic
172C22×C13#46412yes—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—82no—
176C4×C13#45212yes—
177C4×C13#45512yes—
178C4×C13#47312yes—
179C4×C13#49511yescharacteristic
180C4×C13#49711yescharacteristic
181Dic13—82no—
182Dic13—81no—
183Dic13—81no—
184C22×Q8—21no—
185C22×Q8—132no—
186C2×Q16—264no—
187C2×M16—21no—
188C2×M16—132no—
189C22×C8—261no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—131no—
194C4⋊Q8—131no—
195C4⋊Q8—261no—
196C4⋊Q8—261no—
197C4⋊Q8—261no—
198C4⋊Q8—261no—
199C4⋊Q8D5212yes—
200#125—261no—
201C22⋊Q8—261no—
202C22⋊Q8—261no—
203C4×Q8—261no—
204C4×Q8—261no—
205#117—261no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4—261no—
210C2×C42C22×D1311yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8C22⋊D1312yes—
214#103—268no—
215#103—264no—
216#103—264no—
217#103—264no—
218C22⋊C8—21no—
219#97—261no—
220C4×C8—21no—
221C4×C8—132no—
222C4×C8—261no—
223C4×C8—261no—
224C2×C13—22no—
225C2×C13#200411yescharacteristic
226C2×C13#201511yescharacteristic
227C2×C13#202011yescharacteristic
228C2×Q8—22no—
229C2×Q8—41no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—262no—
233C2×Q8—261no—
234C2×Q8—262no—
235C2×Q8—261no—
236C2×Q8—524no—
237C22×C4—41no—
238C22×C4—262no—
239C22×C4#612711yescharacteristic
240C22×C4D4×D1311yescharacteristic
241C22×C4D4×D1311yescharacteristic
242Q16—1044no—
243M16—42no—
244M16—262no—
245M16—262no—
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—262no—
249C2×C8—262no—
250C2×C8—522no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C22⋊C4—521no—
266C42—521no—
267C42C2×D5211yescharacteristic
268C42D4×D1311yescharacteristic
269C42D4×D1311yescharacteristic
270C42C2×C22⋊D1311yescharacteristic
271C13#1017111yescharacteristic, complemented, Sylow
272C23#8813811yescharacteristic
273Q8—44no—
274Q8—81no—
275Q8—81no—
276Q8—524no—
277Q8—522no—
278Q8—522no—
279Q8—524no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—82no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—522no—
287C2×C4—1042no—
288C2×C4#8813611yescharacteristic
289C2×C4#8813611yescharacteristic
290C2×C4#8813811yescharacteristic
291C2×C4#8816612yes—
292C2×C4#8816912yes—
293C2×C4#8818411yescharacteristic
294C2×C4#8819111yescharacteristic
295C2×C4#8819411yescharacteristic
296C8—42no—
297C8—81no—
298C8—522no—
299C8—522no—
300C22—21no—
301C22—21no—
302C22#1171842812yes—
303C22#1171862111yescharacteristic
304C4—21no—
305C4—21no—
306C4—82no—
307C4—1041no—
308C4—1042no—
309C4—1041no—
310C4#1171841612yes—
311C4#1171844412yes—
312C4#1171881611yescharacteristic
313C4#1171882811yescharacteristic
314C4#1171886312yes—
315C2—22no—
316C2#1311586611yescharacteristic
317C2#1311593211yescharacteristic
318C2#1311595611yescharacteristic
subgroupG/H
centerC22#11718621
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1546C2
socleC22×C13#392
prime radicalC23×C13#121
hypercenter#1546D13
hypocenterC13#10171
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
271. C13#10171semidirect

Maximal subgroups

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

subgroupindex
#131257862
#131252162
C2×#117187542
#131158242
#131132902
#131126722
C13×#15462
#1017113