Finite Group Databasebeta

← #15764855

Subgroups — #15764855

Order 3328.

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

normal subgroups only

This group has 476 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#13125989C211yesmaximal, characteristic
2C2×#11718740C211yesmaximal, characteristic
3#13125216C211yesmaximal, 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#11718743—22no—
15#11718742—21no—
16#11718742—21no—
17#11718740—22no—
18#11718740—22no—
19C2×#88048—22no—
20C4×#6099C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718511—22no—
23#11718383—22no—
24#11718343—21no—
25#11718342—21no—
26C13×#332—22no—
27#11718146—22no—
28#11718076—22no—
29C22×Q8×C13—21no—
30C22×Dic26—21no—
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⋊Dic13D412yes—
42#88178—21no—
43#88178—21no—
44C2×#6099D412yes—
45C22×#1055—21no—
46#88124—21no—
47#88123—21no—
48#88123—21no—
49#88123—21no—
50#88123—21no—
51#88123D411yescharacteristic
52#88123D411yescharacteristic
53C4×Dic26—21no—
54C4×Dic26—21no—
55C13×C4⋊C8—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8D412yes—
58C13×C22⋊C8—21no—
59C4×C8×C13—21no—
60#88075—24no—
61#88075—24no—
62#88058—24no—
63#88056—24no—
64#88048—28no—
65#88043—21no—
66C4×#1055—21no—
67C4×#1055—21no—
68C4×#1055D412yes—
69#10173—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—21no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26—82no—
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—22no—
100C4⋊Dic13—22no—
101C4⋊Dic13—21no—
102C4⋊Dic13—41no—
103C4⋊Dic13—41no—
104#6101—41no—
105#6101—41no—
106C4×Dic13—41no—
107#6099—22no—
108#6099—22no—
109C2×#1055—24no—
110C2×#1055—22no—
111C2×#1055—22no—
112#3230—131no—
113C2×#498—131no—
114#3139—131no—
115#1997—131no—
116#1546D1311yescharacteristic
117#1493—131no—
118#1278—131no—
119C23×C13#12111yescharacteristic
120Q8×C13—44no—
121Q8×C13—81no—
122Q8×C13—81no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—42no—
126C2×C4×C13—82no—
127C2×C4×C13#12011yescharacteristic
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12111yescharacteristic
131C2×C4×C13#12111yescharacteristic
132C2×C4×C13#12711yescharacteristic
133C2×C4×C13#13512yes—
134C2×C4×C13#13712yes—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—42no—
138C2×Dic13—82no—
139Dic26—42no—
140Dic26—42no—
141Dic26—82no—
142Dic26—82no—
143C8×C13—42no—
144C8×C13—81no—
145#1055—24no—
146#1055—42no—
147#533—131no—
148C2×C4⋊Q8—131no—
149C2×C4⋊Q8C2×D1311yescharacteristic
150#500—261no—
151#498—262no—
152#498—262no—
153#491—262no—
154#487—261no—
155#487—261no—
156#487—261no—
157#484—262no—
158#477—262no—
159#431C2×D1311yescharacteristic
160C2×#106—262no—
161#423C2×D1311yescharacteristic
162#419—262no—
163C4×M16—131no—
164C2×C4×C8—131no—
165#343—262no—
166#332—22no—
167Q8⋊C8—262no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13#39211yescharacteristic
171C22×C13#46412yes—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—82no—
175C4×C13#45212yes—
176C4×C13#45612yes—
177C4×C13#47112yes—
178C4×C13#49511yescharacteristic
179C4×C13#49711yescharacteristic
180Dic13—81no—
181Dic13—81no—
182Dic13—82no—
183C22×Q8—21no—
184C22×Q8—261no—
185C2×M16—21no—
186C2×M16—132no—
187C22×C8—261no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—131no—
192C4⋊Q8—131no—
193C4⋊Q8—261no—
194C4⋊Q8—261no—
195C4⋊Q8—261no—
196C4⋊Q8—261no—
197C4⋊Q8D5212yes—
198#125—261no—
199C22⋊Q8—261no—
200C22⋊Q8—261no—
201C4×Q8—261no—
202C4×Q8—261no—
203#117—261no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—132no—
207C2×C4⋊C4—261no—
208C2×C42C22×D1311yescharacteristic
209#107—264no—
210#106—268no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8C22⋊D1312yes—
214#103—264no—
215#103—264no—
216#103—264no—
217C22⋊C8—21no—
218#97—261no—
219C4×C8—21no—
220C4×C8—132no—
221C4×C8—261no—
222C4×C8—261no—
223C2×C13—22no—
224C2×C13#200511yescharacteristic
225C2×C13#201511yescharacteristic
226C2×C13#201911yescharacteristic
227C2×Q8—22no—
228C2×Q8—41no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—261no—
232C2×Q8—261no—
233C2×Q8—521no—
234C2×Q8—521no—
235C2×Q8—1042no—
236C22×C4—41no—
237C22×C4—262no—
238C22×C4#612711yescharacteristic
239C22×C4D4×D1311yescharacteristic
240C22×C4D4×D1311yescharacteristic
241M16—42no—
242M16—262no—
243M16—262no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—264no—
247C2×C8—262no—
248C2×C8—262no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—262no—
256C4⋊C4—261no—
257C4⋊C4—262no—
258C4⋊C4—261no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C22⋊C4—521no—
264C42—521no—
265C42C2×D5211yescharacteristic
266C42D4×D1311yescharacteristic
267C42D4×D1311yescharacteristic
268C42C2×C22⋊D1311yescharacteristic
269C13#1017311yescharacteristic, complemented, Sylow
270C23#8813811yescharacteristic
271Q8—44no—
272Q8—81no—
273Q8—81no—
274Q8—522no—
275Q8—522no—
276Q8—1042no—
277Q8—1042no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—42no—
281C2×C4—82no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—522no—
285C2×C4—1042no—
286C2×C4#8813611yescharacteristic
287C2×C4#8813611yescharacteristic
288C2×C4#8813811yescharacteristic
289C2×C4#8816612yes—
290C2×C4#8816912yes—
291C2×C4#8818411yescharacteristic
292C2×C4#8819111yescharacteristic
293C2×C4#8819411yescharacteristic
294C8—42no—
295C8—81no—
296C8—264no—
297C8—522no—
298C22—21no—
299C22—21no—
300C22#1171842812yes—
301C22#1171862111yescharacteristic
302C4—21no—
303C4—21no—
304C4—82no—
305C4—1042no—
306C4—1041no—
307C4—1041no—
308C4#1171841512yes—
309C4#1171844412yes—
310C4#1171881611yescharacteristic
311C4#1171882811yescharacteristic
312C4#1171886612yes—
313C2—22no—
314C2#1311587311yescharacteristic
315C2#1311593211yescharacteristic
316C2#1311594911yescharacteristic
subgroupG/H
centerC22#11718621
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1546C2
socleC22×C13#392
prime radicalC23×C13#121
hypercenter#1546D13
hypocenterC13#10173
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
269. C13#10173semidirect

Maximal subgroups

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

subgroupindex
#131259892
C2×#117187402
#131252162
#131158242
#131132902
#131126722
C13×#15462
#1017313