Finite Group Databasebeta

← #15767317

Subgroups — #15767317

Order 3328.

490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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#13125611C211yesmaximal, characteristic
2#13115821C212yesmaximal
3#13115259C212yesmaximal
4#13112704C211yesmaximal, characteristic
5C13×#1850C211yesmaximal, characteristic
6C23×C8×C13C2211yescharacteristic
7C2×#88178C2212yes—
8C2×C13×C4⋊C8—21no—
9C2×C13×C22⋊C8C2211yescharacteristic
10C4×C13×C22⋊C4C2211yescharacteristic
11#11718873C2212yes—
12#11718777—21no—
13#11718777—21no—
14C2×#88056—22no—
15#11718400—22no—
16#11718383—22no—
17C13×#336—21no—
18#11718143—22no—
19#11718119—22no—
20#11718119—22no—
21C23×C4×C13C2311yescharacteristic
22C22×Dic26D412yes—
23C22×C8×C13—21no—
24C22×C8×C13—22no—
25C22×C8×C13—42no—
26C22×C8×C13D411yescharacteristic
27C22×C8×C13D411yescharacteristic
28C2×C13×C22⋊C4D411yescharacteristic
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C42×C13—21no—
31C2×C22⋊Dic13—22no—
32C2×C22⋊Dic13—22no—
33C2×C4⋊Dic13—22no—
34C2×C4⋊Dic13D412yes—
35#88178—22no—
36#88178—22no—
37#88178—22no—
38#88178—22no—
39C2×#6101—22no—
40C2×Dic52—21no—
41C2×Dic52—21no—
42C13×C4⋊C8—42no—
43C13×C22⋊C8—22no—
44C13×#95—21no—
45#88071—22no—
46#88058—21no—
47#88058—21no—
48#88056—22no—
49#88056—22no—
50#88056—44no—
51#10566—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—41no—
56C22×C4×C13—41no—
57C22×C4×C13C2×D412yes—
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13#4111yescharacteristic
60C22×C4×C13#4112yes—
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—42no—
64C2×Dic26—22no—
65C2×Dic26—22no—
66C2×Dic26—42no—
67C2×Dic26—42no—
68C2×C8×C13—22no—
69C2×C8×C13—24no—
70C2×C8×C13—21no—
71C2×C8×C13—21no—
72C2×C8×C13—42no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C13×C22⋊C4—21no—
78C13×C22⋊C4—22no—
79C13×C22⋊C4Q1612yescomplemented
80C42×C13—41no—
81C42×C13—41no—
82C22⋊Dic13—42no—
83C22⋊Dic13—42no—
84C22⋊Dic13—42no—
85C22⋊Dic13—42no—
86C4⋊Dic13—22no—
87C4⋊Dic13—22no—
88C4⋊Dic13—42no—
89C4⋊Dic13—42no—
90#6101—42no—
91#6101—42no—
92Dic52—81no—
93Dic52—81no—
94#3189—131no—
95#1996—132no—
96#1892—132no—
97#1850D1311yescharacteristic
98#1289—131no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13#12112yes—
102C23×C13#12111yescharacteristic
103C23×C13C2×Q1611yescharacteristic
104C23×C13#13511yescharacteristic
105C23×C13#13712yes—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—41no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13#12011yescharacteristic
119C2×C4×C13#12312yes—
120C2×C4×C13#12411yescharacteristic
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—82no—
124C2×Dic13—82no—
125C2×Dic13—82no—
126C2×Dic13—82no—
127C2×Dic13—82no—
128Dic26—44no—
129Dic26—42no—
130Dic26—42no—
131C8×C13—41no—
132C8×C13—42no—
133C8×C13—41no—
134C23×C8C2×D1311yescharacteristic
135C2×C22⋊Q8—132no—
136#484—262no—
137#467—261no—
138#467—261no—
139#451—262no—
140C2×C4⋊C8—21no—
141C2×#103—262no—
142C2×C22⋊C8C2×D1311yescharacteristic
143#380—132no—
144C4×C22⋊C4C2×D1311yescharacteristic
145#342—262no—
146#342—262no—
147#340—262no—
148#336—21no—
149C22×C13—22no—
150C22×C13—21no—
151C22×C13—22no—
152C22×C13—21no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—42no—
156C22×C13#39411yescharacteristic
157C22×C13#46212yes—
158C22×C13#46412yes—
159C22×C13#46711yescharacteristic
160C22×C13#47011yescharacteristic
161C4×C13—22no—
162C4×C13—21no—
163C4×C13—42no—
164C4×C13—81no—
165C4×C13B(4,𝔽2)11yescharacteristic
166C4×C13#45811yescharacteristic
167Dic13—82no—
168Dic13—82no—
169Dic13—162no—
170C22×Q8—132no—
171C23×C4C22×D1311yescharacteristic
172C2×Q16—261no—
173C2×Q16—261no—
174C22×C8—22no—
175C22×C8—21no—
176C22×C8—42no—
177C22×C8C22⋊D1311yescharacteristic
178C22×C8C22⋊D1311yescharacteristic
179C22⋊Q8—262no—
180C22⋊Q8—262no—
181C22⋊Q8—262no—
182C22⋊Q8—262no—
183C2×C4⋊C4—132no—
184C2×C4⋊C4—262no—
185C2×C4⋊C4—262no—
186C2×C22⋊C4—262no—
187C2×C22⋊C4—262no—
188C2×C22⋊C4D5211yescharacteristic
189C2×C22⋊C4D5211yescharacteristic
190C2×C42—21no—
191#107—261no—
192#107—261no—
193C4⋊C8—42no—
194#103—262no—
195#103—262no—
196#103—524no—
197C22⋊C8—22no—
198#95—21no—
199#95—262no—
200C2×C13—22no—
201C2×C13—21no—
202C2×C13—21no—
203C2×C13—22no—
204C2×C13#204411yescharacteristic
205C2×C13#205311yescharacteristic
206C2×C13#205611yescharacteristic
207C24C2×D5211yescharacteristic
208C2×Q8—262no—
209C2×Q8—262no—
210C2×Q8—522no—
211C2×Q8—522no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—262no—
217C22×C4—262no—
218C22×C4—522no—
219C22×C4#612711yescharacteristic
220C22×C4D4×D1312yes—
221C22×C4#613112yes—
222C22×C4C2×C22⋊D1311yescharacteristic
223Q16—1041no—
224Q16—1041no—
225C2×C8—24no—
226C2×C8—22no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—41no—
230C2×C8—42no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C4⋊C4—262no—
235C4⋊C4—262no—
236C4⋊C4—522no—
237C4⋊C4—522no—
238C4⋊C4—522no—
239C4⋊C4—522no—
240C22⋊C4—21no—
241C22⋊C4—22no—
242C22⋊C4—522no—
243C22⋊C4—522no—
244C22⋊C4—522no—
245C22⋊C4—522no—
246C22⋊C4Dic5212yescomplemented
247C42—41no—
248C42—41no—
249C13#1056611yescharacteristic, complemented, Sylow
250C23—41no—
251C23—41no—
252C23#8814912yes—
253C23#8815811yescharacteristic
254C23C2×Dic5211yescharacteristic
255C23#8816312yes—
256C23#8818411yescharacteristic
257Q8—524no—
258Q8—522no—
259Q8—522no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—522no—
273C2×C4—522no—
274C2×C4—1042no—
275C2×C4—1042no—
276C2×C4—1042no—
277C2×C4—1042no—
278C2×C4—1042no—
279C2×C4#8814812yes—
280C2×C4#8819111yescharacteristic
281C2×C4#8820111yescharacteristic
282C8—42no—
283C8—41no—
284C8—41no—
285C22—21no—
286C22—22no—
287C22—21no—
288C22—22no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22#1171850612yes—
293C22#1171851012yes—
294C22#1171865211yescharacteristic
295C22#1171877711yescharacteristic
296C22#1171879811yescharacteristic
297C4—22no—
298C4—21no—
299C4—42no—
300C4—81no—
301C4—1042no—
302C4—1042no—
303C4—2082no—
304C4#1171869311yescharacteristic
305C4#1171871411yescharacteristic
306C2—21no—
307C2—21no—
308C2—22no—
309C2—22no—
310C2#1311608711yescharacteristic
311C2#1311614211yescharacteristic
312C2#1311615911yescharacteristic
subgroupG/H
centerC22#11718652
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1850C2
socleC22×C13#394
prime radicalC24×C13C2×D4
hypercenter#1850D13
hypocenterC13#10566
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
79. C13×C22⋊C4Q16semidirect
246. C22⋊C4Dic52semidirect
249. C13#10566semidirect

Maximal subgroups

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

subgroupindex
#131256112
#131158212
#131152592
#131127042
C13×#18502
#1056613