Finite Group Databasebeta

← #15763515

Subgroups — #15763515

Order 3328.

632 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#11718382C212yesmaximal
2#13120950C211yesmaximal, characteristic
3C2×#11718059C212yesmaximal
4#13113103C211yesmaximal, characteristic
5C13×#1280C211yesmaximal, characteristic
6C22×C4⋊Dic13C2211yescharacteristic
7C2×#88178C2212yes—
8C2×C13×C22⋊C8C2212yes—
9C2×C13×#95C2211yescharacteristic
10#11718873—22no—
11C2×#88071—22no—
12C2×#88071C2211yescharacteristic
13C2×#88057—22no—
14C2×#88056—22no—
15#11718382—24no—
16#11718382—24no—
17#11718322—22no—
18#11718317—22no—
19#11718059—24no—
20C23×C4×C13D412yes—
21C23×C4×C13C2311yescharacteristic
22C23×Dic13—21no—
23C23×Dic13—21no—
24C22×Dic26D412yes—
25C22×C8×C13—22no—
26C2×C22⋊Dic13—22no—
27C2×C4⋊Dic13—22no—
28C2×C4⋊Dic13—22no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—22no—
31C2×C4⋊Dic13—22no—
32C2×C4⋊Dic13D412yes—
33C2×C4⋊Dic13D412yes—
34#88178—22no—
35#88178—22no—
36#88178—22no—
37#88178—22no—
38C2×#6101—22no—
39C13×C22⋊C8—22no—
40C13×C22⋊C8D414yes—
41C13×#95—22no—
42#88071—24no—
43#88071—22no—
44#88071—44no—
45#88057—28no—
46#88056—28no—
47#9973—131nomaximal, Sylow
48C24×C13C2×D411yescharacteristic
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—42no—
52C22×C4×C13—42no—
53C22×C4×C13—42no—
54C22×C4×C13SD1614yes—
55C22×C4×C13C2×D412yes—
56C22×C4×C13C2×D412yes—
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13#4111yescharacteristic
59C22×Dic13—22no—
60C22×Dic13—22no—
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—41no—
64C22×Dic13—42no—
65C22×Dic13—41no—
66C22×Dic13—41no—
67C22×Dic13—41no—
68C22×Dic13—42no—
69C22×Dic13—42no—
70C22×Dic13—42no—
71C2×Dic26—22no—
72C2×Dic26—22no—
73C2×Dic26—44no—
74C2×C8×C13—24no—
75C2×C8×C13—44no—
76C22⋊Dic13—42no—
77C22⋊Dic13—42no—
78C4⋊Dic13—22no—
79C4⋊Dic13—24no—
80C4⋊Dic13—22no—
81C4⋊Dic13—42no—
82C4⋊Dic13—82no—
83C4⋊Dic13—82no—
84#6101—42no—
85#6101—42no—
86C2×#483—132no—
87#2659—131no—
88C2×#328—132no—
89#1445—131no—
90#1280D1311yescharacteristic
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—22no—
94C23×C13#12011yescharacteristic
95C23×C13#12111yescharacteristic
96C23×C13#12711yescharacteristic
97C23×C13C2×SD1612yes—
98C23×C13#13712yes—
99C2×C4×C13—24no—
100C2×C4×C13—24no—
101C2×C4×C13—41no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—44no—
107C2×C4×C13—82no—
108C2×C4×C13#12012yes—
109C2×C4×C13#12112yes—
110C2×Dic13—44no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13—44no—
118C2×Dic13—44no—
119C2×Dic13—82no—
120C2×Dic13—81no—
121C2×Dic13—82no—
122C2×Dic13—81no—
123C2×Dic13—81no—
124C2×Dic13—81no—
125Dic26—44no—
126Dic26—82no—
127C8×C13—44no—
128C2×C22⋊Q8—132no—
129C22×C4⋊C4—131no—
130#483—264no—
131#483—264no—
132C2×#106—262no—
133C2×#103—262no—
134C2×C22⋊C8C2×D1312yes—
135#398—262no—
136#395—262no—
137#380—262no—
138C2×#95—131no—
139C2×#95—262no—
140C2×#95C2×D1311yescharacteristic
141#328—264no—
142C22×C13—22no—
143C22×C13—22no—
144C22×C13—22no—
145C22×C13—22no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13#39211yescharacteristic
151C22×C13#44812yes—
152C22×C13#45511yescharacteristic
153C22×C13#45611yescharacteristic
154C22×C13#45812yes—
155C22×C13#46112yes—
156C22×C13#49211yescharacteristic
157C22×C13#49711yescharacteristic
158C4×C13—22no—
159C4×C13—22no—
160C4×C13—44no—
161Dic13—82no—
162Dic13—82no—
163Dic13—82no—
164Dic13—82no—
165C22×Q8—132no—
166C23×C4—261no—
167C23×C4—261no—
168C23×C4D5212yes—
169C23×C4C22×D1311yescharacteristic
170C22×C8—22no—
171C22⋊Q8—262no—
172C22⋊Q8—262no—
173C22⋊Q8—262no—
174C22⋊Q8—262no—
175C2×C4⋊C4—132no—
176C2×C4⋊C4—132no—
177C2×C4⋊C4—262no—
178C2×C4⋊C4—262no—
179C2×C4⋊C4—262no—
180C2×C4⋊C4—261no—
181C2×C4⋊C4—262no—
182C2×C4⋊C4—262no—
183C2×C22⋊C4—262no—
184#106—268no—
185#103—268no—
186C22⋊C8—22no—
187C22⋊C8D5214yes—
188#95—22no—
189#95—264no—
190#95—262no—
191#95—524no—
192C2×C13—21no—
193C2×C13—22no—
194C2×C13—21no—
195C2×C13#160812yes—
196C2×C13#161112yes—
197C2×C13#200711yescharacteristic
198C2×C13#201311yescharacteristic
199C2×C13#202211yescharacteristic
200C24C2×D5211yescharacteristic
201C2×Q8—262no—
202C2×Q8—262no—
203C2×Q8—524no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—262no—
210C22×C4—262no—
211C22×C4—262no—
212C22×C4—262no—
213C22×C4—522no—
214C22×C4—521no—
215C22×C4—521no—
216C22×C4—521no—
217C22×C4—521no—
218C22×C4—522no—
219C22×C4—522no—
220C22×C4—522no—
221C22×C4#609514yes—
222C22×C4C2×D5212yes—
223C22×C4D4×D1312yes—
224C22×C4D4×D1311yescharacteristic
225C22×C4#613111yescharacteristic
226C2×C8—24no—
227C2×C8—44no—
228C4⋊C4—264no—
229C4⋊C4—262no—
230C4⋊C4—262no—
231C4⋊C4—522no—
232C4⋊C4—522no—
233C4⋊C4—522no—
234C4⋊C4—1042no—
235C4⋊C4—1042no—
236C22⋊C4—522no—
237C22⋊C4—522no—
238C13#997311yescharacteristic, complemented, Sylow
239C23—22no—
240C23—21no—
241C23—21no—
242C23#8812811yescharacteristic
243C23#8813611yescharacteristic
244C23#8814911yescharacteristic
245C23C2×#609512yes—
246C23#8816312yes—
247Q8—524no—
248Q8—1042no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—82no—
258C2×C4—522no—
259C2×C4—524no—
260C2×C4—524no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—524no—
264C2×C4—522no—
265C2×C4—522no—
266C2×C4—522no—
267C2×C4—1041no—
268C2×C4—1042no—
269C2×C4—1041no—
270C2×C4—1041no—
271C2×C4—1041no—
272C2×C4—1042no—
273C2×C4#8813612yes—
274C2×C4#8814912yes—
275C8—44no—
276C22—21no—
277C22—21no—
278C22—22no—
279C22—22no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—22no—
284C22#1171833211yescharacteristic
285C22#1171835411yescharacteristic
286C22#1171837611yescharacteristic
287C22#1171839912yes—
288C22#1171840312yes—
289C22#1171840711yescharacteristic
290C22#1171841311yescharacteristic
291C22#1171850212yes—
292C4—22no—
293C4—22no—
294C4—44no—
295C4—1042no—
296C4—1042no—
297C4—1042no—
298C4—1042no—
299C2—21no—
300C2—22no—
301C2—21no—
302C2#1311382912yes—
303C2#1311384612yes—
304C2#1311588511yescharacteristic
305C2#1311592111yescharacteristic
306C2#1311596811yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1280C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenter#1280D13
hypocenterC13#9973
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
238. C13#9973semidirect

Maximal subgroups

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

subgroupindex
C2×#117183822
#131209502
C2×#117180592
#131131032
C13×#12802
#997313