Finite Group Databasebeta

← #15872371

Subgroups — #15872371

Order 3328.

1130 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 235 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×#11719188C211yesmaximal, characteristic
2#13117432C212yesmaximal
3#13115819C218yesmaximal, complemented
4#13114910C211yesmaximal, characteristic
5#13114908C212yesmaximal
6C13×#1819C211yesmaximal, characteristic
7C22×C13×C22⋊C4C2211yescharacteristic
8C22×C22⋊Dic13C2211yescharacteristic
9C22×C22⋊Dic13C2211yescharacteristic
10C2×#88178C414yescomplemented
11#11719188—24no—
12#11719188—24no—
13C2×#88132C414yescomplemented
14C2×#88132C2214yes—
15C13×#379C2212yes—
16#11718908C2212yes—
17#11718606—24no—
18#11718605—24no—
19#11718603C2214yes—
20C22⋊C4×Dic13C2214yes—
21C13×#342C2214yes—
22#11718119C2218yes—
23#11718118C2214yes—
24C25×C13C2311yescharacteristic
25C23×C4×C13C2×C412yes—
26C23×Dic13C2×C412yes—
27C23×Dic13C2312yes—
28C22×Dic26C2×C414yes—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4C2×C412yes—
34C2×C13×C22⋊C4C2314yes—
35C2×C13×C22⋊C4C2312yes—
36C2×C22⋊Dic13—22no—
37C2×C22⋊Dic13—22no—
38C2×C22⋊Dic13—22no—
39C2×C22⋊Dic13—22no—
40C2×C22⋊Dic13C2×C412yes—
41C2×C22⋊Dic13C2×C412yes—
42C2×C22⋊Dic13C2×C412yes—
43C2×C22⋊Dic13D414yes—
44C2×C22⋊Dic13D414yes—
45C2×C22⋊Dic13C2314yes—
46C2×C22⋊Dic13C2312yes—
47C2×C4⋊Dic13C2×C414yes—
48#88178—28no—
49#88178—28no—
50C2×#6101—24no—
51C2×#6101C2×C418yes—
52C2×C4×Dic13—24no—
53#88132—28no—
54#88132—28no—
55#88132—28no—
56#88132—28no—
57#88071—24no—
58#88071—24no—
59#21827—131nomaximal, Sylow
60C24×C13—24no—
61C24×C13—82no—
62C24×C13C22×C411yescharacteristic
63C24×C13C22×C411yescharacteristic
64C24×C13C2×D412yes—
65C24×C13C2×D412yes—
66C24×C13C2411yescharacteristic
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—24no—
70C22×C4×C13—82no—
71C22×C4×C13C22×C414yes—
72C22×Dic13—22no—
73C22×Dic13—22no—
74C22×Dic13—24no—
75C22×Dic13—82no—
76C22×Dic13—82no—
77C22×Dic13C22×C414yes—
78C22×Dic13C22×C414yes—
79C22×Dic13C2×D414yes—
80C22×Dic13C2×D414yes—
81C2×Dic26—28no—
82C2×Dic26—84no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—24no—
86C13×C22⋊C4—28no—
87C13×C22⋊C4—82no—
88C13×C22⋊C4—82no—
89C22⋊Dic13—24no—
90C22⋊Dic13—24no—
91C22⋊Dic13—28no—
92C22⋊Dic13—82no—
93C22⋊Dic13—82no—
94C22⋊Dic13C22⋊C414yes—
95C22⋊Dic13C22⋊C414yes—
96C22⋊Dic13C22⋊C418yes—
97C4⋊Dic13—28no—
98#6101—216no—
99#6101—84no—
100C4×Dic13—84no—
101C2×#543—131no—
102#2312—132no—
103#1996—138no—
104#1819—132no—
105#1819—131no—
106#1819D1311yescharacteristic
107C23×C13—22no—
108C23×C13—22no—
109C23×C13—24no—
110C23×C13—24no—
111C23×C13—42no—
112C23×C13—42no—
113C23×C13—42no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—88no—
119C23×C13C2×C22⋊C412yes—
120C23×C13C2×C22⋊C411yescharacteristic
121C23×C13C2×C22⋊C411yescharacteristic
122C23×C13C23×C411yescharacteristic
123C23×C13C22×D412yes—
124C23×C132−1+414yes—
125C2×C4×C13—24no—
126C2×C4×C13—44no—
127C2×C4×C13—44no—
128C2×C4×C13—44no—
129C2×C4×C13—44no—
130C2×C4×C13—82no—
131C2×C4×C13—82no—
132C2×Dic13—24no—
133C2×Dic13—44no—
134C2×Dic13—44no—
135C2×Dic13—44no—
136C2×Dic13—44no—
137C2×Dic13—44no—
138C2×Dic13—44no—
139C2×Dic13—44no—
140C2×Dic13—82no—
141C2×Dic13—82no—
142C2×Dic13C2×C22⋊C418yes—
143Dic26—88no—
144#543—264no—
145#543—264no—
146C2×C22⋊Q8—134no—
147C2×C22⋊Q8—134no—
148C2×C22⋊Q8—134no—
149C22×C22⋊C4—131no—
150C22×C22⋊C4—131no—
151C22×C22⋊C4C2×D1311yescharacteristic
152#388—264no—
153#388—264no—
154#380—134no—
155#379—132no—
156#379C2×D1312yes—
157C4×C22⋊C4—134no—
158#342—134no—
159#342—138no—
160#342C2×D1314yes—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—22no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—22no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—22no—
171C22×C13—44no—
172C22×C13—44no—
173C22×C13—44no—
174C22×C13—84no—
175C22×C13—84no—
176C22×C13C22×C22⋊C411yescharacteristic
177C22×C13#51912yes—
178C22×C13#53614yes—
179C4×C13—44no—
180C4×C13—84no—
181Dic13—28no—
182Dic13—44no—
183Dic13—84no—
184C25C22×D1311yescharacteristic
185C22×Q8—134no—
186C23×C4—132no—
187C23×C4—132no—
188C23×C4C4×D1312yes—
189C22⋊Q8—268no—
190C22⋊Q8—268no—
191C22⋊Q8—268no—
192C22⋊Q8—268no—
193C22⋊Q8—268no—
194C22⋊Q8—268no—
195C2×C4⋊C4—138no—
196C2×C4⋊C4—134no—
197C2×C4⋊C4—264no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—132no—
203C2×C22⋊C4—132no—
204C2×C22⋊C4—134no—
205C2×C22⋊C4—134no—
206C2×C22⋊C4—132no—
207C2×C22⋊C4—132no—
208C2×C22⋊C4—134no—
209C2×C22⋊C4—262no—
210C2×C22⋊C4—262no—
211C2×C22⋊C4—262no—
212C2×C22⋊C4—262no—
213C2×C22⋊C4C4×D1312yes—
214C2×C22⋊C4C22×D1314yes—
215C2×C22⋊C4C22×D1312yes—
216C2×C42—264no—
217#95—264no—
218#95—264no—
219C2×C13—24no—
220C2×C13—22no—
221C2×C13—41no—
222C2×C13—41no—
223C2×C13—42no—
224C2×C13#231011yescharacteristic
225C2×C13#288312yes—
226C24—24no—
227C24—82no—
228C24C2×C4×D1311yescharacteristic
229C24C2×C4×D1311yescharacteristic
230C24D4×D1312yes—
231C24D4×D1312yes—
232C24C23×D1311yescharacteristic
233C2×Q8—268no—
234C2×Q8—1044no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—24no—
238C22×C4—82no—
239C22×C4—134no—
240C22×C4—134no—
241C22×C4—134no—
242C22×C4—134no—
243C22×C4—262no—
244C22×C4—262no—
245C22×C4—264no—
246C22×C4—1042no—
247C22×C4—1042no—
248C22×C4C2×C4×D1314yes—
249C4⋊C4—2616no—
250C4⋊C4—268no—
251C4⋊C4—1044no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—24no—
255C22⋊C4—28no—
256C22⋊C4—82no—
257C22⋊C4—82no—
258C22⋊C4—134no—
259C22⋊C4—134no—
260C22⋊C4—138no—
261C22⋊C4—264no—
262C22⋊C4—264no—
263C22⋊C4—268no—
264C22⋊C4—1042no—
265C22⋊C4—1042no—
266C42—1044no—
267C13#2182711yescharacteristic, complemented, Sylow
268C23—22no—
269C23—22no—
270C23—24no—
271C23—24no—
272C23—42no—
273C23—42no—
274C23—42no—
275C23—42no—
276C23—42no—
277C23—42no—
278C23—42no—
279C23—88no—
280C23C22⋊C4×D1311yescharacteristic
281C23C22⋊C4×D1311yescharacteristic
282C23C22⋊C4×D1312yes—
283C23C22×C4×D1311yescharacteristic
284C23C2×D4×D1312yes—
285C23#8825714yes—
286Q8—1048no—
287C2×C4—24no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4—138no—
295C2×C4—264no—
296C2×C4—524no—
297C2×C4—524no—
298C2×C4—524no—
299C2×C4—524no—
300C2×C4—524no—
301C2×C4—524no—
302C2×C4—524no—
303C2×C4—1042no—
304C2×C4—1042no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—44no—
316C22—44no—
317C22—44no—
318C22—84no—
319C22—84no—
320C22C2×C22⋊C4×D1311yescharacteristic
321C22#1171922112yes—
322C22#1171935314yes—
323C4—44no—
324C4—84no—
325C4—268no—
326C4—524no—
327C4—1044no—
328C2—24no—
329C2—22no—
330C2—42no—
331C2—41no—
332C2—41no—
333C2#1311742111yescharacteristic
334C2#1312329412yes—
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC13×#1819C2
socleC22×C13C22×C22⋊C4
prime radicalC25×C13C23
cosocleC24×C13C24
hypercenter#1819D13
hypocenterC13#21827
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
3. #13115819C2semidirect
10. C2×#88178C4semidirect
13. C2×#88132C4semidirect
267. C13#21827semidirect

Maximal subgroups

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

subgroupindex
C2×#117191882
#131174322
#131158192
#131149102
#131149082
C13×#18192
#2182713