Finite Group Databasebeta

← #15755098

Subgroups — #15755098

Order 3328.

718 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 131 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#13114913C211yesmaximal, characteristic, complemented
2#13114907C211yesmaximal, characteristic, complemented
3#13113392C212yesmaximal, complemented
4#13113392C212yesmaximal, complemented
5C13×#3493C211yesmaximal, characteristic
6C13×#556—22no—
7C13×#555—22no—
8C13×#553—22no—
9C13×#552—22no—
10C13×#544C411yescharacteristic, complemented
11C13×#538—22no—
12C13×#537C411yescharacteristic, complemented
13C13×#529—22no—
14C13×#525C2212yes—
15C13×#520C412yescomplemented
16C2×C13×#117C2211yescharacteristic
17#11718872C2212yes—
18C2×C22⋊#1055C2211yescharacteristic
19C2×C22⋊#1055C2211yescharacteristic
20#11718130—22no—
21#11718130—22no—
22#11718129—22no—
23#11718129—22no—
24#11718118—22no—
25#11718116—22no—
26C2×C13×#41C2×C412yes—
27C23×C4×C13C2311yescharacteristic
28C13×C4⋊Q8—22no—
29C13×#126—24no—
30C13×#126—24no—
31C13×#125—22no—
32C13×#125—22no—
33C13×#124—22no—
34C13×#124—24no—
35C13×#123—24no—
36C13×#123—22no—
37C13×C22⋊Q8—22no—
38C13×C22⋊Q8—22no—
39C13×C22⋊Q8D412yes—
40C13×C22⋊Q8D412yes—
41C13×#121—24no—
42C13×#121—22no—
43C13×#121—22no—
44C13×#121D412yes—
45C13×#121D412yes—
46C13×#120—22no—
47C4×Q8×C13—22no—
48C4×Q8×C13—22no—
49C4×D4×C13—22no—
50C4×D4×C13—22no—
51C4×D4×C13—24no—
52C4×D4×C13—22no—
53C4×D4×C13—22no—
54C13×#117—24no—
55C13×#117—22no—
56C13×#117—22no—
57C13×#117—22no—
58C13×#117C2×C412yes—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4C2×C411yescharacteristic
61C2×C13×C4⋊C4C2×C411yescharacteristic
62C2×C13×C22⋊C4D412yes—
63C2×C42×C13D412yes—
64C2×C22⋊Dic13—22no—
65C22×#1055—21no—
66C22×#1055—21no—
67#88071—22no—
68#88071—22no—
69C22⋊#1055—22no—
70C22⋊#1055—22no—
71#8463—131nomaximal, Sylow
72C24×C13C2×D411yescharacteristic
73C13×#41—44no—
74C2×Q8×C13—22no—
75C2×Q8×C13C22⋊C412yes—
76C2×D4×C13—22no—
77C2×D4×C13—22no—
78C2×D4×C13—22no—
79C2×D4×C13—22no—
80C2×D4×C13C22⋊C412yes—
81C22×C4×C13—24no—
82C22×C4×C13—22no—
83C22×C4×C13—42no—
84C22×C4×C13C22⋊C412yes—
85C22×C4×C13C22⋊C412yes—
86C22×C4×C13C22×C411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D412yes—
89C22×C4×C13C2×D412yes—
90C22×Dic13—42no—
91C13×C4⋊C4—24no—
92C13×C4⋊C4—24no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4C22⋊C412yes—
100C13×C4⋊C4C22⋊C412yes—
101C13×C22⋊C4—24no—
102C13×C22⋊C4—24no—
103C13×C22⋊C4—22no—
104C13×C22⋊C4—24no—
105C13×C22⋊C4—22no—
106C13×C22⋊C4—22no—
107C13×C22⋊C4—22no—
108C13×C22⋊C4—22no—
109C42×C13—24no—
110C42×C13—22no—
111C42×C13—22no—
112C42×C13—22no—
113C22⋊Dic13—44no—
114C2×#1055—42no—
115C2×#1055—42no—
116C2×#1055—41no—
117C2×#1055—41no—
118#3493D1311yescharacteristic
119#1820—131no—
120#1818—131no—
121#1516—132no—
122#1516—132no—
123C23×C13—22no—
124C23×C13—22no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13C2×C22⋊C411yescharacteristic
128C23×C13#12012yes—
129Q8×C13—42no—
130Q8×C13—82no—
131D4×C13—42no—
132D4×C13—44no—
133D4×C13—82no—
134D4×C13—82no—
135D4×C13—82no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—44no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—84no—
149C2×C4×C13C2×C22⋊C412yes—
150C2×C4×C13#12011yescharacteristic
151C2×C4×C13#12011yescharacteristic
152C2×Dic13—82no—
153C2×Dic13—82no—
154C2×Dic13—82no—
155#1055—81no—
156#1055—81no—
157#556—22no—
158#555—22no—
159#553—22no—
160#552—22no—
161#544Dic1311yescharacteristic, complemented
162#538—22no—
163#537Dic1311yescharacteristic, complemented
164#529—22no—
165#525C2×D1312yes—
166#520Dic1312yescomplemented
167C2×#117C2×D1311yescharacteristic
168C2×C22⋊C8—131no—
169C2×C22⋊C8—131no—
170#381—132no—
171#342—262no—
172#336—262no—
173#328—262no—
174#328—262no—
175#327—262no—
176#327—262no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—42no—
183C22×C13—42no—
184C22×C13—42no—
185C22×C13—82no—
186C22×C13#37911yescharacteristic
187C22×C13#41012yes—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—22no—
191C4×C13—42no—
192C4×C13—42no—
193C4×C13—42no—
194C4×C13—42no—
195C4×C13—42no—
196Dic13—162no—
197C2×#41C2×Dic1312yes—
198C23×C4C22×D1311yescharacteristic
199C22×C8—261no—
200C22×C8—261no—
201C4⋊Q8—22no—
202#126—24no—
203#126—24no—
204#125—22no—
205#125—22no—
206#124—22no—
207#124—24no—
208#123—24no—
209#123—22no—
210C22⋊Q8—22no—
211C22⋊Q8—22no—
212C22⋊Q8C22⋊D1312yes—
213C22⋊Q8C22⋊D1312yes—
214#121—24no—
215#121—22no—
216#121—22no—
217#121C22⋊D1312yes—
218#121C22⋊D1312yes—
219#120—22no—
220C4×Q8—22no—
221C4×Q8—22no—
222C4×D4—22no—
223C4×D4—22no—
224C4×D4—24no—
225C4×D4—22no—
226C4×D4—22no—
227#117—24no—
228#117—22no—
229#117—22no—
230#117—22no—
231#117C2×Dic1312yes—
232C2×C4⋊C4—22no—
233C2×C4⋊C4C2×Dic1311yescharacteristic
234C2×C4⋊C4C2×Dic1311yescharacteristic
235C2×C22⋊C4—262no—
236C2×C22⋊C4C22⋊D1312yes—
237C2×C42C22⋊D1312yes—
238C22⋊C8—262no—
239C22⋊C8—262no—
240#95—262no—
241#95—262no—
242C2×C13—22no—
243C2×C13—42no—
244C2×C13—82no—
245C2×C13#178211yescharacteristic
246C2×C13#179411yescharacteristic
247C2×C13#179411yescharacteristic
248C24C2×C22⋊D1311yescharacteristic
249#41—44no—
250C2×Q8—22no—
251C2×Q8C22⋊Dic1312yes—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4C22⋊Dic1312yes—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—42no—
260C22×C4—522no—
261C22×C4C22⋊Dic1312yes—
262C22×C4C22⋊Dic1312yes—
263C22×C4C22×Dic1311yescharacteristic
264C22×C4C2×C22⋊D1311yescharacteristic
265C22×C4C2×C22⋊D1312yes—
266C22×C4C2×C22⋊D1312yes—
267C2×C8—522no—
268C2×C8—522no—
269C2×C8—521no—
270C2×C8—521no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4C22⋊Dic1312yes—
280C4⋊C4C22⋊Dic1312yes—
281C22⋊C4—24no—
282C22⋊C4—24no—
283C22⋊C4—22no—
284C22⋊C4—24no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—524no—
290C42—24no—
291C42—22no—
292C42—22no—
293C42—22no—
294C13#846311yescharacteristic, complemented, Sylow
295C23—22no—
296C23—22no—
297C23—41no—
298C23—41no—
299C23C2×C22⋊Dic1311yescharacteristic
300C23#8820712yes—
301Q8—42no—
302Q8—82no—
303D4—42no—
304D4—44no—
305D4—82no—
306D4—82no—
307D4—82no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—84no—
321C2×C4—1042no—
322C2×C4—1042no—
323C2×C4—1042no—
324C2×C4C2×C22⋊Dic1312yes—
325C2×C4#8820711yescharacteristic
326C2×C4#8820711yescharacteristic
327C8—1041no—
328C8—1041no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—82no—
338C22#1171890112yes—
339C22#1171890811yescharacteristic
340C4—21no—
341C4—21no—
342C4—22no—
343C4—42no—
344C4—42no—
345C4—42no—
346C4—42no—
347C4—42no—
348C4—2082no—
349C2—22no—
350C2—42no—
351C2—82no—
352C2#1311475411yescharacteristic
353C2#1311480011yescharacteristic
354C2#1311480011yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC13×#3493C2
socleC22×C13#379
cosocleC23×C4×C13C23
hypercenter#3493D13
hypocenterC13#8463
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3493

Complements

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

NH ≅ G/Ntype
1. #13114913C2semidirect
2. #13114907C2semidirect
3. #13113392C2semidirect
4. #13113392C2semidirect
10. C13×#544C4semidirect
12. C13×#537C4semidirect
15. C13×#520C4semidirect
161. #544Dic13semidirect
163. #537Dic13semidirect
166. #520Dic13semidirect
294. C13#8463semidirect

Maximal subgroups

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

subgroupindex
#131149132
#131149072
#131133922
C13×#34932
#846313