Finite Group Databasebeta

← #15754652

Subgroups — #15754652

Order 3328.

738 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 151 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#13114828C211yesmaximal, characteristic
2#13113508C212yesmaximal, complemented
3#13113265C212yesmaximal, complemented
4#13113157C211yesmaximal, characteristic
5C2×C13×#556C211yesmaximal, characteristic
6C13×#556—24no—
7C13×#556—24no—
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×#126—22no—
10C2×C13×#124—21no—
11C2×C13×C22⋊Q8C412yes—
12C2×C4×Q8×C13—21no—
13C2×C4×Q8×C13C2211yescharacteristic
14C2×C4×D4×C13C2211yescharacteristic
15C2×C13×#117C412yes—
16C2×#88073—21no—
17#11718586C2212yes—
18#11718585C2212yes—
19#11718139—24no—
20Q8⋊#1055—24no—
21#11718122—21no—
22#11718117—22no—
23C22×Q8×C13—21no—
24C22×Q8×C13C2×C411yescharacteristic
25C22×D4×C13D411yescharacteristic
26C23×C4×C13C2×C412yes—
27C13×C4⋊Q8—22no—
28C13×C4⋊Q8D414yes—
29C13×#126—216no—
30C13×#124—28no—
31C13×C22⋊Q8—24no—
32C13×C22⋊Q8—24no—
33C4×Q8×C13—28no—
34C4×Q8×C13—22no—
35C4×Q8×C13D414yes—
36C4×D4×C13—22no—
37C4×D4×C13—22no—
38C13×#117—24no—
39C13×#117—24no—
40C2×C13×C4⋊C4—22no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4C2×C411yescharacteristic
44C2×C13×C4⋊C4C2×C412yes—
45C2×C13×C4⋊C4D411yescharacteristic
46C2×C13×C22⋊C4—22no—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊C4D412yes—
49C2×C42×C13—22no—
50C2×C42×C13—21no—
51C2×C42×C13C2311yescharacteristic
52C2×#6099—22no—
53#88073—42no—
54C22⋊#1055—22no—
55C4⋊#1055—22no—
56C4⋊#1055—22no—
57C4⋊#1055—22no—
58C4×#1055—22no—
59#8389—131nomaximal, Sylow
60C24×C13C22⋊C412yes—
61C2×Q8×C13—21no—
62C2×Q8×C13—24no—
63C2×Q8×C13—42no—
64C2×Q8×C13—42no—
65C2×Q8×C13—41no—
66C2×Q8×C13—41no—
67C2×Q8×C13C22⋊C412yes—
68C2×D4×C13—22no—
69C2×D4×C13—22no—
70C2×D4×C13—21no—
71C2×D4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—22no—
75C22×C4×C13—22no—
76C22×C4×C13—22no—
77C22×C4×C13—44no—
78C22×C4×C13C22⋊C412yes—
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C13×C4⋊C4—28no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—24no—
86C13×C4⋊C4—24no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4C22⋊C412yes—
89C13×C4⋊C4C22⋊C414yes—
90C13×C22⋊C4—28no—
91C13×C22⋊C4—28no—
92C13×C22⋊C4—24no—
93C42×C13—28no—
94C42×C13—24no—
95C42×C13C2×D412yes—
96C42×C13C2×D412yes—
97#6099—42no—
98#6099—42no—
99C2×#1055—42no—
100C2×#1055—42no—
101C2×#556D1311yescharacteristic
102#1800—131no—
103#1546—132no—
104#1487—132no—
105#1460—131no—
106C23×C13—22no—
107C23×C13—22no—
108C23×C13—22no—
109C23×C13—42no—
110C23×C13—42no—
111C23×C13C2×C22⋊C411yescharacteristic
112Q8×C13—24no—
113Q8×C13—42no—
114Q8×C13—44no—
115Q8×C13—44no—
116D4×C13—42no—
117D4×C13—42no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—24no—
123C2×C4×C13—41no—
124C2×C4×C13—44no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—44no—
130C2×C4×C13—42no—
131C2×C4×C13C2×C22⋊C411yescharacteristic
132C2×C4×C13C2×C22⋊C411yescharacteristic
133C2×C4×C13#12012yes—
134C2×C4×C13#12012yes—
135C2×C4×C13#13512yes—
136C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C13#13711yescharacteristic
138#1055—82no—
139#1055—82no—
140#556—24no—
141#556—24no—
142C2×C4⋊Q8C2×D1311yescharacteristic
143C2×#126—22no—
144C2×#124—21no—
145C2×C22⋊Q8Dic1312yes—
146C2×C4×Q8—21no—
147C2×C4×Q8C2×D1311yescharacteristic
148C2×C4×D4C2×D1311yescharacteristic
149C2×#117Dic1312yes—
150#431—132no—
151#423—132no—
152C2×#100—261no—
153#343—261no—
154#332—264no—
155Q8⋊C8—264no—
156#323—262no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—42no—
162C22×C13—82no—
163C22×C13—82no—
164C22×C13#37911yescharacteristic
165C22×C13#41611yescharacteristic
166C22×C13#41711yescharacteristic
167C4×C13—22no—
168C4×C13—21no—
169C4×C13—42no—
170C4×C13—42no—
171C4×C13—42no—
172C4×C13—44no—
173C4×C13#41312yes—
174C4×C13#44912yes—
175C4×C13#45212yes—
176C22×Q8—21no—
177C22×Q8C2×Dic1311yescharacteristic
178C22×D4C22⋊D1311yescharacteristic
179C23×C4C2×Dic1312yes—
180C2×M16—262no—
181C4⋊Q8—22no—
182C4⋊Q8C22⋊D1314yes—
183#126—216no—
184#124—28no—
185C22⋊Q8—24no—
186C22⋊Q8—24no—
187C4×Q8—28no—
188C4×Q8—22no—
189C4×Q8C22⋊D1314yes—
190C4×D4—22no—
191C4×D4—22no—
192#117—24no—
193#117—24no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×Dic1311yescharacteristic
198C2×C4⋊C4C2×Dic1312yes—
199C2×C4⋊C4C22⋊D1311yescharacteristic
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4C22⋊D1312yes—
203C2×C42—22no—
204C2×C42—21no—
205C2×C42C22×D1311yescharacteristic
206C4⋊C8—262no—
207C4⋊C8—262no—
208C4⋊C8—262no—
209#100—522no—
210C22⋊C8—262no—
211C4×C8—262no—
212C2×C13—21no—
213C2×C13—21no—
214C2×C13—82no—
215C2×C13#178511yescharacteristic
216C2×C13#178811yescharacteristic
217C2×C13#179611yescharacteristic
218C24C22⋊Dic1312yes—
219C2×Q8—21no—
220C2×Q8—24no—
221C2×Q8—42no—
222C2×Q8—41no—
223C2×Q8—42no—
224C2×Q8—41no—
225C2×Q8C22⋊Dic1312yes—
226C2×D4—21no—
227C2×D4—22no—
228C2×D4—21no—
229C2×D4—22no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—44no—
236C22×C4C22⋊Dic1312yes—
237C22×C4C22×Dic1311yescharacteristic
238C22×C4C2×C22⋊D1311yescharacteristic
239C22×C4C2×C22⋊D1311yescharacteristic
240M16—522no—
241M16—522no—
242C2×C8—522no—
243C2×C8—522no—
244C4⋊C4—28no—
245C4⋊C4—21no—
246C4⋊C4—22no—
247C4⋊C4—24no—
248C4⋊C4—24no—
249C4⋊C4—22no—
250C4⋊C4C22⋊Dic1312yes—
251C4⋊C4C22⋊Dic1314yes—
252C22⋊C4—28no—
253C22⋊C4—28no—
254C22⋊C4—24no—
255C42—28no—
256C42—24no—
257C42C2×C22⋊D1312yes—
258C42C2×C22⋊D1312yes—
259C13#838911yescharacteristic, complemented, Sylow
260C23—22no—
261C23—22no—
262C23—22no—
263C23—42no—
264C23—42no—
265C23C2×C22⋊Dic1311yescharacteristic
266Q8—24no—
267Q8—42no—
268Q8—44no—
269Q8—44no—
270D4—42no—
271D4—42no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—24no—
277C2×C4—41no—
278C2×C4—44no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4#8820311yescharacteristic
286C2×C4#8820412yes—
287C2×C4#8820511yescharacteristic
288C2×C4C2×C22⋊Dic1311yescharacteristic
289C2×C4C2×C22⋊Dic1311yescharacteristic
290C2×C4#8820712yes—
291C2×C4#8820712yes—
292C8—1042no—
293C8—1042no—
294C22—21no—
295C22—21no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—82no—
300C22—82no—
301C22#1171889311yescharacteristic
302C22#1171889411yescharacteristic
303C22#1171890811yescharacteristic
304C4—21no—
305C4—22no—
306C4—42no—
307C4—42no—
308C4—44no—
309C4—42no—
310C4#1171889812yes—
311C4#1171889912yes—
312C4#1171890012yes—
313C2—21no—
314C2—21no—
315C2—82no—
316C2#1311476411yescharacteristic
317C2#1311477611yescharacteristic
318C2#1311481111yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#556C2
socleC22×C13#379
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenterC2×#556D13
hypocenterC13#8389
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. #13113508C2semidirect
3. #13113265C2semidirect
259. C13#8389semidirect

Maximal subgroups

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

subgroupindex
#131148282
#131135082
#131132652
#131131572
C2×C13×#5562
#838913