Finite Group Databasebeta

← #16786957

Subgroups — #16786957

Order 3328.

360 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 88 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#13131198C211yesmaximal, characteristic, complemented
2#13131194C211yesmaximal, characteristic, complemented
3#13129759C212yesmaximal, complemented
4#13129758C212yesmaximal, complemented
5#13123546C211yesmaximal, characteristic
6C2×C13×#131C411yescharacteristic
7#11719537C411yescharacteristic
8C2×#88155C411yescharacteristic
9#11718895C2211yescharacteristic
10#11718790C2211yescharacteristic
11#11718789—21no—
12#11718789—21no—
13#11718779C411yescharacteristic
14C8×C22⋊D13—21no—
15C8×C22⋊D13—21no—
16C2×C8×Dic13C2211yescharacteristic
17C22⋊#6092C2212yes—
18C22⋊#6092C2212yes—
19#11718260—21no—
20#11718260—21no—
21#11718258—21no—
22#11718257—21no—
23C2×C13×#41C2×C411yescharacteristic
24C2×#6127C2×C411yescharacteristic
25C13×#131—42no—
26C2×C13×M16—21no—
27C2×C13×M16C2×C411yescharacteristic
28C22×C8×C13—21no—
29C22×C8×C13C2×C411yescharacteristic
30#88201C811yescharacteristic
31#88198C811yescharacteristic
32#88194C811yescharacteristic
33#88193—21no—
34#88193—21no—
35#88190C811yescharacteristic
36C4×C22⋊D13—21no—
37C4×C22⋊D13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×#6099C2×C411yescharacteristic
40C22×#1055C2311yescharacteristic
41#88155—42no—
42C2×#6094—21no—
43C2×C8×D13—21no—
44C2×#6092—22no—
45C2×#6092—22no—
46C22⋊#1055—21no—
47C22⋊#1055—21no—
48#88060—21no—
49#88060—21no—
50#88054—21no—
51#88054—21no—
52C8×Dic13D411yescharacteristic
53C8×Dic13D411yescharacteristic
54C8×Dic13D411yescharacteristic
55C8×Dic13D411yescharacteristic
56#11492—131nomaximal, Sylow
57C13×#41—41no—
58C13×#41—41no—
59C2×Q8×C13C2×C811yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13C2×C811yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13C22×C411yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C22×Dic13M1611yescharacteristic
68C22×Dic13M1611yescharacteristic
69#6127—41no—
70#6127—41no—
71C2×D52C2×C811yescharacteristic
72C2×C4×D13—21no—
73C2×Dic26C2×C811yescharacteristic
74C13×M16—42no—
75C13×M16—41no—
76C2×C8×C13—22no—
77C2×C8×C13—21no—
78C2×C8×C13—42no—
79C2×C8×C13C22⋊C411yescharacteristic
80C2×C8×C13C22⋊C411yescharacteristic
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83#6103—21no—
84#6103—21no—
85#6101—21no—
86#6101—21no—
87C4×Dic13C22⋊C411yescharacteristic
88C4×Dic13C22⋊C411yescharacteristic
89C4×Dic13C2×C811yescharacteristic
90C4×Dic13C2×C811yescharacteristic
91#6099—41no—
92C2×#1055—21no—
93C2×#1055—41no—
94C2×#1055C2×D411yescharacteristic
95C2×#1055C2×D411yescharacteristic
96#6094—42no—
97C8×D13—42no—
98#6092—42no—
99#6092—42no—
100#2931—131no—
101#2163—131no—
102#2162—131no—
103#1315—132no—
104#1315—132no—
105C23×C13—21no—
106C23×C13C2×M1611yescharacteristic
107C22×D13—21no—
108Q8×C13—41no—
109D4×C13—41no—
110D4×C13—42no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13C2×C22⋊C411yescharacteristic
117C2×C4×C13C22×C811yescharacteristic
118C22⋊D13—42no—
119C22⋊D13—42no—
120C22⋊D13—42no—
121C2×Dic13—22no—
122C2×Dic13—21no—
123C2×Dic13—41no—
124C2×Dic13C22⋊C811yescharacteristic
125C2×Dic13C22⋊C811yescharacteristic
126C2×Dic13C22⋊C811yescharacteristic
127C2×Dic13C22⋊C811yescharacteristic
128D52—41no—
129C4×D13—41no—
130C4×D13—41no—
131Dic26—41no—
132C8×C13—21no—
133C8×C13—41no—
134C8×C13#10012yes—
135#1055—21no—
136#1055—21no—
137#1055—41no—
138C2×#131—131no—
139C2×#131#26111yescharacteristic
140#532—131no—
141#436—261no—
142#436—261no—
143C8×D4—261no—
144C8×D4—261no—
145#423—131no—
146#408—131no—
147#408—131no—
148C2×C4×C8—131no—
149C4⋊C16—261no—
150C4⋊C16—261no—
151C22⋊C16—132no—
152C22⋊C16—132no—
153#346—261no—
154C4×C16—261no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13C2×C22⋊C811yescharacteristic
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—41no—
165C4×C13—21no—
166C4×C13—41no—
167C4×C13#41011yescharacteristic
168C4×C13C2×#10011yescharacteristic
169Dic13—21no—
170Dic13—21no—
171Dic13—21no—
172Dic13—41no—
173Dic13#35012yes—
174C2×#41—131no—
175C2×#41C2×#26111yescharacteristic
176#131—42no—
177#131—522no—
178C2×M16—21no—
179C2×M16—131no—
180C2×M16—261no—
181C2×M16C2×#26111yescharacteristic
182C22×C8—21no—
183C22×C8—131no—
184C22×C8—261no—
185C22×C8C2×#26111yescharacteristic
186C4⋊Q8—131no—
187#127—131no—
188#124—131no—
189#124—131no—
190#121—261no—
191#121—261no—
192C4×D4—261no—
193C4×D4—261no—
194C2×C42—131no—
195C2×C16—262no—
196C2×C16—262no—
197C4⋊C8—261no—
198C4⋊C8—261no—
199C22⋊C8—261no—
200C22⋊C8—261no—
201C22⋊C8—261no—
202C22⋊C8—261no—
203C4×C8—131no—
204C4×C8—131no—
205C4×C8—131no—
206C4×C8—131no—
207C2×C13—41no—
208C2×C13—81no—
209C2×C13#146011yescharacteristic
210C2×C13C2×#35011yescharacteristic
211C2×C13#211711yescharacteristic
212D13—81no—
213#41—41no—
214#41—41no—
215#41—521no—
216#41—521no—
217C2×Q8—131no—
218C2×Q8D13⋊C811yescharacteristic
219C2×D4—21no—
220C2×D4—131no—
221C2×D4—261no—
222C2×D4—261no—
223C2×D4—261no—
224C2×D4D13⋊C811yescharacteristic
225C22×C4—21no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—261no—
229C22×C4C22×#26111yescharacteristic
230M16—42no—
231M16—41no—
232M16—522no—
233M16—521no—
234C2×C8—22no—
235C2×C8—21no—
236C2×C8—42no—
237C2×C8—131no—
238C2×C8—131no—
239C2×C8—261no—
240C2×C8—522no—
241C2×C8—521no—
242C2×C8C22⋊#26111yescharacteristic
243C2×C8C22⋊#26111yescharacteristic
244C4⋊C4—261no—
245C4⋊C4—261no—
246C22⋊C4—261no—
247C22⋊C4—261no—
248C22⋊C4—261no—
249C22⋊C4—261no—
250C42—131no—
251C42—131no—
252C42—131no—
253C42—131no—
254C16—522no—
255C16—522no—
256C13#1149211yescharacteristic, complemented, Sylow
257C23—21no—
258C23—261no—
259C23D13⋊M1611yescharacteristic
260Q8—41no—
261Q8—521no—
262D4—41no—
263D4—42no—
264D4—521no—
265D4—522no—
266D4—522no—
267D4—522no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—131no—
274C2×C4—131no—
275C2×C4—131no—
276C2×C4—131no—
277C2×C4—262no—
278C2×C4—261no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4C2×D13⋊C811yescharacteristic
283C2×C4C2×C22⋊#26111yescharacteristic
284C8—21no—
285C8—41no—
286C8—261no—
287C8—261no—
288C8—521no—
289C8#8812112yes—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—521no—
297C22—521no—
298C22—521no—
299C22D13⋊(C22⋊C8)11yescharacteristic
300C4—21no—
301C4—41no—
302C4—132no—
303C4—261no—
304C4—261no—
305C4—261no—
306C4—521no—
307C4#1171911611yescharacteristic
308C4C2×#8812111yescharacteristic
309C2—41no—
310C2—81no—
311C2—1041no—
312C2#1313007511yescharacteristic
313C2D13⋊#35011yescharacteristic
314C2#1313107911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#131C4
socleC22×C13C2×C22⋊C8
prime radical#11719537C4
cosocleC22×#1055C23
hypercenterC2×#131#261
hypocenterC13#11492
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #13131198C2semidirect
2. #13131194C2semidirect
3. #13129759C2semidirect
4. #13129758C2semidirect
256. C13#11492semidirect

Maximal subgroups

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

subgroupindex
#131311982
#131311942
#131297592
#131297582
#131235462
#1149213