Finite Group Databasebeta

← #15760331

Subgroups — #15760331

Order 3328.

570 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 109 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#13123876C211yesmaximal, characteristic
2#13119790C211yesmaximal, characteristic
3#13114825C211yesmaximal, characteristic
4#13113521C211yesmaximal, characteristic, complemented
5#13112738C211yesmaximal, characteristic, complemented
6#13112737C211yesmaximal, characteristic, complemented
7C13×#1549C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88200—22no—
10C2×C4×D52C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#423C2211yescharacteristic
13C2×#88063—21no—
14#11718653C414yes—
15#11718649—21no—
16#11718637—21no—
17C4×C4⋊Dic13C2211yescharacteristic
18#11718586C2211yescharacteristic
19#11718585C2211yescharacteristic
20#11718499—22no—
21#11718387—22no—
22#11718349—22no—
23C13×#332—22no—
24#11718146—21no—
25#11718139—22no—
26C22×Q8×C13—21no—
27C22×D52D411yescharacteristic
28C22×C4×D13D412yes—
29C2×C13×M16—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C412yes—
36C2×C42×C13C2311yescharacteristic
37#88200—48no—
38C2×#6103—24no—
39C2×#6103C2×C412yes—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13D411yescharacteristic
42C2×#6101—24no—
43C2×C4×Dic13—21no—
44C2×#6099—21no—
45C2×#6094—24no—
46C4×D52—21no—
47C4×D52—21no—
48C4×D52—21no—
49C4×D52—21no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8D412yes—
53C13×C22⋊C8—21no—
54C4×C8×C13—21no—
55#88071C2×C412yes—
56C22⋊#1055—21no—
57#88063—42no—
58#88060—24no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055D412yes—
62C4×#1055—21no—
63#9403—131nomaximal, Sylow
64C23×D13C22⋊C412yes—
65C2×Q8×C13—44no—
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C22×C4×C13—22no—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—22no—
73C22×Dic13C22⋊C412yes—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52—21no—
79C2×D52—21no—
80C2×C4×D13—22no—
81C2×C4×D13—22no—
82C2×C4×D13—44no—
83C13×M16—41no—
84C13×M16—41no—
85C2×C8×C13—22no—
86C2×C8×C13—41no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C42×C13C2×D411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13#4111yescharacteristic
94C42×C13#4111yescharacteristic
95#6103—22no—
96#6103—22no—
97#6103—48no—
98C4⋊Dic13—24no—
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101#6101—48no—
102C4×Dic13—41no—
103C4×Dic13—41no—
104#6099—41no—
105#6099—41no—
106C2×#1055—22no—
107C2×#1055—41no—
108#6094—84no—
109#2975—131no—
110#2542—131no—
111#1800—131no—
112#1549—131no—
113#1549D1311yescharacteristic, complemented
114#1303—131no—
115#1303—131no—
116C23×C13C2×C22⋊C411yescharacteristic
117C22×D13—22no—
118C22×D13—22no—
119C22×D13—22no—
120C22×D13—42no—
121C22×D13—42no—
122Q8×C13—82no—
123Q8×C13—82no—
124C2×C4×C13—22no—
125C2×C4×C13—41no—
126C2×C4×C13—44no—
127C2×C4×C13—42no—
128C2×C4×C13C4×D411yescharacteristic
129C2×C4×C13C4×D411yescharacteristic
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12111yescharacteristic
132C2×C4×C13#12111yescharacteristic
133C2×C4×C13#12311yescharacteristic
134C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C13#13711yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C2×C4×C13#13711yescharacteristic
138C2×Dic13—24no—
139C2×Dic13—22no—
140C2×Dic13—42no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143D52—41no—
144D52—41no—
145D52—41no—
146D52—41no—
147C4×D13—44no—
148C4×D13—82no—
149C8×C13—42no—
150C8×C13—81no—
151#1055—42no—
152#1055—81no—
153C2×C4⋊Q8C2×D1311yescharacteristic
154C2×C22⋊Q8—262no—
155C2×C4×D4—131no—
156#436—262no—
157#436—262no—
158#431—131no—
159#431C2×D1311yescharacteristic
160#423—131no—
161#423C2×D1311yescharacteristic
162C2×#100—261no—
163#407—262no—
164#399—134no—
165#390—261no—
166#384—261no—
167C4×C4⋊C4—131no—
168#343—261no—
169#332—22no—
170#332—262no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13#38611yescharacteristic
174C22×C13#41711yescharacteristic
175C22×C13#41911yescharacteristic
176C2×D13—44no—
177C2×D13—42no—
178C2×D13—42no—
179C2×D13—42no—
180C2×D13—82no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—82no—
185C4×C13#45312yes—
186C4×C13#46811yescharacteristic
187C4×C13#46811yescharacteristic
188C4×C13#47011yescharacteristic
189C4×C13#47011yescharacteristic
190Dic13—44no—
191Dic13—42no—
192C22×Q8—21no—
193C22×D4—131no—
194C23×C4—132no—
195C2×M16—21no—
196C2×M16—264no—
197C2×M16—261no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C22⋊Q8—528no—
203C4×D4—261no—
204C4×D4—261no—
205C4×D4—261no—
206C4×D4—261no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4—264no—
211C2×C4⋊C4C4×D1312yes—
212C2×C22⋊C4—132no—
213C2×C22⋊C4—264no—
214C2×C42—261no—
215C2×C42C22×D1311yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—132no—
219C4⋊C8—261no—
220C4⋊C8—261no—
221C4⋊C8C22⋊D1312yes—
222#100—522no—
223C22⋊C8—21no—
224C22⋊C8—264no—
225C22⋊C8—261no—
226C4×C8—21no—
227C4×C8—261no—
228#95—132no—
229C2×C13—21no—
230C2×C13—21no—
231C2×C13#188711yescharacteristic
232C2×C13#189411yescharacteristic
233C2×C13#191511yescharacteristic
234D13—82no—
235C24—132no—
236C2×Q8—44no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×D4—261no—
240C2×D4—261no—
241C2×D4—261no—
242C2×D4—261no—
243C2×D4—261no—
244C2×D4—261no—
245C22×C4—22no—
246C22×C4—132no—
247C22×C4—262no—
248C22×C4—262no—
249C22×C4—262no—
250C22×C4—524no—
251C22×C4C2×C4×D1311yescharacteristic
252C22×C4D4×D1311yescharacteristic
253C22×C4D4×D1311yescharacteristic
254M16—41no—
255M16—41no—
256M16—521no—
257M16—521no—
258M16—1044no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—262no—
262C2×C8—521no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—264no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—528no—
271C22⋊C4—262no—
272C22⋊C4—262no—
273C22⋊C4—528no—
274C42—521no—
275C42—521no—
276C42#612711yescharacteristic
277C42D4×D1311yescharacteristic
278C42#612911yescharacteristic
279C42C2×C22⋊D1311yescharacteristic
280C13#940311yescharacteristic, complemented, Sylow
281C23—262no—
282C23—262no—
283C23—262no—
284C23—522no—
285C23—522no—
286C23C22⋊C4×D1311yescharacteristic
287Q8—82no—
288Q8—82no—
289D4—521no—
290D4—521no—
291D4—521no—
292D4—521no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—264no—
298C2×C4—262no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—524no—
302C2×C4—522no—
303C2×C4—1042no—
304C2×C4#8813511yescharacteristic
305C2×C4#8813711yescharacteristic
306C2×C4#8813811yescharacteristic
307C2×C4#8816811yescharacteristic
308C2×C4#8816911yescharacteristic
309C2×C4#8817211yescharacteristic
310C2×C4#8817211yescharacteristic
311C2×C4C4×C22⋊D1311yescharacteristic
312C2×C4#8819111yescharacteristic
313C2×C4#8819211yescharacteristic
314C8—42no—
315C8—81no—
316C8—522no—
317C8—1041no—
318C22—21no—
319C22—21no—
320C22—524no—
321C22—522no—
322C22—522no—
323C22—522no—
324C22—1042no—
325C22#1171846311yescharacteristic
326C22#1171846411yescharacteristic
327C22#1171861711yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—82no—
332C4—524no—
333C4—522no—
334C4#1171847311yescharacteristic
335C4#1171847711yescharacteristic
336C4#1171883511yescharacteristic
337C4#1171885011yescharacteristic
338C4#1171885912yes—
339C2—21no—
340C2—21no—
341C2—1042no—
342C2#1311523111yescharacteristic
343C2#1311526611yescharacteristic
344C2#1311538511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1549C2
socleC22×C13#386
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1549D13
hypocenterC13#9403
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
4. #13113521C2semidirect
5. #13112738C2semidirect
6. #13112737C2semidirect
7. C13×#1549C2semidirect
113. #1549D13semidirect
280. C13#9403semidirect

Maximal subgroups

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

subgroupindex
#131238762
#131197902
#131148252
#131135212
#131127382
#131127372
C13×#15492
#940313