Finite Group Databasebeta

← #16778525

Subgroups — #16778525

Order 3328.

478 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 102 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#13130764C211yesmaximal, characteristic, complemented
2#13130752C211yesmaximal, characteristic, complemented
3#13129654C212yesmaximal, complemented
4#13129652C212yesmaximal
5#13117301C211yesmaximal, characteristic
6C2×C4×D4×C13C411yescharacteristic
7C2×#88180—21no—
8C2×#88112—21no—
9#11718882C411yescharacteristic
10#11718882C2211yescharacteristic
11C4×C22⋊Dic13—21no—
12#11718646C411yescharacteristic
13#11718646C2211yescharacteristic
14#11718612—21no—
15#11718612—21no—
16C4×C4⋊Dic13C411yescharacteristic
17C42×Dic13C2211yescharacteristic
18#11718290—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13—21no—
25C22×#1057—22no—
26C22×#1057—22no—
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4—21no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36#88180—42no—
37#88180—42no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×C4×Dic13—21no—
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13C2311yescharacteristic
49#88112—42no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#7642—131nomaximal, Sylow
54C24×C13—21no—
55C2×D4×C13—21no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13M1612yes—
59C22×C4×C13—24no—
60C22×C4×C13—21no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C2×D411yescharacteristic
71C22×Dic13C2×D411yescharacteristic
72C2×#1057—42no—
73C2×#1057—42no—
74C2×#1057—42no—
75C2×#1057—42no—
76C2×#1057—42no—
77C2×#1057—42no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4M1612yes—
80C13×C22⋊C4—24no—
81C42×C13—21no—
82C42×C13—21no—
83C22⋊Dic13—42no—
84C22⋊Dic13—42no—
85C22⋊Dic13—41no—
86C22⋊Dic13—41no—
87C22⋊Dic13—42no—
88C4⋊Dic13—42no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93C4×Dic13—22no—
94C4×Dic13—41no—
95C4×Dic13—41no—
96C4×Dic13—41no—
97C4×Dic13—41no—
98C4×Dic13—42no—
99C4×Dic13D812yes—
100C4×Dic13SD1612yes—
101#2293—131no—
102#1839—131no—
103#1831—131no—
104#1271—132no—
105#1270—132no—
106C23×C13—22no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13C2×C22⋊C411yescharacteristic
114D4×C13—42no—
115D4×C13—42no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—22no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—48no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13#10212yes—
128C2×C4×C13C2×M1611yescharacteristic
129C2×C4×C13C2×M1611yescharacteristic
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13#10212yes—
146C2×Dic13C2×D811yescharacteristic
147C2×Dic13C2×SD1611yescharacteristic
148C2×Dic13#13512yes—
149#1057—82no—
150#1057—82no—
151C2×C4×D4#26111yescharacteristic
152C2×#117—261no—
153C2×C4⋊C8—261no—
154#390—131no—
155#390—131no—
156#389—131no—
157#389—131no—
158#388—261no—
159#388—261no—
160C4×C4⋊C4—131no—
161C4×C22⋊C4—261no—
162C43—131no—
163#336—132no—
164#336—132no—
165#336—261no—
166#336—261no—
167#336—261no—
168C22×C13—42no—
169C22×C13—42no—
170C22×C13—42no—
171C22×C13—81no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13—81no—
175C22×C13#40711yescharacteristic
176C22×C13#41011yescharacteristic
177C22×C13#41311yescharacteristic
178C22×C13C2×#10211yescharacteristic
179C22×C13#41611yescharacteristic
180C22×C13#42111yescharacteristic
181C22×C13#42111yescharacteristic
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—22no—
185C4×C13—42no—
186C4×C13—41no—
187Dic13—22no—
188Dic13—21no—
189Dic13—21no—
190Dic13—22no—
191Dic13—41no—
192Dic13—81no—
193Dic13—81no—
194C22×D4C2×#26111yescharacteristic
195C23×C4—21no—
196C22×C8—262no—
197C22×C8—262no—
198C4×D4—22no—
199C4×D4—22no—
200#117—522no—
201#117—522no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4C2×#26111yescharacteristic
207C2×C22⋊C4—21no—
208C2×C22⋊C4—261no—
209C2×C22⋊C4—261no—
210C2×C22⋊C4—261no—
211C2×C22⋊C4—261no—
212C2×C42—131no—
213C2×C42—131no—
214C2×C42—131no—
215C2×C42—131no—
216C2×C42—131no—
217C2×C42—131no—
218C2×C42—261no—
219C2×C42C2×#26111yescharacteristic
220C4⋊C8—522no—
221#95—261no—
222#95—261no—
223#95—261no—
224C2×C13—82no—
225C2×C13#146411yescharacteristic
226C2×C13#148611yescharacteristic
227C2×C13#148811yescharacteristic
228C2×C13#151711yescharacteristic
229C2×C13#152111yescharacteristic
230C2×C13#153511yescharacteristic
231C2×C13#154011yescharacteristic
232C24—21no—
233C2×D4—21no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4#612212yes—
237C22×C4—24no—
238C22×C4—21no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—131no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4C22⋊#26111yescharacteristic
248C22×C4C22⋊#26111yescharacteristic
249C22×C4C22×#26111yescharacteristic
250C2×C8—522no—
251C2×C8—522no—
252C2×C8—522no—
253C2×C8—522no—
254C2×C8—522no—
255C2×C8—522no—
256C4⋊C4—21no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—522no—
261C4⋊C4—521no—
262C4⋊C4#612212yes—
263C22⋊C4—24no—
264C22⋊C4—521no—
265C22⋊C4—522no—
266C22⋊C4—521no—
267C22⋊C4—522no—
268C22⋊C4—522no—
269C42—21no—
270C42—21no—
271C42—132no—
272C42—132no—
273C42—262no—
274C42—521no—
275C42—521no—
276C42—521no—
277C42—521no—
278C42—522no—
279C13#764211yescharacteristic, complemented, Sylow
280C23—22no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23C2×C22⋊#26111yescharacteristic
288D4—42no—
289D4—42no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—48no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—131no—
302C2×C4—132no—
303C2×C4—131no—
304C2×C4—132no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4#8811512yes—
321C2×C4C2×#612211yescharacteristic
322C2×C4C2×#612211yescharacteristic
323C8—1042no—
324C8—1042no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22#1171911611yescharacteristic
333C22#1171913211yescharacteristic
334C22C2×#8811511yescharacteristic
335C22#1171914011yescharacteristic
336C22#1171916511yescharacteristic
337C22#1171916611yescharacteristic
338C22#1171916911yescharacteristic
339C4—21no—
340C4—21no—
341C4—22no—
342C4—42no—
343C4—41no—
344C4—261no—
345C4—261no—
346C4—262no—
347C4—262no—
348C4—521no—
349C4—1041no—
350C4—1041no—
351C2—82no—
352C2#1313008711yescharacteristic
353C2#1313016111yescharacteristic
354C2#1313016711yescharacteristic
355C2#1313026611yescharacteristic
356C2#1313027811yescharacteristic
357C2#1313032011yescharacteristic
358C2#1313033311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×D4×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×D4#261
hypocenterC13#7642
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #13130764C2semidirect
2. #13130752C2semidirect
3. #13129654C2semidirect
279. C13#7642semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131307522
#131296542
#131296522
#131173012
#764213