Finite Group Databasebeta

← #15756480

Subgroups — #15756480

Order 3328.

472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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#13114824C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112715C212yesmaximal, complemented
4#13112703C212yesmaximal, complemented
5C13×#2353C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C13×#388—21no—
8C13×#387—21no—
9C13×#386—21no—
10C13×#383C411yescharacteristic, complemented
11C13×#381C411yescharacteristic, complemented
12C13×#380C2211yescharacteristic
13C4×C13×C22⋊C4—21no—
14C4×C13×C22⋊C4C411yescharacteristic, complemented
15C13×#376C411yescharacteristic, complemented
16C2×C13×#95C2211yescharacteristic
17C2×#88074—21no—
18#11718873C2212yes—
19C2×C22⋊#1055C2212yes—
20#11718120—21no—
21#11718118—21no—
22#11718117—21no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13—21no—
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C22⋊C4—21no—
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C42×C13—21no—
37C2×C42×C13—21no—
38C2×C42×C13C2×C411yescharacteristic
39C2×C22⋊Dic13—22no—
40C2×C4⋊Dic13—22no—
41C22×#1055—22no—
42C13×#95—21no—
43C13×#95—21no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95C2×C411yescharacteristic
48C13×#95C2×C411yescharacteristic
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51#88074—42no—
52#88071—22no—
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55#8763—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C24×C13C2×D411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—81no—
71C22×C4×C13—81no—
72C22×C4×C13—81no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13#4112yes—
79C22×C4×C13#4112yes—
80C22×Dic13—42no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—81no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—81no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—42no—
92C42×C13—81no—
93C22⋊Dic13—42no—
94C22⋊Dic13—42no—
95C4⋊Dic13—82no—
96C2×#1055—42no—
97C2×#1055—82no—
98#2353D1311yescharacteristic
99#1799—131no—
100#1459—131no—
101#1294—132no—
102#1289—132no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13C2×C22⋊C411yescharacteristic
111C23×C13#12312yes—
112C23×C13#13512yes—
113C23×C13AGL(1,ℤ/8)11yescharacteristic
114C23×C13#13711yescharacteristic
115D4×C13—42no—
116D4×C13—42no—
117C2×C4×C13—22no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13—84no—
143C2×C4×C13#11711yescharacteristic
144C2×C4×C13#11711yescharacteristic
145C2×C4×C13#12312yes—
146C2×Dic13—82no—
147C2×Dic13—82no—
148C2×Dic13—82no—
149#1055—82no—
150C2×C4×D4C2×D1311yescharacteristic
151C2×#99—261no—
152C2×C22⋊C8—132no—
153#388—21no—
154#387—21no—
155#386—21no—
156#383Dic1311yescharacteristic, complemented
157#381Dic1311yescharacteristic, complemented
158#380—132no—
159#380C2×D1311yescharacteristic
160C4×C22⋊C4—21no—
161C4×C22⋊C4Dic1311yescharacteristic, complemented
162#376Dic1311yescharacteristic, complemented
163C2×#95C2×D1311yescharacteristic
164#342—261no—
165#324—261no—
166#323—261no—
167C22×C13—22no—
168C22×C13—21no—
169C22×C13—22no—
170C22×C13—21no—
171C22×C13—42no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13#38111yescharacteristic
180C22×C13#41611yescharacteristic
181C22×C13#41711yescharacteristic
182C22×C13#48212yes—
183C22×C13#48512yes—
184C4×C13—22no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—42no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—81no—
192C4×C13—81no—
193C4×C13—81no—
194Dic13—162no—
195C22×D4C22⋊D1311yescharacteristic
196C23×C4—21no—
197C23×C4C2×Dic1311yescharacteristic
198C23×C4C22×D1311yescharacteristic
199C22×C8—262no—
200C4×D4—22no—
201C4×D4—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—262no—
204C2×C4⋊C4C22⋊D1311yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—262no—
209C2×C22⋊C4C22⋊D1311yescharacteristic
210C2×C22⋊C4C22⋊D1311yescharacteristic
211C2×C42—21no—
212C2×C42—21no—
213C2×C42C2×Dic1311yescharacteristic
214#99—522no—
215C22⋊C8—262no—
216C22⋊C8—262no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—262no—
223#95C2×Dic1311yescharacteristic
224#95C2×Dic1311yescharacteristic
225#95C2×Dic1311yescharacteristic
226#95C2×Dic1311yescharacteristic
227C2×C13—22no—
228C2×C13—21no—
229C2×C13—21no—
230C2×C13—22no—
231C2×C13—81no—
232C2×C13#182511yescharacteristic
233C2×C13#182711yescharacteristic
234C2×C13#182811yescharacteristic
235C24C22⋊Dic1311yescharacteristic
236C24C2×C22⋊D1311yescharacteristic
237C2×D4—22no—
238C2×D4—21no—
239C2×D4—22no—
240C2×D4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—522no—
253C22×C4C22⋊Dic1311yescharacteristic
254C22×C4C22⋊Dic1311yescharacteristic
255C22×C4C22⋊Dic1311yescharacteristic
256C22×C4#612712yes—
257C22×C4#612712yes—
258C22×C4C22×Dic1311yescharacteristic
259C22×C4C2×C22⋊D1311yescharacteristic
260C2×C8—522no—
261C2×C8—1042no—
262C4⋊C4—22no—
263C4⋊C4—81no—
264C4⋊C4—1042no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—42no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—81no—
271C22⋊C4—522no—
272C22⋊C4—522no—
273C42—21no—
274C42—21no—
275C42—42no—
276C42—81no—
277C13#876311yescharacteristic, complemented, Sylow
278C23—21no—
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23#8818312yes—
286C23#8820311yescharacteristic
287C23#8820412yes—
288C23#8820511yescharacteristic
289C23C2×C22⋊Dic1311yescharacteristic
290D4—42no—
291D4—42no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—84no—
318C2×C4—1042no—
319C2×C4—1042no—
320C2×C4—1042no—
321C2×C4#8818011yescharacteristic
322C2×C4#8818011yescharacteristic
323C2×C4#8818312yes—
324C8—1042no—
325C22—21no—
326C22—22no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22—81no—
337C22#1171865712yes—
338C22#1171866412yes—
339C22#1171887211yescharacteristic
340C22#1171889311yescharacteristic
341C22#1171889411yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—42no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—2082no—
353C2—21no—
354C2—21no—
355C2—22no—
356C2—22no—
357C2—81no—
358C2#1311493111yescharacteristic
359C2#1311494011yescharacteristic
360C2#1311494411yescharacteristic
subgroupG/H
centerC22#11718872
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2353C2
socleC22×C13#381
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2353D13
hypocenterC13#8763
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2353

Complements

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

NH ≅ G/Ntype
3. #13112715C2semidirect
4. #13112703C2semidirect
10. C13×#383C4semidirect
11. C13×#381C4semidirect
14. C4×C13×C22⋊C4C4semidirect
15. C13×#376C4semidirect
156. #383Dic13semidirect
157. #381Dic13semidirect
161. C4×C22⋊C4Dic13semidirect
162. #376Dic13semidirect
277. C13#8763semidirect

Maximal subgroups

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

subgroupindex
#131148242
#131131542
#131127152
#131127032
C13×#23532
#876313