Finite Group Databasebeta

← #15756472

Subgroups — #15756472

Order 3328.

472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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#13117776C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112714C212yesmaximal, complemented
4#13112703C212yesmaximal, complemented
5C13×#1799C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×C13×#99—21no—
8C13×#380C2212yes—
9#11718881—21no—
10#11718873C2211yescharacteristic
11#11718872C411yescharacteristic, complemented
12C4×C22⋊Dic13C411yescharacteristic, complemented
13C2×#88071C2211yescharacteristic
14C2×C22⋊#1055C2212yes—
15#11718642—21no—
16#11718612—21no—
17C22⋊C4×Dic13—21no—
18#11718598C411yescharacteristic, complemented
19#11718593C411yescharacteristic, complemented
20C13×#342—21no—
21#11718120—21no—
22#11718117—21no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×Dic13—21no—
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13C2×C411yescharacteristic
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C22×#1055—22no—
42C13×#99—42no—
43C13×#95—22no—
44#88071—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071C2×C411yescharacteristic
50#88071C2×C411yescharacteristic
51#88071C2×C411yescharacteristic
52#88071C2×C411yescharacteristic
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55#8762—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—42no—
65C22×C4×C13—81no—
66C22×C4×C13—81no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13#4112yes—
73C22×C4×C13#4112yes—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—42no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13—81no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—82no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C42×C13—21no—
89C42×C13—21no—
90C22⋊Dic13—42no—
91C22⋊Dic13—42no—
92C22⋊Dic13—81no—
93C4⋊Dic13—81no—
94C4×Dic13—42no—
95C4×Dic13—81no—
96C2×#1055—42no—
97C2×#1055—82no—
98#2353—131no—
99#1799D1311yescharacteristic
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—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13—82no—
131C2×C4×C13—82no—
132C2×C4×C13—82no—
133C2×C4×C13#11711yescharacteristic
134C2×C4×C13#11711yescharacteristic
135C2×C4×C13#12312yes—
136C2×Dic13—22no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—82no—
149C2×Dic13—82no—
150#1055—82no—
151C2×C4×D4C2×D1311yescharacteristic
152C2×#99—21no—
153C2×C22⋊C8—132no—
154#388—261no—
155#387—261no—
156#386—261no—
157#383—131no—
158#381—131no—
159#380—131no—
160#380C2×D1312yes—
161C4×C22⋊C4—131no—
162C4×C22⋊C4—261no—
163#376—131no—
164C2×#95—131no—
165#342—21no—
166#324—261no—
167#323—261no—
168C22×C13—21no—
169C22×C13—22no—
170C22×C13—21no—
171C22×C13—22no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—42no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13#38111yescharacteristic
181C22×C13#41611yescharacteristic
182C22×C13#41711yescharacteristic
183C22×C13#48212yes—
184C22×C13#48512yes—
185C4×C13—22no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—162no—
192Dic13—42no—
193Dic13—81no—
194Dic13—81no—
195Dic13—81no—
196C22×D4C22⋊D1311yescharacteristic
197C23×C4—261no—
198C23×C4C4×D1311yescharacteristic
199C23×C4C22×D1311yescharacteristic
200C22×C8—262no—
201C4×D4—22no—
202C4×D4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4D5211yescharacteristic
206C2×C22⋊C4—22no—
207C2×C22⋊C4—261no—
208C2×C22⋊C4—261no—
209C2×C22⋊C4—261no—
210C2×C22⋊C4D5211yescharacteristic
211C2×C22⋊C4C22⋊D1311yescharacteristic
212C2×C42—261no—
213C2×C42—261no—
214C2×C42C4×D1311yescharacteristic
215#99—42no—
216C22⋊C8—262no—
217C22⋊C8—262no—
218#95—22no—
219#95—131no—
220#95—131no—
221#95—131no—
222#95—131no—
223#95—261no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228C2×C13—21no—
229C2×C13—21no—
230C2×C13—22no—
231C2×C13—22no—
232C2×C13—81no—
233C2×C13#182511yescharacteristic
234C2×C13#182711yescharacteristic
235C2×C13#182811yescharacteristic
236C24#610311yescharacteristic
237C24C2×C22⋊D1311yescharacteristic
238C2×D4—21no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4—22no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—42no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4—522no—
252C22×C4—521no—
253C22×C4—521no—
254C22×C4—1041no—
255C22×C4#610311yescharacteristic
256C22×C4#610311yescharacteristic
257C22×C4#610311yescharacteristic
258C22×C4C2×C4×D1311yescharacteristic
259C22×C4C2×D5211yescharacteristic
260C22×C4#612912yes—
261C22×C4#612912yes—
262C2×C8—522no—
263C2×C8—1042no—
264C4⋊C4—22no—
265C4⋊C4—82no—
266C4⋊C4—1041no—
267C22⋊C4—22no—
268C22⋊C4—22no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—522no—
272C22⋊C4—522no—
273C22⋊C4—1041no—
274C42—21no—
275C42—21no—
276C42—522no—
277C42—1041no—
278C13#876211yescharacteristic, complemented, Sylow
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23C2×#610311yescharacteristic
287C23#8818611yescharacteristic
288C23#8818912yes—
289C23#8819611yescharacteristic
290C23#8820412yes—
291D4—42no—
292D4—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—262no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—1042no—
322C2×C4—1042no—
323C2×C4#8813111yescharacteristic
324C2×C4#8813111yescharacteristic
325C2×C4#8814012yes—
326C8—1042no—
327C22—21no—
328C22—22no—
329C22—21no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22#1171860411yescharacteristic
340C22#1171862711yescharacteristic
341C22#1171866311yescharacteristic
342C22#1171869612yes—
343C22#1171870612yes—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—162no—
351C4—522no—
352C4—1041no—
353C4—1041no—
354C4—1041no—
355C2—22no—
356C2—21no—
357C2—21no—
358C2—22no—
359C2—81no—
360C2#1311492811yescharacteristic
361C2#1311493711yescharacteristic
362C2#1311494211yescharacteristic
subgroupG/H
centerC22#11718604
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1799C2
socleC22×C13#381
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#1799D13
hypocenterC13#8762
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13112714C2semidirect
4. #13112703C2semidirect
11. #11718872C4semidirect
12. C4×C22⋊Dic13C4semidirect
18. #11718598C4semidirect
19. #11718593C4semidirect
278. C13#8762semidirect

Maximal subgroups

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

subgroupindex
#131177762
#131131542
#131127142
#131127032
C13×#17992
#876213