Finite Group Databasebeta

← #15773726

Subgroups — #15773726

Order 3328.

416 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 83 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#13118119C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic, complemented
3#13112864C212yesmaximal, complemented
4#13112840C212yesmaximal
5C13×#1467C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×D52C411yescharacteristic
8C13×#432—21no—
9#11718892—21no—
10C2×#88076—21no—
11#11718654—21no—
12#11718652C411yescharacteristic
13#11718652C2211yescharacteristic
14#11718647C411yescharacteristic
15#11718647C2211yescharacteristic
16C4×#6103—21no—
17C4×#6103—21no—
18#11718593C411yescharacteristic
19#11718585—21no—
20C13×#324—21no—
21C13×#324C2212yes—
22#11718122C2212yes—
23C22×Q8×C13D411yescharacteristic
24C22×D52C2×C411yescharacteristic
25C22×C4×D13—21no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×#6103—21no—
35C2×#6103—21no—
36C2×#6103—21no—
37C2×#6103—21no—
38C2×#6103—21no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4×Dic13—21no—
41C2×#6099—22no—
42C4×D52—41no—
43C4×D52—41no—
44C13×C4⋊C8—41no—
45C13×C22⋊C8—22no—
46C13×#97—41no—
47#88076—42no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071C2×C411yescharacteristic
54#88071C2×C411yescharacteristic
55C4⋊#1055—41no—
56C4⋊#1055—41no—
57#11829—131nomaximal, Sylow
58C23×D13—21no—
59C2×Q8×C13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C2×D52—41no—
74C2×D52—42no—
75C2×C4×D13—42no—
76C2×C4×D13—42no—
77C2×C4×D13—41no—
78C2×C4×D13—41no—
79C2×C8×C13—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89#6103—42no—
90#6103—42no—
91#6103—42no—
92#6103—42no—
93#6103—41no—
94#6103—41no—
95C4⋊Dic13—41no—
96C4×Dic13—42no—
97#6099—42no—
98#6099—42no—
99C2×#1055—42no—
100#2398—131no—
101#1801—131no—
102#1467D1311yescharacteristic, complemented
103#1353—132no—
104#1345—132no—
105C23×C13C2×C22⋊C411yescharacteristic
106C22×D13—22no—
107C22×D13—41no—
108C22×D13—41no—
109C22×D13—41no—
110C22×D13—41no—
111C22×D13—41no—
112C22×D13—41no—
113Q8×C13—42no—
114Q8×C13—42no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
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—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13#9911yescharacteristic
131C2×C4×C13#9911yescharacteristic
132C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C13#13711yescharacteristic
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143D52—42no—
144D52—42no—
145C4×D13—82no—
146C4×D13—82no—
147C8×C13—82no—
148#1055—82no—
149C2×C4×Q8C2×D1311yescharacteristic
150C2×C4×D4—131no—
151#432—21no—
152#423—261no—
153C2×#101—261no—
154#400—131no—
155#400—131no—
156#397—261no—
157#394—131no—
158#394—131no—
159#393—261no—
160C4×C22⋊C4—261no—
161C4×C22⋊C4—261no—
162#376—131no—
163#343—132no—
164#324—21no—
165#324C2×D1312yes—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13C2×#9911yescharacteristic
169C22×C13#41711yescharacteristic
170C22×C13#42111yescharacteristic
171C2×D13—42no—
172C2×D13—42no—
173C2×D13—42no—
174C2×D13—81no—
175C2×D13—81no—
176C2×D13—81no—
177C2×D13—81no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13#35512yes—
187Dic13—81no—
188Dic13—81no—
189Dic13—81no—
190C22×Q8D5211yescharacteristic
191C22×D4—131no—
192C23×C4—261no—
193C2×M16—262no—
194C4×Q8—41no—
195C4×Q8—41no—
196C4×D4—521no—
197C4×D4—521no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4C4×D1311yescharacteristic
200C2×C4⋊C4C22⋊D1311yescharacteristic
201C2×C4⋊C4C22×D1311yescharacteristic
202C2×C22⋊C4—261no—
203C2×C22⋊C4—261no—
204C2×C22⋊C4—261no—
205C2×C22⋊C4—261no—
206C2×C22⋊C4—261no—
207C2×C42—261no—
208C2×C42C4×D1311yescharacteristic
209C2×C42D5211yescharacteristic
210C2×C42C22⋊D1311yescharacteristic
211C4⋊C8—41no—
212C4⋊C8—521no—
213C4⋊C8—521no—
214#101—522no—
215C22⋊C8—22no—
216#97—41no—
217#95—131no—
218#95—131no—
219#95—261no—
220#95—261no—
221#95—261no—
222#95—261no—
223#95—261no—
224C2×C13—21no—
225C2×C13—21no—
226C2×C13#151311yescharacteristic
227C2×C13#212011yescharacteristic
228C2×C13C2×#35511yescharacteristic
229D13—82no—
230C24—261no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×D4—521no—
236C2×D4—522no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—522no—
241C22×C4—522no—
242C22×C4—521no—
243C22×C4—521no—
244C22×C4#610311yescharacteristic
245C22×C4#610311yescharacteristic
246C22×C4#610311yescharacteristic
247C22×C4#610311yescharacteristic
248C22×C4C2×C4×D1311yescharacteristic
249C22×C4C2×D5211yescharacteristic
250C22×C4C2×C22⋊D1311yescharacteristic
251M16—522no—
252M16—522no—
253C2×C8—42no—
254C2×C8—522no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—521no—
259C22⋊C4—522no—
260C22⋊C4—522no—
261C22⋊C4—522no—
262C22⋊C4—522no—
263C22⋊C4—521no—
264C22⋊C4—521no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—522no—
272C13#1182911yescharacteristic, complemented, Sylow
273C23—262no—
274C23—521no—
275C23—521no—
276C23—521no—
277C23—521no—
278C23—521no—
279C23—521no—
280C23C2×#610311yescharacteristic
281Q8—42no—
282Q8—42no—
283D4—522no—
284D4—522no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—1042no—
310C2×C4—1042no—
311C2×C4#8804611yescharacteristic
312C2×C4#8804611yescharacteristic
313C2×C4#8816211yescharacteristic
314C2×C4#8816311yescharacteristic
315C8—82no—
316C8—1042no—
317C22—21no—
318C22—21no—
319C22—522no—
320C22—522no—
321C22—522no—
322C22—1041no—
323C22—1041no—
324C22—1041no—
325C22—1041no—
326C22C2×#8804611yescharacteristic
327C22#1171879411yescharacteristic
328C22#1171880011yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—1041no—
338C4—1041no—
339C4—1041no—
340C4#1171806912yes—
341C2—21no—
342C2—21no—
343C2—1042no—
344C2#1311338011yescharacteristic
345C2#1311647511yescharacteristic
346C2C2×#1171806911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1467C2
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1467D13
hypocenterC13#11829
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. #13114832C2semidirect
3. #13112864C2semidirect
5. C13×#1467C2semidirect
102. #1467D13semidirect
272. C13#11829semidirect

Maximal subgroups

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

subgroupindex
#131181192
#131148322
#131128642
#131128402
C13×#14672
#1182913