Finite Group Databasebeta

← #15751398

Subgroups — #15751398

Order 3328.

464 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123203C211yesmaximal, characteristic
2C4×C4⋊#1055C211yesmaximal, characteristic, complemented
3#13112660C212yesmaximal, complemented
4#13112656C212yesmaximal
5C13×#1767C211yesmaximal, characteristic, complemented
6C2×#88130—21no—
7C2×C13×C4⋊C8—21no—
8C2×C13×#97—21no—
9C43×C13C2211yescharacteristic
10#11718601—21no—
11#11718601—21no—
12#11718601—21no—
13#11718600C411yescharacteristic
14#11718600C411yescharacteristic
15#11718600C2211yescharacteristic
16#11718589C411yescharacteristic
17#11718589C411yescharacteristic
18#11718589C2211yescharacteristic
19C2×C4⋊#1055—21no—
20C2×C4×#1055—21no—
21C13×#336C2212yes—
22#11718116C2212yes—
23C22×D52C2×C411yescharacteristic
24C22×C8×C13—22no—
25C2×C42×C13C2×C411yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13C2311yescharacteristic
32C2×#6103—21no—
33C2×#6103—21no—
34C2×#6103—21no—
35C2×#6103—21no—
36C2×#6103—21no—
37C2×#6103—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C22×#1055—22no—
45#88130—42no—
46#88130—42no—
47C13×C4⋊C8—24no—
48C13×#97—42no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52C4⋊#1055—24no—
53C4×#1055—42no—
54#7686—131nomaximal, Sylow
55C23×D13—21no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C2×D52—22no—
67C2×D52—41no—
68C2×D52—41no—
69C2×C8×C13—24no—
70C2×C8×C13—42no—
71C2×C8×C13—42no—
72C42×C13—22no—
73C42×C13—22no—
74C42×C13—22no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—41no—
78C42×C13—41no—
79C42×C13D812yes—
80C42×C13SD1612yes—
81#6103—42no—
82#6103—42no—
83#6103—42no—
84#6103—42no—
85#6103—41no—
86#6103—41no—
87#6103—41no—
88#6103—41no—
89C4⋊Dic13—22no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92#6101—42no—
93#6101—42no—
94#6101—41no—
95#6101—41no—
96C2×#1055—24no—
97C2×#1055—42no—
98C2×#1055—42no—
99#2860—131no—
100#1767D1311yescharacteristic, complemented
101C4×C4⋊C8—131no—
102#1271—132no—
103#1270—132no—
104C23×C13C2×C22⋊C411yescharacteristic
105C22×D13—41no—
106C22×D13—41no—
107C22×D13—41no—
108C22×D13—41no—
109C22×D13—41no—
110C22×D13—41no—
111C22×D13—41no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
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#10212yes—
127C2×C4×C13#10212yes—
128C2×C4×C13#10412yes—
129C2×C4×C13#10412yes—
130C2×C4×C13#13112yes—
131C2×C4×C13C2×D811yescharacteristic
132C2×C4×C13C2×SD1611yescharacteristic
133C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C13#13711yescharacteristic
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144D52—82no—
145C8×C13—44no—
146#1055—44no—
147C2×#126—261no—
148C2×C4⋊C8—21no—
149C2×C4⋊C8—261no—
150C2×#97—21no—
151C2×C4×C8—261no—
152#390—131no—
153#390—131no—
154#390—131no—
155#389—131no—
156#389—131no—
157#389—131no—
158#388—261no—
159#388—261no—
160#388—261no—
161C43C2×D1311yescharacteristic
162#336—132no—
163#336C2×D1312yes—
164C22×C13#40811yescharacteristic
165C22×C13#41011yescharacteristic
166C22×C13#41311yescharacteristic
167C22×C13C2×#10211yescharacteristic
168C22×C13#41711yescharacteristic
169C22×C13C2×#10411yescharacteristic
170C22×C13C2×#10411yescharacteristic
171C2×D13—81no—
172C2×D13—81no—
173C2×D13—81no—
174C2×D13—81no—
175C2×D13—81no—
176C2×D13—81no—
177C2×D13—81no—
178C4×C13—22no—
179C4×C13—22no—
180C4×C13—22no—
181C4×C13—22no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—22no—
187Dic13—81no—
188Dic13—81no—
189Dic13—81no—
190C22×D4—131no—
191C22×C8—22no—
192C22×C8—262no—
193#126—522no—
194#126—522no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C22⋊C4—261no—
202C2×C22⋊C4—261no—
203C2×C22⋊C4—261no—
204C2×C22⋊C4—261no—
205C2×C22⋊C4—261no—
206C2×C22⋊C4—261no—
207C2×C42C4×D1311yescharacteristic
208C2×C42C4×D1311yescharacteristic
209C2×C42D5211yescharacteristic
210C2×C42D5211yescharacteristic
211C2×C42C22⋊D1311yescharacteristic
212C2×C42C22⋊D1311yescharacteristic
213C2×C42C22×D1311yescharacteristic
214C4⋊C8—24no—
215C4⋊C8—264no—
216#97—42no—
217C4×C8—522no—
218#95—261no—
219#95—261no—
220#95—261no—
221C2×C13#147311yescharacteristic
222C2×C13#148311yescharacteristic
223C2×C13#149211yescharacteristic
224C2×C13#150211yescharacteristic
225C2×C13#150911yescharacteristic
226C2×C13#152411yescharacteristic
227C2×C13#154711yescharacteristic
228D13—161no—
229C24—261no—
230C2×D4—262no—
231C2×D4—521no—
232C2×D4—521no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4#610311yescharacteristic
237C22×C4#610311yescharacteristic
238C22×C4#610311yescharacteristic
239C22×C4#610311yescharacteristic
240C22×C4C2×C4×D1311yescharacteristic
241C22×C4C2×D5211yescharacteristic
242C22×C4C2×C22⋊D1311yescharacteristic
243C2×C8—24no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—264no—
247C2×C8—522no—
248C2×C8—522no—
249C4⋊C4—262no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C4⋊C4—521no—
253C4⋊C4—521no—
254C4⋊C4—522no—
255C4⋊C4—522no—
256C22⋊C4—522no—
257C22⋊C4—521no—
258C22⋊C4—521no—
259C22⋊C4—521no—
260C22⋊C4—521no—
261C22⋊C4—522no—
262C22⋊C4—522no—
263C22⋊C4—522no—
264C42—22no—
265C42—22no—
266C42—21no—
267C42—21no—
268C42—22no—
269C42—41no—
270C42—41no—
271C42#610412yes—
272C42#610612yes—
273C13#768611yescharacteristic, complemented, Sylow
274C23—521no—
275C23—521no—
276C23—521no—
277C23—521no—
278C23—521no—
279C23—521no—
280C23—521no—
281C23C2×#610311yescharacteristic
282D4—1042no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
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—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4#8804512yes—
307C2×C4#8804912yes—
308C2×C4#8804912yes—
309C2×C4#8806512yes—
310C2×C4#8816112yes—
311C2×C4#8816211yescharacteristic
312C2×C4#8816311yescharacteristic
313C2×C4C2×#610411yescharacteristic
314C2×C4C2×#610611yescharacteristic
315C8—44no—
316C8—524no—
317C22—1041no—
318C22—1041no—
319C22—1041no—
320C22—1041no—
321C22—1041no—
322C22—1041no—
323C22—1041no—
324C22C2×#8804511yescharacteristic
325C22C2×#8804911yescharacteristic
326C22#1171866711yescharacteristic
327C22#1171879011yescharacteristic
328C22#1171879311yescharacteristic
329C22#1171879411yescharacteristic
330C22C2×#8806511yescharacteristic
331C4—21no—
332C4—21no—
333C4—22no—
334C4—22no—
335C4—22no—
336C4—22no—
337C4—22no—
338C4—21no—
339C4—21no—
340C4—1041no—
341C4—1041no—
342C4—1041no—
343C2—2081no—
344C2#1311320611yescharacteristic
345C2#1311325011yescharacteristic
346C2#1311328611yescharacteristic
347C2#1311333011yescharacteristic
348C2#1311336211yescharacteristic
349C2#1311342211yescharacteristic
350C2#1311351411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1767C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1767D13
hypocenterC13#7686
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#1055C2semidirect
3. #13112660C2semidirect
5. C13×#1767C2semidirect
100. #1767D13semidirect
273. C13#7686semidirect

Maximal subgroups

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

subgroupindex
#131232032
C4×C4⋊#10552
#131126602
#131126562
C13×#17672
#768613