Finite Group Databasebeta

← #15750914

Subgroups — #15750914

Order 3328.

520 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117300C211yesmaximal, characteristic
2C4×C4⋊#1055C211yesmaximal, characteristic, complemented
3#13112660C212yesmaximal, complemented
4#13112656C212yesmaximal
5C13×#1831C211yesmaximal, characteristic, complemented
6C2×C4×D52C411yescharacteristic
7C2×#88126—21no—
8C2×C13×C4⋊C8—21no—
9C43×C13C2211yescharacteristic
10#11718601—21no—
11#11718601—21no—
12#11718600C411yescharacteristic
13#11718600C2211yescharacteristic
14C4×#6103—21no—
15C4×C4⋊Dic13C411yescharacteristic
16#11718589C411yescharacteristic
17#11718589C2211yescharacteristic
18C2×C4⋊#1055—21no—
19C2×C4×#1055—21no—
20C13×#336—21no—
21C13×#336C2212yes—
22#11718116C2212yes—
23C22×D52C2×C411yescharacteristic
24C22×C4×D13—21no—
25C22×C8×C13—22no—
26C2×C42×C13C2×C411yescharacteristic
27C2×C42×C13C2×C411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13C2311yescharacteristic
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×C4×Dic13—21no—
44C22×#1055—22no—
45C4×D52—22no—
46C4×D52C814yescomplemented
47#88126—42no—
48#88126—42no—
49C13×C4⋊C8—42no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53C4⋊#1055—24no—
54C4×#1055—42no—
55#7574—131nomaximal, Sylow
56C23×D13—21no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C2×D52—21no—
68C2×D52—41no—
69C2×D52—41no—
70C2×D52C2×C812yes—
71C2×C4×D13—24no—
72C2×C4×D13—42no—
73C2×C4×D13—42no—
74C2×C8×C13—42no—
75C2×C8×C13—42no—
76C2×C8×C13—42no—
77C42×C13—22no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—41no—
81C42×C13—41no—
82C42×C13—41no—
83C42×C13C2×C812yes—
84C42×C13M1612yes—
85C42×C13D812yes—
86C42×C13SD1612yes—
87#6103—24no—
88#6103—42no—
89#6103—42no—
90#6103—41no—
91#6103—41no—
92#6103—41no—
93#6103—41no—
94C4⋊Dic13—21no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97C4⋊Dic13C2×C812yes—
98#6101—42no—
99#6101—41no—
100#6101—41no—
101C4×Dic13—42no—
102C2×#1055—24no—
103C2×#1055—42no—
104C2×#1055—42no—
105#2293—131no—
106#1831D1311yescharacteristic, complemented
107C4×C4⋊C8—131no—
108#1271—132no—
109#1270—132no—
110C23×C13C2×C22⋊C411yescharacteristic
111C22×D13—22no—
112C22×D13—41no—
113C22×D13—41no—
114C22×D13—41no—
115C22×D13—41no—
116C22×D13—41no—
117C22×D13—41no—
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—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13C22⋊C812yes—
132C2×C4×C13C22⋊C812yes—
133C2×C4×C13#10212yes—
134C2×C4×C13#10212yes—
135C2×C4×C13#10412yes—
136C2×C4×C13C22×C811yescharacteristic
137C2×C4×C13C2×M1611yescharacteristic
138C2×C4×C13C2×D811yescharacteristic
139C2×C4×C13C2×SD1611yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13#13711yescharacteristic
142C2×Dic13—22no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151D52—42no—
152D52—42no—
153C4×D13—48no—
154C8×C13—82no—
155#1055—44no—
156C2×C4×D4—131no—
157C2×#117—261no—
158C2×C4⋊C8—21no—
159C2×C4⋊C8—261no—
160C2×C4×C8—261no—
161#390—131no—
162#390—131no—
163#389—131no—
164#389—131no—
165#388—261no—
166#388—261no—
167C4×C4⋊C4—131no—
168C4×C22⋊C4—261no—
169C43C2×D1311yescharacteristic
170#336—21no—
171#336—132no—
172#336C2×D1312yes—
173C22×C13C2×C22⋊C811yescharacteristic
174C22×C13#41011yescharacteristic
175C22×C13#41311yescharacteristic
176C22×C13C2×#10211yescharacteristic
177C22×C13#41711yescharacteristic
178C22×C13C2×#10411yescharacteristic
179C22×C13#42111yescharacteristic
180C2×D13—42no—
181C2×D13—42no—
182C2×D13—42no—
183C2×D13—81no—
184C2×D13—81no—
185C2×D13—81no—
186C2×D13—81no—
187C4×C13—22no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—22no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—41no—
196C4×C13D4⋊C814yes—
197Dic13—42no—
198Dic13—81no—
199Dic13—81no—
200C22×D4—131no—
201C23×C4—261no—
202C22×C8—22no—
203C22×C8—262no—
204C4×D4—134no—
205C4×D4—262no—
206#117—522no—
207#117—522no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C22⋊C4—261no—
214C2×C22⋊C4—261no—
215C2×C22⋊C4—261no—
216C2×C22⋊C4—261no—
217C2×C22⋊C4—261no—
218C2×C42—261no—
219C2×C42C4×D1311yescharacteristic
220C2×C42C4×D1311yescharacteristic
221C2×C42D5211yescharacteristic
222C2×C42D5211yescharacteristic
223C2×C42C22⋊D1311yescharacteristic
224C2×C42C22⋊D1311yescharacteristic
225C2×C42C22×D1311yescharacteristic
226C4⋊C8—42no—
227C4⋊C8—264no—
228C4×C8—522no—
229#95—261no—
230#95—261no—
231#95—261no—
232C2×C13#145811yescharacteristic
233C2×C13C2×D4⋊C811yescharacteristic
234C2×C13#147711yescharacteristic
235C2×C13#150911yescharacteristic
236C2×C13#151711yescharacteristic
237C2×C13#152911yescharacteristic
238C2×C13#154711yescharacteristic
239D13—82no—
240C24—261no—
241C2×D4—132no—
242C2×D4—261no—
243C2×D4—521no—
244C2×D4—521no—
245C22×C4—261no—
246C22×C4—264no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4—522no—
250C22×C4—522no—
251C22×C4#610311yescharacteristic
252C22×C4#610311yescharacteristic
253C22×C4#610311yescharacteristic
254C22×C4#610311yescharacteristic
255C22×C4C2×C4×D1311yescharacteristic
256C22×C4C2×D5211yescharacteristic
257C22×C4C2×C22⋊D1311yescharacteristic
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—264no—
262C2×C8—522no—
263C2×C8—522no—
264C4⋊C4—132no—
265C4⋊C4—261no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C4⋊C4—521no—
269C4⋊C4—521no—
270C4⋊C4—522no—
271C22⋊C4—264no—
272C22⋊C4—522no—
273C22⋊C4—521no—
274C22⋊C4—521no—
275C22⋊C4—521no—
276C22⋊C4—521no—
277C22⋊C4—522no—
278C42—22no—
279C42—21no—
280C42—21no—
281C42—41no—
282C42—41no—
283C42—41no—
284C42—522no—
285C42C8×D1312yes—
286C42#609412yes—
287C42#610412yes—
288C42#610612yes—
289C13#757411yescharacteristic, complemented, Sylow
290C23—262no—
291C23—521no—
292C23—521no—
293C23—521no—
294C23—521no—
295C23—521no—
296C23—521no—
297C23C2×#610311yescharacteristic
298D4—522no—
299D4—522no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—262no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—528no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4#8804912yes—
324C2×C4#8804912yes—
325C2×C4#8806012yes—
326C2×C4#8806012yes—
327C2×C4#8806512yes—
328C2×C4C2×C8×D1311yescharacteristic
329C2×C4C2×#609411yescharacteristic
330C2×C4#8816211yescharacteristic
331C2×C4#8816311yescharacteristic
332C2×C4C2×#610411yescharacteristic
333C2×C4C2×#610611yescharacteristic
334C8—82no—
335C8—524no—
336C22—522no—
337C22—522no—
338C22—522no—
339C22—1041no—
340C22—1041no—
341C22—1041no—
342C22—1041no—
343C22C2×#8804911yescharacteristic
344C22#1171866611yescharacteristic
345C22#1171866711yescharacteristic
346C22C2×#8806011yescharacteristic
347C22#1171879311yescharacteristic
348C22#1171879411yescharacteristic
349C22C2×#8806511yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—22no—
357C4—22no—
358C4—41no—
359C4—522no—
360C4—1041no—
361C4—1041no—
362C4#1171807514yes—
363C2—1042no—
364C2#1311314811yescharacteristic
365C2C2×#1171807511yescharacteristic
366C2#1311322411yescharacteristic
367C2#1311336211yescharacteristic
368C2#1311339511yescharacteristic
369C2#1311344411yescharacteristic
370C2#1311351411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1831C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1831D13
hypocenterC13#7574
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#1055C2semidirect
3. #13112660C2semidirect
5. C13×#1831C2semidirect
46. C4×D52C8semidirect
106. #1831D13semidirect
289. C13#7574semidirect

Maximal subgroups

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

subgroupindex
#131173002
C4×C4⋊#10552
#131126602
#131126562
C13×#18312
#757413