Finite Group Databasebeta

← #16784439

Subgroups — #16784439

Order 3328.

384 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130751C211yesmaximal, characteristic
2C4×C4⋊#1057C211yesmaximal, characteristic
3C2×#11718256C211yesmaximal, characteristic
4C2×#11718255C211yesmaximal, characteristic
5#13129666C211yesmaximal, characteristic
6#13129666C211yesmaximal, characteristic
7C4⋊C8×Dic13C211yesmaximal, characteristic
8C2×C4⋊#1057C2211yescharacteristic
9C2×C4⋊#1057C2211yescharacteristic
10C2×C4⋊#1057C2211yescharacteristic
11C2×C4⋊#1057C2211yescharacteristic
12C2×C4×#1057—21no—
13C2×C13×C4⋊C8C411yescharacteristic
14C2×C8×Dic13C2211yescharacteristic
15C2×C8×Dic13C2211yescharacteristic
16C42×Dic13C2211yescharacteristic
17C2×C4⋊#1055C411yescharacteristic
18#11718290—21no—
19#11718290—21no—
20#11718290—21no—
21#11718256—22no—
22#11718255—22no—
23#11718142C411yescharacteristic
24#11718142C411yescharacteristic
25C22×#1057—21no—
26C22×#1057—21no—
27C22×#1057—21no—
28C22×#1057—21no—
29C22×C8×C13C2×C411yescharacteristic
30C22×C8×C13C2×C411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D411yescharacteristic
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13Q811yescharacteristic
36C2×C4×Dic13Q811yescharacteristic
37C2×C4×Dic13C2311yescharacteristic
38C22×#1055C2×C411yescharacteristic
39C22×#1055C2×C411yescharacteristic
40C4⋊#1057—21no—
41C4⋊#1057—21no—
42C4⋊#1057—21no—
43C4⋊#1057—21no—
44C4⋊#1057—21no—
45C4⋊#1057—21no—
46C4⋊#1057D412yes—
47C4⋊#1057Q812yes—
48C4×#1057—42no—
49C13×C4⋊C8—22no—
50C8×Dic13—21no—
51C8×Dic13—21no—
52C8×Dic13—21no—
53C8×Dic13—21no—
54C4⋊#1055C814yescomplemented
55#9603—131nomaximal, Sylow
56C22×C4×C13C4⋊C411yescharacteristic
57C22×C4×C13C4⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×Dic13C4⋊C411yescharacteristic
60C22×Dic13C4⋊C411yescharacteristic
61C22×Dic13C2×D411yescharacteristic
62C22×Dic13C2×Q811yescharacteristic
63C2×#1057—22no—
64C2×#1057—22no—
65C2×#1057—41no—
66C2×#1057—41no—
67C2×#1057—41no—
68C2×#1057—41no—
69C2×#1057—41no—
70C2×#1057—41no—
71C2×#1057—41no—
72C2×#1057—41no—
73C2×#1057—41no—
74C2×#1057—41no—
75C2×C8×C13—21no—
76C2×C8×C13—21no—
77C2×C8×C13—21no—
78C2×C8×C13—21no—
79C2×C8×C13—21no—
80C2×C8×C13—21no—
81C42×C13C2×C812yes—
82C42×C13M1612yes—
83C4×Dic13—21no—
84C4×Dic13—21no—
85C4×Dic13—22no—
86C4×Dic13—21no—
87C4×Dic13—21no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90C4×Dic13—41no—
91C4×Dic13C2×D411yescharacteristic
92C4×Dic13C2×Q811yescharacteristic
93C4×Dic13#4111yescharacteristic
94C4×Dic13#4111yescharacteristic
95C2×#1055—21no—
96C2×#1055—21no—
97C2×#1055—21no—
98C2×#1055—21no—
99C2×#1055C2×C812yes—
100C2×#1055C2×C812yes—
101#1831—131no—
102C4×C4⋊C8—131no—
103C4×C4⋊C8—131no—
104C2×#335—131no—
105C2×#334—131no—
106#1277—131no—
107#1277—131no—
108C23×C13C2×C4⋊C411yescharacteristic
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13C4⋊C812yes—
114C2×C4×C13C4⋊C812yes—
115C2×C4×C13C4×D411yescharacteristic
116C2×C4×C13C4×Q811yescharacteristic
117C2×C4×C13C22×C811yescharacteristic
118C2×C4×C13C2×M1611yescharacteristic
119C2×C4×C13#13111yescharacteristic
120C2×C4×C13#13111yescharacteristic
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13#10812yes—
129C2×Dic13#12111yescharacteristic
130C2×Dic13C22⋊Q811yescharacteristic
131C2×Dic13#12511yescharacteristic
132C2×Dic13C4⋊Q811yescharacteristic
133C2×Dic13#13511yescharacteristic
134C2×Dic13#13511yescharacteristic
135C2×Dic13AGL(1,ℤ/8)11yescharacteristic
136C2×Dic13#13711yescharacteristic
137#1057—42no—
138#1057—42no—
139#1057—81no—
140#1057—81no—
141C8×C13—41no—
142C8×C13—41no—
143#1055—22no—
144#1055—22no—
145C2×C4⋊C8—131no—
146C2×C4⋊C8—131no—
147C2×C4⋊C8—131no—
148C2×C4⋊C8—131no—
149C2×C4⋊C8—131no—
150C2×C4⋊C8#26111yescharacteristic
151C2×C4×C8—131no—
152C2×C4×C8—131no—
153C2×C4×C8—261no—
154C43—131no—
155#336—131no—
156#336—131no—
157#336—261no—
158#336—261no—
159#336—261no—
160#335—262no—
161#334—262no—
162C22×C13#38911yescharacteristic
163C22×C13C2×C4⋊C811yescharacteristic
164C22×C13#42411yescharacteristic
165C22×C13#42711yescharacteristic
166C22×C13#42811yescharacteristic
167C22×C13C2×#10811yescharacteristic
168C22×C13#43011yescharacteristic
169C4×C13—22no—
170C4×C13—22no—
171C4×C13C8×D411yescharacteristic
172C4×C13#43611yescharacteristic
173C4×C13C8×Q811yescharacteristic
174C4×C13#44611yescharacteristic
175Dic13—22no—
176Dic13—21no—
177Dic13—21no—
178Dic13—41no—
179Dic13#46311yescharacteristic
180Dic13#46411yescharacteristic
181Dic13#47811yescharacteristic
182Dic13#47911yescharacteristic
183C22×C8—131no—
184C22×C8—131no—
185C22×C8—261no—
186C22×C8—261no—
187C22×C8—261no—
188C22×C8—261no—
189C22×C8C2×#26111yescharacteristic
190C22×C8C2×#26111yescharacteristic
191C2×C42—131no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—131no—
197C2×C42C2×#26111yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—132no—
200C4⋊C8—132no—
201C4⋊C8—134no—
202C4⋊C8—261no—
203C4⋊C8—261no—
204C4⋊C8—261no—
205C4⋊C8—261no—
206C4⋊C8—261no—
207C4⋊C8—261no—
208C4×C8—261no—
209C4×C8—261no—
210C4×C8—261no—
211C4×C8—261no—
212C4×C8—522no—
213C2×C13#156411yescharacteristic
214C2×C13#156511yescharacteristic
215C2×C13#157211yescharacteristic
216C2×C13#157311yescharacteristic
217C2×C13#193911yescharacteristic
218C2×C13#194911yescharacteristic
219C2×C13#195011yescharacteristic
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—131no—
223C22×C4—131no—
224C22×C4C4⋊#26111yescharacteristic
225C22×C4C4⋊#26111yescharacteristic
226C22×C4C22×#26111yescharacteristic
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—132no—
234C2×C8—132no—
235C2×C8—261no—
236C2×C8—261no—
237C2×C8—261no—
238C2×C8—261no—
239C2×C8—262no—
240C2×C8—262no—
241C2×C8—521no—
242C2×C8—521no—
243C2×C8—521no—
244C2×C8—521no—
245C2×C8—521no—
246C2×C8—521no—
247C2×C8—521no—
248C2×C8—521no—
249C2×C8—521no—
250C2×C8—521no—
251C42—131no—
252C42—131no—
253C42—131no—
254C42—131no—
255C42—261no—
256C42—261no—
257C42—261no—
258C42—262no—
259C42—261no—
260C42—261no—
261C42—261no—
262C42—521no—
263C42D13⋊C812yes—
264C42#612212yes—
265C13#960311yescharacteristic, complemented, Sylow
266C23C2×C4⋊#26111yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—131no—
272C2×C4—131no—
273C2×C4—131no—
274C2×C4—131no—
275C2×C4—131no—
276C2×C4—131no—
277C2×C4—131no—
278C2×C4—131no—
279C2×C4—132no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4#8811212yes—
288C2×C4#8811212yes—
289C2×C4C2×D13⋊C811yescharacteristic
290C2×C4#8823811yescharacteristic
291C2×C4D4×#26111yescharacteristic
292C2×C4#8824011yescharacteristic
293C2×C4Q8×#26111yescharacteristic
294C2×C4C2×#612211yescharacteristic
295C8—41no—
296C8—41no—
297C8—262no—
298C8—262no—
299C8—522no—
300C8—522no—
301C8—1041no—
302C8—1041no—
303C22#1171907911yescharacteristic
304C22#1171908311yescharacteristic
305C22#1171909211yescharacteristic
306C22D13⋊#10811yescharacteristic
307C22#1171909811yescharacteristic
308C22#1171910011yescharacteristic
309C22C2×#8811211yescharacteristic
310C4—22no—
311C4—22no—
312C4—131no—
313C4—131no—
314C4—131no—
315C4—131no—
316C4—262no—
317C4—261no—
318C4—261no—
319C4—521no—
320C4#1171907311yescharacteristic
321C4#1171907411yescharacteristic
322C4#1171914511yescharacteristic
323C4#1171915811yescharacteristic
324C2#1313038511yescharacteristic
325C2#1313038911yescharacteristic
326C2#1313040811yescharacteristic
327C2#1313041011yescharacteristic
328C2#1313093411yescharacteristic
329C2#1313094911yescharacteristic
330C2#1313095211yescharacteristic
subgroupG/H
centerC23C2×C4⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊C8C4
socle, prime radicalC23×C13C2×C4⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4⋊C8#261
hypocenterC13#9603
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
54. C4⋊#1055C8semidirect
265. C13#9603semidirect

Maximal subgroups

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

subgroupindex
#131307512
C4×C4⋊#10572
C2×#117182562
C2×#117182552
#131296662
C4⋊C8×Dic132
#960313