Finite Group Databasebeta

← #16785055

Subgroups — #16785055

Order 3328.

458 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130769C211yesmaximal, characteristic
2#13130550C211yesmaximal, characteristic
3#13129672C212yesmaximal
4#13129672C212yesmaximal
5#13117395C211yesmaximal, characteristic
6C2×#88144C411yescharacteristic
7C2×#88112—21no—
8C2×#88112—21no—
9C2×C4⋊#1057C2212yes—
10C2×C4×#1057C2212yes—
11C13×#389C411yescharacteristic
12#11718639—21no—
13#11718638C411yescharacteristic
14C4⋊C4×Dic13—21no—
15C4⋊C4×Dic13C2211yescharacteristic
16C4⋊C4×Dic13C2211yescharacteristic
17C42×Dic13C2211yescharacteristic
18#11718589C411yescharacteristic
19#11718314—21no—
20#11718310—21no—
21#11718290—21no—
22#11718290—21no—
23C22×#1057—22no—
24C22×#1057—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×#6101—21no—
34C2×C4×Dic13—21no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13C2311yescharacteristic
42#88144—22no—
43#88144C814yescomplemented
44#88112—42no—
45#88112—42no—
46C4⋊#1057—24no—
47C4×#1057—22no—
48C4×#1057Q814yes—
49C13×#95—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#9872—131nomaximal, Sylow
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C22×Dic13C2×D411yescharacteristic
67C2×#1057—24no—
68C2×#1057—42no—
69C2×#1057—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4C2×C812yes—
77C42×C13—22no—
78C4⋊Dic13—21no—
79C4⋊Dic13—24no—
80C4⋊Dic13—22no—
81C4⋊Dic13C2×C812yes—
82#6101—24no—
83#6101—42no—
84C4×Dic13—21no—
85C4×Dic13—21no—
86C4×Dic13—21no—
87C4×Dic13—21no—
88C4×Dic13—41no—
89C4×Dic13—41no—
90C4×Dic13—41no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93C4×Dic13—41no—
94C4×Dic13C2×C812yes—
95C4×Dic13M1612yes—
96C4×Dic13C2×Q812yes—
97C4×Dic13#4112yes—
98C4×#125—131no—
99#1842—131no—
100#1744—131no—
101#1279—132no—
102#1279—132no—
103C23×C13C2×C22⋊C411yescharacteristic
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13C4×Q812yes—
117C2×C4×C13C22×C811yescharacteristic
118C2×C4×C13C2×M1611yescharacteristic
119C2×C4×C13#13112yes—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—22no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13C22⋊C812yes—
133C2×Dic13C22⋊C812yes—
134C2×Dic13C22⋊Q812yes—
135C2×Dic13#12411yescharacteristic
136C2×Dic13C4⋊Q811yescharacteristic
137C2×Dic13AGL(1,ℤ/8)11yescharacteristic
138C2×Dic13AGL(1,ℤ/8)11yescharacteristic
139C2×Dic13#13711yescharacteristic
140C2×Dic13#13711yescharacteristic
141#1057—44no—
142#1057—82no—
143C2×#125—131no—
144C2×C4⋊C8—132no—
145C2×C4⋊C8—261no—
146C2×C4⋊C8—261no—
147C2×C4×C8—132no—
148#389—131no—
149#389#26111yescharacteristic
150#387—261no—
151#387—261no—
152#382—131no—
153C4×C4⋊C4—131no—
154C4×C4⋊C4—131no—
155C4×C4⋊C4—261no—
156C4×C4⋊C4—261no—
157C43—131no—
158#336—261no—
159#336—261no—
160C22×C13#39111yescharacteristic
161C22×C13C2×C22⋊C811yescharacteristic
162C22×C13#40811yescharacteristic
163C22×C13#41711yescharacteristic
164C22×C13#41711yescharacteristic
165C22×C13#42111yescharacteristic
166C22×C13#42111yescharacteristic
167C4×C13—42no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—81no—
171C4×C13C8×Q812yes—
172C4×C13#44612yes—
173Dic13—22no—
174Dic13—22no—
175Dic13—22no—
176Dic13—42no—
177Dic13—81no—
178Dic13#49011yescharacteristic
179Dic13#49111yescharacteristic
180Dic13#50111yescharacteristic
181Dic13#50111yescharacteristic
182C22×C8—262no—
183C22×C8—262no—
184#125—134no—
185#125—262no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4C2×#26111yescharacteristic
193C2×C4⋊C4C2×#26111yescharacteristic
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—131no—
200C2×C42—261no—
201C2×C42—261no—
202C2×C42C2×#26111yescharacteristic
203C4⋊C8—264no—
204C4⋊C8—522no—
205C4⋊C8—522no—
206C4×C8—134no—
207C4×C8—262no—
208#95—21no—
209#95—261no—
210#95—261no—
211#95—261no—
212#95—261no—
213#95—261no—
214C2×C13#147711yescharacteristic
215C2×C13#147711yescharacteristic
216C2×C13#149511yescharacteristic
217C2×C13#149511yescharacteristic
218C2×C13#198411yescharacteristic
219C2×C13#199211yescharacteristic
220C2×C13#199511yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4C22⋊#26111yescharacteristic
230C22×C4C22⋊#26111yescharacteristic
231C22×C4C22×#26111yescharacteristic
232C2×C8—264no—
233C2×C8—522no—
234C2×C8—522no—
235C2×C8—522no—
236C2×C8—522no—
237C2×C8—522no—
238C4⋊C4—21no—
239C4⋊C4—22no—
240C4⋊C4—42no—
241C4⋊C4—132no—
242C4⋊C4—264no—
243C4⋊C4—264no—
244C4⋊C4—261no—
245C4⋊C4—262no—
246C4⋊C4—522no—
247C4⋊C4D13⋊C812yes—
248C42—22no—
249C42—132no—
250C42—132no—
251C42—132no—
252C42—132no—
253C42—261no—
254C42—261no—
255C42—261no—
256C42—261no—
257C42—521no—
258C42—521no—
259C42—521no—
260C42—521no—
261C42—521no—
262C42—521no—
263C13#987211yescharacteristic, complemented, Sylow
264C23C2×C22⋊#26111yescharacteristic
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—131no—
278C2×C4—131no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—131no—
282C2×C4—131no—
283C2×C4—132no—
284C2×C4—132no—
285C2×C4—132no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—262no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4C2×D13⋊C811yescharacteristic
299C2×C4D13⋊M1611yescharacteristic
300C2×C4#8823812yes—
301C2×C4Q8×#26112yes—
302C8—524no—
303C8—1042no—
304C22D13⋊(C22⋊C8)11yescharacteristic
305C22#1171914011yescharacteristic
306C22#1171914611yescharacteristic
307C22#1171915511yescharacteristic
308C22(C2×#261)⋊Q811yescharacteristic
309C22#1171916411yescharacteristic
310C22#1171916411yescharacteristic
311C4—42no—
312C4—41no—
313C4—41no—
314C4—81no—
315C4—131no—
316C4—131no—
317C4—131no—
318C4—131no—
319C4—262no—
320C4—262no—
321C4—262no—
322C4—522no—
323C4—1041no—
324C4#1171907412yes—
325C4#1171907812yes—
326C2#1313013211yescharacteristic
327C2#1313013411yescharacteristic
328C2#1313019111yescharacteristic
329C2#1313019311yescharacteristic
330C2#1313100711yescharacteristic
331C2#1313101911yescharacteristic
332C2#1313102411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#9872
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
43. #88144C8semidirect
263. C13#9872semidirect

Maximal subgroups

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

subgroupindex
#131307692
#131305502
#131296722
#131173952
#987213