Finite Group Databasebeta

← #16786862

Subgroups — #16786862

Order 3328.

418 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 92 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#13131064C211yesmaximal, characteristic, complemented
2D13⋊(C22⋊C16)C211yesmaximal, characteristic, complemented
3#13129773C212yesmaximal, complemented
4#13129756C212yesmaximal, complemented
5C2×#11718788C211yesmaximal, characteristic
6C22×C13×M16C411yescharacteristic
7C2×C4×C22⋊D13C411yescharacteristic
8C22×C8×D13C2211yescharacteristic
9C2×#88098—21no—
10C2×D13⋊C16—21no—
11C2×C22⋊#1055C2211yescharacteristic
12#11718788—21no—
13#11718788—21no—
14#11718788—21no—
15#11718788—21no—
16C2×#88060C411yescharacteristic
17C2×#88055C411yescharacteristic
18C2×#88054C2211yescharacteristic
19C22⋊#6092C2212yes—
20C22⋊#6092C2212yes—
21#11718259—21no—
22#11718259—21no—
23C23×C4×C13C2×C411yescharacteristic
24C22×C22⋊D13C811yescharacteristic
25C22×C4×D13C2×C411yescharacteristic
26C2×C13×M16—21no—
27C2×C13×M16—21no—
28C2×C13×M16—42no—
29C22×C8×C13C2×C411yescharacteristic
30C22×C8×C13C2×C411yescharacteristic
31C2×C22⋊Dic13C811yescharacteristic
32C4×C22⋊D13—21no—
33C4×C22⋊D13—21no—
34C4×C22⋊D13—21no—
35C4×C22⋊D13—21no—
36C2×#6103C811yescharacteristic
37C2×#6101C811yescharacteristic
38C2×C4×Dic13C2×C411yescharacteristic
39C22×#1055C2×C411yescharacteristic
40C22×#1055C2311yescharacteristic
41C2×C8×D13—42no—
42C2×C8×D13D411yescharacteristic
43C2×C8×D13D411yescharacteristic
44C2×C8×D13D411yescharacteristic
45C2×C8×D13D411yescharacteristic
46C2×#6092—22no—
47C2×#6092—22no—
48#88098—42no—
49D13⋊C16—42no—
50C22⋊#1055—21no—
51C22⋊#1055—21no—
52#88060—21no—
53#88060—21no—
54#88055—21no—
55#88055—21no—
56#88054—21no—
57#88054—21no—
58#11467—131nomaximal, Sylow
59C24×C13C2×C811yescharacteristic
60C23×D13C2×C811yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13C2×C811yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13—42no—
70C22×Dic13C2×C811yescharacteristic
71C22×Dic13C2×C811yescharacteristic
72C22×Dic13C2×C811yescharacteristic
73C2×C4×D13—41no—
74C2×C4×D13—41no—
75C2×C4×D13C22⋊C411yescharacteristic
76C2×C4×D13C22⋊C411yescharacteristic
77C2×C4×D13M1611yescharacteristic
78C2×C4×D13M1611yescharacteristic
79C13×M16—42no—
80C13×M16—42no—
81C2×C8×C13—22no—
82C2×C8×C13—21no—
83C2×C8×C13—41no—
84C2×C8×C13C22⋊C411yescharacteristic
85C2×C8×C13C22⋊C411yescharacteristic
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88#6103—21no—
89#6103—21no—
90#6101—21no—
91#6101—21no—
92C4×Dic13—21no—
93C4×Dic13—21no—
94C2×#1055—21no—
95C2×#1055—41no—
96C2×#1055—41no—
97C2×#1055C2×D411yescharacteristic
98C2×#1055C2×D411yescharacteristic
99C8×D13—22no—
100C8×D13—22no—
101C8×D13—41no—
102C8×D13—41no—
103#6092—42no—
104#6092—42no—
105C2×#435—131no—
106#2112—131no—
107C2×C22⋊C16—131no—
108#1322—132no—
109#1314—132no—
110C23×C13—21no—
111C23×C13—22no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13C22×C811yescharacteristic
115C22×D13—22no—
116C22×D13—22no—
117C22×D13—41no—
118C22×D13C22⋊C811yescharacteristic
119C22×D13C22⋊C811yescharacteristic
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—42no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13C2×C22⋊C411yescharacteristic
128C2×C4×C13C2×M1611yescharacteristic
129C22⋊D13—42no—
130C22⋊D13—42no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—22no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13C22⋊C811yescharacteristic
137C2×Dic13C22⋊C811yescharacteristic
138C4×D13—21no—
139C4×D13—21no—
140C4×D13—21no—
141C4×D13—21no—
142C4×D13—41no—
143C4×D13—41no—
144C8×C13—21no—
145C8×C13—41no—
146C8×C13#9912yes—
147#1055—21no—
148#1055—21no—
149#1055—41no—
150C22×M16#26111yescharacteristic
151C23×C8—131no—
152C2×C4×D4—131no—
153C2×M32—261no—
154C22×C16—261no—
155#435—261no—
156#435—261no—
157#435—261no—
158#435—261no—
159C2×C4⋊C8—131no—
160C2×C22⋊C8—131no—
161C2×C22⋊C8—131no—
162C2×#97—131no—
163C22⋊C16—132no—
164C22⋊C16—132no—
165C22⋊C16—261no—
166C22⋊C16—261no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—82no—
173C22×C13C2×C22⋊C811yescharacteristic
174C22×C13#50412yes—
175C2×D13—21no—
176C2×D13—21no—
177C2×D13—21no—
178C2×D13—21no—
179C2×D13—21no—
180C2×D13—44no—
181C2×D13#34912yes—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13C2×#9911yescharacteristic
185C4×C13#41311yescharacteristic
186Dic13—21no—
187Dic13—21no—
188Dic13—41no—
189Dic13—41no—
190C22×D4—131no—
191C23×C4—131no—
192C23×C4C2×#26111yescharacteristic
193C2×M16—21no—
194C2×M16—21no—
195C2×M16—42no—
196C22×C8—131no—
197C22×C8—131no—
198C22×C8—131no—
199C22×C8—131no—
200C22×C8—131no—
201C22×C8—131no—
202C22×C8—522no—
203C22×C8C2×#26111yescharacteristic
204C22×C8C2×#26111yescharacteristic
205C4×D4—261no—
206C4×D4—261no—
207C4×D4—261no—
208C4×D4—261no—
209C2×C4⋊C4—131no—
210C2×C22⋊C4—131no—
211C2×C22⋊C4—131no—
212C2×C42—131no—
213M32—522no—
214C2×C16—262no—
215C2×C16—262no—
216C2×C16—522no—
217C4⋊C8—261no—
218C4⋊C8—261no—
219C22⋊C8—261no—
220C22⋊C8—261no—
221C22⋊C8—261no—
222C22⋊C8—261no—
223#97—261no—
224#97—261no—
225C2×C13—22no—
226C2×C13—81no—
227C2×C13#145911yescharacteristic
228C2×C13#211311yescharacteristic
229C2×C13C2×#34911yescharacteristic
230D13—22no—
231D13—41no—
232C24—131no—
233C24D13⋊C811yescharacteristic
234C2×D4—261no—
235C2×D4—261no—
236C2×D4—522no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—131no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—521no—
249C22×C4—521no—
250C22×C4D13⋊C811yescharacteristic
251C22×C4C22×#26111yescharacteristic
252M16—42no—
253M16—42no—
254C2×C8—22no—
255C2×C8—21no—
256C2×C8—41no—
257C2×C8—131no—
258C2×C8—131no—
259C2×C8—262no—
260C2×C8—262no—
261C2×C8—261no—
262C2×C8—521no—
263C2×C8—521no—
264C2×C8—521no—
265C2×C8—521no—
266C2×C8C22⋊#26111yescharacteristic
267C2×C8C22⋊#26111yescharacteristic
268C4⋊C4—261no—
269C4⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C42—261no—
275C42—261no—
276C16—522no—
277C16—522no—
278C13#1146711yescharacteristic, complemented, Sylow
279C23—21no—
280C23—22no—
281C23—41no—
282C23—41no—
283C23—131no—
284C23—131no—
285C23—262no—
286C23—262no—
287C23—521no—
288C23C2×D13⋊C811yescharacteristic
289D4—522no—
290D4—522no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—262no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4D13⋊M1611yescharacteristic
312C2×C4C2×C22⋊#26111yescharacteristic
313C8—21no—
314C8—41no—
315C8—261no—
316C8—261no—
317C8—521no—
318C8#8811912yes—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—82no—
325C22—132no—
326C22—261no—
327C22—261no—
328C22—261no—
329C22—261no—
330C22—261no—
331C22—524no—
332C22#1171909612yes—
333C22D13⋊(C22⋊C8)11yescharacteristic
334C4—21no—
335C4—41no—
336C4—261no—
337C4—261no—
338C4—521no—
339C4—521no—
340C4#1171913211yescharacteristic
341C4C2×#8811911yescharacteristic
342C2—22no—
343C2—81no—
344C2—262no—
345C2—521no—
346C2#1313007111yescharacteristic
347C2#1313106711yescharacteristic
348C2D13⋊#34911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC23×C13C22×C8
FrattiniC22×C4C22×#261
FittingC22×C13×M16C4
socleC22×C13C2×C22⋊C8
prime radicalC22×C22⋊D13C8
cosocleC22×#1055C23
hypercenterC22×M16#261
hypocenterC13#11467
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. #13131064C2semidirect
2. D13⋊(C22⋊C16)C2semidirect
3. #13129773C2semidirect
4. #13129756C2semidirect
278. C13#11467semidirect

Maximal subgroups

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

subgroupindex
#131310642
D13⋊(C22⋊C16)2
#131297732
#131297562
C2×#117187882
#1146713