Finite Group Databasebeta

← #16786948

Subgroups — #16786948

Order 3328.

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

normal subgroups only

This group has 390 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#13131198C211yesmaximal, characteristic, complemented
2#13131194C211yesmaximal, characteristic, complemented
3#13129757C212yesmaximal, complemented
4#13129756C212yesmaximal, complemented
5C2×#11718789C211yesmaximal, characteristic
6C22×C13×M16C411yescharacteristic
7C2×C4×C22⋊D13C411yescharacteristic
8C22×#6094C411yescharacteristic
9C2×C22⋊#1055C2211yescharacteristic
10#11718789—21no—
11#11718789—21no—
12#11718789—21no—
13#11718789—21no—
14C2×#88060C2211yescharacteristic
15C2×#88054C411yescharacteristic
16C2×C8×Dic13C2211yescharacteristic
17C22⋊#6092C2212yes—
18C22⋊#6092C2212yes—
19#11718260—21no—
20#11718260—21no—
21#11718258—21no—
22#11718257—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×#6094—21no—
42C2×#6094—21no—
43C2×#6094—42no—
44C2×#6092—22no—
45C2×#6092—22no—
46C22⋊#1055—21no—
47C22⋊#1055—21no—
48#88060—21no—
49#88060—21no—
50#88054—21no—
51#88054—21no—
52C8×Dic13D411yescharacteristic
53C8×Dic13D411yescharacteristic
54C8×Dic13D411yescharacteristic
55C8×Dic13D411yescharacteristic
56#11489—131nomaximal, Sylow
57C24×C13C2×C811yescharacteristic
58C23×D13C2×C811yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13C2×C811yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—42no—
68C22×Dic13C2×C811yescharacteristic
69C22×Dic13C2×C811yescharacteristic
70C22×Dic13C2×C811yescharacteristic
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13—41no—
74C2×C4×D13—41no—
75C13×M16—42no—
76C13×M16—42no—
77C2×C8×C13—22no—
78C2×C8×C13—21no—
79C2×C8×C13—41no—
80C2×C8×C13C22⋊C411yescharacteristic
81C2×C8×C13C22⋊C411yescharacteristic
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84#6103—21no—
85#6103—21no—
86#6101—21no—
87#6101—21no—
88C4×Dic13C22⋊C411yescharacteristic
89C4×Dic13C22⋊C411yescharacteristic
90C4×Dic13M1611yescharacteristic
91C4×Dic13M1611yescharacteristic
92C2×#1055—21no—
93C2×#1055—41no—
94C2×#1055—41no—
95C2×#1055C2×D411yescharacteristic
96C2×#1055C2×D411yescharacteristic
97#6094—42no—
98#6094—42no—
99#6092—42no—
100#6092—42no—
101C2×#436—131no—
102#2163—131no—
103#2162—131no—
104#1314—132no—
105#1314—132no—
106C23×C13—21no—
107C23×C13—22no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13C22×C811yescharacteristic
111C22×D13—21no—
112C22×D13—22no—
113C22×D13—41no—
114C22×D13—41no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13C2×C22⋊C411yescharacteristic
123C2×C4×C13C2×M1611yescharacteristic
124C22⋊D13—42no—
125C22⋊D13—42no—
126C2×Dic13—22no—
127C2×Dic13—22no—
128C2×Dic13—21no—
129C2×Dic13—41no—
130C2×Dic13C22⋊C811yescharacteristic
131C2×Dic13C22⋊C811yescharacteristic
132C2×Dic13C22⋊C811yescharacteristic
133C2×Dic13C22⋊C811yescharacteristic
134C4×D13—42no—
135C4×D13—41no—
136C4×D13—41no—
137C8×C13—21no—
138C8×C13—41no—
139C8×C13#10012yes—
140#1055—21no—
141#1055—21no—
142#1055—41no—
143C22×M16—131no—
144C22×M16#26111yescharacteristic
145C2×C4×D4—131no—
146#436—261no—
147#436—261no—
148#436—261no—
149#436—261no—
150C2×C4⋊C8—131no—
151C2×C22⋊C8—131no—
152C2×C22⋊C8—131no—
153C2×C4×C8—131no—
154C4⋊C16—261no—
155C4⋊C16—261no—
156C22⋊C16—132no—
157C22⋊C16—132no—
158#346—261no—
159C4×C16—261no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—82no—
166C22×C13C2×C22⋊C811yescharacteristic
167C22×C13#50412yes—
168C2×D13—41no—
169C2×D13—41no—
170C2×D13—41no—
171C2×D13—82no—
172C4×C13—21no—
173C4×C13—41no—
174C4×C13#41011yescharacteristic
175C4×C13C2×#10011yescharacteristic
176Dic13—21no—
177Dic13—21no—
178Dic13—21no—
179Dic13—41no—
180Dic13#34912yes—
181C22×D4—131no—
182C23×C4—131no—
183C23×C4C2×#26111yescharacteristic
184C2×M16—21no—
185C2×M16—21no—
186C2×M16—42no—
187C2×M16—261no—
188C2×M16—261no—
189C2×M16—522no—
190C22×C8—131no—
191C22×C8—131no—
192C22×C8C2×#26111yescharacteristic
193C22×C8C2×#26111yescharacteristic
194C4×D4—261no—
195C4×D4—261no—
196C4×D4—261no—
197C4×D4—261no—
198C2×C4⋊C4—131no—
199C2×C22⋊C4—131no—
200C2×C22⋊C4—131no—
201C2×C42—131no—
202C2×C16—262no—
203C2×C16—262no—
204C4⋊C8—261no—
205C4⋊C8—261no—
206C22⋊C8—261no—
207C22⋊C8—261no—
208C22⋊C8—261no—
209C22⋊C8—261no—
210C4×C8—131no—
211C4×C8—131no—
212C4×C8—131no—
213C4×C8—131no—
214C2×C13—22no—
215C2×C13—81no—
216C2×C13#146011yescharacteristic
217C2×C13#211311yescharacteristic
218C2×C13C2×#34911yescharacteristic
219D13—81no—
220C24—131no—
221C24D13⋊C811yescharacteristic
222C2×D4—261no—
223C2×D4—261no—
224C2×D4—522no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—521no—
235C22×C4—521no—
236C22×C4D13⋊C811yescharacteristic
237C22×C4C22×#26111yescharacteristic
238M16—42no—
239M16—42no—
240M16—522no—
241M16—522no—
242C2×C8—22no—
243C2×C8—21no—
244C2×C8—41no—
245C2×C8—131no—
246C2×C8—131no—
247C2×C8—261no—
248C2×C8—521no—
249C2×C8—521no—
250C2×C8C22⋊#26111yescharacteristic
251C2×C8C22⋊#26111yescharacteristic
252C4⋊C4—261no—
253C4⋊C4—261no—
254C22⋊C4—261no—
255C22⋊C4—261no—
256C22⋊C4—261no—
257C22⋊C4—261no—
258C42—131no—
259C42—131no—
260C42—131no—
261C42—131no—
262C16—522no—
263C16—522no—
264C13#1148911yescharacteristic, complemented, Sylow
265C23—21no—
266C23—22no—
267C23—41no—
268C23—41no—
269C23—261no—
270C23—262no—
271C23—521no—
272C23—521no—
273C23C2×D13⋊C811yescharacteristic
274D4—522no—
275D4—522no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—131no—
287C2×C4—262no—
288C2×C4—262no—
289C2×C4—261no—
290C2×C4—522no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4D13⋊M1611yescharacteristic
295C2×C4C2×C22⋊#26111yescharacteristic
296C8—21no—
297C8—41no—
298C8—261no—
299C8—261no—
300C8—521no—
301C8#8812112yes—
302C22—21no—
303C22—21no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—82no—
308C22—521no—
309C22—521no—
310C22—521no—
311C22—1042no—
312C22#1171909612yes—
313C22D13⋊(C22⋊C8)11yescharacteristic
314C4—21no—
315C4—41no—
316C4—132no—
317C4—261no—
318C4—261no—
319C4—261no—
320C4—521no—
321C4#1171911611yescharacteristic
322C4C2×#8812111yescharacteristic
323C2—22no—
324C2—81no—
325C2—1041no—
326C2#1313007511yescharacteristic
327C2#1313106711yescharacteristic
328C2D13⋊#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#11489
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. #13131198C2semidirect
2. #13131194C2semidirect
3. #13129757C2semidirect
4. #13129756C2semidirect
264. C13#11489semidirect

Maximal subgroups

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

subgroupindex
#131311982
#131311942
#131297572
#131297562
C2×#117187892
#1148913