Finite Group Databasebeta

← #16786775

Subgroups — #16786775

Order 3328.

392 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 94 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
2D13⋊(C22⋊C16)C211yesmaximal, characteristic
3#13129773C212yesmaximal, complemented
4#13129772C212yesmaximal, complemented
5C2×#11718500C211yesmaximal, characteristic
6C22×#6094C411yescharacteristic
7C22×C8×D13C2211yescharacteristic
8C2×#88126C411yescharacteristic
9C2×#88098—21no—
10C2×D13⋊C16—21no—
11C2×C13×C4⋊C8C411yescharacteristic
12C2×#88054C411yescharacteristic
13C2×#88054C2211yescharacteristic
14C2×C4⋊#1055C2211yescharacteristic
15#11718500—21no—
16#11718500—21no—
17#11718500—21no—
18#11718500—21no—
19C22⋊#6092C2212yes—
20C22⋊#6092C2212yes—
21#11718259—21no—
22#11718259—21no—
23C22×C4×D13C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25C22×C8×C13C2×C411yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×#6103C811yescharacteristic
28C2×#6103C811yescharacteristic
29C2×#6101C811yescharacteristic
30C2×#6101C811yescharacteristic
31C2×C4×Dic13C2×C411yescharacteristic
32C22×#1055C2×C411yescharacteristic
33C22×#1055C2311yescharacteristic
34C2×#6094—21no—
35C2×#6094—21no—
36C2×#6094—42no—
37C2×C8×D13—42no—
38C2×C8×D13D411yescharacteristic
39C2×C8×D13D411yescharacteristic
40C2×C8×D13D411yescharacteristic
41C2×C8×D13D411yescharacteristic
42#88126—21no—
43#88126—21no—
44#88126—21no—
45#88126—21no—
46C2×#6092—22no—
47C2×#6092—22no—
48#88098—42no—
49D13⋊C16—42no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52#88054—21no—
53#88054—21no—
54#88054—21no—
55#88054—21no—
56C4⋊#1055—21no—
57C4⋊#1055—21no—
58#11441—131nomaximal, Sylow
59C23×D13C2×C811yescharacteristic
60C22×C4×C13C2×C811yescharacteristic
61C22×C4×C13C2×C811yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×Dic13C2×C811yescharacteristic
64C22×Dic13C2×C811yescharacteristic
65C22×Dic13C2×C811yescharacteristic
66C2×C4×D13—22no—
67C2×C4×D13—22no—
68C2×C4×D13C22⋊C411yescharacteristic
69C2×C4×D13C22⋊C411yescharacteristic
70C2×C4×D13M1611yescharacteristic
71C2×C4×D13M1611yescharacteristic
72C2×C8×C13—21no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C2×C8×C13C22⋊C411yescharacteristic
76C2×C8×C13C22⋊C411yescharacteristic
77C42×C13—21no—
78C42×C13—21no—
79#6103—21no—
80#6103—21no—
81#6103—21no—
82#6103—21no—
83#6101—21no—
84#6101—21no—
85#6101—21no—
86#6101—21no—
87C4×Dic13—21no—
88C4×Dic13—21no—
89C2×#1055—21no—
90C2×#1055—41no—
91C2×#1055—41no—
92C2×#1055C2×D411yescharacteristic
93C2×#1055C2×D411yescharacteristic
94#6094—42no—
95#6094—42no—
96C8×D13—22no—
97C8×D13—22no—
98C8×D13—41no—
99C8×D13—41no—
100#6092—42no—
101#6092—42no—
102C2×#424—131no—
103#2112—131no—
104C2×C22⋊C16—131no—
105#1322—132no—
106#1322—132no—
107C23×C13C22×C811yescharacteristic
108C22×D13—22no—
109C22×D13—22no—
110C22×D13—41no—
111C22×D13C22⋊C811yescharacteristic
112C22×D13C22⋊C811yescharacteristic
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—22no—
118C2×C4×C13—41no—
119C2×C4×C13C2×C22⋊C411yescharacteristic
120C2×C4×C13C2×M1611yescharacteristic
121C2×Dic13—22no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—22no—
125C2×Dic13—41no—
126C2×Dic13C22⋊C811yescharacteristic
127C2×Dic13C22⋊C811yescharacteristic
128C4×D13—22no—
129C4×D13—21no—
130C4×D13—21no—
131C4×D13—22no—
132C4×D13#9912yes—
133C4×D13#10112yes—
134C8×C13—21no—
135C8×C13—21no—
136C8×C13—41no—
137#1055—21no—
138#1055—21no—
139#1055—41no—
140C22×M16—131no—
141C23×C8—131no—
142C2×#117—131no—
143C2×M32—261no—
144C22×C16—261no—
145#424—261no—
146#424—261no—
147#424—261no—
148#424—261no—
149C2×C4⋊C8—131no—
150C2×C4⋊C8—131no—
151C2×C4⋊C8—131no—
152C2×C4⋊C8#26111yescharacteristic
153C22⋊C16—132no—
154C22⋊C16—132no—
155C22⋊C16—261no—
156C22⋊C16—261no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13C2×C22⋊C811yescharacteristic
160C22×C13#50412yes—
161C2×D13—21no—
162C2×D13—21no—
163C2×D13—21no—
164C2×D13—21no—
165C2×D13—21no—
166C2×D13—44no—
167C2×D13#32412yes—
168C4×C13—21no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13C2×#9911yescharacteristic
172C4×C13C2×#10111yescharacteristic
173Dic13—21no—
174Dic13—41no—
175Dic13—41no—
176Dic13#32412yes—
177C23×C4—131no—
178C2×M16—261no—
179C2×M16—261no—
180C2×M16—522no—
181C22×C8—131no—
182C22×C8—131no—
183C22×C8—131no—
184C22×C8—131no—
185C22×C8—131no—
186C22×C8—131no—
187C22×C8—522no—
188C22×C8C2×#26111yescharacteristic
189C22×C8C2×#26111yescharacteristic
190#117—261no—
191#117—261no—
192#117—261no—
193#117—261no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—131no—
196C2×C22⋊C4—131no—
197C2×C22⋊C4—131no—
198C2×C42—131no—
199C2×C42C2×#26111yescharacteristic
200M32—522no—
201C2×C16—262no—
202C2×C16—262no—
203C2×C16—522no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—261no—
207C4⋊C8—261no—
208C4⋊C8—261no—
209C4⋊C8—261no—
210C4⋊C8—261no—
211C4⋊C8—261no—
212C2×C13—22no—
213C2×C13C2×#32411yescharacteristic
214C2×C13#211311yescharacteristic
215C2×C13#211511yescharacteristic
216D13—22no—
217D13—41no—
218C24—131no—
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—131no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—262no—
227C22×C4—262no—
228C22×C4D13⋊C811yescharacteristic
229C22×C4D13⋊C811yescharacteristic
230C22×C4C22×#26111yescharacteristic
231M16—522no—
232M16—522no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—131no—
237C2×C8—131no—
238C2×C8—262no—
239C2×C8—262no—
240C2×C8—261no—
241C2×C8—521no—
242C2×C8—521no—
243C2×C8—521no—
244C2×C8—521no—
245C2×C8C22⋊#26111yescharacteristic
246C2×C8C22⋊#26111yescharacteristic
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C22⋊C4—261no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C22⋊C4—261no—
255C42—21no—
256C42—21no—
257C42—261no—
258C42—261no—
259C16—522no—
260C16—522no—
261C13#1144111yescharacteristic, complemented, Sylow
262C23—131no—
263C23—131no—
264C23—262no—
265C23—262no—
266C23—521no—
267C23C2×D13⋊C811yescharacteristic
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—131no—
275C2×C4—132no—
276C2×C4—132no—
277C2×C4—131no—
278C2×C4—262no—
279C2×C4—262no—
280C2×C4—262no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—262no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—521no—
287C2×C4D13⋊M1611yescharacteristic
288C2×C4C2×C22⋊#26111yescharacteristic
289C8—21no—
290C8—21no—
291C8—41no—
292C8—261no—
293C8—261no—
294C8—521no—
295C22—21no—
296C22—21no—
297C22—132no—
298C22—261no—
299C22—261no—
300C22—261no—
301C22—261no—
302C22—261no—
303C22—524no—
304C22#1171909612yes—
305C22D13⋊(C22⋊C8)11yescharacteristic
306C4—21no—
307C4—41no—
308C4—41no—
309C4—132no—
310C4—261no—
311C4—521no—
312C4—521no—
313C4D13⋊#9911yescharacteristic
314C4D13⋊#10111yescharacteristic
315C2—22no—
316C2—262no—
317C2—521no—
318C2D13⋊#32411yescharacteristic
319C2#1313106711yescharacteristic
320C2#1313107311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC23×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊C8C4
socleC22×C13C2×C22⋊C8
prime radicalC23×D13C2×C8
cosocleC22×#1055C23
hypercenterC2×C4⋊C8#261
hypocenterC13#11441
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #13129773C2semidirect
4. #13129772C2semidirect
261. C13#11441semidirect

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
#131297722
C2×#117185002
#1144113