Finite Group Databasebeta

← #15760619

Subgroups — #15760619

Order 3328.

554 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 111 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#13123865C211yesmaximal, characteristic
2#13113553C212yesmaximal, complemented
3#13113177C211yesmaximal, characteristic
4#13112692C212yesmaximal, complemented
5C13×#2542C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×C22⋊Q8—21no—
8C2×C13×C22⋊Q8—21no—
9C2×C4×D4×C13C2211yescharacteristic
10C13×#399—21no—
11C13×#399—21no—
12C13×#390C412yes—
13C13×#384C412yes—
14C4×C13×C4⋊C4C2211yescharacteristic
15#11718868—21no—
16C2×C22⋊#1055—21no—
17#11718672—24no—
18#11718587C2212yes—
19#11718587C2212yes—
20#11718139—24no—
21#11718117—21no—
22#11718117—21no—
23C22×Q8×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C4⋊Q8—22no—
28C13×C4⋊Q8—22no—
29C13×C22⋊Q8—44no—
30C13×C22⋊Q8—44no—
31C4×D4×C13—22no—
32C4×D4×C13—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—22no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C412yes—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C42×C13C2×C412yes—
44C2×C42×C13C2311yescharacteristic
45C2×#6099—22no—
46C22×#1055—22no—
47C13×#95—21no—
48C22⋊#1055—22no—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52C4⋊#1055—22no—
53C4⋊#1055D414yes—
54#88043—22no—
55#88043—22no—
56#9455—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C24×C13C22⋊C411yescharacteristic
59C2×Q8×C13—42no—
60C2×Q8×C13—42no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×D4×C13—22no—
64C2×D4×C13—22no—
65C2×D4×C13—41no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—22no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C13×C4⋊C4—24no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—24no—
82C13×C4⋊C4—44no—
83C13×C4⋊C4—44no—
84C13×C4⋊C4—42no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—22no—
87C13×C22⋊C4—44no—
88C13×C22⋊C4—44no—
89C42×C13—42no—
90C42×C13C2×D412yes—
91C42×C13#4112yes—
92#6099—82no—
93C2×#1055—24no—
94C2×#1055—42no—
95C2×#1055—82no—
96#2973—131no—
97#2542D1311yescharacteristic
98#1556—132no—
99#1466—131no—
100#1285—132no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13#10112yes—
111C23×C13C2×C22⋊C411yescharacteristic
112Q8×C13—82no—
113Q8×C13—82no—
114D4×C13—44no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—22no—
118C2×C4×C13—24no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13C4×D412yes—
134C2×C4×C13#12011yescharacteristic
135C2×C4×C13#12112yes—
136C2×C4×C13#12311yescharacteristic
137#1055—44no—
138#1055—82no—
139C2×C4⋊Q8C2×D1311yescharacteristic
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—21no—
142C2×C4×D4C2×D1311yescharacteristic
143#435—264no—
144#432—132no—
145#432—132no—
146#407—261no—
147C2×C22⋊C8—261no—
148#399—21no—
149#399—21no—
150#390Dic1312yes—
151#384Dic1312yes—
152C4×C4⋊C4C2×D1311yescharacteristic
153#332—264no—
154#323—261no—
155#323—261no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—22no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—81no—
167C22×C13—81no—
168C22×C13#38611yescharacteristic
169C22×C13C2×#10111yescharacteristic
170C22×C13#41311yescharacteristic
171C4×C13—21no—
172C4×C13—22no—
173C4×C13—22no—
174C4×C13—44no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—82no—
178C4×C13#45312yes—
179C22×Q8—21no—
180C22×D4C2×Dic1311yescharacteristic
181C23×C4C22⋊D1311yescharacteristic
182C23×C4C22⋊D1311yescharacteristic
183C2×M16—262no—
184C22×C8—262no—
185C4⋊Q8—22no—
186C4⋊Q8—22no—
187C22⋊Q8—44no—
188C22⋊Q8—44no—
189C4×D4—22no—
190C4×D4—22no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4C2×Dic1312yes—
196C2×C4⋊C4C2×Dic1311yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4C22⋊D1311yescharacteristic
200C2×C22⋊C4C22⋊D1311yescharacteristic
201C2×C42C2×Dic1312yes—
202C2×C42C22×D1311yescharacteristic
203C4⋊C8—134no—
204C4⋊C8—262no—
205C22⋊C8—262no—
206C22⋊C8—262no—
207C22⋊C8—262no—
208C22⋊C8—262no—
209#97—262no—
210#97—262no—
211#95—21no—
212C2×C13—21no—
213C2×C13—21no—
214C2×C13—42no—
215C2×C13—81no—
216C2×C13#188711yescharacteristic
217C2×C13#190111yescharacteristic
218C2×C13#190911yescharacteristic
219C24C22⋊Dic1311yescharacteristic
220C24C22⋊Dic1311yescharacteristic
221C2×Q8—42no—
222C2×Q8—42no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—41no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4C22⋊Dic1311yescharacteristic
237C22×C4C22⋊Dic1311yescharacteristic
238C22×C4C22×Dic1311yescharacteristic
239C22×C4C2×C22⋊D1311yescharacteristic
240C22×C4C2×C22⋊D1311yescharacteristic
241M16—1042no—
242C2×C8—264no—
243C2×C8—522no—
244C2×C8—1042no—
245C4⋊C4—24no—
246C4⋊C4—22no—
247C4⋊C4—24no—
248C4⋊C4—44no—
249C4⋊C4—44no—
250C4⋊C4—42no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—44no—
254C22⋊C4—44no—
255C42—42no—
256C42D4×D1312yes—
257C42#612912yes—
258C13#945511yescharacteristic, complemented, Sylow
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23#8807612yes—
269C23C2×C22⋊Dic1311yescharacteristic
270Q8—82no—
271Q8—82no—
272D4—44no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—24no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4D4×Dic1312yes—
292C2×C4#8818911yescharacteristic
293C2×C4#8819111yescharacteristic
294C2×C4#8819312yes—
295C8—524no—
296C8—1042no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—42no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22—81no—
309C22#1171888111yescharacteristic
310C22C2×#8807611yescharacteristic
311C22#1171889811yescharacteristic
312C4—21no—
313C4—22no—
314C4—22no—
315C4—44no—
316C4—41no—
317C4—41no—
318C4—82no—
319C4#1171873812yes—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—81no—
324C2#1311523511yescharacteristic
325C2#1311530511yescharacteristic
326C2#1311535911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2542C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#2542D13
hypocenterC13#9455
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2542

Complements

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

NH ≅ G/Ntype
2. #13113553C2semidirect
4. #13112692C2semidirect
258. C13#9455semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131135532
#131131772
#131126922
C13×#25422
#945513