Finite Group Databasebeta

← #15757994

Subgroups — #15757994

Order 3328.

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

normal subgroups only

This group has 484 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#13123921C211yesmaximal, characteristic
2C4×#88076C211yesmaximal, characteristic
3#13113283C212yesmaximal
4#13112729C212yesmaximal
5C13×#2399C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#398—21no—
9C13×#398C411yescharacteristic
10C13×#398C411yescharacteristic
11C13×#395—21no—
12C13×#395C411yescharacteristic
13C13×#395C411yescharacteristic
14C4×C13×C4⋊C4—21no—
15C4×C13×C4⋊C4—21no—
16C13×#376C2211yescharacteristic
17C2×#88076—21no—
18#11718685—24no—
19#11718587—21no—
20#11718587C2212yes—
21#11718586—21no—
22C4×#6099C2212yes—
23Q8⋊#1055—24no—
24#11718122—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×Q8×C13D411yescharacteristic
27C4×Q8×C13—22no—
28C4×Q8×C13—22no—
29C4×Q8×C13—22no—
30C4×Q8×C13—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C42×C13—21no—
41C2×C42×C13—21no—
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C42×C13C2311yescharacteristic
45C2×#6099—22no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95C2×C411yescharacteristic
52C13×#95C2×C411yescharacteristic
53#88076—24no—
54C22⋊#1055—22no—
55C4⋊#1055—22no—
56C4⋊#1055—22no—
57C4⋊#1055D414yes—
58#88043—22no—
59#88043—22no—
60#88043—22no—
61C4×#1055—22no—
62C4×#1055—22no—
63#9030—131nomaximal, Sylow
64C2×Q8×C13—22no—
65C2×Q8×C13—22no—
66C2×Q8×C13—22no—
67C2×Q8×C13—41no—
68C2×Q8×C13—42no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C13×C4⋊C4—22no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—42no—
89C42×C13—24no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—41no—
95C42×C13—41no—
96C42×C13C2×D412yes—
97C42×C13#4112yes—
98#6099—24no—
99#6099—42no—
100C2×#1055—24no—
101C2×#1055—42no—
102#2983—131no—
103#2399D1311yescharacteristic
104C4×#101—131no—
105#1491—132no—
106#1300—132no—
107C23×C13C2×C22⋊C411yescharacteristic
108Q8×C13—24no—
109Q8×C13—44no—
110Q8×C13—42no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13#10412yes—
137C2×C4×C13C4×D412yes—
138C2×C4×C13#12011yescharacteristic
139C2×C4×C13#12112yes—
140C2×C4×C13#12311yescharacteristic
141#1055—44no—
142#1055—44no—
143C2×C4×Q8C2×D1311yescharacteristic
144C2×C4×Q8C2×D1311yescharacteristic
145#446—264no—
146#432—132no—
147#432—261no—
148#431—261no—
149C2×#101—261no—
150C4×M16—132no—
151#398—21no—
152#398Dic1311yescharacteristic
153#398Dic1311yescharacteristic
154#395—21no—
155#395Dic1311yescharacteristic
156#395Dic1311yescharacteristic
157C4×C4⋊C4—21no—
158C4×C4⋊C4—21no—
159#376C2×D1311yescharacteristic
160#343—261no—
161Q8⋊C8—264no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13#38611yescharacteristic
165C22×C13C2×#10411yescharacteristic
166C22×C13#42111yescharacteristic
167C4×C13—22no—
168C4×C13—22no—
169C4×C13—21no—
170C4×C13—22no—
171C4×C13—42no—
172C4×C13—42no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—42no—
177C4×C13—81no—
178C4×C13#45612yes—
179C22×Q8C2×Dic1311yescharacteristic
180C22×Q8C22⋊D1311yescharacteristic
181C2×M16—262no—
182C4×Q8—22no—
183C4×Q8—22no—
184C4×Q8—22no—
185C4×Q8—22no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C2×Dic1311yescharacteristic
192C2×C4⋊C4C2×Dic1311yescharacteristic
193C2×C4⋊C4C2×Dic1311yescharacteristic
194C2×C4⋊C4C22⋊D1311yescharacteristic
195C2×C42—21no—
196C2×C42—21no—
197C2×C42C22⋊D1311yescharacteristic
198C2×C42C22⋊D1311yescharacteristic
199C2×C42C22×D1311yescharacteristic
200C4⋊C8—134no—
201C4⋊C8—262no—
202C4⋊C8—262no—
203#101—264no—
204C22⋊C8—262no—
205#97—262no—
206#97—262no—
207#97—262no—
208C4×C8—262no—
209C4×C8—262no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95C2×Dic1311yescharacteristic
216#95C2×Dic1311yescharacteristic
217C2×C13—21no—
218C2×C13—21no—
219C2×C13#187111yescharacteristic
220C2×C13#188611yescharacteristic
221C2×C13#189111yescharacteristic
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—42no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4C22⋊Dic1311yescharacteristic
232C22×C4C22⋊Dic1311yescharacteristic
233C22×C4C22⋊Dic1311yescharacteristic
234C22×C4C22⋊Dic1311yescharacteristic
235C22×C4C22×Dic1311yescharacteristic
236C22×C4C2×C22⋊D1311yescharacteristic
237C22×C4C2×C22⋊D1311yescharacteristic
238M16—264no—
239M16—522no—
240C2×C8—264no—
241C2×C8—522no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C42—24no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—41no—
257C42—41no—
258C42D4×D1312yes—
259C42#612912yes—
260C13#903011yescharacteristic, complemented, Sylow
261C23C2×C22⋊Dic1311yescharacteristic
262Q8—24no—
263Q8—44no—
264Q8—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4#8807712yes—
291C2×C4D4×Dic1312yes—
292C2×C4#8818911yescharacteristic
293C2×C4#8819111yescharacteristic
294C2×C4#8819312yes—
295C8—524no—
296C8—524no—
297C22—21no—
298C22—21no—
299C22#1171888111yescharacteristic
300C22C2×#8807711yescharacteristic
301C22#1171889711yescharacteristic
302C4—22no—
303C4—22no—
304C4—21no—
305C4—22no—
306C4—42no—
307C4—42no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—42no—
312C4—81no—
313C4#1171875612yes—
314C2—21no—
315C2—21no—
316C2#1311513911yescharacteristic
317C2#1311523011yescharacteristic
318C2#1311525511yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2399C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2399D13
hypocenterC13#9030
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
260. C13#9030semidirect

Maximal subgroups

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

subgroupindex
#131239212
C4×#880762
#131132832
#131127292
C13×#23992
#903013