Finite Group Databasebeta

← #15779173

Subgroups — #15779173

Order 3328.

914 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 115 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#13114751C212yesmaximal
2#13112961C214yesmaximal, complemented
3C2×C13×#390C211yesmaximal, characteristic
4C23×D4×C13C2211yescharacteristic
5C22×C13×C4⋊C4C411yescharacteristic, complemented
6C22×C13×C22⋊C4—22no—
7C22×C42×C13C411yescharacteristic, complemented
8C13×#390—22no—
9C13×#390C412yescomplemented
10C13×#390C2212yes—
11#11718908—22no—
12C2×#88074—22no—
13C2×#88074C2214yes—
14C25×C13D412yes—
15C22×D4×C13—24no—
16C22×D4×C13—42no—
17C22×D4×C13—41no—
18C22×D4×C13—41no—
19C22×D4×C13C2×C411yescharacteristic
20C22×D4×C13D412yes—
21C22×D4×C13C2311yescharacteristic
22C23×C4×C13—21no—
23C23×C4×C13—21no—
24C23×C4×C13C2×C411yescharacteristic
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—41no—
27C2×C13×C4⋊C4—41no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C22⋊C4—24no—
30C2×C13×C22⋊C4—24no—
31C2×C13×C22⋊C4—48no—
32C2×C42×C13—21no—
33C2×C42×C13—42no—
34C2×C42×C13C2×C412yes—
35C2×C22⋊Dic13—24no—
36C2×C22⋊Dic13—42no—
37C2×C22⋊Dic13—42no—
38#88074—28no—
39#88074—44no—
40#12856—131nomaximal, Sylow
41C24×C13—24no—
42C24×C13—22no—
43C24×C13—22no—
44C24×C13—42no—
45C24×C13—44no—
46C24×C13—44no—
47C24×C13C22⋊C412yes—
48C24×C13C22⋊C411yescharacteristic
49C24×C13C2×D412yes—
50C2×D4×C13—24no—
51C2×D4×C13—24no—
52C2×D4×C13—22no—
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13—42no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13—48no—
59C2×D4×C13—48no—
60C2×D4×C13#4114yes—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—24no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—44no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×Dic13—44no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C13×C22⋊C4—48no—
79C13×C22⋊C4—48no—
80C42×C13—42no—
81C42×C13—42no—
82C22⋊Dic13—44no—
83C22⋊Dic13—44no—
84C22⋊Dic13—84no—
85C22⋊Dic13—84no—
86C2×#390D1311yescharacteristic
87#1781—132no—
88#1393—134no—
89C23×C13—22no—
90C23×C13—22no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—22no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—44no—
99C23×C13—44no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—416no—
105C23×C13—44no—
106C23×C13—44no—
107C23×C13—82no—
108C23×C13—82no—
109C23×C13—88no—
110C23×C13#9911yescharacteristic
111C23×C13#9911yescharacteristic
112C23×C13C2×C22⋊C411yescharacteristic
113C23×C13#12314yes—
114D4×C13—44no—
115D4×C13—48no—
116D4×C13—44no—
117C2×C4×C13—24no—
118C2×C4×C13—24no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—24no—
124C2×C4×C13—48no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—44no—
128C2×C4×C13—42no—
129C2×C4×C13—82no—
130C2×C4×C13—82no—
131C2×C4×C13#9912yes—
132C2×C4×C13#11712yes—
133C2×Dic13—84no—
134C2×Dic13—84no—
135C2×Dic13—84no—
136C23×D4C2×D1311yescharacteristic
137C22×C4⋊C4Dic1311yescharacteristic, complemented
138C22×C22⋊C4—22no—
139C22×C42Dic1311yescharacteristic, complemented
140C2×#99—134no—
141C2×#99—262no—
142#390—22no—
143#390Dic1312yescomplemented
144#390C2×D1312yes—
145#379—262no—
146C22×C13—24no—
147C22×C13—24no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—24no—
155C22×C13—44no—
156C22×C13—44no—
157C22×C13—42no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—42no—
162C22×C13—82no—
163C22×C13—88no—
164C22×C13—88no—
165C22×C13—82no—
166C22×C13#35312yes—
167C22×C13#35412yes—
168C22×C13#38111yescharacteristic
169C22×C13C2×#9911yescharacteristic
170C22×C13C2×#9911yescharacteristic
171C4×C13—22no—
172C4×C13—22no—
173C4×C13—44no—
174C4×C13—82no—
175Dic13—164no—
176C25C22⋊D1312yes—
177C22×D4—24no—
178C22×D4—42no—
179C22×D4—41no—
180C22×D4—41no—
181C22×D4C2×Dic1311yescharacteristic
182C22×D4C22⋊D1312yes—
183C22×D4C22×D1311yescharacteristic
184C23×C4—21no—
185C23×C4—21no—
186C23×C4C2×Dic1311yescharacteristic
187C2×C4⋊C4—21no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4C2×Dic1312yes—
191C2×C22⋊C4—24no—
192C2×C22⋊C4—24no—
193C2×C22⋊C4—48no—
194C2×C22⋊C4—264no—
195C2×C22⋊C4—522no—
196C2×C22⋊C4—522no—
197C2×C42—21no—
198C2×C42—42no—
199C2×C42C2×Dic1312yes—
200#99—268no—
201#99—524no—
202C2×C13—21no—
203C2×C13—21no—
204C2×C13—22no—
205C2×C13—22no—
206C2×C13—44no—
207C2×C13—82no—
208C2×C13#181911yescharacteristic
209C2×C13C2×#35311yescharacteristic
210C2×C13C2×#35411yescharacteristic
211C24—24no—
212C24—22no—
213C24—22no—
214C24—42no—
215C24—44no—
216C24—44no—
217C24C22⋊Dic1312yes—
218C24C22⋊Dic1311yescharacteristic
219C24C2×C22⋊D1312yes—
220C2×D4—24no—
221C2×D4—24no—
222C2×D4—22no—
223C2×D4—41no—
224C2×D4—41no—
225C2×D4—42no—
226C2×D4—41no—
227C2×D4—41no—
228C2×D4—48no—
229C2×D4—48no—
230C2×D4#612714yes—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—24no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—44no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—524no—
244C22×C4C22⋊Dic1311yescharacteristic
245C22×C4C22×Dic1311yescharacteristic
246C4⋊C4—42no—
247C4⋊C4—42no—
248C22⋊C4—48no—
249C22⋊C4—48no—
250C22⋊C4—524no—
251C22⋊C4—524no—
252C22⋊C4—1044no—
253C22⋊C4—1044no—
254C42—42no—
255C42—42no—
256C13#1285611yescharacteristic, complemented, Sylow
257C23—21no—
258C23—21no—
259C23—22no—
260C23—22no—
261C23—22no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—44no—
267C23—44no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—416no—
273C23—44no—
274C23—44no—
275C23—82no—
276C23—82no—
277C23—88no—
278C23#8807411yescharacteristic
279C23#8807411yescharacteristic
280C23#8818314yes—
281C23C2×C22⋊Dic1311yescharacteristic
282D4—44no—
283D4—48no—
284D4—44no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—24no—
292C2×C4—48no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—1044no—
300C2×C4—1044no—
301C2×C4—1044no—
302C2×C4#8807412yes—
303C2×C4#8818012yes—
304C22—24no—
305C22—24no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—24no—
313C22—44no—
314C22—44no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22—82no—
321C22—88no—
322C22—88no—
323C22—82no—
324C22#1171813312yes—
325C22#1171813712yes—
326C22#1171887211yescharacteristic
327C22C2×#8807411yescharacteristic
328C22C2×#8807411yescharacteristic
329C4—22no—
330C4—22no—
331C4—44no—
332C4—82no—
333C4—2084no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—22no—
338C2—44no—
339C2—82no—
340C2#1311491011yescharacteristic
341C2C2×#1171813711yescharacteristic
342C2C2×#1171813311yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC2×C13×#390C2
socleC22×C13C2×#99
prime radicalC23×D4×C13C22
cosocleC22×D4×C13C23
hypercenterC2×#390D13
hypocenterC13#12856
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. #13112961C2semidirect
5. C22×C13×C4⋊C4C4semidirect
7. C22×C42×C13C4semidirect
9. C13×#390C4semidirect
137. C22×C4⋊C4Dic13semidirect
139. C22×C42Dic13semidirect
143. #390Dic13semidirect
256. C13#12856semidirect

Maximal subgroups

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

subgroupindex
#131147512
#131129612
C2×C13×#3902
#1285613