Finite Group Databasebeta

← #15773579

Subgroups — #15773579

Order 3328.

572 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 95 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#13114910C211yesmaximal, characteristic
2#13113163C211yesmaximal, characteristic
3#13112836C214yesmaximal, complemented
4C2×C13×#397C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic, complemented
6C22×C13×C22⋊C4—21no—
7C22×C13×C22⋊C4C2211yescharacteristic
8C13×#397—21no—
9C13×#397—21no—
10C13×#397C412yescomplemented
11C13×#397C2212yes—
12C2×C13×#95—21no—
13C2×C13×#95C411yescharacteristic, complemented
14#11718908—21no—
15#11718868—21no—
16#11718118—21no—
17#11718118C2212yes—
18#11718117—21no—
19#11718117C2212yes—
20C25×C13D411yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—41no—
27C2×C13×C4⋊C4—41no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—41no—
32C2×C13×C22⋊C4—41no—
33C2×C13×C22⋊C4—44no—
34C2×C13×C22⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C13×C22⋊C4D411yescharacteristic
37C2×C13×C22⋊C4C2311yescharacteristic
38C2×C22⋊Dic13—22no—
39C2×C22⋊Dic13—41no—
40C2×C22⋊Dic13—41no—
41C2×#6099—41no—
42C13×#95—21no—
43C13×#95—22no—
44C13×#95—22no—
45C13×#95C2×C412yes—
46C22⋊#1055—22no—
47C22⋊#1055—41no—
48#11797—131nomaximal, Sylow
49C24×C13—22no—
50C24×C13—21no—
51C24×C13—21no—
52C24×C13—41no—
53C24×C13—42no—
54C24×C13—42no—
55C24×C13C22⋊C411yescharacteristic
56C24×C13C22⋊C411yescharacteristic
57C24×C13C2×D411yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×Dic13—42no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—44no—
85C13×C22⋊C4—44no—
86C22⋊Dic13—42no—
87C22⋊Dic13—42no—
88C22⋊Dic13—82no—
89C22⋊Dic13—82no—
90#6099—82no—
91C2×#1055—42no—
92C2×#397D1311yescharacteristic
93#1819—131no—
94#1462—131no—
95#1344—134no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—48no—
112C23×C13—42no—
113C23×C13—42no—
114C23×C13—81no—
115C23×C13—81no—
116C23×C13—84no—
117C23×C13#9911yescharacteristic
118C23×C13#9911yescharacteristic
119C23×C13C2×C22⋊C411yescharacteristic
120C23×C13AGL(1,ℤ/8)12yes—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—81no—
139C2×C4×C13—84no—
140C2×C4×C13—82no—
141C2×C4×C13—82no—
142C2×Dic13—82no—
143C2×Dic13—82no—
144C2×Dic13—82no—
145#1055—82no—
146C22×C4⋊C4Dic1311yescharacteristic, complemented
147C22×C22⋊C4—21no—
148C22×C22⋊C4C2×D1311yescharacteristic
149#407—261no—
150#397—21no—
151#397—21no—
152#397Dic1312yescomplemented
153#397C2×D1312yes—
154#379—261no—
155C2×#95—21no—
156C2×#95Dic1311yescharacteristic, complemented
157#342—132no—
158#342—261no—
159#323—132no—
160#323—261no—
161C22×C13—24no—
162C22×C13—24no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—22no—
170C22×C13—42no—
171C22×C13—42no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—81no—
178C22×C13—84no—
179C22×C13—84no—
180C22×C13—81no—
181C22×C13#35212yes—
182C22×C13#35412yes—
183C22×C13C2×#9911yescharacteristic
184C22×C13#41811yescharacteristic
185C22×C13#42111yescharacteristic
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—82no—
191C4×C13—82no—
192Dic13—162no—
193C25C22⋊D1311yescharacteristic
194C23×C4—21no—
195C23×C4—21no—
196C23×C4C2×Dic1311yescharacteristic
197C23×C4C22⋊D1311yescharacteristic
198C2×M16—521no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—41no—
201C2×C4⋊C4—41no—
202C2×C4⋊C4C2×Dic1312yes—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—41no—
206C2×C22⋊C4—41no—
207C2×C22⋊C4—44no—
208C2×C22⋊C4—262no—
209C2×C22⋊C4—521no—
210C2×C22⋊C4—521no—
211C2×C22⋊C4C2×Dic1311yescharacteristic
212C2×C22⋊C4C22⋊D1311yescharacteristic
213C2×C22⋊C4C22⋊D1311yescharacteristic
214C2×C22⋊C4C22×D1311yescharacteristic
215C22⋊C8—262no—
216C22⋊C8—521no—
217#95—22no—
218#95—21no—
219#95—22no—
220#95C2×Dic1312yes—
221C2×C13—21no—
222C2×C13—22no—
223C2×C13—22no—
224C2×C13—21no—
225C2×C13—42no—
226C2×C13—81no—
227C2×C13#151011yescharacteristic
228C2×C13C2×#35211yescharacteristic
229C2×C13C2×#35411yescharacteristic
230C24—22no—
231C24—21no—
232C24—21no—
233C24—41no—
234C24—42no—
235C24—42no—
236C24C22⋊Dic1311yescharacteristic
237C24C22⋊Dic1311yescharacteristic
238C24C2×C22⋊D1311yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—522no—
255C22×C4C22⋊Dic1311yescharacteristic
256C22×C4C22⋊Dic1311yescharacteristic
257C22×C4C22×Dic1311yescharacteristic
258C22×C4C2×C22⋊D1311yescharacteristic
259M16—1042no—
260C2×C8—522no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—44no—
268C22⋊C4—44no—
269C22⋊C4—522no—
270C22⋊C4—522no—
271C22⋊C4—1042no—
272C22⋊C4—1042no—
273C13#1179711yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—22no—
277C23—22no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—42no—
284C23—42no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—48no—
290C23—42no—
291C23—42no—
292C23—81no—
293C23—81no—
294C23—84no—
295C23#8807411yescharacteristic
296C23#8807411yescharacteristic
297C23#8818612yes—
298C23C2×C22⋊Dic1311yescharacteristic
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—84no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—1042no—
321C2×C4—1042no—
322C2×C4—1042no—
323C8—1042no—
324C22—24no—
325C22—24no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—81no—
341C22—84no—
342C22—84no—
343C22—81no—
344C22#1171813112yes—
345C22#1171813312yes—
346C22#1171887611yescharacteristic
347C22C2×#8807411yescharacteristic
348C22#1171889711yescharacteristic
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—82no—
354C4—82no—
355C4—2082no—
356C2—21no—
357C2—21no—
358C2—22no—
359C2—22no—
360C2—42no—
361C2—81no—
362C2#1311336511yescharacteristic
363C2C2×#1171813111yescharacteristic
364C2C2×#1171813311yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC2×C13×#397C2
socleC22×C13C2×#99
prime radicalC25×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenterC2×#397D13
hypocenterC13#11797
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
3. #13112836C2semidirect
5. C22×C13×C4⋊C4C4semidirect
10. C13×#397C4semidirect
13. C2×C13×#95C4semidirect
146. C22×C4⋊C4Dic13semidirect
152. #397Dic13semidirect
156. C2×#95Dic13semidirect
273. C13#11797semidirect

Maximal subgroups

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

subgroupindex
#131149102
#131131632
#131128362
C2×C13×#3972
#1179713