Finite Group Databasebeta

← #16778355

Subgroups — #16778355

Order 3328.

566 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 110 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#13130728C211yesmaximal, characteristic
2#13130728C211yesmaximal, characteristic
3#13129655C212yesmaximal, complemented
4#13129654C212yesmaximal, complemented
5D13×#389C211yesmaximal, characteristic
6C2×C4⋊C4×D13—21no—
7C2×C4⋊C4×D13C411yescharacteristic
8C2×C4⋊C4×D13C411yescharacteristic
9C2×C42×D13C2211yescharacteristic
10C2×#88111—21no—
11C2×#88111—21no—
12C13×#389C411yescharacteristic
13#11718646C2211yescharacteristic
14#11718634C2211yescharacteristic
15#11718633—21no—
16#11718589C411yescharacteristic
17D13×#95—21no—
18#11718308—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×C4×D13—21no—
24C22×C4×D13—21no—
25C22×C4×D13C2×C411yescharacteristic
26C22×C4×D13D411yescharacteristic
27C22×C4×D13D411yescharacteristic
28C22×#1057—22no—
29C22×#1057—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C42×C13C2×C411yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13C2311yescharacteristic
44C4⋊C4×D13—22no—
45C4⋊C4×D13—42no—
46C4⋊C4×D13—44no—
47C4⋊C4×D13C814yescomplemented
48C42×D13—42no—
49#88111—42no—
50#88111—42no—
51C13×#95—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#7593—131nomaximal, Sylow
56C23×D13C22⋊C411yescharacteristic
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C22×Dic13C2×D411yescharacteristic
67C2×C4×D13—22no—
68C2×C4×D13—22no—
69C2×C4×D13—24no—
70C2×C4×D13—22no—
71C2×C4×D13—22no—
72C2×C4×D13—22no—
73C2×C4×D13—22no—
74C2×C4×D13—41no—
75C2×C4×D13—41no—
76C2×C4×D13—42no—
77C2×C4×D13—42no—
78C2×C4×D13—42no—
79C2×C4×D13—42no—
80C2×C4×D13—42no—
81C2×C4×D13C2×C812yes—
82C2×C4×D13M1612yes—
83C2×#1057—42no—
84C2×#1057—42no—
85C2×#1057—42no—
86C2×#1057—42no—
87C2×#1057—42no—
88C2×#1057—42no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4C2×C812yes—
93C42×C13—41no—
94C4⋊Dic13—21no—
95C4⋊Dic13—42no—
96C4⋊Dic13—41no—
97C4⋊Dic13C2×C812yes—
98#6101—24no—
99#6101—42no—
100#6101—42no—
101#6101—42no—
102C4×Dic13—41no—
103C4×Dic13—41no—
104C4×Dic13—41no—
105C2×#389—131no—
106#1817—131no—
107#1817—131no—
108#1271—132no—
109#1271—132no—
110C23×C13C2×C22⋊C411yescharacteristic
111C22×D13—21no—
112C22×D13—21no—
113C22×D13—21no—
114C22×D13—21no—
115C22×D13C22⋊C812yes—
116C22×D13#9912yes—
117C22×D13#10112yes—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—22no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13C22×C811yescharacteristic
133C2×C4×C13C2×M1611yescharacteristic
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—22no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13C22⋊C812yes—
147C2×Dic13AGL(1,ℤ/8)12yes—
148C2×Dic13#13712yes—
149C4×D13—24no—
150C4×D13—24no—
151C4×D13—44no—
152C4×D13—44no—
153C4×D13—48no—
154C4×D13—84no—
155#1057—82no—
156#1057—82no—
157C22×C4⋊C4—131no—
158C22×C4⋊C4—131no—
159C22×C4⋊C4—261no—
160C22×C42—131no—
161C2×C22⋊C8—261no—
162C2×C22⋊C8—261no—
163#389—131no—
164#389—131no—
165#389—131no—
166#389—261no—
167#389—261no—
168#389#26111yescharacteristic
169C2×#95—261no—
170#336—132no—
171#336—132no—
172#336—261no—
173#336—261no—
174C22×C13C2×C22⋊C811yescharacteristic
175C22×C13C2×#9911yescharacteristic
176C22×C13C2×#10111yescharacteristic
177C22×C13#41811yescharacteristic
178C22×C13#41911yescharacteristic
179C22×C13#42111yescharacteristic
180C22×C13#42111yescharacteristic
181C2×D13—22no—
182C2×D13—22no—
183C2×D13—22no—
184C2×D13—22no—
185C2×D13—22no—
186C2×D13—22no—
187C2×D13#32414yes—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—42no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13—81no—
194Dic13—22no—
195Dic13—22no—
196Dic13—22no—
197Dic13—42no—
198Dic13—81no—
199C23×C4—131no—
200C23×C4—131no—
201C23×C4—131no—
202C23×C4—261no—
203C23×C4—261no—
204C22×C8—262no—
205C22×C8—262no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—134no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—262no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—522no—
217C2×C4⋊C4—524no—
218C2×C4⋊C4C2×#26111yescharacteristic
219C2×C4⋊C4C2×#26111yescharacteristic
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—131no—
223C2×C42—522no—
224C2×C42C2×#26111yescharacteristic
225C22⋊C8—522no—
226C22⋊C8—522no—
227#95—21no—
228#95—261no—
229#95—261no—
230#95—261no—
231C2×C13C2×#32411yescharacteristic
232C2×C13#147811yescharacteristic
233C2×C13#147911yescharacteristic
234C2×C13#151011yescharacteristic
235C2×C13#151111yescharacteristic
236C2×C13#153411yescharacteristic
237C2×C13#155611yescharacteristic
238D13—24no—
239C24—131no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—132no—
246C22×C4—132no—
247C22×C4—262no—
248C22×C4—262no—
249C22×C4—262no—
250C22×C4—262no—
251C22×C4—262no—
252C22×C4—262no—
253C22×C4—264no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—521no—
257C22×C4—521no—
258C22×C4—522no—
259C22×C4—522no—
260C22×C4—522no—
261C22×C4—522no—
262C22×C4—522no—
263C22×C4C22⋊#26111yescharacteristic
264C22×C4C22⋊#26111yescharacteristic
265C22×C4C22×#26111yescharacteristic
266C2×C8—522no—
267C2×C8—522no—
268C2×C8—522no—
269C2×C8—522no—
270C2×C8—522no—
271C2×C8—522no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—42no—
275C4⋊C4—132no—
276C4⋊C4—264no—
277C4⋊C4—261no—
278C4⋊C4—521no—
279C4⋊C4—522no—
280C4⋊C4—522no—
281C4⋊C4—522no—
282C4⋊C4—522no—
283C4⋊C4D13⋊C812yes—
284C42—41no—
285C42—521no—
286C42—521no—
287C42—521no—
288C13#759311yescharacteristic, complemented, Sylow
289C23—132no—
290C23—132no—
291C23—132no—
292C23—261no—
293C23—261no—
294C23—261no—
295C23—261no—
296C23C2×C22⋊#26111yescharacteristic
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—132no—
312C2×C4—132no—
313C2×C4—132no—
314C2×C4—264no—
315C2×C4—264no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—262no—
323C2×C4—524no—
324C2×C4—524no—
325C2×C4—528no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—1044no—
332C2×C4C2×D13⋊C811yescharacteristic
333C2×C4D13⋊M1611yescharacteristic
334C8—1042no—
335C8—1042no—
336C22—134no—
337C22—262no—
338C22—262no—
339C22—262no—
340C22—262no—
341C22—262no—
342C22—262no—
343C22D13⋊(C22⋊C8)11yescharacteristic
344C22#1171913811yescharacteristic
345C22D13⋊#9911yescharacteristic
346C22#1171915311yescharacteristic
347C22D13⋊#10111yescharacteristic
348C22#1171916611yescharacteristic
349C22#1171916611yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—42no—
355C4—81no—
356C4—262no—
357C4—262no—
358C4—262no—
359C4—522no—
360C4—1041no—
361C2—264no—
362C2D13⋊#32411yescharacteristic
363C2#1313013611yescharacteristic
364C2#1313013911yescharacteristic
365C2#1313024211yescharacteristic
366C2#1313024511yescharacteristic
367C2#1313031911yescharacteristic
368C2#1313036611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#389C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#7593
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #13129655C2semidirect
4. #13129654C2semidirect
47. C4⋊C4×D13C8semidirect
288. C13#7593semidirect

Maximal subgroups

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

subgroupindex
#131307282
#131296552
#131296542
D13×#3892
#759313