Finite Group Databasebeta

← #15781599

Subgroups — #15781599

Order 3328.

492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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#13114824C211yesmaximal, characteristic
2C4×#88074C211yesmaximal, characteristic
3#13112961C212yesmaximal
4#13112961C212yesmaximal
5C13×#2566C211yesmaximal, characteristic
6C2×C13×#125C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#396—21no—
9C13×#396—21no—
10C13×#390C2211yescharacteristic
11C13×#390C2211yescharacteristic
12C13×#385—21no—
13C13×#385—21no—
14C13×#384C411yescharacteristic, complemented
15C13×#382C411yescharacteristic, complemented
16C4×C13×C4⋊C4C411yescharacteristic, complemented
17C2×#88074C2212yes—
18C2×#88074C2212yes—
19#11718873—21no—
20C4×C22⋊Dic13—21no—
21#11718118—21no—
22#11718118—21no—
23C22×D4×C13C2311yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C13×#125—41no—
27C13×#125—41no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C42×C13C2×C411yescharacteristic
45C2×C42×C13C2×C411yescharacteristic
46C2×C42×C13C2×C411yescharacteristic
47C2×C22⋊Dic13—22no—
48C2×C22⋊Dic13—22no—
49C2×C4⋊Dic13—41no—
50C2×C4×Dic13—41no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54#88074—22no—
55#88074—24no—
56#88074Q814yes—
57#88071—41no—
58#88071—41no—
59#13300—131nomaximal, Sylow
60C24×C13C2×D411yescharacteristic
61C24×C13C2×D411yescharacteristic
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13C2×Q812yes—
65C2×D4×C13#4112yes—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—81no—
75C22×C4×C13—81no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22×C411yescharacteristic
81C22×Dic13—42no—
82C22×Dic13—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—81no—
91C13×C4⋊C4—81no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—81no—
97C13×C22⋊C4—81no—
98C42×C13—21no—
99C42×C13—21no—
100C42×C13—41no—
101C42×C13—41no—
102C22⋊Dic13—24no—
103C22⋊Dic13—42no—
104C22⋊Dic13—42no—
105C22⋊Dic13—42no—
106C4⋊Dic13—82no—
107C4×Dic13—82no—
108#2566D1311yescharacteristic
109#1799—131no—
110C4×#99—131no—
111#1393—132no—
112#1393—132no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13C2×C22⋊C411yescharacteristic
122C23×C13C22⋊Q812yes—
123C23×C13#12411yescharacteristic
124C23×C13C4⋊Q811yescharacteristic
125D4×C13—42no—
126D4×C13—42no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—22no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13#9911yescharacteristic
153C2×C4×C13#9911yescharacteristic
154C2×C4×C13C4×Q812yes—
155C2×Dic13—44no—
156C2×Dic13—82no—
157C2×Dic13—82no—
158C2×Dic13—82no—
159C2×Dic13—82no—
160C2×Dic13—82no—
161C2×#125Dic1311yescharacteristic, complemented
162C2×C4×D4C2×D1311yescharacteristic
163C2×#99—132no—
164C2×#99—132no—
165#396—21no—
166#396—21no—
167#390C2×D1311yescharacteristic
168#390C2×D1311yescharacteristic
169#385—21no—
170#385—21no—
171#384Dic1311yescharacteristic, complemented
172#382Dic1311yescharacteristic, complemented
173#380—261no—
174C4×C4⋊C4Dic1311yescharacteristic, complemented
175C4×C22⋊C4—261no—
176#342—261no—
177#342—261no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—22no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—42no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—81no—
191C22×C13—81no—
192C22×C13#39111yescharacteristic
193C22×C13C2×#9911yescharacteristic
194C22×C13#41011yescharacteristic
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—22no—
198C4×C13—42no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13—41no—
202C4×C13—81no—
203C4×C13—81no—
204C4×C13—81no—
205Dic13—84no—
206Dic13—162no—
207C22×D4C22×D1311yescharacteristic
208C23×C4C22⋊D1311yescharacteristic
209C23×C4C22⋊D1311yescharacteristic
210#125—41no—
211#125—41no—
212C4×D4—41no—
213C4×D4—41no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—521no—
220C2×C4⋊C4C2×Dic1311yescharacteristic
221C2×C4⋊C4C2×Dic1311yescharacteristic
222C2×C4⋊C4C2×Dic1311yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—262no—
228C2×C22⋊C4—262no—
229C2×C22⋊C4C22⋊D1311yescharacteristic
230C2×C22⋊C4C22⋊D1311yescharacteristic
231C2×C42—521no—
232C2×C42C2×Dic1311yescharacteristic
233C2×C42C2×Dic1311yescharacteristic
234C2×C42C2×Dic1311yescharacteristic
235#99—134no—
236#99—262no—
237#99—264no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—521no—
242#95—521no—
243C2×C13—21no—
244C2×C13—21no—
245C2×C13—42no—
246C2×C13—41no—
247C2×C13—41no—
248C2×C13#199611yescharacteristic
249C2×C13#212611yescharacteristic
250C2×C13#212711yescharacteristic
251C24C2×C22⋊D1311yescharacteristic
252C24C2×C22⋊D1311yescharacteristic
253C2×D4—41no—
254C2×D4—41no—
255C2×D4Q8×D1312yes—
256C2×D4#613112yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—81no—
266C22×C4—81no—
267C22×C4—522no—
268C22×C4—522no—
269C22×C4C22⋊Dic1311yescharacteristic
270C22×C4C22⋊Dic1311yescharacteristic
271C22×C4C22⋊Dic1311yescharacteristic
272C22×C4C22⋊Dic1311yescharacteristic
273C22×C4C22×Dic1311yescharacteristic
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—81no—
282C4⋊C4—81no—
283C4⋊C4—1042no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—81no—
289C22⋊C4—81no—
290C22⋊C4—264no—
291C22⋊C4—522no—
292C22⋊C4—522no—
293C22⋊C4—522no—
294C42—21no—
295C42—21no—
296C42—41no—
297C42—41no—
298C42—1042no—
299C13#1330011yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23#8819811yescharacteristic
309C23#8820012yes—
310C23#8820111yescharacteristic
311C23C2×C22⋊Dic1311yescharacteristic
312D4—42no—
313D4—42no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—524no—
340C2×C4—1042no—
341C2×C4—1042no—
342C2×C4—1042no—
343C2×C4—1042no—
344C2×C4—1042no—
345C2×C4#8807411yescharacteristic
346C2×C4#8807411yescharacteristic
347C2×C4Q8×Dic1312yes—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—42no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22C2×#8807411yescharacteristic
363C22#1171889111yescharacteristic
364C22#1171890111yescharacteristic
365C4—21no—
366C4—21no—
367C4—22no—
368C4—42no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—81no—
373C4—81no—
374C4—81no—
375C4—1044no—
376C4—2082no—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—41no—
381C2—41no—
382C2#1311582211yescharacteristic
383C2#1311650111yescharacteristic
384C2#1311650511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2566C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#2566D13
hypocenterC13#13300
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2566

Complements

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

NH ≅ G/Ntype
6. C2×C13×#125C4semidirect
14. C13×#384C4semidirect
15. C13×#382C4semidirect
16. C4×C13×C4⋊C4C4semidirect
161. C2×#125Dic13semidirect
171. #384Dic13semidirect
172. #382Dic13semidirect
174. C4×C4⋊C4Dic13semidirect
299. C13#13300semidirect

Maximal subgroups

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

subgroupindex
#131148242
C4×#880742
#131129612
C13×#25662
#1330013