Finite Group Databasebeta

← #15781586

Subgroups — #15781586

Order 3328.

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

normal subgroups only

This group has 488 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#13114828C211yesmaximal, characteristic
2C4×#88074C211yesmaximal, characteristic
3#13112954C212yesmaximal
4#13112954C212yesmaximal
5C13×#2579C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic, complemented
8C13×#398—21no—
9C13×#396—21no—
10C13×#387—21no—
11C13×#386C2211yescharacteristic
12C13×#386C2211yescharacteristic
13C13×#385—21no—
14C13×#385C411yescharacteristic, complemented
15C13×#385C411yescharacteristic, complemented
16C13×#380C411yescharacteristic, complemented
17C2×#88074C2212yes—
18C2×#88073C2212yes—
19C4×C22⋊Dic13—21no—
20#11718585—21no—
21#11718122—21no—
22#11718118—21no—
23C22×D4×C13C2311yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13D411yescharacteristic
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⋊C4—41no—
36C2×C13×C4⋊C4—41no—
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C22⋊Dic13—22no—
46C2×C4×Dic13—41no—
47C2×#6099—22no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53#88074—22no—
54#88074Q814yes—
55#88073—24no—
56#88071—41no—
57C4⋊#1055—41no—
58C4⋊#1055—41no—
59#13297—131nomaximal, Sylow
60C24×C13C22×C411yescharacteristic
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—42no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13—81no—
78C22×C4×C13—81no—
79C22×C4×C13—81no—
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×Dic13—42no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—81no—
92C13×C4⋊C4—81no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—81no—
99C42×C13—21no—
100C42×C13—21no—
101C22⋊Dic13—24no—
102C22⋊Dic13—42no—
103C4×Dic13—82no—
104#6099—42no—
105#6099—42no—
106C2×#1055—42no—
107#2579D1311yescharacteristic
108#1800—131no—
109C4×#99—131no—
110#1390—132no—
111#1390—132no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13C2×C22⋊C411yescharacteristic
121C23×C13C4×Q812yes—
122C23×C13C22⋊Q812yes—
123D4×C13—42no—
124D4×C13—42no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—22no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
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—81no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13—82no—
153C2×C4×C13#9911yescharacteristic
154C2×C4×C13#9911yescharacteristic
155C2×C4×C13#12411yescharacteristic
156C2×C4×C13C4⋊Q811yescharacteristic
157C2×Dic13—44no—
158C2×Dic13—82no—
159C2×Dic13—82no—
160#1055—82no—
161C2×C4×D4C2×D1311yescharacteristic
162C22×C4⋊C4Dic1311yescharacteristic, complemented
163#423—261no—
164C2×#100—132no—
165C2×#99—132no—
166#398—21no—
167#396—21no—
168#387—21no—
169#386C2×D1311yescharacteristic
170#386C2×D1311yescharacteristic
171#385—21no—
172#385Dic1311yescharacteristic, complemented
173#385Dic1311yescharacteristic, complemented
174#380Dic1311yescharacteristic, complemented
175C4×C22⋊C4—261no—
176#343—261no—
177#342—261no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—42no—
183C22×C13—42no—
184C22×C13—42no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—81no—
190C22×C13#39111yescharacteristic
191C22×C13C2×#9911yescharacteristic
192C22×C13#41011yescharacteristic
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—41no—
198C4×C13—42no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13—81no—
202C4×C13—81no—
203C4×C13—81no—
204Dic13—84no—
205C22×D4C22×D1311yescharacteristic
206C23×C4C2×Dic1311yescharacteristic
207C23×C4C2×Dic1311yescharacteristic
208C23×C4C2×Dic1311yescharacteristic
209C23×C4C22⋊D1311yescharacteristic
210C2×M16—262no—
211C4×D4—41no—
212C4×D4—41no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4C22⋊D1311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—262no—
224C2×C22⋊C4C2×Dic1311yescharacteristic
225C2×C22⋊C4C2×Dic1311yescharacteristic
226C2×C22⋊C4C2×Dic1311yescharacteristic
227C2×C22⋊C4C22⋊D1311yescharacteristic
228C2×C42—521no—
229C2×C42C22⋊D1311yescharacteristic
230C4⋊C8—521no—
231C4⋊C8—521no—
232#100—264no—
233#99—134no—
234#99—262no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—521no—
241C2×C13—21no—
242C2×C13—21no—
243C2×C13—42no—
244C2×C13—42no—
245C2×C13#199611yescharacteristic
246C2×C13#212011yescharacteristic
247C2×C13#212111yescharacteristic
248C24C22×Dic1311yescharacteristic
249C24C2×C22⋊D1311yescharacteristic
250C2×D4—41no—
251C2×D4—41no—
252C2×D4Q8×D1312yes—
253C2×D4#613112yes—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—42no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—81no—
266C22×C4—81no—
267C22×C4—81no—
268C22×C4—522no—
269C22×C4C22⋊Dic1311yescharacteristic
270C22×C4C22⋊Dic1311yescharacteristic
271C22×C4C22⋊Dic1311yescharacteristic
272C22×C4C22⋊Dic1311yescharacteristic
273C22×C4C2×C22⋊D1311yescharacteristic
274M16—522no—
275M16—522no—
276C2×C8—522no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—81no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—81no—
290C22⋊C4—264no—
291C22⋊C4—522no—
292C42—21no—
293C42—21no—
294C42—1042no—
295C13#1329711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23Q8×Dic1312yes—
305C23#8820012yes—
306C23C2×C22⋊Dic1311yescharacteristic
307D4—42no—
308D4—42no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
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—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—82no—
337C2×C4—524no—
338C2×C4—1042no—
339C2×C4—1042no—
340C2×C4#8807411yescharacteristic
341C2×C4#8807411yescharacteristic
342C2×C4#8819811yescharacteristic
343C2×C4#8820111yescharacteristic
344C8—1042no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—22no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—81no—
357C22C2×#8807411yescharacteristic
358C22#1171889111yescharacteristic
359C22#1171890111yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—41no—
365C4—42no—
366C4—41no—
367C4—41no—
368C4—81no—
369C4—81no—
370C4—81no—
371C4—1044no—
372C2—21no—
373C2—21no—
374C2—42no—
375C2—42no—
376C2#1311582211yescharacteristic
377C2#1311647711yescharacteristic
378C2#1311648211yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2579C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#2579D13
hypocenterC13#13297
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2579

Complements

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

NH ≅ G/Ntype
7. C22×C13×C4⋊C4C4semidirect
14. C13×#385C4semidirect
15. C13×#385C4semidirect
16. C13×#380C4semidirect
162. C22×C4⋊C4Dic13semidirect
172. #385Dic13semidirect
173. #385Dic13semidirect
174. #380Dic13semidirect
295. C13#13297semidirect

Maximal subgroups

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

subgroupindex
#131148282
C4×#880742
#131129542
C13×#25792
#1329713