Finite Group Databasebeta

← #15781600

Subgroups — #15781600

Order 3328.

404 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 93 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#13120053C211yesmaximal, characteristic
2#13114830C211yesmaximal, characteristic
3#101×Dic13C211yesmaximal, characteristic
4#13112963C211yesmaximal, characteristic
5#13112962C211yesmaximal, characteristic
6#13112962C211yesmaximal, characteristic
7C13×#1394C211yesmaximal, characteristic
8C2×Q8×Dic13C2211yescharacteristic
9C2×#88142C411yescharacteristic
10C2×C13×#101C2211yescharacteristic
11C2×C13×#101C2211yescharacteristic
12C13×#391C2211yescharacteristic
13#11718891C2211yescharacteristic
14C2×#88076C2211yescharacteristic
15C2×#88076C2211yescharacteristic
16#11718779—21no—
17M16×Dic13—21no—
18#11718638C411yescharacteristic
19#11718597C411yescharacteristic
20C4×#6101C411yescharacteristic
21#11718321—21no—
22#11718321—21no—
23#11718307—21no—
24#11718307—21no—
25#11718146—21no—
26#11718146—21no—
27C22×Q8×C13C2311yescharacteristic
28C22×Dic26—21no—
29C2×C13×M16—21no—
30C2×C13×M16—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33Q8×Dic13—41no—
34Q8×Dic13—41no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D411yescharacteristic
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×#6099—21no—
46C2×#6099—21no—
47#88142—41no—
48#88142—41no—
49C13×#101—21no—
50C13×#101—21no—
51C13×#101—21no—
52C13×#101Q812yescomplemented
53C13×#95—21no—
54C13×#95—21no—
55#88076—21no—
56#88076—21no—
57#88076—21no—
58#88076Q812yescomplemented
59#88071—21no—
60#88071—21no—
61#88071—21no—
62#88071—21no—
63#88071—21no—
64#88071—21no—
65#88071—21no—
66#88055—41no—
67#88054—41no—
68#88054—41no—
69C8×Dic13—41no—
70#13301—131nomaximal, Sylow
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13C2×Q811yescharacteristic
74C2×Q8×C13C2×Q811yescharacteristic
75C2×Q8×C13#4111yescharacteristic
76C2×Q8×C13#4111yescharacteristic
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13C22⋊C411yescharacteristic
85C22×Dic13C22⋊C411yescharacteristic
86C22×Dic13C22⋊C411yescharacteristic
87C22×Dic13C22⋊C411yescharacteristic
88C2×Dic26—44no—
89C2×Dic26—41no—
90C2×Dic26—41no—
91C13×M16—22no—
92C13×M16—41no—
93C13×M16—41no—
94C13×M16—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C13×C4⋊C4—41no—
98C42×C13—41no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102C4⋊Dic13—41no—
103#6101—42no—
104#6101—42no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108C4×Dic13—21no—
109C4×Dic13—21no—
110C4×Dic13—21no—
111C4×Dic13—41no—
112#6099—22no—
113#6099—41no—
114#6099—41no—
115#6099—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118#2568—131no—
119#1801—131no—
120C4×#101—131no—
121#1394—131no—
122#1394—131no—
123#1394—131no—
124#1394D1311yescharacteristic
125C23×C13C2×C22⋊C411yescharacteristic
126Q8×C13—41no—
127Q8×C13—41no—
128Q8×C13—41no—
129Q8×C13—41no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13C4×Q811yescharacteristic
142C2×C4×C13C4×Q811yescharacteristic
143C2×C4×C13C22⋊Q811yescharacteristic
144C2×C4×C13C22⋊Q811yescharacteristic
145C2×C4×C13#12411yescharacteristic
146C2×C4×C13C4⋊Q811yescharacteristic
147C2×Dic13—22no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—42no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13#9911yescharacteristic
160C2×Dic13#9911yescharacteristic
161Dic26—82no—
162Dic26—82no—
163C8×C13—42no—
164C8×C13—81no—
165#1055—42no—
166#1055—81no—
167C2×C4⋊Q8—131no—
168C2×C4×Q8—131no—
169#423—261no—
170C2×#101—131no—
171C2×#101—131no—
172C2×#101C2×D1311yescharacteristic
173C2×#101C2×D1311yescharacteristic
174C4×M16—261no—
175#400—261no—
176#400—261no—
177#391—131no—
178#391—261no—
179#391—261no—
180#391C2×D1311yescharacteristic
181#382—131no—
182#382—131no—
183C4×C4⋊C4—131no—
184#343—261no—
185#343—261no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13#39111yescharacteristic
189C22×C13C2×#9911yescharacteristic
190C22×C13#41011yescharacteristic
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—81no—
198C4×C13—81no—
199Dic13—21no—
200Dic13—41no—
201Dic13—41no—
202Dic13—41no—
203Dic13—81no—
204Dic13—81no—
205Dic13#35512yes—
206C22×Q8—261no—
207C22×Q8C22×D1311yescharacteristic
208C2×M16—21no—
209C2×M16—21no—
210C2×M16—261no—
211C2×M16—261no—
212C4⋊Q8—521no—
213C4⋊Q8—521no—
214C4×Q8—521no—
215C4×Q8—521no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—131no—
219C2×C4⋊C4—131no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4C4×D1311yescharacteristic
223C2×C42—131no—
224C2×C42—131no—
225C2×C42—131no—
226C2×C42—131no—
227C2×C42C4×D1311yescharacteristic
228C4⋊C8—521no—
229C4⋊C8—521no—
230#101—21no—
231#101—21no—
232#101—21no—
233#101—132no—
234#101—261no—
235#101—261no—
236#101—261no—
237#101Dic2612yescomplemented
238#97—521no—
239C4×C8—521no—
240#95—21no—
241#95—21no—
242#95—261no—
243#95—261no—
244#95—261no—
245#95—261no—
246#95—261no—
247#95—261no—
248#95—261no—
249C2×C13—21no—
250C2×C13—21no—
251C2×C13#199611yescharacteristic
252C2×C13C2×#35511yescharacteristic
253C2×C13#213511yescharacteristic
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—521no—
257C2×Q8—521no—
258C2×Q8—524no—
259C2×Q8C2×Dic2611yescharacteristic
260C2×Q8#612711yescharacteristic
261C2×Q8#612911yescharacteristic
262C2×Q8Q8×D1311yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4C2×C4×D1311yescharacteristic
272C22×C4D4×D1311yescharacteristic
273C22×C4D4×D1311yescharacteristic
274M16—22no—
275M16—41no—
276M16—41no—
277M16—41no—
278M16—262no—
279M16—521no—
280M16—521no—
281M16—521no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—521no—
285C2×C8—521no—
286C4⋊C4—41no—
287C4⋊C4—521no—
288C4⋊C4—521no—
289C4⋊C4—521no—
290C4⋊C4—521no—
291C4⋊C4—522no—
292C4⋊C4—522no—
293C42—41no—
294C42—261no—
295C42—261no—
296C42—261no—
297C42—261no—
298C42—261no—
299C42—261no—
300C42—521no—
301C13#1330111yescharacteristic, complemented, Sylow
302C23C22⋊C4×D1311yescharacteristic
303Q8—41no—
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—1042no—
308Q8—1042no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—131no—
321C2×C4—131no—
322C2×C4—262no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—522no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4C4×Dic2611yescharacteristic
335C2×C4#8813211yescharacteristic
336C2×C4#8813911yescharacteristic
337C2×C4#8814111yescharacteristic
338C2×C4#8814211yescharacteristic
339C2×C4#8815011yescharacteristic
340C8—42no—
341C8—81no—
342C8—522no—
343C8—1041no—
344C22—21no—
345C22—21no—
346C22#1171830711yescharacteristic
347C22#1171840111yescharacteristic
348C22D13×#9911yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—132no—
358C4—261no—
359C4—521no—
360C4—521no—
361C4—521no—
362C4—1041no—
363C4—1041no—
364C2—21no—
365C2—21no—
366C2#1311581911yescharacteristic
367C2D13×#35511yescharacteristic
368C2#1311652911yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#1394C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#1394D13
hypocenterC13#13301
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
52. C13×#101Q8semidirect
58. #88076Q8semidirect
237. #101Dic26semidirect
301. C13#13301semidirect

Maximal subgroups

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

subgroupindex
#131200532
#131148302
#101×Dic132
#131129632
#131129622
C13×#13942
#1330113