Finite Group Databasebeta

← #15775923

Subgroups — #15775923

Order 3328.

428 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 63 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#13116186C211yesmaximal, characteristic, complemented
2#13113843C211yesmaximal, characteristic, complemented
3#13113775C211yesmaximal, characteristic
4#13112842C211yesmaximal, characteristic, complemented
5#13112839C211yesmaximal, characteristic
6#13112780C211yesmaximal, characteristic, complemented
7C13×#2609C211yesmaximal, characteristic
8C2×C13×#117—21no—
9#11719205C2211yescharacteristic
10C13×#398C2211yescharacteristic
11C13×#396—21no—
12C13×#394C2211yescharacteristic
13C13×#388—21no—
14C13×#387—21no—
15C13×#386—21no—
16C13×#385—21no—
17C13×#382C2211yescharacteristic
18#11718879—21no—
19#11718632—21no—
20#11718625—21no—
21#11718122C2211yescharacteristic
22#11718120C2211yescharacteristic
23#11718120C2211yescharacteristic
24#11718115—21no—
25#11718044—21no—
26#11718044—21no—
27C22×D4×C13D411yescharacteristic
28C23×C4×C13—21no—
29C13×#117—42no—
30C13×#117—42no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4C2311yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C42×C13—21no—
43C2×C42×C13D411yescharacteristic
44C2×#6105—41no—
45#88180—21no—
46#88178—21no—
47#88178—21no—
48C2×#6099—21no—
49#88144—41no—
50#88142—41no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95D411yescharacteristic
56C13×#95D411yescharacteristic
57#88072—41no—
58C22⋊#1055—21no—
59C22⋊#1055—21no—
60#88050—41no—
61#88048—41no—
62#88048—41no—
63#88047—41no—
64#12248—131nomaximal, Sylow
65C24×C13—21no—
66C2×D4×C13—41no—
67C2×D4×C13—42no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—42no—
74C22×C4×C13—42no—
75C22×C4×C13—42no—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C2×Dic26—21no—
80C2×Dic26—21no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—81no—
94C42×C13—21no—
95C42×C13—42no—
96C42×C13SD1612yescomplemented
97C22⋊Dic13—41no—
98#6105—82no—
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13—21no—
103#6101—41no—
104#6101—41no—
105C4×Dic13—41no—
106#6099—22no—
107#6099—41no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111#2609D1311yescharacteristic
112#2061—131no—
113#1611—131no—
114#1599—131no—
115#1346—131no—
116#1345—131no—
117#1324—131no—
118C23×C13—22no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13#12011yescharacteristic
126D4×C13—42no—
127D4×C13—81no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—48no—
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×C13C2×SD1611yescharacteristic
151C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
152C2×Dic13—41no—
153C2×Dic13—41no—
154Dic26—81no—
155Dic26—81no—
156#1055—42no—
157#1055—81no—
158#1055—81no—
159#544—131no—
160C2×#117—21no—
161#483—261no—
162#450—261no—
163#428—261no—
164#398C2×D1311yescharacteristic
165#396—21no—
166#394C2×D1311yescharacteristic
167#388—21no—
168#387—21no—
169#386—21no—
170#385—21no—
171#382C2×D1311yescharacteristic
172#343—131no—
173#339—261no—
174#328—261no—
175#328—261no—
176#324—131no—
177#324—131no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—42no—
181C22×C13—42no—
182C22×C13—42no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13#45011yescharacteristic
188C22×C13#45611yescharacteristic
189C22×C13B(4,𝔽2)11yescharacteristic
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—42no—
193C4×C13—42no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13—81no—
199Dic13—81no—
200Dic13—81no—
201C22×D4C22⋊D1311yescharacteristic
202C23×C4—21no—
203C2×SD16—521no—
204C2×M16—261no—
205C4⋊Q8—521no—
206#125—521no—
207C22⋊Q8—261no—
208C22⋊Q8—261no—
209#117—42no—
210#117—42no—
211#117—261no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C22⋊D1311yescharacteristic
216C2×C4⋊C4C22⋊D1311yescharacteristic
217C2×C4⋊C4C22×D1311yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C42—21no—
224C2×C42C22⋊D1311yescharacteristic
225#107—521no—
226#106—521no—
227#106—521no—
228#103—521no—
229#102—521no—
230C22⋊C8—261no—
231C22⋊C8—261no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95C22⋊D1311yescharacteristic
237#95C22⋊D1311yescharacteristic
238C2×C13—21no—
239C2×C13—21no—
240C2×C13—82no—
241C2×C13#160411yescharacteristic
242C2×C13#219711yescharacteristic
243C2×C13#220411yescharacteristic
244C24—21no—
245C2×Q8—261no—
246C2×Q8—261no—
247C2×D4—41no—
248C2×D4—42no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4C2×C22⋊D1311yescharacteristic
258C22×C4C2×C22⋊D1311yescharacteristic
259C22×C4C2×C22⋊D1311yescharacteristic
260SD16—1042no—
261M16—262no—
262M16—521no—
263C2×C8—521no—
264C2×C8—521no—
265C2×C8—521no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—521no—
278C4⋊C4—521no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—81no—
285C22⋊C4—521no—
286C42—21no—
287C42—42no—
288C42—521no—
289C42#610512yescomplemented
290C13#1224811yescharacteristic, complemented, Sylow
291C23—22no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23#8820711yescharacteristic
299Q8—1041no—
300Q8—1041no—
301D4—42no—
302D4—81no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—48no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4#8818611yescharacteristic
328C2×C4C2×#610511yescharacteristic
329C8—522no—
330C8—1041no—
331C8—1041no—
332C22—21no—
333C22—21no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22#1171887911yescharacteristic
342C22#1171890511yescharacteristic
343C22#1171890711yescharacteristic
344C4—21no—
345C4—21no—
346C4—42no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—1041no—
354C4—1041no—
355C2—21no—
356C2—21no—
357C2—82no—
358C2#1311380511yescharacteristic
359C2#1311682611yescharacteristic
360C2#1311686211yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2609C2
socleC22×C13B(4,𝔽2)
prime radicalC22×D4×C13D4
hypercenter#2609D13
hypocenterC13#12248
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2609

Complements

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

NH ≅ G/Ntype
1. #13116186C2semidirect
2. #13113843C2semidirect
4. #13112842C2semidirect
6. #13112780C2semidirect
96. C42×C13SD16semidirect
289. C42#6105semidirect
290. C13#12248semidirect

Maximal subgroups

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

subgroupindex
#131161862
#131138432
#131137752
#131128422
#131128392
#131127802
C13×#26092
#1224813