Finite Group Databasebeta

← #15775930

Subgroups — #15775930

Order 3328.

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

normal subgroups only

This group has 386 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#13116181C211yesmaximal, characteristic, complemented
2#13113843C211yesmaximal, characteristic, complemented
3#13113775C211yesmaximal, characteristic
4#13112842C211yesmaximal, characteristic, complemented
5#13112839C211yesmaximal, characteristic
6#13112782C211yesmaximal, characteristic, complemented
7C13×#2823C211yesmaximal, characteristic
8C2×C13×#126—21no—
9#11719205C2211yescharacteristic
10C13×#398—21no—
11C13×#398C2211yescharacteristic
12C13×#396—21no—
13C13×#396—21no—
14C13×#396—21no—
15C13×#394—21no—
16C13×#394C2211yescharacteristic
17C13×#384C2211yescharacteristic
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
28C13×#126—42no—
29C13×#126—42no—
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—21no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4C2311yescharacteristic
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C42×C13D411yescharacteristic
46C2×#6105—41no—
47#88180—21no—
48#88178—21no—
49#88178—21no—
50C2×#6099—21no—
51#88144—41no—
52#88142—41no—
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#12249—131nomaximal, Sylow
65C24×C13—21no—
66C2×D4×C13—41no—
67C2×D4×C13—81no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C2×Dic26—21no—
77C2×Dic26—21no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—81no—
86C13×C4⋊C4—81no—
87C13×C4⋊C4—81no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—81no—
93C13×C22⋊C4—81no—
94C13×C22⋊C4—81no—
95C42×C13—21no—
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#2823D1311yescharacteristic
112#2060—131no—
113#1611—131no—
114#1599—131no—
115#1346—131no—
116#1345—131no—
117#1325—131no—
118C23×C13—41no—
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—21no—
132C2×C4×C13—21no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
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×C13C2×SD1611yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
151C2×Dic13—41no—
152C2×Dic13—41no—
153Dic26—81no—
154Dic26—81no—
155#1055—42no—
156#1055—81no—
157#1055—81no—
158#544—131no—
159C2×#126—21no—
160#483—261no—
161#450—261no—
162#428—261no—
163#398—21no—
164#398C2×D1311yescharacteristic
165#396—21no—
166#396—21no—
167#396—21no—
168#394—21no—
169#394C2×D1311yescharacteristic
170#384C2×D1311yescharacteristic
171#343—131no—
172#339—261no—
173#328—261no—
174#328—261no—
175#324—131no—
176#324—131no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13#45011yescharacteristic
187C22×C13#45611yescharacteristic
188C22×C13B(4,𝔽2)11yescharacteristic
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—42no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—81no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13—81no—
198Dic13—81no—
199Dic13—81no—
200C22×D4C22⋊D1311yescharacteristic
201C2×SD16—521no—
202C2×M16—261no—
203C4⋊Q8—521no—
204#126—42no—
205#126—42no—
206#125—521no—
207C22⋊Q8—261no—
208C22⋊Q8—261no—
209#117—261no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C22⋊D1311yescharacteristic
217C2×C4⋊C4C22⋊D1311yescharacteristic
218C2×C4⋊C4C22×D1311yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C42C22⋊D1311yescharacteristic
226#107—521no—
227#106—521no—
228#106—521no—
229#103—521no—
230#102—521no—
231C22⋊C8—261no—
232C22⋊C8—261no—
233#95—21no—
234#95—21no—
235#95C22⋊D1311yescharacteristic
236#95C22⋊D1311yescharacteristic
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—161no—
240C2×C13#160411yescharacteristic
241C2×C13#220011yescharacteristic
242C2×C13#220311yescharacteristic
243C24—21no—
244C2×Q8—261no—
245C2×Q8—261no—
246C2×D4—41no—
247C2×D4—81no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C2×C22⋊D1311yescharacteristic
254C22×C4C2×C22⋊D1311yescharacteristic
255C22×C4C2×C22⋊D1311yescharacteristic
256SD16—1042no—
257M16—262no—
258M16—521no—
259C2×C8—521no—
260C2×C8—521no—
261C2×C8—521no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—521no—
277C4⋊C4—521no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—81no—
283C22⋊C4—81no—
284C22⋊C4—81no—
285C22⋊C4—521no—
286C42—21no—
287C42—521no—
288C42#610512yescomplemented
289C13#1224911yescharacteristic, complemented, Sylow
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#8820711yescharacteristic
298Q8—1041no—
299Q8—1041no—
300D4—42no—
301D4—81no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
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—521no—
324C2×C4—521no—
325C2×C4#8818611yescharacteristic
326C2×C4C2×#610511yescharacteristic
327C8—522no—
328C8—1041no—
329C8—1041no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22#1171887911yescharacteristic
340C22#1171890511yescharacteristic
341C22#1171890711yescharacteristic
342C4—21no—
343C4—21no—
344C4—42no—
345C4—41no—
346C4—41no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—1041no—
352C4—1041no—
353C2—21no—
354C2—21no—
355C2—161no—
356C2#1311380511yescharacteristic
357C2#1311684311yescharacteristic
358C2#1311685711yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2823C2
socleC22×C13B(4,𝔽2)
prime radicalC22×D4×C13D4
hypercenter#2823D13
hypocenterC13#12249
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2823

Complements

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

NH ≅ G/Ntype
1. #13116181C2semidirect
2. #13113843C2semidirect
4. #13112842C2semidirect
6. #13112782C2semidirect
96. C42×C13SD16semidirect
288. C42#6105semidirect
289. C13#12249semidirect

Maximal subgroups

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

subgroupindex
#131161812
#131138432
#131137752
#131128422
#131128392
#131127822
C13×#28232
#1224913