Finite Group Databasebeta

← #15775749

Subgroups — #15775749

Order 3328.

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

normal subgroups only

This group has 346 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#13115997C211yesmaximal, characteristic
2#13113877C211yesmaximal, characteristic
3#13113809C211yesmaximal, characteristic
4#13112866C211yesmaximal, characteristic
5#13112863C211yesmaximal, characteristic
6#13112770C211yesmaximal, characteristic
7C13×#2799C211yesmaximal, characteristic
8#11719205C2211yescharacteristic
9C13×#400—21no—
10C13×#400C2211yescharacteristic
11C13×#398—21no—
12C13×#395C2211yescharacteristic
13C13×#391—21no—
14C13×#391—21no—
15C13×#391C2211yescharacteristic
16C13×#387—21no—
17C13×#387—21no—
18#11718889—21no—
19#11718886—21no—
20#11718631—21no—
21#11718122C2211yescharacteristic
22#11718120C2211yescharacteristic
23#11718120C2211yescharacteristic
24#11718115—21no—
25#11718044—21no—
26#11718044—21no—
27C22×Q8×C13D411yescharacteristic
28C22×Q8×C13D411yescharacteristic
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C42×C13—21no—
36C2×C42×C13D411yescharacteristic
37C2×#6107—41no—
38#88180—21no—
39#88178—21no—
40#88178—21no—
41C2×#6099—21no—
42#88144—41no—
43#88142—41no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95D411yescharacteristic
54C13×#95D411yescharacteristic
55#88075—41no—
56#88075—41no—
57#88075—41no—
58C22⋊#1055—21no—
59C22⋊#1055—21no—
60#88050—41no—
61#88047—41no—
62#12222—131nomaximal, Sylow
63C2×Q8×C13—21no—
64C2×Q8×C13—42no—
65C2×Q8×C13—41no—
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C2×Q8×C13Q1612yescomplemented
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C2×Dic26—21no—
79C2×Dic26—21no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—81no—
85C13×C4⋊C4—81no—
86C42×C13—41no—
87C42×C13—81no—
88C22⋊Dic13—41no—
89#6107—82no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94#6101—41no—
95#6101—41no—
96C4×Dic13—41no—
97#6099—41no—
98#6099—41no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102#2799D1311yescharacteristic
103#2028—131no—
104#1617—131no—
105#1605—131no—
106#1354—131no—
107#1353—131no—
108#1319—131no—
109C23×C13#12011yescharacteristic
110Q8×C13—42no—
111Q8×C13—42no—
112Q8×C13—81no—
113Q8×C13—81no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13C2×Q1611yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C2×Dic13—41no—
140C2×Dic13—41no—
141Dic26—81no—
142Dic26—81no—
143#1055—81no—
144#1055—81no—
145#1055—81no—
146#544—131no—
147#484—261no—
148#451—261no—
149#419—261no—
150#400—21no—
151#400C2×D1311yescharacteristic
152#398—21no—
153#395C2×D1311yescharacteristic
154#391—21no—
155#391—21no—
156#391C2×D1311yescharacteristic
157#387—21no—
158#387—21no—
159#343—131no—
160#339—261no—
161#328—261no—
162#328—261no—
163#324—131no—
164#324—131no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13#45111yescharacteristic
168C22×C13#45511yescharacteristic
169C22×C13B(4,𝔽2)11yescharacteristic
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—42no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—42no—
176C4×C13—81no—
177C4×C13—81no—
178C4×C13—81no—
179C4×C13—81no—
180Dic13—81no—
181Dic13—81no—
182C22×Q8C22⋊D1311yescharacteristic
183C22×Q8C22⋊D1311yescharacteristic
184C2×Q16—521no—
185C2×M16—261no—
186C4⋊Q8—521no—
187#125—521no—
188C22⋊Q8—261no—
189C22⋊Q8—261no—
190#117—261no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4C22⋊D1311yescharacteristic
196C2×C4⋊C4C22×D1311yescharacteristic
197C2×C42—21no—
198C2×C42C22⋊D1311yescharacteristic
199#107—521no—
200#103—521no—
201#103—521no—
202#103—521no—
203#103—521no—
204C22⋊C8—261no—
205C22⋊C8—261no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95C22⋊D1311yescharacteristic
216#95C22⋊D1311yescharacteristic
217C2×C13—21no—
218C2×C13—21no—
219C2×C13#160211yescharacteristic
220C2×C13#219711yescharacteristic
221C2×C13#220311yescharacteristic
222C2×Q8—21no—
223C2×Q8—42no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—261no—
228C2×Q8—261no—
229C2×Q8#610712yescomplemented
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4C2×C22⋊D1311yescharacteristic
237C22×C4C2×C22⋊D1311yescharacteristic
238C22×C4C2×C22⋊D1311yescharacteristic
239Q16—1042no—
240M16—521no—
241M16—521no—
242C2×C8—521no—
243C2×C8—521no—
244C2×C8—521no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—81no—
250C4⋊C4—81no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C22⋊C4—521no—
258C42—41no—
259C42—81no—
260C42—521no—
261C13#1222211yescharacteristic, complemented, Sylow
262C23#8820711yescharacteristic
263Q8—42no—
264Q8—42no—
265Q8—81no—
266Q8—81no—
267Q8—1041no—
268Q8—1041no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4#8819611yescharacteristic
295C2×C4C2×#610711yescharacteristic
296C8—1041no—
297C8—1041no—
298C8—1041no—
299C22—21no—
300C22—21no—
301C22#1171888911yescharacteristic
302C22#1171890311yescharacteristic
303C22#1171890511yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—42no—
309C4—42no—
310C4—81no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—1041no—
315C4—1041no—
316C2—21no—
317C2—21no—
318C2#1311379311yescharacteristic
319C2#1311682611yescharacteristic
320C2#1311685711yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2799C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2799D13
hypocenterC13#12222
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2799

Complements

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

NH ≅ G/Ntype
68. C2×Q8×C13Q16semidirect
229. C2×Q8#6107semidirect
261. C13#12222semidirect

Maximal subgroups

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

subgroupindex
#131159972
#131138772
#131138092
#131128662
#131128632
#131127702
C13×#27992
#1222213