Finite Group Databasebeta

← #15766011

Subgroups — #15766011

Order 3328.

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

normal subgroups only

This group has 416 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#13123212C211yesmaximal, characteristic
2#13115812C211yesmaximal, characteristic
3#13113401C211yesmaximal, characteristic
4#13113399C211yesmaximal, characteristic
5#13112696C211yesmaximal, characteristic
6#13112668C211yesmaximal, characteristic
7C13×#1286C211yesmaximal, characteristic
8C2×#88142—21no—
9#11719175C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C13×#382C2211yescharacteristic
13#11718638—21no—
14#11718597C2211yescharacteristic
15C42×Dic13C2211yescharacteristic
16#11718586C2211yescharacteristic
17#11718307—22no—
18#11718307—22no—
19#11718147—21no—
20#11718147—21no—
21#11718059—22no—
22#11718044—22no—
23C22×Dic26—22no—
24C2×C13×M16—21no—
25C2×C13×C4⋊C4—21no—
26C2×C42×C13C2311yescharacteristic
27#88180—21no—
28C2×C4⋊Dic13—21no—
29#88178—21no—
30#88178—21no—
31C2×#6101—22no—
32C2×C4×Dic13—21no—
33C2×C4×Dic13—21no—
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36#88142—42no—
37#88142—42no—
38#88124—21no—
39#88123Q811yescharacteristic, complemented
40#88123Q811yescharacteristic, complemented
41C4×Dic26—21no—
42C4×Dic26—21no—
43C13×C4⋊C8—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C22⋊C8—21no—
47C4×C8×C13—21no—
48C13×#95—21no—
49C13×#95D412yes—
50#88071—24no—
51#88071—21no—
52#88071D412yes—
53C22⋊#1055—21no—
54C4⋊#1055—21no—
55C4×#1055—21no—
56#10363—131nomaximal, Sylow
57C22×C4×C13—22no—
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13—22no—
64C2×Dic26—21no—
65C2×Dic26—21no—
66C2×Dic26—44no—
67C2×Dic26—44no—
68C2×Dic26—44no—
69C13×M16—41no—
70C13×M16—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C42×C13C2×Q811yescharacteristic
76C42×C13#4111yescharacteristic
77C42×C13#4111yescharacteristic
78C42×C13#4111yescharacteristic
79C22⋊Dic13—41no—
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13—41no—
85C4⋊Dic13—41no—
86#6101—44no—
87#6101—41no—
88#6101—41no—
89C4×Dic13—21no—
90C4×Dic13—21no—
91C4×Dic13—42no—
92C4×Dic13—42no—
93C4×Dic13—41no—
94C4×Dic13SD1612yes—
95C4×Dic13Q1612yes—
96C2×#1055—41no—
97#2862—131no—
98#1994—131no—
99#1518—131no—
100#1518—131no—
101#1286—131no—
102#1286D1311yescharacteristic
103#1276—131no—
104C23×C13#12011yescharacteristic
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13C22⋊Q811yescharacteristic
111C2×C4×C13C22⋊Q811yescharacteristic
112C2×C4×C13C22⋊Q811yescharacteristic
113C2×C4×C13#12411yescharacteristic
114C2×C4×C13#12411yescharacteristic
115C2×C4×C13#12411yescharacteristic
116C2×C4×C13C2×SD1611yescharacteristic
117C2×C4×C13C2×Q1611yescharacteristic
118C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C13#13711yescharacteristic
120C2×Dic13—22no—
121C2×Dic13—22no—
122C2×Dic13—22no—
123C2×Dic13—22no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—42no—
131Dic26—88no—
132Dic26—81no—
133Dic26—81no—
134C8×C13—81no—
135C8×C13—81no—
136#1055—81no—
137#533—131no—
138C2×C4⋊Q8—261no—
139#431—131no—
140#431C2×D1311yescharacteristic
141#423C2×D1311yescharacteristic
142#391—262no—
143#391—262no—
144#382—131no—
145#382—261no—
146#382C2×D1311yescharacteristic
147C43—131no—
148#339—261no—
149#339—261no—
150#328—262no—
151#328—262no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13#39311yescharacteristic
155C22×C13#45011yescharacteristic
156C22×C13#45111yescharacteristic
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—82no—
162C4×C13#47511yescharacteristic
163C4×C13#47711yescharacteristic
164C4×C13#48711yescharacteristic
165C4×C13#48911yescharacteristic
166Dic13—24no—
167Dic13—42no—
168Dic13—82no—
169Dic13—81no—
170Dic13—81no—
171C22×Q8—262no—
172C2×M16—21no—
173C4⋊Q8—131no—
174C4⋊Q8—131no—
175C4⋊Q8—522no—
176C4⋊Q8—522no—
177#125—261no—
178C22⋊Q8—261no—
179C22⋊Q8—261no—
180C4×Q8—261no—
181C4×Q8—261no—
182#117—261no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—262no—
185C2×C4⋊C4—261no—
186C2×C42—131no—
187C2×C42—131no—
188C2×C42—261no—
189C2×C42—261no—
190C2×C42C22×D1311yescharacteristic
191C4⋊C8—21no—
192C4⋊C8—21no—
193C4⋊C8—21no—
194C4⋊C8—261no—
195C22⋊C8—21no—
196C22⋊C8—261no—
197C4×C8—21no—
198C4×C8—261no—
199#95—21no—
200#95—132no—
201#95—264no—
202#95—261no—
203#95D5212yes—
204C2×C13—21no—
205C2×C13—21no—
206C2×C13#202411yescharacteristic
207C2×C13#203111yescharacteristic
208C2×C13#203111yescharacteristic
209C2×Q8—261no—
210C2×Q8—261no—
211C2×Q8—524no—
212C2×Q8—524no—
213C2×Q8—524no—
214C22×C4—22no—
215C22×C4—261no—
216C22×C4—261no—
217C22×C4—262no—
218C22×C4C2×D5211yescharacteristic
219C22×C4D4×D1311yescharacteristic
220C22×C4D4×D1311yescharacteristic
221M16—41no—
222M16—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—521no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—261no—
229C4⋊C4—261no—
230C4⋊C4—261no—
231C4⋊C4—261no—
232C4⋊C4—524no—
233C4⋊C4—521no—
234C4⋊C4—521no—
235C4⋊C4—521no—
236C4⋊C4—521no—
237C22⋊C4—521no—
238C42—132no—
239C42—132no—
240C42—261no—
241C42—261no—
242C42—522no—
243C42—522no—
244C42—521no—
245C42#612711yescharacteristic
246C42#612711yescharacteristic
247C42#612911yescharacteristic
248C42Q8×D1311yescharacteristic
249C13#1036311yescharacteristic, complemented, Sylow
250C23#8813611yescharacteristic
251Q8—1041no—
252Q8—1041no—
253Q8—1048no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—262no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4—522no—
266C2×C4—522no—
267C2×C4—522no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4#8812911yescharacteristic
271C2×C4#8813911yescharacteristic
272C2×C4#8813911yescharacteristic
273C2×C4#8815011yescharacteristic
274C2×C4#8815011yescharacteristic
275C2×C4#8815111yescharacteristic
276C2×C4#8816511yescharacteristic
277C2×C4SD16×D1311yescharacteristic
278C2×C4#8816911yescharacteristic
279C2×C4Q16×D1311yescharacteristic
280C8—81no—
281C8—81no—
282C8—1041no—
283C22—21no—
284C22—21no—
285C22#1171833411yescharacteristic
286C22#1171843711yescharacteristic
287C22#1171846911yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—82no—
293C4—264no—
294C4—522no—
295C4—1042no—
296C4—1041no—
297C4—1041no—
298C4#1171842611yescharacteristic
299C4#1171845311yescharacteristic
300C4#1171851511yescharacteristic
301C4#1171853611yescharacteristic
302C2—21no—
303C2—21no—
304C2#1311597611yescharacteristic
305C2#1311600711yescharacteristic
306C2#1311601111yescharacteristic
subgroupG/H
centerC22#11718334
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1286C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#1286D13
hypocenterC13#10363
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
39. #88123Q8semidirect
40. #88123Q8semidirect
249. C13#10363semidirect

Maximal subgroups

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

subgroupindex
#131232122
#131158122
#131134012
#131133992
#131126962
#131126682
C13×#12862
#1036313