Finite Group Databasebeta

← #15772935

Subgroups — #15772935

Order 3328.

310 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 83 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#13125419C211yesmaximal, characteristic
2#13116637C211yesmaximal, characteristic
3D13×#334C211yesmaximal, characteristic
4#13112807C211yesmaximal, characteristic, complemented
5#13112806C211yesmaximal, characteristic, complemented
6#13112805C211yesmaximal, characteristic, complemented
7C13×#1334C211yesmaximal, characteristic, complemented
8#11719283—21no—
9C4×C13×Q16C2211yescharacteristic
10#11718849C411yescharacteristic
11#11718842C411yescharacteristic
12C4×#6107—21no—
13#11718548C411yescharacteristic
14#11718535C411yescharacteristic
15D13×C4⋊C8—21no—
16#11718474—21no—
17#11718453—21no—
18C4×Dic52C2211yescharacteristic
19C4×C8×D13C2211yescharacteristic
20C13×#346C2211yescharacteristic
21C13×#334C2211yescharacteristic
22#11718099—21no—
23#11718093—21no—
24#11718072—21no—
25#11718053C2211yescharacteristic
26#11718049C2211yescharacteristic
27C2×C13×Q16C2×C411yescharacteristic
28C4×Q8×C13—21no—
29#88200—21no—
30#88198—21no—
31C2×#6107—21no—
32C2×Dic52C2×C411yescharacteristic
33C2×C8×D13—41no—
34C2×C8×D13C2×C411yescharacteristic
35C2×C8×D13D411yescharacteristic
36#88151—21no—
37#88150—41no—
38#88143—41no—
39#88142—21no—
40#88126—41no—
41C42×D13D411yescharacteristic
42C4×Dic26—21no—
43C4×Dic26—41no—
44C2×C13×C16—21no—
45C13×#107C2×C411yescharacteristic
46C13×C4⋊C8—21no—
47C13×#103—21no—
48C4×C8×C13C2311yescharacteristic
49#88075—21no—
50#88058C2×C411yescharacteristic
51#88056—21no—
52#88054—41no—
53C8×Dic13C2×C411yescharacteristic
54C8×Dic13D411yescharacteristic
55C2×#6090—21no—
56#88050—21no—
57#88047—21no—
58C4⋊#1055—21no—
59C4×#1055D411yescharacteristic
60#11655—131nomaximal, Sylow
61C2×Q8×C13—21no—
62C2×C4×D13C22⋊C411yescharacteristic
63C2×C4×D13D811yescharacteristic
64C2×C4×D13SD1611yescharacteristic
65C2×Dic26—21no—
66C2×Dic26—41no—
67C13×Q16—21no—
68C13×Q16—21no—
69C2×C8×C13—41no—
70C2×C8×C13C22×C411yescharacteristic
71C2×C8×C13C2×D411yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4—41no—
74C42×C13—41no—
75C42×C13C2×D411yescharacteristic
76#6107—42no—
77#6103—41no—
78#6103—41no—
79C4⋊Dic13—21no—
80C4⋊Dic13—41no—
81#6101—41no—
82#6101—41no—
83#6101—41no—
84#6101—41no—
85#6101—41no—
86C4×Dic13—41no—
87C4×Dic13C22⋊C411yescharacteristic
88C4×Dic13D811yescharacteristic
89C4×Dic13SD1611yescharacteristic
90C2×#1055—41no—
91C2×#1055C22⋊C411yescharacteristic
92C2×#1055C22⋊C411yescharacteristic
93Dic52—21no—
94Dic52—21no—
95C8×D13—21no—
96C8×D13—21no—
97C8×D13—41no—
98C8×D13—82no—
99C13×C16—41no—
100#6090—41no—
101#3170—131no—
102#2163—131no—
103C2×#334—131no—
104#1334—131no—
105#1334—131no—
106#1334—131no—
107#1334D1311yescharacteristic, complemented
108C22×D13#10211yescharacteristic
109Q8×C13—41no—
110Q8×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13C2×C22⋊C411yescharacteristic
114C2×C4×C13C2×D811yescharacteristic
115C2×C4×C13C2×SD1611yescharacteristic
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13#10211yescharacteristic
119C2×Dic13#10211yescharacteristic
120C2×Dic13#10211yescharacteristic
121C4×D13—22no—
122C4×D13—21no—
123C4×D13—21no—
124C4×D13—22no—
125Dic26—41no—
126Dic26—41no—
127Dic26—82no—
128C8×C13—21no—
129C8×C13—81no—
130C8×C13#13111yescharacteristic
131C8×C13#13111yescharacteristic
132#1055—21no—
133#1055—21no—
134#1055—81no—
135#533—261no—
136#500—131no—
137#494—131no—
138#487—261no—
139#467—131no—
140#467—131no—
141#467—261no—
142C4×Q16—131no—
143C4×Q16—261no—
144C4×Q16C2×D1311yescharacteristic
145C2×C4⋊C8—261no—
146C2×C4×C8—131no—
147C4⋊C16—261no—
148C22⋊C16—261no—
149#346—131no—
150#346C2×D1311yescharacteristic
151#334—131no—
152#334—261no—
153#334C2×D1311yescharacteristic
154C22×C13C2×#10211yescharacteristic
155C2×D13—21no—
156C2×D13—21no—
157C2×D13#36212yes—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—81no—
161C4×C13—81no—
162C4×C13#40811yescharacteristic
163C4×C13#42111yescharacteristic
164Dic13—21no—
165Dic13—21no—
166Dic13—81no—
167Dic13—81no—
168Dic13#36012yes—
169C2×Q16—131no—
170C2×Q16—261no—
171C2×Q16C4×D1311yescharacteristic
172C22×C8—131no—
173C22×C8—131no—
174C22×C8—521no—
175C4⋊Q8—261no—
176C4⋊Q8—261no—
177#125—521no—
178C22⋊Q8—261no—
179C22⋊Q8—261no—
180C22⋊Q8—521no—
181C4×Q8—21no—
182C4×Q8—261no—
183C4×Q8—521no—
184#117—521no—
185C2×C42—131no—
186C2×C16—21no—
187C2×C16—261no—
188#107—131no—
189#107—261no—
190#107C4×D1311yescharacteristic
191C4⋊C8—21no—
192C4⋊C8—261no—
193C4⋊C8—521no—
194#103—21no—
195#103—261no—
196#103—261no—
197#103—261no—
198C4×C8—131no—
199C4×C8—131no—
200C4×C8—131no—
201C4×C8C22×D1311yescharacteristic
202C2×C13#148011yescharacteristic
203C2×C13C2×#36011yescharacteristic
204C2×C13C2×#36211yescharacteristic
205D13—22no—
206C2×Q8—21no—
207C2×Q8—261no—
208C2×Q8—521no—
209C22×C4—131no—
210C22×C4—131no—
211C22×C4—131no—
212Q16—21no—
213Q16—21no—
214Q16—261no—
215Q16—261no—
216Q16—522no—
217C2×C8—41no—
218C2×C8—131no—
219C2×C8—131no—
220C2×C8—261no—
221C2×C8—261no—
222C2×C8—521no—
223C2×C8—521no—
224C2×C8—1042no—
225C2×C8C2×C4×D1311yescharacteristic
226C2×C8D4×D1311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—41no—
229C4⋊C4—261no—
230C4⋊C4—521no—
231C4⋊C4—521no—
232C4⋊C4—521no—
233C4⋊C4—521no—
234C4⋊C4—521no—
235C4⋊C4—521no—
236C22⋊C4—521no—
237C22⋊C4—521no—
238C42—41no—
239C42—131no—
240C42—131no—
241C42—131no—
242C42—521no—
243C42D4×D1311yescharacteristic
244C16—41no—
245C16—521no—
246C13#1165511yescharacteristic, complemented, Sylow
247C23—131no—
248Q8—41no—
249Q8—41no—
250Q8—521no—
251Q8—521no—
252Q8—1042no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—131no—
256C2×C4—131no—
257C2×C4—131no—
258C2×C4—262no—
259C2×C4—262no—
260C2×C4—261no—
261C2×C4—261no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4C22⋊C4×D1311yescharacteristic
265C2×C4D8×D1311yescharacteristic
266C2×C4SD16×D1311yescharacteristic
267C8—21no—
268C8—81no—
269C8—261no—
270C8—261no—
271C8—1041no—
272C8#8815511yescharacteristic
273C8#8816111yescharacteristic
274C22—132no—
275C22—261no—
276C22—261no—
277C22D13×#10211yescharacteristic
278C4—21no—
279C4—21no—
280C4—81no—
281C4—81no—
282C4—132no—
283C4—261no—
284C4—261no—
285C4—1041no—
286C4—1041no—
287C4#1171838811yescharacteristic
288C4#1171848211yescharacteristic
289C2—262no—
290C2#1311323311yescharacteristic
291C2D13×#36011yescharacteristic
292C2D13×#36211yescharacteristic
subgroupG/H
centerC22D13×#102
commutatorC2×C8×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#1334C2
socleC22×C13C2×#102
prime radicalC22×D13#102
cosocleC4×C8×C13C23
hypercenter#1334D13
hypocenterC13#11655
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1334

Complements

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

NH ≅ G/Ntype
4. #13112807C2semidirect
5. #13112806C2semidirect
6. #13112805C2semidirect
7. C13×#1334C2semidirect
107. #1334D13semidirect
246. C13#11655semidirect

Maximal subgroups

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

subgroupindex
#131254192
#131166372
D13×#3342
#131128072
#131128062
#131128052
C13×#13342
#1165513