Finite Group Databasebeta

← #15773320

Subgroups — #15773320

Order 3328.

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

normal subgroups only

This group has 356 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#13125401C211yesmaximal, characteristic
2#13116632C211yesmaximal, characteristic, complemented
3#13114724C211yesmaximal, characteristic, complemented
4#13112849C211yesmaximal, characteristic, complemented
5#13112847C211yesmaximal, characteristic, complemented
6#13112845C211yesmaximal, characteristic
7C13×#1347C211yesmaximal, characteristic
8#11719305—21no—
9C13×#466C2211yescharacteristic
10#11718816C411yescharacteristic, complemented
11D8×Dic13C411yescharacteristic, complemented
12#11718777C2211yescharacteristic
13C2×C8×Dic13C2211yescharacteristic
14#11718702—21no—
15C4⋊C4×Dic13—21no—
16C2×#88048—21no—
17#11718539C411yescharacteristic, complemented
18#11718534C411yescharacteristic, complemented
19#11718429—21no—
20#11718419—21no—
21C13×C22⋊C16C2211yescharacteristic
22C13×#340C2211yescharacteristic
23#11718143C2211yescharacteristic
24C22⋊#6090C2211yescharacteristic
25#11718093—21no—
26C16×Dic13—21no—
27C2×C13×D8C2×C411yescharacteristic
28C22×C8×C13C2311yescharacteristic
29C13×#121—21no—
30C2×C13×C4⋊C4—21no—
31#88190—21no—
32#88189—41no—
33D4×Dic13—21no—
34D4×Dic13—41no—
35C2×#6105—21no—
36C2×C4⋊Dic13—21no—
37#88178—21no—
38C2×C4×Dic13—41no—
39C2×C4×Dic13D411yescharacteristic
40C22×#1055D411yescharacteristic
41C2×Dic52C2×C411yescharacteristic
42#88144—21no—
43#88141—21no—
44#88133—41no—
45#88131—41no—
46C2×C13×C16—21no—
47C13×#107C2×C411yescharacteristic
48C13×#102—21no—
49#88072—21no—
50#88071—41no—
51#88058C2×C411yescharacteristic
52#88056—21no—
53C8×Dic13C2×C411yescharacteristic
54C8×Dic13C2×C411yescharacteristic
55C8×Dic13D411yescharacteristic
56C8×Dic13D411yescharacteristic
57C2×#6090—21no—
58#88050—21no—
59#88048—24no—
60#88048—21no—
61#11741—131nomaximal, Sylow
62C2×D4×C13—21no—
63C2×D4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—41no—
67C22×Dic13—41no—
68C22×Dic13D811yescharacteristic
69C22×Dic13D811yescharacteristic
70C2×Dic26—21no—
71C13×D8—41no—
72C2×C8×C13—41no—
73C2×C8×C13C22×C411yescharacteristic
74C2×C8×C13C2×D411yescharacteristic
75C13×C4⋊C4—22no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—41no—
78C13×C22⋊C4—41no—
79C22⋊Dic13—41no—
80C22⋊Dic13—41no—
81C22⋊Dic13—41no—
82C22⋊Dic13—41no—
83#6105—42no—
84C4⋊Dic13—22no—
85C4⋊Dic13—21no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88#6101—41no—
89#6101—41no—
90#6101—41no—
91C4×Dic13—41no—
92C4×Dic13—82no—
93C4×Dic13C22⋊C411yescharacteristic
94C4×Dic13C22⋊C411yescharacteristic
95C4×Dic13SD1611yescharacteristic
96C4×Dic13SD1611yescharacteristic
97C2×#1055—22no—
98C2×#1055C22⋊C411yescharacteristic
99C2×#1055C22⋊C411yescharacteristic
100Dic52—41no—
101C13×C16—41no—
102#6090—41no—
103#3168—131no—
104#2162—131no—
105C4×#106—131no—
106#1348—131no—
107#1348—131no—
108#1347—131no—
109#1347D1311yescharacteristic
110C23×C13—41no—
111C23×C13C2×D811yescharacteristic
112D4×C13—41no—
113D4×C13—41no—
114D4×C13—81no—
115D4×C13—81no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—81no—
121C2×C4×C13—81no—
122C2×C4×C13C2×C22⋊C411yescharacteristic
123C2×C4×C13C2×SD1611yescharacteristic
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—22no—
127C2×Dic13—42no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—81no—
131C2×Dic13—81no—
132C2×Dic13—82no—
133C2×Dic13#10211yescharacteristic
134C2×Dic13#10211yescharacteristic
135C2×Dic13#10211yescharacteristic
136C2×Dic13#10211yescharacteristic
137Dic26—41no—
138Dic26—41no—
139C8×C13—21no—
140C8×C13—21no—
141#1055—21no—
142#1055#10412yes—
143#529—261no—
144#499—131no—
145#495—131no—
146#488—261no—
147#467—131no—
148#466C2×D1311yescharacteristic
149#465—261no—
150C4×Q16—131no—
151C4×SD16—261no—
152C4×D8—131no—
153C2×#106—261no—
154C2×C4×C8—131no—
155C4×C4⋊C4—261no—
156C4⋊C16—261no—
157C22⋊C16—131no—
158C22⋊C16C2×D1311yescharacteristic
159C4×C16—261no—
160#340—131no—
161#340C2×D1311yescharacteristic
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—81no—
165C22×C13—81no—
166C22×C13—81no—
167C22×C13C2×#10211yescharacteristic
168C22×C13#50811yescharacteristic
169C22×C13#50811yescharacteristic
170C4×C13—21no—
171C4×C13—82no—
172C4×C13—81no—
173C4×C13#41011yescharacteristic
174C4×C13C2×#10411yescharacteristic
175Dic13—21no—
176Dic13—21no—
177Dic13—21no—
178Dic13—82no—
179Dic13—81no—
180Dic13—81no—
181Dic13#36012yes—
182C2×Q16—131no—
183C2×SD16—261no—
184C2×D8C4×D1311yescharacteristic
185C22×C8—131no—
186C22×C8C22×D1311yescharacteristic
187#126—521no—
188#125—261no—
189#124—261no—
190#123—521no—
191C22⋊Q8—261no—
192#121—21no—
193C4×Q8—261no—
194C4×D4—261no—
195C4×D4—521no—
196#117—521no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—261no—
199C2×C42—131no—
200C2×C42—521no—
201C2×C16—21no—
202C2×C16—261no—
203#107—131no—
204#107C4×D1311yescharacteristic
205#106—261no—
206#106—264no—
207#103—261no—
208#103—261no—
209#102—21no—
210#102—261no—
211C4×C8—131no—
212C4×C8—131no—
213C4×C8—131no—
214C4×C8—131no—
215#95—521no—
216C2×C13—21no—
217C2×C13—21no—
218C2×C13—161no—
219C2×C13#150211yescharacteristic
220C2×C13#213811yescharacteristic
221C2×C13C2×#36011yescharacteristic
222C2×Q8—261no—
223C2×D4—21no—
224C2×D4—41no—
225C22×C4—41no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—521no—
229C22×C4—521no—
230C22×C4D4×D1311yescharacteristic
231Q16—521no—
232SD16—522no—
233D8—41no—
234C2×C8—41no—
235C2×C8—131no—
236C2×C8—131no—
237C2×C8—262no—
238C2×C8C2×C4×D1311yescharacteristic
239C2×C8D4×D1311yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—21no—
242C4⋊C4—41no—
243C4⋊C4—262no—
244C4⋊C4—261no—
245C4⋊C4—521no—
246C4⋊C4—521no—
247C4⋊C4—521no—
248C4⋊C4—521no—
249C4⋊C4—521no—
250C22⋊C4—41no—
251C22⋊C4—521no—
252C22⋊C4—521no—
253C22⋊C4—521no—
254C22⋊C4—521no—
255C42—131no—
256C42—131no—
257C42—131no—
258C42—131no—
259C42—521no—
260C42—1042no—
261C16—41no—
262C16—521no—
263C13#1174111yescharacteristic, complemented, Sylow
264C23—41no—
265C23D8×D1311yescharacteristic
266Q8—521no—
267Q8—521no—
268D4—41no—
269D4—41no—
270D4—81no—
271D4—81no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—131no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—131no—
282C2×C4—262no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—522no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—1042no—
289C2×C4—1041no—
290C2×C4—1041no—
291C2×C4C22⋊C4×D1311yescharacteristic
292C2×C4SD16×D1311yescharacteristic
293C8—21no—
294C8—21no—
295C8—132no—
296C8—261no—
297C22—21no—
298C22—21no—
299C22—81no—
300C22—81no—
301C22—81no—
302C22D13×#10211yescharacteristic
303C22#1171857311yescharacteristic
304C22#1171857711yescharacteristic
305C4—21no—
306C4—82no—
307C4—81no—
308C4—132no—
309C4—261no—
310C4—261no—
311C4—261no—
312C4—1042no—
313C4—1041no—
314C4—1041no—
315C4#1171840111yescharacteristic
316C4D13×#10411yescharacteristic
317C2—21no—
318C2—21no—
319C2—161no—
320C2#1311332911yescharacteristic
321C2#1311654011yescharacteristic
322C2D13×#36011yescharacteristic
subgroupG/H
centerC22D13×#102
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1347C2
socleC22×C13C2×#102
prime radicalC13×#466C22
cosocleC22×C8×C13C23
hypercenter#1347D13
hypocenterC13#11741
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1347

Complements

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

NH ≅ G/Ntype
2. #13116632C2semidirect
3. #13114724C2semidirect
4. #13112849C2semidirect
5. #13112847C2semidirect
10. #11718816C4semidirect
11. D8×Dic13C4semidirect
17. #11718539C4semidirect
18. #11718534C4semidirect
263. C13#11741semidirect

Maximal subgroups

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

subgroupindex
#131254012
#131166322
#131147242
#131128492
#131128472
#131128452
C13×#13472
#1174113