Finite Group Databasebeta

← #15766099

Subgroups — #15766099

Order 3328.

360 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 77 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#13115779C211yesmaximal, characteristic
2#13113386C211yesmaximal, characteristic
3#13113347C211yesmaximal, characteristic
4#13112729C211yesmaximal, characteristic
5#13112700C211yesmaximal, characteristic
6#13112692C211yesmaximal, characteristic
7C13×#2605C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C13×#400—21no—
10C13×#395—21no—
11C13×#391—21no—
12C13×#391—21no—
13C13×#387—21no—
14C13×#387—21no—
15C13×#383C2211yescharacteristic
16C4×C13×C4⋊C4C2211yescharacteristic
17C13×#376C2211yescharacteristic
18#11718587C2211yescharacteristic
19#11718587C2211yescharacteristic
20C4×#6099C2211yescharacteristic
21#11718115—21no—
22#11718115—21no—
23#11718044—21no—
24#11718044—21no—
25#11718044—21no—
26#11718044—21no—
27C22×Q8×C13—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C42×C13—21no—
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36#88180—21no—
37#88178—21no—
38#88178—21no—
39C2×#6099—21no—
40#88124—21no—
41#88123Q811yescharacteristic, complemented
42#88123Q811yescharacteristic, complemented
43C4×Dic26—21no—
44C4×Dic26—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
55C13×#95D411yescharacteristic
56C13×#95D411yescharacteristic
57C22⋊#1055—21no—
58C22⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61#88043—21no—
62#88043—21no—
63#88043—21no—
64C4×#1055—21no—
65#10379—131nomaximal, Sylow
66C2×Q8×C13—42no—
67C2×Q8×C13—42no—
68C2×Q8×C13—81no—
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—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—81no—
84C42×C13—41no—
85C42×C13—41no—
86C42×C13—42no—
87C42×C13C2×Q811yescharacteristic
88C42×C13#4111yescharacteristic
89C42×C13#4111yescharacteristic
90C42×C13#4111yescharacteristic
91C22⋊Dic13—41no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96#6101—41no—
97#6101—41no—
98C4×Dic13—41no—
99#6099—22no—
100#6099—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104#2605D1311yescharacteristic
105#1986—131no—
106#1515—131no—
107#1506—131no—
108#1300—131no—
109#1288—131no—
110#1285—131no—
111C23×C13#12011yescharacteristic
112Q8×C13—84no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
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—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13C22⋊Q811yescharacteristic
136C2×C4×C13C22⋊Q811yescharacteristic
137C2×C4×C13C22⋊Q811yescharacteristic
138C2×C4×C13#12411yescharacteristic
139C2×C4×C13#12411yescharacteristic
140C2×C4×C13#12411yescharacteristic
141C2×Dic13—41no—
142C2×Dic13—41no—
143Dic26—81no—
144Dic26—81no—
145#1055—42no—
146#1055—81no—
147#1055—81no—
148#533—131no—
149#432—131no—
150#432—131no—
151C4×M16—131no—
152#400—21no—
153#395—21no—
154#391—21no—
155#391—21no—
156#387—21no—
157#387—21no—
158#383C2×D1311yescharacteristic
159C4×C4⋊C4C2×D1311yescharacteristic
160#376C2×D1311yescharacteristic
161#339—261no—
162#339—261no—
163#328—261no—
164#328—261no—
165#328—261no—
166#328—261no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13#39311yescharacteristic
170C22×C13#45511yescharacteristic
171C22×C13#45611yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—42no—
179C4×C13—42no—
180C4×C13—81no—
181C4×C13—81no—
182C4×C13—81no—
183C4×C13—81no—
184Dic13—81no—
185Dic13—81no—
186C22×Q8—21no—
187C2×M16—261no—
188C4⋊Q8—131no—
189C4⋊Q8—131no—
190#125—261no—
191C22⋊Q8—261no—
192C22⋊Q8—261no—
193C4×Q8—261no—
194C4×Q8—261no—
195#117—261no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C42—21no—
201C2×C42C22⋊D1311yescharacteristic
202C2×C42C22⋊D1311yescharacteristic
203C2×C42C22×D1311yescharacteristic
204C4⋊C8—261no—
205C4⋊C8—261no—
206C22⋊C8—261no—
207C22⋊C8—261no—
208#97—261no—
209#97—261no—
210#97—261no—
211C4×C8—261no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95C22⋊D1311yescharacteristic
221#95C22⋊D1311yescharacteristic
222#95C22⋊D1311yescharacteristic
223#95C22⋊D1311yescharacteristic
224C2×C13—21no—
225C2×C13—21no—
226C2×C13#202811yescharacteristic
227C2×C13#203111yescharacteristic
228C2×C13#203111yescharacteristic
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—81no—
232C2×Q8—261no—
233C2×Q8—261no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4C2×C22⋊D1311yescharacteristic
241C22×C4C2×C22⋊D1311yescharacteristic
242C22×C4C2×C22⋊D1311yescharacteristic
243M16—262no—
244M16—521no—
245C2×C8—521no—
246C2×C8—521no—
247C2×C8—521no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—81no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C22⋊C4—521no—
259C42—41no—
260C42—41no—
261C42—42no—
262C42—521no—
263C42Q8×D1311yescharacteristic
264C42#613111yescharacteristic
265C42#613111yescharacteristic
266C42#613111yescharacteristic
267C13#1037911yescharacteristic, complemented, Sylow
268C23#8820711yescharacteristic
269Q8—84no—
270Q8—1041no—
271Q8—1041no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
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—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4#8820011yescharacteristic
297C2×C4#8820011yescharacteristic
298C2×C4#8820011yescharacteristic
299C2×C4#8820111yescharacteristic
300C2×C4#8820111yescharacteristic
301C2×C4#8820111yescharacteristic
302C8—522no—
303C8—1041no—
304C8—1041no—
305C22—21no—
306C22—21no—
307C22#1171889211yescharacteristic
308C22#1171890311yescharacteristic
309C22#1171890711yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—42no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4—1041no—
323C4—1041no—
324C2—21no—
325C2—21no—
326C2#1311599411yescharacteristic
327C2#1311600511yescharacteristic
328C2#1311600511yescharacteristic
subgroupG/H
centerC22#11718892
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2605C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#2605D13
hypocenterC13#10379
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2605

Complements

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

NH ≅ G/Ntype
41. #88123Q8semidirect
42. #88123Q8semidirect
267. C13#10379semidirect

Maximal subgroups

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

subgroupindex
#131157792
#131133862
#131133472
#131127292
#131127002
#131126922
C13×#26052
#1037913