Finite Group Databasebeta

← #15752250

Subgroups — #15752250

Order 3328.

350 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 87 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#13116399C211yesmaximal, characteristic
2#13116399C211yesmaximal, characteristic
3#13116374C211yesmaximal, characteristic
4#13112662C211yesmaximal, characteristic
5#13112659C211yesmaximal, characteristic
6#13112659C211yesmaximal, characteristic
7C13×#2805C211yesmaximal, characteristic
8C13×#400—21no—
9C13×#400—21no—
10C13×#395—21no—
11C13×#391C2211yescharacteristic
12C13×#389—21no—
13C13×#389C2211yescharacteristic
14C13×#389C2211yescharacteristic
15C13×#387—21no—
16C13×#387—21no—
17C2×#88075—21no—
18C2×#88047—21no—
19#11718596C2211yescharacteristic
20#11718121—21no—
21#11718121—21no—
22#11718121—21no—
23#11718121—21no—
24#11718116C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C22×#1055—21no—
43C22×#1055—21no—
44C22×#1055—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×#95—21no—
54#88075—42no—
55#88047—42no—
56#7835—131nomaximal, Sylow
57C2×Q8×C13—21no—
58C2×Q8×C13—21no—
59C2×Q8×C13—41no—
60C2×Q8×C13—41no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—41no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—81no—
82C13×C4⋊C4—81no—
83C13×C4⋊C4Q1612yes—
84C42×C13—41no—
85C42×C13—81no—
86C4⋊Dic13—41no—
87C4⋊Dic13—42no—
88C4⋊Dic13—42no—
89C4⋊Dic13—41no—
90C2×#1055—22no—
91C2×#1055—41no—
92C2×#1055—41no—
93C2×#1055—41no—
94C2×#1055—41no—
95C2×#1055—41no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99#2805D1311yescharacteristic
100#2100—131no—
101#2100—131no—
102#2095—131no—
103#1272—131no—
104#1271—131no—
105#1271—131no—
106C23×C13#12011yescharacteristic
107Q8×C13—42no—
108Q8×C13—81no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—41no—
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×C13C2×Q1611yescharacteristic
134C2×C4×C13#13511yescharacteristic
135C2×C4×C13#13511yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C2×C4×C13#13711yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C2×Dic13—81no—
140C2×Dic13—81no—
141C2×Dic13—81no—
142#1055—42no—
143#1055—81no—
144#1055—81no—
145C2×#107—261no—
146C2×#103—261no—
147#400—21no—
148#400—21no—
149#395—21no—
150#391C2×D1311yescharacteristic
151#389—21no—
152#389C2×D1311yescharacteristic
153#389C2×D1311yescharacteristic
154#387—21no—
155#387—21no—
156#384—131no—
157#340—261no—
158#340—261no—
159#340—261no—
160#340—261no—
161#336—131no—
162#336—131no—
163#336—131no—
164C22×C13#45111yescharacteristic
165C22×C13#45211yescharacteristic
166C22×C13#45211yescharacteristic
167C22×C13#45311yescharacteristic
168C22×C13#45411yescharacteristic
169C22×C13#45411yescharacteristic
170C22×C13#45811yescharacteristic
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—42no—
178C4×C13—81no—
179C4×C13—81no—
180C4×C13—81no—
181C4×C13—81no—
182C4×C13—81no—
183Dic13—161no—
184C22×Q8C22⋊D1311yescharacteristic
185C22×C8—261no—
186C22×C8—261no—
187C22×C8—261no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4C22⋊D1311yescharacteristic
196C2×C4⋊C4C22⋊D1311yescharacteristic
197C2×C4⋊C4C22⋊D1311yescharacteristic
198C2×C4⋊C4C22⋊D1311yescharacteristic
199C2×C4⋊C4C22⋊D1311yescharacteristic
200C2×C42—21no—
201C2×C42C22×D1311yescharacteristic
202#107—522no—
203#103—522no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213C2×C13#161511yescharacteristic
214C2×C13#161711yescharacteristic
215C2×C13#161811yescharacteristic
216C2×C13#163211yescharacteristic
217C2×C13#163611yescharacteristic
218C2×C13#163811yescharacteristic
219C2×C13#165711yescharacteristic
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8—41no—
223C2×Q8—41no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—521no—
231C22×C4C2×C22⋊D1311yescharacteristic
232C22×C4C2×C22⋊D1311yescharacteristic
233C22×C4C2×C22⋊D1311yescharacteristic
234C2×C8—262no—
235C2×C8—521no—
236C2×C8—521no—
237C2×C8—521no—
238C2×C8—521no—
239C2×C8—521no—
240C2×C8—521no—
241C2×C8—521no—
242C2×C8—521no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—81no—
254C4⋊C4—81no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—522no—
258C4⋊C4—522no—
259C4⋊C4#610712yes—
260C42—41no—
261C42—81no—
262C13#783511yescharacteristic, complemented, Sylow
263C23#8820711yescharacteristic
264Q8—42no—
265Q8—81no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
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—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—1041no—
291C2×C4—1041no—
292C2×C4—1041no—
293C2×C4#8819611yescharacteristic
294C2×C4C2×#610711yescharacteristic
295C2×C4#8820411yescharacteristic
296C2×C4#8820411yescharacteristic
297C2×C4#8820511yescharacteristic
298C2×C4#8820511yescharacteristic
299C8—522no—
300C8—1041no—
301C8—1041no—
302C22#1171888911yescharacteristic
303C22#1171890011yescharacteristic
304C22#1171890011yescharacteristic
305C22#1171890211yescharacteristic
306C22#1171890411yescharacteristic
307C22#1171890611yescharacteristic
308C22#1171890611yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—81no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—2081no—
322C2#1311386711yescharacteristic
323C2#1311387811yescharacteristic
324C2#1311388411yescharacteristic
325C2#1311397011yescharacteristic
326C2#1311399411yescharacteristic
327C2#1311400811yescharacteristic
328C2#1311413411yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2805C2
socle, prime radicalC23×C13#120
hypercenter#2805D13
hypocenterC13#7835
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2805

Complements

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

NH ≅ G/Ntype
262. C13#7835semidirect

Maximal subgroups

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

subgroupindex
#131163992
#131163742
#131126622
#131126592
C13×#28052
#783513