Finite Group Databasebeta

← #15763023

Subgroups — #15763023

Order 3328.

388 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123221C211yesmaximal, characteristic
2#13114690C211yesmaximal, characteristic
3#13114584C211yesmaximal, characteristic
4#13112718C211yesmaximal, characteristic
5#13112718C211yesmaximal, characteristic
6#13112717C211yesmaximal, characteristic
7C13×#1295C211yesmaximal, characteristic
8C2×C13×#97C2211yescharacteristic
9C2×C13×#97C2211yescharacteristic
10C13×#382C2211yescharacteristic
11C2×#88054—21no—
12#11718646C411yescharacteristic
13#11718646C411yescharacteristic
14#11718634C411yescharacteristic
15#11718634C411yescharacteristic
16#11718597C2211yescharacteristic
17C42×Dic13C2211yescharacteristic
18C2×#88043C2211yescharacteristic
19C2×#88043C2211yescharacteristic
20#11718316—21no—
21#11718316—21no—
22#11718315—21no—
23#11718315—21no—
24#11718142—21no—
25#11718142—21no—
26#11718142—21no—
27C22×C8×C13—21no—
28C22×C8×C13—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C22×#1055—21no—
45C22×#1055—21no—
46C13×#97—21no—
47C13×#97—21no—
48C13×#97—21no—
49C13×#97Q812yes—
50C13×#95—21no—
51C13×#95—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88054—24no—
59#88043—21no—
60#88043—21no—
61#88043—21no—
62#88043Q812yes—
63#9893—131nomaximal, Sylow
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13C22⋊C411yescharacteristic
75C2×C8×C13—22no—
76C2×C8×C13—22no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C42×C13C2×Q811yescharacteristic
84C42×C13C2×Q811yescharacteristic
85C42×C13#4111yescharacteristic
86C42×C13#4111yescharacteristic
87C4⋊Dic13—42no—
88C4⋊Dic13—42no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91#6101—42no—
92#6101—42no—
93C4×Dic13—22no—
94C4×Dic13—41no—
95C4×Dic13—41no—
96C4×Dic13—41no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99C2×#1055—22no—
100C2×#1055—22no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105#2864—131no—
106#1767—131no—
107#1745—131no—
108#1295—131no—
109#1295—131no—
110#1295—131no—
111#1295D1311yescharacteristic
112C23×C13C2×C22⋊C411yescharacteristic
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
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×C13C4×Q811yescharacteristic
126C2×C4×C13C4×Q811yescharacteristic
127C2×C4×C13C22⋊Q811yescharacteristic
128C2×C4×C13C22⋊Q811yescharacteristic
129C2×C4×C13#12411yescharacteristic
130C2×C4×C13C4⋊Q811yescharacteristic
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13#10412yes—
149C8×C13—42no—
150C8×C13—42no—
151#1055—42no—
152#1055—42no—
153C2×C4⋊C8—261no—
154C2×#97—131no—
155C2×#97—131no—
156C2×#97C2×D1311yescharacteristic
157C2×#97C2×D1311yescharacteristic
158#389—131no—
159#389—131no—
160#389—131no—
161#389—131no—
162#387—261no—
163#387—261no—
164#387—261no—
165#387—261no—
166#382—131no—
167#382C2×D1311yescharacteristic
168C43—131no—
169#336—261no—
170#336—261no—
171#336—261no—
172C22×C13#39111yescharacteristic
173C22×C13#41311yescharacteristic
174C22×C13#41311yescharacteristic
175C22×C13C2×#10411yescharacteristic
176C22×C13#42111yescharacteristic
177C22×C13#42111yescharacteristic
178C22×C13#42111yescharacteristic
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—81no—
186C4×C13—81no—
187Dic13—22no—
188Dic13—41no—
189Dic13—41no—
190Dic13—41no—
191Dic13—81no—
192Dic13—81no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—261no—
196C22×C8—261no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4C4×D1311yescharacteristic
204C2×C4⋊C4C4×D1311yescharacteristic
205C2×C42—131no—
206C2×C42—131no—
207C2×C42—131no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42C22×D1311yescharacteristic
212C4⋊C8—264no—
213#97—21no—
214#97—21no—
215#97—21no—
216#97—132no—
217#97—261no—
218#97—261no—
219#97—261no—
220#97Dic2612yes—
221#95—21no—
222#95—21no—
223#95—261no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228#95—261no—
229C2×C13#152911yescharacteristic
230C2×C13#153211yescharacteristic
231C2×C13#153511yescharacteristic
232C2×C13#153511yescharacteristic
233C2×C13#198611yescharacteristic
234C2×C13#199511yescharacteristic
235C2×C13#199811yescharacteristic
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4C2×C4×D1311yescharacteristic
245C22×C4D4×D1311yescharacteristic
246C22×C4D4×D1311yescharacteristic
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—262no—
254C2×C8—262no—
255C2×C8—521no—
256C2×C8—521no—
257C2×C8—521no—
258C2×C8—521no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—522no—
264C4⋊C4—522no—
265C4⋊C4—522no—
266C4⋊C4—522no—
267C42—262no—
268C42—521no—
269C42—521no—
270C42—521no—
271C42—521no—
272C42—521no—
273C42C2×Dic2611yescharacteristic
274C42#612711yescharacteristic
275C42#612911yescharacteristic
276C42Q8×D1311yescharacteristic
277C13#989311yescharacteristic, complemented, Sylow
278C23C22⋊C4×D1311yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—132no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4C4×Dic2611yescharacteristic
310C2×C4#8813211yescharacteristic
311C2×C4#8813911yescharacteristic
312C2×C4#8814111yescharacteristic
313C2×C4#8814211yescharacteristic
314C2×C4#8815011yescharacteristic
315C8—42no—
316C8—42no—
317C8—522no—
318C8—522no—
319C22#1171830711yescharacteristic
320C22#1171840611yescharacteristic
321C22#1171841211yescharacteristic
322C22D13×#10411yescharacteristic
323C22#1171848211yescharacteristic
324C22#1171848211yescharacteristic
325C22#1171848211yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—81no—
333C4—81no—
334C4—262no—
335C4—521no—
336C4—521no—
337C4—521no—
338C4—1041no—
339C4—1041no—
340C2#1311344011yescharacteristic
341C2#1311345511yescharacteristic
342C2#1311346411yescharacteristic
343C2#1311346611yescharacteristic
344C2#1311577811yescharacteristic
345C2#1311581511yescharacteristic
346C2#1311582711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1295C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1295D13
hypocenterC13#9893
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
277. C13#9893semidirect

Maximal subgroups

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

subgroupindex
#131232212
#131146902
#131145842
#131127182
#131127172
C13×#12952
#989313