Finite Group Databasebeta

← #15751132

Subgroups — #15751132

Order 3328.

462 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117405C211yesmaximal, characteristic
2#13114978C211yesmaximal, characteristic
3#13114688C211yesmaximal, characteristic
4#13112662C211yesmaximal, characteristic
5#13112661C211yesmaximal, characteristic
6#13112661C211yesmaximal, characteristic
7C13×#1272C211yesmaximal, characteristic
8C2×Q8×Dic13C411yescharacteristic
9C2×#88198C411yescharacteristic
10C2×#88141C411yescharacteristic
11C13×#391C2211yescharacteristic
12C2×#88055—21no—
13C2×#88054—21no—
14#11718637C411yescharacteristic
15C42×Dic13C2211yescharacteristic
16#11718590C2211yescharacteristic
17#11718310—21no—
18#11718310—21no—
19#11718308—21no—
20#11718308—21no—
21C13×#336C2211yescharacteristic
22C13×#336C2211yescharacteristic
23#11718142—21no—
24#11718142—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13C2×C411yescharacteristic
28C22×Dic26C2×C411yescharacteristic
29C22×C8×C13—21no—
30C22×C8×C13—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33Q8×Dic13—42no—
34#88198—22no—
35#88198—22no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13—21no—
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C2×C4×Dic13D411yescharacteristic
51C22×#1055—21no—
52C22×#1055—21no—
53#88141—42no—
54C13×#95—21no—
55C13×#95—21no—
56#88071—21no—
57#88071—21no—
58#88055—42no—
59#88054—24no—
60#7624—131nomaximal, Sylow
61C2×Q8×C13—21no—
62C2×Q8×C13—41no—
63C2×Q8×C13—41no—
64C2×Q8×C13M1612yes—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C22⋊C411yescharacteristic
76C2×Dic26—21no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C2×Dic26M1612yes—
80C2×C8×C13—22no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C13×C4⋊C4—41no—
87C42×C13—41no—
88C4⋊Dic13—42no—
89C4⋊Dic13—41no—
90#6101—24no—
91#6101—24no—
92#6101—42no—
93#6101—42no—
94#6101—42no—
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—22no—
100C4×Dic13—22no—
101C4×Dic13—41no—
102C4×Dic13—42no—
103C4×Dic13—42no—
104C4×Dic13SD1612yes—
105C4×Dic13Q1612yes—
106C2×#1055—22no—
107C2×#1055—41no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112C4×C4⋊Q8—131no—
113#1839—131no—
114#1767—131no—
115#1272—131no—
116#1272—131no—
117#1272—131no—
118#1272D1311yescharacteristic
119C23×C13C2×C22⋊C411yescharacteristic
120Q8×C13—42no—
121Q8×C13—42no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—22no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13C2×M1611yescharacteristic
135C2×C4×C13C2×M1611yescharacteristic
136C2×C4×C13C2×SD1611yescharacteristic
137C2×C4×C13C2×Q1611yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C2×C4×C13#13711yescharacteristic
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—22no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13#10012yes—
155C2×Dic13#10312yes—
156C2×Dic13#10312yes—
157C2×Dic13#10412yes—
158Dic26—42no—
159Dic26—42no—
160C8×C13—42no—
161C8×C13—81no—
162#1055—42no—
163#1055—81no—
164C2×C4⋊Q8—131no—
165C2×C4×Q8—131no—
166C2×C4×Q8—131no—
167C2×C4⋊C8—261no—
168C2×#97—261no—
169#391—131no—
170#391C2×D1311yescharacteristic
171#389—261no—
172#389—261no—
173#384—131no—
174C4×C4⋊C4—261no—
175C4×C4⋊C4—261no—
176C43—131no—
177#336—131no—
178#336—131no—
179#336—261no—
180#336—261no—
181#336C2×D1311yescharacteristic
182#336C2×D1311yescharacteristic
183C22×C13#40711yescharacteristic
184C22×C13#41011yescharacteristic
185C22×C13C2×#10011yescharacteristic
186C22×C13C2×#10311yescharacteristic
187C22×C13#41911yescharacteristic
188C22×C13C2×#10411yescharacteristic
189C22×C13#42111yescharacteristic
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—42no—
197C4×C13—81no—
198Dic13—22no—
199Dic13—22no—
200Dic13—22no—
201Dic13—22no—
202Dic13—42no—
203Dic13—81no—
204C22×Q8—131no—
205C22×Q8C4×D1311yescharacteristic
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—261no—
209C22×C8—261no—
210C4⋊Q8—262no—
211C4⋊Q8—262no—
212C4×Q8—522no—
213C4×Q8—522no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4C4×D1311yescharacteristic
222C2×C42—131no—
223C2×C42—131no—
224C2×C42—131no—
225C2×C42—131no—
226C2×C42—131no—
227C2×C42—131no—
228C2×C42—261no—
229C2×C42—261no—
230C2×C42C22×D1311yescharacteristic
231C4⋊C8—264no—
232#97—522no—
233#95—21no—
234#95—21no—
235#95—261no—
236#95—261no—
237C2×C13#146611yescharacteristic
238C2×C13#148711yescharacteristic
239C2×C13#149111yescharacteristic
240C2×C13#150311yescharacteristic
241C2×C13#151511yescharacteristic
242C2×C13#153011yescharacteristic
243C2×C13#154811yescharacteristic
244C2×Q8—21no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—132no—
248C2×Q8—261no—
249C2×Q8—521no—
250C2×Q8—521no—
251C2×Q8#609412yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—131no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4C2×C4×D1311yescharacteristic
261C22×C4D4×D1311yescharacteristic
262C22×C4D4×D1311yescharacteristic
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—262no—
270C2×C8—521no—
271C2×C8—521no—
272C2×C8—521no—
273C2×C8—521no—
274C2×C8—521no—
275C4⋊C4—41no—
276C4⋊C4—264no—
277C4⋊C4—264no—
278C4⋊C4—521no—
279C4⋊C4—522no—
280C4⋊C4—522no—
281C4⋊C4—522no—
282C4⋊C4—522no—
283C42—41no—
284C42—132no—
285C42—132no—
286C42—262no—
287C42—262no—
288C42—261no—
289C42—261no—
290C42—261no—
291C42—261no—
292C42—521no—
293C42—522no—
294C42—522no—
295C13#762411yescharacteristic, complemented, Sylow
296C23C22⋊C4×D1311yescharacteristic
297Q8—42no—
298Q8—42no—
299Q8—522no—
300Q8—522no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—132no—
314C2×C4—132no—
315C2×C4—132no—
316C2×C4—132no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—262no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4C2×#609411yescharacteristic
332C2×C4M16×D1311yescharacteristic
333C2×C4SD16×D1311yescharacteristic
334C2×C4#8816911yescharacteristic
335C2×C4Q16×D1311yescharacteristic
336C2×C4#8817211yescharacteristic
337C8—42no—
338C8—81no—
339C8—522no—
340C8—1041no—
341C22#1171838711yescharacteristic
342C22#1171840111yescharacteristic
343C22D13×#10011yescharacteristic
344C22D13×#10311yescharacteristic
345C22#1171846311yescharacteristic
346C22D13×#10411yescharacteristic
347C22#1171848211yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—81no—
356C4—262no—
357C4—262no—
358C4—262no—
359C4—262no—
360C4—522no—
361C4—1041no—
362C2#1311317511yescharacteristic
363C2#1311326311yescharacteristic
364C2#1311328111yescharacteristic
365C2#1311333311yescharacteristic
366C2#1311338511yescharacteristic
367C2#1311344511yescharacteristic
368C2#1311351511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1272C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1272D13
hypocenterC13#7624
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
295. C13#7624semidirect

Maximal subgroups

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

subgroupindex
#131174052
#131149782
#131146882
#131126622
#131126612
C13×#12722
#762413