Finite Group Databasebeta

← #15755810

Subgroups — #15755810

Order 3328.

550 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×C22⋊D13C211yesmaximal, characteristic
2#13114861C211yesmaximal, characteristic, complemented
3#13114821C212yesmaximal
4#13112703C212yesmaximal, complemented
5C13×#1807C211yesmaximal, characteristic, complemented
6C23×C8×C13C2211yescharacteristic
7C2×C4×C22⋊D13C2211yescharacteristic
8C22×C8×D13C411yescharacteristic, complemented
9C2×C13×#106—21no—
10C13×#380C2212yes—
11#11718873C2212yes—
12C2×C22⋊#1055C2211yescharacteristic
13C8×C22⋊D13—21no—
14C8×C22⋊D13—21no—
15C8×C22⋊D13—21no—
16C8×C22⋊D13—21no—
17C2×#88060C411yescharacteristic, complemented
18C2×#88057—21no—
19C2×#88054C411yescharacteristic, complemented
20C2×C8×Dic13C411yescharacteristic, complemented
21C2×#88046—22no—
22C13×#340—21no—
23#11718143—21no—
24#11718119—22no—
25C23×C4×C13C2311yescharacteristic
26C22×C22⋊D13D411yescharacteristic
27C22×C4×D13C2×C411yescharacteristic
28C22×C8×C13—42no—
29C22×C8×C13C2×C411yescharacteristic
30C22×C8×C13C2×C411yescharacteristic
31C22×C8×C13D411yescharacteristic
32C22×C8×C13D411yescharacteristic
33C22×C8×C13D411yescharacteristic
34C22×C8×C13D411yescharacteristic
35C2×C13×C4⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C22⋊Dic13—22no—
38C2×C22⋊Dic13D411yescharacteristic
39C4×C22⋊D13—21no—
40C4×C22⋊D13—21no—
41C4×C22⋊D13—21no—
42C4×C22⋊D13—21no—
43C2×#6103Q811yescharacteristic
44C2×C4⋊Dic13—22no—
45C2×#6101Q811yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47C22×#1055C2×C411yescharacteristic
48C22×#1055C2×C411yescharacteristic
49C2×C8×D13—21no—
50C2×C8×D13—21no—
51C2×C8×D13—42no—
52C13×#106—42no—
53C13×#95—22no—
54#88071—22no—
55C22⋊#1055—21no—
56C22⋊#1055—21no—
57#88060—21no—
58#88060—21no—
59#88057—42no—
60#88054—21no—
61#88054—21no—
62C8×Dic13—21no—
63C8×Dic13—21no—
64#88046—44no—
65#8608—131nomaximal, Sylow
66C24×C13C2×D411yescharacteristic
67C23×D13C4⋊C411yescharacteristic
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—42no—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×Q811yescharacteristic
75C22×C4×C13#4111yescharacteristic
76C22×C4×C13#4111yescharacteristic
77C2×C22⋊D13—21no—
78C2×C22⋊D13—21no—
79C2×C22⋊D13—22no—
80C2×C22⋊D13SD1614yes—
81C22×Dic13—42no—
82C22×Dic13C4⋊C411yescharacteristic
83C22×Dic13C4⋊C411yescharacteristic
84C22×Dic13C4⋊C411yescharacteristic
85C2×C4×D13—21no—
86C2×C4×D13—21no—
87C2×C4×D13—41no—
88C2×C4×D13—41no—
89C2×C8×C13—22no—
90C2×C8×C13—22no—
91C2×C8×C13—22no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C2×C8×C13C22⋊C411yescharacteristic
96C2×C8×C13C22⋊C411yescharacteristic
97C2×C8×C13C22⋊C411yescharacteristic
98C2×C8×C13C22⋊C411yescharacteristic
99C13×C4⋊C4—42no—
100C13×C4⋊C4—42no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—42no—
103C22⋊Dic13—21no—
104C22⋊Dic13—21no—
105C22⋊Dic13—42no—
106C22⋊Dic13—42no—
107#6103—21no—
108#6103—21no—
109C4⋊Dic13—42no—
110C4⋊Dic13—42no—
111#6101—21no—
112#6101—21no—
113C4×Dic13—21no—
114C4×Dic13—21no—
115C2×#1055—21no—
116C2×#1055—21no—
117C2×#1055—41no—
118C2×#1055—41no—
119C8×D13—42no—
120C8×D13—42no—
121C2×C8×D4—131no—
122#1807—131no—
123#1807D1311yescharacteristic, complemented
124#1799—132no—
125#1289—132no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13C2×C4⋊C411yescharacteristic
129C23×C13#12111yescharacteristic
130C23×C13#12111yescharacteristic
131C23×C13C2×SD1612yes—
132C23×C13#13512yes—
133C22×D13—21no—
134C22×D13—21no—
135C22×D13—41no—
136C22×D13—41no—
137C22×D13#10612yescomplemented
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—82no—
148C2×C4×C13—82no—
149C2×C4×C13—82no—
150C2×C4×C13C2×C22⋊C411yescharacteristic
151C2×C4×C13#11711yescharacteristic
152C2×C4×C13C22⋊Q811yescharacteristic
153C2×C4×C13C22⋊Q811yescharacteristic
154C22⋊D13—24no—
155C22⋊D13—24no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—82no—
163C2×Dic13—82no—
164C2×Dic13—82no—
165C2×Dic13#10612yescomplemented
166C4×D13—42no—
167C4×D13—41no—
168C4×D13—41no—
169C8×C13—21no—
170C8×C13—21no—
171C8×C13—21no—
172C8×C13#9912yescomplemented
173#1055—41no—
174#1055—41no—
175C23×C8—131no—
176C23×C8C2×D1311yescharacteristic
177C2×C4×D4—131no—
178C8×D4—261no—
179C8×D4—261no—
180C8×D4—261no—
181C8×D4—261no—
182C2×#106—21no—
183C2×#106—261no—
184C2×C4⋊C8—131no—
185C2×#99—262no—
186C2×C22⋊C8—131no—
187C2×C22⋊C8—131no—
188C2×C4×C8—131no—
189#380—132no—
190#380C2×D1312yes—
191#342—262no—
192#340—21no—
193#340—261no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—42no—
201C22×C13—42no—
202C22×C13#38011yescharacteristic
203C22×C13C2×#10611yescharacteristic
204C22×C13#42711yescharacteristic
205C22×C13#46512yes—
206C22×C13#46512yes—
207C2×D13—22no—
208C2×D13—42no—
209C2×D13—41no—
210C2×D13—41no—
211C2×D13—42no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—162no—
216C4×C13C2×#9911yescharacteristic
217C4×C13#41011yescharacteristic
218Dic13—22no—
219Dic13—41no—
220Dic13—41no—
221Dic13—162no—
222C22×D4—131no—
223C23×C4—131no—
224C23×C4C22×D1311yescharacteristic
225C22×C8—42no—
226C22×C8—131no—
227C22×C8—131no—
228C22×C8—261no—
229C22×C8—261no—
230C22×C8—522no—
231C22×C8C4×D1311yescharacteristic
232C22×C8C4×D1311yescharacteristic
233C22×C8D5211yescharacteristic
234C22×C8D5211yescharacteristic
235C22×C8C22⋊D1311yescharacteristic
236C22×C8C22⋊D1311yescharacteristic
237C4×D4—261no—
238C4×D4—261no—
239C4×D4—261no—
240C4×D4—261no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—131no—
243C2×C4⋊C4—262no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—131no—
246C2×C22⋊C4—131no—
247C2×C22⋊C4—262no—
248C2×C42—131no—
249#106—42no—
250#106—522no—
251C4⋊C8—261no—
252C4⋊C8—261no—
253#99—524no—
254C22⋊C8—261no—
255C22⋊C8—261no—
256C22⋊C8—261no—
257C22⋊C8—261no—
258C4×C8—261no—
259C4×C8—261no—
260#95—22no—
261#95—262no—
262C2×C13—22no—
263C2×C13—22no—
264C2×C13—21no—
265C2×C13—21no—
266C2×C13#179911yescharacteristic
267C2×C13#180711yescharacteristic
268C2×C13#181211yescharacteristic
269D13—42no—
270C24—131no—
271C24D4×D1311yescharacteristic
272C2×D4—134no—
273C2×D4—261no—
274C2×D4—262no—
275C2×D4—261no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—42no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4—522no—
287C22×C4C2×C4×D1311yescharacteristic
288C22×C4C2×D5211yescharacteristic
289C22×C4#612911yescharacteristic
290C22×C4Q8×D1311yescharacteristic
291C22×C4#613111yescharacteristic
292C22×C4C2×C22⋊D1311yescharacteristic
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—261no—
300C2×C8—261no—
301C2×C8—522no—
302C2×C8—522no—
303C2×C8—521no—
304C2×C8—521no—
305C2×C8#610311yescharacteristic
306C2×C8#610311yescharacteristic
307C2×C8#610311yescharacteristic
308C2×C8#610311yescharacteristic
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—261no—
312C4⋊C4—261no—
313C4⋊C4—522no—
314C4⋊C4—522no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—261no—
318C22⋊C4—261no—
319C22⋊C4—261no—
320C22⋊C4—261no—
321C22⋊C4—522no—
322C22⋊C4—522no—
323C42—261no—
324C42—261no—
325C13#860811yescharacteristic, complemented, Sylow
326C23—41no—
327C23—41no—
328C23—132no—
329C23—261no—
330C23—261no—
331C23—521no—
332C23—521no—
333C23C4⋊C4×D1311yescharacteristic
334C23#8814911yescharacteristic
335C23SD16×D1312yes—
336C23#8817012yes—
337C23#8819211yescharacteristic
338D4—264no—
339D4—264no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—132no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—522no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—1042no—
363C2×C4—1042no—
364C2×C4—1042no—
365C2×C4#8814611yescharacteristic
366C2×C4#8815111yescharacteristic
367C2×C4C2×#610311yescharacteristic
368C2×C4#8820011yescharacteristic
369C8—21no—
370C8—21no—
371C8—21no—
372C8—521no—
373C8—521no—
374C8#8804612yescomplemented
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—42no—
382C22—42no—
383C22—262no—
384C22—522no—
385C22—522no—
386C22—521no—
387C22—521no—
388C22D13×#10611yescharacteristic
389C22#1171852111yescharacteristic
390C22#1171852512yes—
391C22#1171864811yescharacteristic
392C22#1171883212yes—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—162no—
397C4—262no—
398C4—521no—
399C4—521no—
400C4—2082no—
401C4C2×#8804611yescharacteristic
402C4#1171866711yescharacteristic
403C2—22no—
404C2—22no—
405C2—21no—
406C2—21no—
407C2—522no—
408C2#1311482111yescharacteristic
409C2#1311485811yescharacteristic
410C2#1311487911yescharacteristic
subgroupG/H
centerC22#11718648
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1807C2
socleC22×C13#380
prime radicalC22×C22⋊D13D4
cosocleC23×C4×C13C23
hypercenter#1807D13
hypocenterC13#8608
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
2. #13114861C2semidirect
4. #13112703C2semidirect
5. C13×#1807C2semidirect
8. C22×C8×D13C4semidirect
17. C2×#88060C4semidirect
19. C2×#88054C4semidirect
20. C2×C8×Dic13C4semidirect
123. #1807D13semidirect
137. C22×D13#106semidirect
165. C2×Dic13#106semidirect
172. C8×C13#99semidirect
325. C13#8608semidirect
374. C8#88046semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C22⋊D132
#131148612
#131148212
#131127032
C13×#18072
#860813