Finite Group Databasebeta

← #15755774

Subgroups — #15755774

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718346C211yesmaximal, characteristic
2#13114813C211yesmaximal, characteristic
3#13114813C211yesmaximal, characteristic
4C2×#11718071C211yesmaximal, characteristic, complemented
5C2×#11718072C211yesmaximal, characteristic, complemented
6#13112671C211yesmaximal, characteristic, complemented
7C13×#1277C211yesmaximal, characteristic, complemented
8C2×C42×D13C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C2×#88060—21no—
13C2×#88060—21no—
14C2×#88060C411yescharacteristic
15C2×#88060C411yescharacteristic
16C2×#88054C411yescharacteristic
17C2×#88054C411yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21#11718346—22no—
22#11718346—22no—
23#11718142—21no—
24#11718142—21no—
25#11718072—22no—
26#11718071—22no—
27C22×C4×D13C2×C411yescharacteristic
28C22×C4×D13D411yescharacteristic
29C22×C4×D13Q811yescharacteristic
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C22×C8×C13C2×C411yescharacteristic
33C22×C8×C13C2×C411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13Q811yescharacteristic
38C22×#1055—21no—
39C22×#1055—21no—
40C22×#1055C2×C411yescharacteristic
41C22×#1055C2×C411yescharacteristic
42C42×D13—21no—
43C42×D13—21no—
44C42×D13—21no—
45C42×D13—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C4×C8×C13—21no—
51C4×C8×C13—21no—
52#88060—22no—
53#88060—22no—
54#88060—42no—
55#88060—42no—
56#88054—22no—
57#88054—22no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4×#1055D412yes—
63C4×#1055D412yes—
64#8600—131nomaximal, Sylow
65C23×D13C4⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×Q811yescharacteristic
69C22×Dic13C4⋊C411yescharacteristic
70C22×Dic13C4⋊C411yescharacteristic
71C22×Dic13C4⋊C411yescharacteristic
72C2×C4×D13—22no—
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13—22no—
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×C4×D13—21no—
83C2×C4×D13—21no—
84C2×C4×D13—21no—
85C2×C4×D13—21no—
86C2×C4×D13—21no—
87C2×C4×D13—21no—
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13—21no—
93C2×C8×C13—21no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C42×C13C2×D411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C42×C13#4111yescharacteristic
103C42×C13#4111yescharacteristic
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108C4×Dic13—21no—
109C4×Dic13—21no—
110C2×#1055—21no—
111C2×#1055—21no—
112C2×#1055—21no—
113C2×#1055—21no—
114C2×#1055—41no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—41no—
119C2×#1055—41no—
120C2×#1055C22⋊C412yes—
121C2×#1055C22⋊C412yes—
122C2×#431—131no—
123#1797—131no—
124#1797—131no—
125C2×#335—131no—
126C2×#334—131no—
127#1277—131no—
128#1277D1311yescharacteristic, complemented
129C23×C13C2×C4⋊C411yescharacteristic
130C22×D13—21no—
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—21no—
134C22×D13—21no—
135C22×D13—21no—
136C22×D13#10812yes—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13C2×C22⋊C411yescharacteristic
140C2×C4×C13#11711yescharacteristic
141C2×C4×C13#12111yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13C22⋊Q811yescharacteristic
144C2×C4×C13C22⋊Q811yescharacteristic
145C2×C4×C13#13111yescharacteristic
146C2×C4×C13#13111yescharacteristic
147C2×C4×C13#13111yescharacteristic
148C2×C4×C13#13111yescharacteristic
149C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C13#13711yescharacteristic
152C2×C4×C13#13711yescharacteristic
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13#10812yes—
162C4×D13—24no—
163C4×D13—24no—
164C4×D13—41no—
165C4×D13—41no—
166C4×D13—41no—
167C4×D13—41no—
168C4×D13—41no—
169C4×D13—41no—
170C4×D13—41no—
171C4×D13—41no—
172C8×C13—41no—
173C8×C13—41no—
174C8×C13—81no—
175C8×C13—81no—
176#1055—22no—
177#1055—22no—
178#1055—81no—
179#1055—81no—
180C22×C42—131no—
181#431—262no—
182#431—262no—
183C2×C4⋊C8—131no—
184C2×C4⋊C8—131no—
185C2×C4⋊C8—131no—
186C2×C4⋊C8—131no—
187C2×C4⋊C8C2×D1311yescharacteristic
188C2×C4⋊C8C2×D1311yescharacteristic
189C2×C22⋊C8—131no—
190C2×C22⋊C8—131no—
191C2×C22⋊C8—261no—
192C2×C22⋊C8—261no—
193C2×C4×C8—131no—
194C2×C4×C8C2×D1311yescharacteristic
195#336—261no—
196#336—261no—
197#335—262no—
198#334—262no—
199C22×C13#38011yescharacteristic
200C22×C13#42411yescharacteristic
201C22×C13#42411yescharacteristic
202C22×C13#42811yescharacteristic
203C22×C13#42811yescharacteristic
204C22×C13C2×#10811yescharacteristic
205C22×C13C2×#10811yescharacteristic
206C2×D13—22no—
207C2×D13—22no—
208C2×D13—22no—
209C2×D13—41no—
210C2×D13—41no—
211C2×D13—41no—
212C2×D13—41no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13#40811yescharacteristic
216C4×C13#40811yescharacteristic
217C4×C13#43311yescharacteristic
218C4×C13#43311yescharacteristic
219C4×C13#46811yescharacteristic
220C4×C13#46811yescharacteristic
221C4×C13#46911yescharacteristic
222C4×C13#47011yescharacteristic
223Dic13—22no—
224Dic13—41no—
225Dic13—41no—
226C23×C4—131no—
227C23×C4—131no—
228C23×C4—131no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—131no—
232C22×C8—131no—
233C22×C8—261no—
234C22×C8—261no—
235C22×C8C4×D1311yescharacteristic
236C22×C8C4×D1311yescharacteristic
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—261no—
241C2×C42—261no—
242C2×C42—261no—
243C2×C42—261no—
244C2×C42C22×D1311yescharacteristic
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—262no—
250C4⋊C8—262no—
251C4⋊C8—261no—
252C4⋊C8—261no—
253C4⋊C8—261no—
254C4⋊C8—261no—
255C22⋊C8—262no—
256C22⋊C8—262no—
257C22⋊C8—522no—
258C22⋊C8—522no—
259C4×C8—21no—
260C4×C8—21no—
261C4×C8—132no—
262C4×C8—132no—
263C2×C13#157311yescharacteristic
264C2×C13#157311yescharacteristic
265C2×C13#157411yescharacteristic
266C2×C13#157411yescharacteristic
267C2×C13#179811yescharacteristic
268C2×C13#180911yescharacteristic
269C2×C13#181011yescharacteristic
270D13—42no—
271C24—131no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—262no—
276C22×C4—262no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—261no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4—261no—
291C22×C4C2×C4×D1311yescharacteristic
292C22×C4D4×D1311yescharacteristic
293C22×C4Q8×D1311yescharacteristic
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—132no—
307C2×C8—132no—
308C2×C8—261no—
309C2×C8—261no—
310C2×C8—261no—
311C2×C8—261no—
312C2×C8—521no—
313C2×C8—521no—
314C2×C8—521no—
315C2×C8—521no—
316C2×C8—521no—
317C2×C8—521no—
318C42—261no—
319C42—261no—
320C42—261no—
321C42—261no—
322C42—261no—
323C42—261no—
324C42#612711yescharacteristic
325C42#612711yescharacteristic
326C42D4×D1311yescharacteristic
327C42D4×D1311yescharacteristic
328C13#860011yescharacteristic, complemented, Sylow
329C23—132no—
330C23—261no—
331C23—261no—
332C23—261no—
333C23—261no—
334C23—261no—
335C23—261no—
336C23C4⋊C4×D1311yescharacteristic
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—132no—
340C2×C4—264no—
341C2×C4—264no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—521no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4#8812611yescharacteristic
359C2×C4C22⋊C4×D1311yescharacteristic
360C2×C4#8813811yescharacteristic
361C2×C4#8813811yescharacteristic
362C2×C4#8815011yescharacteristic
363C2×C4#8815011yescharacteristic
364C2×C4#8815511yescharacteristic
365C2×C4#8815511yescharacteristic
366C2×C4#8816111yescharacteristic
367C2×C4#8816111yescharacteristic
368C2×C4#8816511yescharacteristic
369C2×C4#8816811yescharacteristic
370C2×C4#8816911yescharacteristic
371C2×C4#8817211yescharacteristic
372C8—41no—
373C8—41no—
374C8—81no—
375C8—81no—
376C8—262no—
377C8—262no—
378C8—1041no—
379C8—1041no—
380C22—262no—
381C22—262no—
382C22—262no—
383C22—521no—
384C22—521no—
385C22—521no—
386C22—521no—
387C22#1171832811yescharacteristic
388C22#1171850011yescharacteristic
389C22#1171850011yescharacteristic
390C22#1171852211yescharacteristic
391C22#1171854211yescharacteristic
392C22D13×#10811yescharacteristic
393C22D13×#10811yescharacteristic
394C4—21no—
395C4—21no—
396C4—262no—
397C4—521no—
398C4—521no—
399C4#1171835111yescharacteristic
400C4#1171837011yescharacteristic
401C4#1171838811yescharacteristic
402C4#1171838811yescharacteristic
403C4#1171844111yescharacteristic
404C4#1171844311yescharacteristic
405C4#1171847311yescharacteristic
406C4#1171847711yescharacteristic
407C2—522no—
408C2#1311361811yescharacteristic
409C2#1311362011yescharacteristic
410C2#1311362311yescharacteristic
411C2#1311362611yescharacteristic
412C2#1311481911yescharacteristic
413C2#1311486811yescharacteristic
414C2#1311487311yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1277C2
socleC23×C13C2×C4⋊C4
prime radicalC23×D13C4⋊C4
cosocleC2×C42×C13C23
hypercenter#1277D13
hypocenterC13#8600
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
4. C2×#11718071C2semidirect
5. C2×#11718072C2semidirect
6. #13112671C2semidirect
7. C13×#1277C2semidirect
128. #1277D13semidirect
328. C13#8600semidirect

Maximal subgroups

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

subgroupindex
C2×#117183462
#131148132
C2×#117180712
C2×#117180722
#131126712
C13×#12772
#860013