Finite Group Databasebeta

← #15758566

Subgroups — #15758566

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718494C211yesmaximal, characteristic
2#13123183C211yesmaximal, characteristic
3#13114813C211yesmaximal, characteristic
4C2×#11718139C211yesmaximal, characteristic, complemented
5#13112720C211yesmaximal, characteristic, complemented
6#13112720C211yesmaximal, characteristic, complemented
7C2×C13×#332C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88200—21no—
10C2×C42×D13C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13#11718891—21no—
14C2×#88060—21no—
15C2×#88060—21no—
16C2×C8×Dic13—21no—
17#11718648—21no—
18#11718648C412yes—
19#11718634—21no—
20#11718634C412yes—
21#11718596C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24#11718494—22no—
25#11718494—22no—
26C13×#332—22no—
27#11718142—21no—
28#11718139—22no—
29C22×Q8×C13—21no—
30C22×C4×D13C2×C411yescharacteristic
31C22×C4×D13D411yescharacteristic
32C22×C4×D13D411yescharacteristic
33C22×C8×C13—21no—
34C22×C8×C13—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4C2×C412yes—
41C2×C42×C13C2311yescharacteristic
42#88200—42no—
43#88200—42no—
44C2×#6103—22no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13C2×C412yes—
48C2×#6101—22no—
49C2×C4×Dic13C2×C411yescharacteristic
50C2×C4×Dic13D411yescharacteristic
51C2×C4×Dic13D411yescharacteristic
52C22×#1055—21no—
53C22×#1055—21no—
54C42×D13—21no—
55C42×D13—21no—
56C42×D13—21no—
57C42×D13—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8—21no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8D412yes—
62#88071—22no—
63#88071—22no—
64#88060—24no—
65#88060—42no—
66C8×Dic13—24no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055D412yes—
71#9130—131nomaximal, Sylow
72C23×D13C22⋊C411yescharacteristic
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C22×C4×C13—22no—
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×Dic13—22no—
84C22×Dic13C22⋊C411yescharacteristic
85C22×Dic13C22⋊C411yescharacteristic
86C22×Dic13C22⋊C411yescharacteristic
87C2×C4×D13—21no—
88C2×C4×D13—21no—
89C2×C4×D13—21no—
90C2×C4×D13—21no—
91C2×C4×D13—21no—
92C2×C4×D13—21no—
93C2×C4×D13—21no—
94C2×C4×D13—21no—
95C2×C4×D13—21no—
96C2×C4×D13—21no—
97C2×C4×D13—21no—
98C2×C4×D13—21no—
99C2×C4×D13—22no—
100C2×C4×D13—41no—
101C2×C4×D13D812yes—
102C2×C4×D13SD1612yes—
103C2×C8×C13—22no—
104C2×C8×C13—41no—
105C2×C8×C13—41no—
106C2×C8×C13—41no—
107C2×C8×C13—41no—
108C2×C8×C13—41no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C42×C13C2×D411yescharacteristic
114C42×C13C2×D411yescharacteristic
115C42×C13#4111yescharacteristic
116C42×C13#4111yescharacteristic
117#6103—44no—
118C4⋊Dic13—41no—
119C4⋊Dic13—41no—
120C4⋊Dic13—41no—
121C4⋊Dic13—41no—
122C4⋊Dic13—42no—
123#6101—44no—
124C4×Dic13—21no—
125C4×Dic13—21no—
126C4×Dic13—21no—
127C4×Dic13—21no—
128C4×Dic13—21no—
129C4×Dic13—21no—
130C2×#1055—22no—
131C2×#1055—41no—
132C2×#1055—41no—
133C2×#1055—41no—
134C2×#1055—41no—
135C2×#1055—41no—
136C2×#431—131no—
137#2857—131no—
138#1797—131no—
139C2×#332—131no—
140C2×#332D1311yescharacteristic, complemented
141#1296—131no—
142#1296—131no—
143C23×C13C2×C22⋊C411yescharacteristic
144C22×D13—21no—
145C22×D13—21no—
146C22×D13—21no—
147C22×D13—21no—
148C22×D13—21no—
149C22×D13—21no—
150C22×D13#10212yes—
151Q8×C13—81no—
152Q8×C13—81no—
153Q8×C13—81no—
154Q8×C13—81no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13C4×D411yescharacteristic
161C2×C4×C13C4×D411yescharacteristic
162C2×C4×C13#12011yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12111yescharacteristic
165C2×C4×C13#12311yescharacteristic
166C2×C4×C13C2×D811yescharacteristic
167C2×C4×C13C2×SD1611yescharacteristic
168C2×C4×C13#13511yescharacteristic
169C2×C4×C13#13511yescharacteristic
170C2×C4×C13#13511yescharacteristic
171C2×C4×C13#13511yescharacteristic
172C2×C4×C13#13711yescharacteristic
173C2×C4×C13#13711yescharacteristic
174C2×Dic13—21no—
175C2×Dic13—21no—
176C2×Dic13—21no—
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—21no—
181C2×Dic13—42no—
182C2×Dic13—42no—
183C2×Dic13—42no—
184C2×Dic13#10112yes—
185C2×Dic13#10212yes—
186C4×D13—22no—
187C4×D13—22no—
188C4×D13—22no—
189C4×D13—22no—
190C4×D13—42no—
191C4×D13—42no—
192C4×D13—41no—
193C4×D13—41no—
194C4×D13—41no—
195C4×D13—41no—
196C8×C13—42no—
197C8×C13—81no—
198#1055—42no—
199#1055—81no—
200C2×C4⋊Q8C2×D1311yescharacteristic
201C2×C22⋊Q8—261no—
202C22×C42—131no—
203#431—262no—
204#431—262no—
205C2×C4⋊C8—131no—
206C2×C4⋊C8—131no—
207C2×C4⋊C8C2×D1311yescharacteristic
208C2×C4⋊C8C2×D1311yescharacteristic
209C2×C22⋊C8—261no—
210C2×C22⋊C8—261no—
211C2×C4×C8—261no—
212#391—261no—
213#389—132no—
214#389—261no—
215#384—131no—
216#380—132no—
217#380—261no—
218#336—261no—
219#332—22no—
220#332—262no—
221C22×C13#38611yescharacteristic
222C22×C13C2×#10111yescharacteristic
223C22×C13#41311yescharacteristic
224C22×C13C2×#10211yescharacteristic
225C22×C13#41611yescharacteristic
226C22×C13#41611yescharacteristic
227C22×C13#41911yescharacteristic
228C2×D13—22no—
229C2×D13—22no—
230C2×D13—22no—
231C2×D13—41no—
232C2×D13—41no—
233C2×D13—41no—
234C2×D13—41no—
235C4×C13—21no—
236C4×C13—21no—
237C4×C13—82no—
238C4×C13#45211yescharacteristic
239C4×C13#45211yescharacteristic
240C4×C13#46511yescharacteristic
241C4×C13#46511yescharacteristic
242C4×C13#46611yescharacteristic
243C4×C13#46611yescharacteristic
244C4×C13#48511yescharacteristic
245C4×C13#48511yescharacteristic
246Dic13—22no—
247Dic13—22no—
248Dic13—41no—
249Dic13—82no—
250C22×Q8—21no—
251C23×C4—131no—
252C23×C4—131no—
253C23×C4—131no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—261no—
257C22×C8—261no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C22⋊Q8—522no—
263C22⋊Q8—522no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—132no—
266C2×C4⋊C4—262no—
267C2×C4⋊C4—261no—
268C2×C4⋊C4—261no—
269C2×C4⋊C4C4×D1312yes—
270C2×C22⋊C4—262no—
271C2×C42—131no—
272C2×C42—131no—
273C2×C42—131no—
274C2×C42—261no—
275C2×C42—261no—
276C2×C42—261no—
277C2×C42—261no—
278C2×C42C22×D1311yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—132no—
283C4⋊C8—261no—
284C4⋊C8—261no—
285C4⋊C8—261no—
286C4⋊C8C22⋊D1312yes—
287C22⋊C8—264no—
288C22⋊C8—522no—
289C4×C8—264no—
290#95—262no—
291#95—262no—
292C2×C13#154011yescharacteristic
293C2×C13#154411yescharacteristic
294C2×C13#154611yescharacteristic
295C2×C13#155411yescharacteristic
296C2×C13#187311yescharacteristic
297C2×C13#189311yescharacteristic
298C2×C13#190111yescharacteristic
299D13—42no—
300C24—131no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C22×C4—22no—
308C22×C4—131no—
309C22×C4—131no—
310C22×C4—132no—
311C22×C4—132no—
312C22×C4—131no—
313C22×C4—262no—
314C22×C4—261no—
315C22×C4—261no—
316C22×C4—261no—
317C22×C4—261no—
318C22×C4—261no—
319C22×C4—261no—
320C22×C4—261no—
321C22×C4—261no—
322C22×C4—261no—
323C22×C4—261no—
324C22×C4—261no—
325C22×C4—261no—
326C22×C4—262no—
327C22×C4—521no—
328C22×C4C2×C4×D1311yescharacteristic
329C22×C4D4×D1311yescharacteristic
330C22×C4D4×D1311yescharacteristic
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—262no—
338C2×C8—521no—
339C2×C8—521no—
340C2×C8—521no—
341C2×C8—521no—
342C2×C8—521no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—522no—
348C4⋊C4—524no—
349C4⋊C4—521no—
350C4⋊C4—521no—
351C4⋊C4—521no—
352C4⋊C4—521no—
353C22⋊C4—524no—
354C42—261no—
355C42—261no—
356C42—261no—
357C42—261no—
358C42—261no—
359C42—261no—
360C42#612711yescharacteristic
361C42D4×D1311yescharacteristic
362C42#612911yescharacteristic
363C42C2×C22⋊D1311yescharacteristic
364C13#913011yescharacteristic, complemented, Sylow
365C23—132no—
366C23—261no—
367C23—261no—
368C23—261no—
369C23—261no—
370C23—261no—
371C23—261no—
372C23C22⋊C4×D1311yescharacteristic
373Q8—81no—
374Q8—81no—
375Q8—81no—
376Q8—81no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—132no—
383C2×C4—132no—
384C2×C4—261no—
385C2×C4—261no—
386C2×C4—261no—
387C2×C4—261no—
388C2×C4—262no—
389C2×C4—262no—
390C2×C4—262no—
391C2×C4—262no—
392C2×C4—261no—
393C2×C4—261no—
394C2×C4—261no—
395C2×C4—522no—
396C2×C4—522no—
397C2×C4—521no—
398C2×C4—521no—
399C2×C4—521no—
400C2×C4—521no—
401C2×C4—522no—
402C2×C4—522no—
403C2×C4—522no—
404C2×C4#8813511yescharacteristic
405C2×C4#8813711yescharacteristic
406C2×C4#8813811yescharacteristic
407C2×C4D8×D1311yescharacteristic
408C2×C4#8816611yescharacteristic
409C2×C4SD16×D1311yescharacteristic
410C2×C4#8816911yescharacteristic
411C2×C4#8817011yescharacteristic
412C2×C4#8817011yescharacteristic
413C2×C4#8817211yescharacteristic
414C2×C4#8817311yescharacteristic
415C2×C4C4×C22⋊D1311yescharacteristic
416C2×C4#8819111yescharacteristic
417C2×C4#8819211yescharacteristic
418C8—42no—
419C8—81no—
420C8—522no—
421C8—1041no—
422C22—262no—
423C22—262no—
424C22—262no—
425C22—521no—
426C22—521no—
427C22—521no—
428C22—521no—
429C22D13×#10111yescharacteristic
430C22#1171841211yescharacteristic
431C22D13×#10211yescharacteristic
432C22#1171843311yescharacteristic
433C22#1171846311yescharacteristic
434C22#1171846511yescharacteristic
435C22#1171861711yescharacteristic
436C4—21no—
437C4—21no—
438C4—82no—
439C4—262no—
440C4—262no—
441C4—521no—
442C4—1042no—
443C4#1171843611yescharacteristic
444C4#1171843911yescharacteristic
445C4#1171847511yescharacteristic
446C4#1171847611yescharacteristic
447C4#1171881811yescharacteristic
448C4#1171883211yescharacteristic
449C4#1171883411yescharacteristic
450C4#1171884811yescharacteristic
451C2—522no—
452C2#1311348411yescharacteristic
453C2#1311349911yescharacteristic
454C2#1311350611yescharacteristic
455C2#1311354311yescharacteristic
456C2#1311514511yescharacteristic
457C2#1311526111yescharacteristic
458C2#1311530111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#332C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenterC2×#332D13
hypocenterC13#9130
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
4. C2×#11718139C2semidirect
5. #13112720C2semidirect
6. #13112720C2semidirect
7. C2×C13×#332C2semidirect
140. C2×#332D13semidirect
364. C13#9130semidirect

Maximal subgroups

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

subgroupindex
C2×#117184942
#131231832
#131148132
C2×#117181392
#131127202
C2×C13×#3322
#913013