Finite Group Databasebeta

← #15766332

Subgroups — #15766332

Order 3328.

520 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119832C211yesmaximal, characteristic
2#13115798C211yesmaximal, characteristic, complemented
3#13115595C211yesmaximal, characteristic, complemented
4#13114837C211yesmaximal, characteristic
5C2×#11718075C211yesmaximal, characteristic
6#13112675C211yesmaximal, characteristic, complemented
7C2×C13×#332C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88201—21no—
10C2×C4×D52C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13#11718891—21no—
14C2×#88061—21no—
15C2×#88058—21no—
16#11718654—22no—
17#11718648—21no—
18#11718648—21no—
19#11718596C2211yescharacteristic
20C4×C4⋊Dic13C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22C13×#332—22no—
23#11718143—21no—
24#11718143—21no—
25#11718121—22no—
26#11718075—22no—
27C22×Q8×C13—21no—
28C22×D52D411yescharacteristic
29C22×C4×D13—21no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4D412yes—
38C2×C42×C13C2311yescharacteristic
39#88201—42no—
40#88201—42no—
41C2×#6103—22no—
42C2×#6103—22no—
43C2×#6103—21no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13D411yescharacteristic
48C2×C4⋊Dic13D411yescharacteristic
49C2×C4⋊Dic13D411yescharacteristic
50C2×C4×Dic13—21no—
51C22×#1055—21no—
52C4×D52—21no—
53C4×D52—21no—
54C4×D52—21no—
55C4×D52—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8D412yes—
60#88071—22no—
61#88071—22no—
62#88071—21no—
63#88061—42no—
64#88058—42no—
65C4×#1055—21no—
66C4×#1055—21no—
67#10416—131nomaximal, Sylow
68C23×D13—21no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C22×C4×C13—22no—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—41no—
83C2×D52—21no—
84C2×D52—21no—
85C2×D52—21no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52D812yes—
89C2×C4×D13—41no—
90C2×C4×D13—41no—
91C2×C4×D13—41no—
92C2×C4×D13—41no—
93C2×C4×D13—41no—
94C2×C4×D13—41no—
95C2×C8×C13—22no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C42×C13C2×D411yescharacteristic
106C42×C13#4111yescharacteristic
107C42×C13#4111yescharacteristic
108C42×C13#4111yescharacteristic
109#6103—44no—
110#6103—44no—
111#6103—41no—
112#6103—41no—
113C4⋊Dic13—21no—
114C4⋊Dic13—21no—
115C4⋊Dic13—21no—
116C4⋊Dic13—21no—
117C4⋊Dic13—21no—
118C4⋊Dic13—21no—
119C4⋊Dic13—42no—
120C4⋊Dic13—41no—
121C4⋊Dic13—41no—
122C4⋊Dic13—41no—
123C4⋊Dic13—41no—
124C4×Dic13—41no—
125C4×Dic13—41no—
126C2×#1055—22no—
127C2×#1055—41no—
128C2×#1055—41no—
129#2547—131no—
130#1990—131no—
131#1947—131no—
132#1802—131no—
133C2×#332D1311yescharacteristic, complemented
134C2×D4⋊C8—131no—
135#1279—131no—
136C23×C13#12011yescharacteristic
137C22×D13—22no—
138C22×D13—41no—
139C22×D13—41no—
140C22×D13—41no—
141C22×D13—41no—
142C22×D13—41no—
143C22×D13—41no—
144Q8×C13—81no—
145Q8×C13—81no—
146Q8×C13—81no—
147Q8×C13—81no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13#12111yescharacteristic
154C2×C4×C13#12111yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13#12311yescharacteristic
157C2×C4×C13#12311yescharacteristic
158C2×C4×C13#12411yescharacteristic
159C2×C4×C13C2×D811yescharacteristic
160C2×C4×C13#13511yescharacteristic
161C2×C4×C13#13511yescharacteristic
162C2×C4×C13#13511yescharacteristic
163C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C13#13711yescharacteristic
166C2×C4×C13#13711yescharacteristic
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—41no—
171C2×Dic13—41no—
172C2×Dic13—41no—
173C2×Dic13—41no—
174C2×Dic13—41no—
175C2×Dic13—41no—
176C2×Dic13—81no—
177C2×Dic13—81no—
178C2×Dic13—81no—
179D52—22no—
180D52—22no—
181D52—41no—
182D52—41no—
183C4×D13—81no—
184C4×D13—81no—
185C4×D13—81no—
186C4×D13—81no—
187C8×C13—42no—
188C8×C13—81no—
189#1055—42no—
190C2×C4⋊Q8C2×D1311yescharacteristic
191C2×#124—261no—
192C2×C4×D4—131no—
193C2×#107—261no—
194C2×C4⋊C8C2×D1311yescharacteristic
195C2×C4⋊C8C2×D1311yescharacteristic
196C2×#102—261no—
197C2×C4×C8—131no—
198#397—262no—
199#391—261no—
200#384—131no—
201#380—261no—
202#380—261no—
203C4×C4⋊C4—131no—
204#340—261no—
205#340—261no—
206#340—262no—
207#332—22no—
208D4⋊C8—262no—
209C22×C13#39411yescharacteristic
210C22×C13#44711yescharacteristic
211C22×C13#44911yescharacteristic
212C22×C13#45211yescharacteristic
213C22×C13#45211yescharacteristic
214C22×C13#45411yescharacteristic
215C22×C13#45611yescharacteristic
216C2×D13—42no—
217C2×D13—42no—
218C2×D13—42no—
219C2×D13—81no—
220C2×D13—81no—
221C2×D13—81no—
222C2×D13—81no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—82no—
226C4×C13#46311yescharacteristic
227C4×C13#46411yescharacteristic
228C4×C13#46611yescharacteristic
229C4×C13#46811yescharacteristic
230C4×C13#48011yescharacteristic
231C4×C13#48211yescharacteristic
232C4×C13#48811yescharacteristic
233C4×C13#48911yescharacteristic
234Dic13—81no—
235Dic13—81no—
236Dic13—81no—
237Dic13—161no—
238C22×Q8—21no—
239C22×D4—131no—
240C23×C4—261no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—261no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248#124—522no—
249#124—522no—
250C4×D4—261no—
251C4×D4—261no—
252C4×D4—261no—
253C4×D4—261no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—131no—
256C2×C4⋊C4—131no—
257C2×C4⋊C4—131no—
258C2×C4⋊C4—261no—
259C2×C4⋊C4—261no—
260C2×C4⋊C4—261no—
261C2×C4⋊C4D5212yes—
262C2×C22⋊C4—262no—
263C2×C22⋊C4—262no—
264C2×C22⋊C4—261no—
265C2×C42—261no—
266C2×C42C22×D1311yescharacteristic
267#107—522no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8C22⋊D1312yes—
272#102—522no—
273C4×C8—261no—
274C4×C8—261no—
275#95—262no—
276#95—262no—
277#95—261no—
278C2×C13#162511yescharacteristic
279C2×C13#163811yescharacteristic
280C2×C13#164711yescharacteristic
281C2×C13#165211yescharacteristic
282C2×C13#203311yescharacteristic
283C2×C13#203811yescharacteristic
284C2×C13#204211yescharacteristic
285D13—82no—
286C24—261no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×D4—132no—
294C2×D4—261no—
295C2×D4—261no—
296C2×D4—261no—
297C2×D4—261no—
298C2×D4—261no—
299C22×C4—22no—
300C22×C4—261no—
301C22×C4—261no—
302C22×C4—261no—
303C22×C4—521no—
304C22×C4—521no—
305C22×C4—521no—
306C22×C4—521no—
307C22×C4—521no—
308C22×C4—521no—
309C22×C4—521no—
310C22×C4C2×D5211yescharacteristic
311C22×C4D4×D1311yescharacteristic
312C22×C4D4×D1311yescharacteristic
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—262no—
320C2×C8—521no—
321C2×C8—521no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—261no—
327C4⋊C4—261no—
328C4⋊C4—261no—
329C4⋊C4—261no—
330C4⋊C4—261no—
331C4⋊C4—261no—
332C4⋊C4—522no—
333C4⋊C4—521no—
334C4⋊C4—521no—
335C4⋊C4—521no—
336C4⋊C4—521no—
337C22⋊C4—524no—
338C22⋊C4—524no—
339C22⋊C4—521no—
340C22⋊C4—521no—
341C42—521no—
342C42—521no—
343C42#612711yescharacteristic
344C42#612911yescharacteristic
345C42#612911yescharacteristic
346C42C2×C22⋊D1311yescharacteristic
347C13#1041611yescharacteristic, complemented, Sylow
348C23—262no—
349C23—521no—
350C23—521no—
351C23—521no—
352C23—521no—
353C23—521no—
354C23—521no—
355C23#8813611yescharacteristic
356Q8—81no—
357Q8—81no—
358Q8—81no—
359Q8—81no—
360D4—262no—
361D4—262no—
362D4—521no—
363D4—521no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—521no—
370C2×C4—521no—
371C2×C4—521no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4—521no—
375C2×C4—521no—
376C2×C4—521no—
377C2×C4—521no—
378C2×C4—1041no—
379C2×C4—1041no—
380C2×C4—1041no—
381C2×C4—1041no—
382C2×C4—1041no—
383C2×C4—1041no—
384C2×C4—1041no—
385C2×C4#8813711yescharacteristic
386C2×C4#8813911yescharacteristic
387C2×C4#8814011yescharacteristic
388C2×C4D8×D1311yescharacteristic
389C2×C4#8816611yescharacteristic
390C2×C4#8816811yescharacteristic
391C2×C4#8816811yescharacteristic
392C2×C4#8816911yescharacteristic
393C2×C4#8817011yescharacteristic
394C2×C4#8817211yescharacteristic
395C2×C4#8817311yescharacteristic
396C2×C4#8818411yescharacteristic
397C2×C4#8819211yescharacteristic
398C2×C4#8819311yescharacteristic
399C8—42no—
400C8—81no—
401C8—522no—
402C22—522no—
403C22—522no—
404C22—522no—
405C22—1041no—
406C22—1041no—
407C22—1041no—
408C22—1041no—
409C22#1171841311yescharacteristic
410C22#1171841411yescharacteristic
411C22#1171843411yescharacteristic
412C22#1171844411yescharacteristic
413C22#1171847111yescharacteristic
414C22#1171847211yescharacteristic
415C22#1171862211yescharacteristic
416C4—21no—
417C4—21no—
418C4—82no—
419C4—1041no—
420C4—1041no—
421C4—1041no—
422C4—2081no—
423C4#1171843511yescharacteristic
424C4#1171844511yescharacteristic
425C4#1171845611yescharacteristic
426C4#1171846111yescharacteristic
427C4#1171881811yescharacteristic
428C4#1171882611yescharacteristic
429C4#1171883511yescharacteristic
430C4#1171884611yescharacteristic
431C2—1042no—
432C2#1311392611yescharacteristic
433C2#1311400911yescharacteristic
434C2#1311407211yescharacteristic
435C2#1311410711yescharacteristic
436C2#1311601711yescharacteristic
437C2#1311605411yescharacteristic
438C2#1311607411yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#332C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenterC2×#332D13
hypocenterC13#10416
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #13115798C2semidirect
3. #13115595C2semidirect
6. #13112675C2semidirect
7. C2×C13×#332C2semidirect
133. C2×#332D13semidirect
347. C13#10416semidirect

Maximal subgroups

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

subgroupindex
#131198322
#131157982
#131155952
#131148372
C2×#117180752
#131126752
C2×C13×#3322
#1041613