Finite Group Databasebeta

← #15872836

Subgroups — #15872836

Order 3328.

1118 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719433C211yesmaximal, characteristic
2C2×D13×C4⋊C8C211yesmaximal, characteristic
3#13117232C211yesmaximal, characteristic
4#13115788C211yesmaximal, characteristic, complemented
5#13115787C211yesmaximal, characteristic, complemented
6#13115760C211yesmaximal, characteristic, complemented
7#13115256C214yesmaximal
8#13114849C214yesmaximal, complemented
9C13×#1981C211yesmaximal, characteristic, complemented
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×#88200C2212yes—
12C2×Q8×Dic13C2212yes—
13C22×C8×D13C2212yes—
14#11719433—24no—
15#11719433C418yescomplemented
16C2×#88151—21no—
17C2×#88146—21no—
18C2×#88144—21no—
19C2×#88141—21no—
20C2×C42×D13C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×#103C2214yes—
24C4×C13×C4⋊C4C2211yescharacteristic
25C2×#88075C2214yes—
26C2×#88054C2212yes—
27#11718648C2212yes—
28#11718638C2212yes—
29C4×#6103—21no—
30C4×C4⋊Dic13C2211yescharacteristic
31#11718593—21no—
32C2×C4⋊#1055C2211yescharacteristic
33D13×C4⋊C8—24no—
34#11718325—21no—
35#11718312—21no—
36#11718143C2214yes—
37#11718121C2214yes—
38C22×Q8×C13C2312yes—
39C22×C4×D13D411yescharacteristic
40C22×C4×D13D411yescharacteristic
41C22×C4×D13C2311yescharacteristic
42C22×Dic26—21no—
43C22×C8×C13C2312yes—
44C13×C4⋊Q8—22no—
45C13×C4⋊Q8C2×C414yes—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4C2312yes—
49C2×C42×C13—21no—
50C2×C42×C13C2311yescharacteristic
51#88200—24no—
52#88200C2×C418yes—
53Q8×Dic13—24no—
54Q8×Dic13C2×C418yes—
55C2×#6103—22no—
56C2×#6103—22no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13C2312yes—
60C2×C4⋊Dic13C2312yes—
61C2×#6101—22no—
62C2×C4×Dic13—22no—
63C2×C4×Dic13—21no—
64C2×C4×Dic13D411yescharacteristic
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13C2311yescharacteristic
67C22×#1055C2312yes—
68C2×C8×D13—24no—
69C2×C8×D13—44no—
70#88151—28no—
71#88146—28no—
72#88144—28no—
73#88141—28no—
74C42×D13C2×C414yes—
75C42×D13D414yes—
76#88123—22no—
77#88123C2×C414yes—
78C13×C4⋊C8—22no—
79C13×#103—44no—
80C13×#95—21no—
81#88075—44no—
82#88071—21no—
83#88071—22no—
84#88071—22no—
85#88071—22no—
86#88054—24no—
87C4⋊#1055—22no—
88#21889—131nomaximal, Sylow
89C23×D13C2×D411yescharacteristic
90C2×Q8×C13—22no—
91C2×Q8×C13—24no—
92C2×Q8×C13—24no—
93C2×Q8×C13C22×C414yes—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2411yescharacteristic
99C22×Dic13—22no—
100C22×Dic13—22no—
101C22×Dic13C2×D411yescharacteristic
102C22×Dic13C2×D411yescharacteristic
103C22×Dic13C2×D411yescharacteristic
104C2×C4×D13—24no—
105C2×C4×D13—22no—
106C2×C4×D13—22no—
107C2×C4×D13—22no—
108C2×C4×D13—22no—
109C2×C4×D13C22⋊C414yes—
110C2×C4×D13C22⋊C414yes—
111C2×C4×D13C22×C412yes—
112C2×C4×D13C2×D412yes—
113C2×Dic26—24no—
114C2×Dic26—42no—
115C2×Dic26—42no—
116C2×C8×C13—22no—
117C2×C8×C13—24no—
118C13×C4⋊C4—24no—
119C13×C4⋊C4—24no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—22no—
122C42×C13—42no—
123C42×C13C22×C412yes—
124C42×C13C2×D412yes—
125#6103—28no—
126#6103—44no—
127C4⋊Dic13—24no—
128C4⋊Dic13—22no—
129C4⋊Dic13—28no—
130C4⋊Dic13—22no—
131C4⋊Dic13—22no—
132C4⋊Dic13C22×C414yes—
133#6101—28no—
134C4×Dic13—28no—
135C4×Dic13—42no—
136C4×Dic13C22⋊C414yes—
137C4×Dic13C22⋊C414yes—
138C4×Dic13C22×C412yes—
139C4×Dic13C2×D412yes—
140C2×#1055—22no—
141C2×#1055—24no—
142C8×D13—48no—
143C2×#533—131no—
144C22×C4⋊C8—131no—
145#2283—131no—
146#1988—131no—
147#1988—131no—
148#1981—131no—
149#1981D1311yescharacteristic, complemented
150#1892—134no—
151#1805—134no—
152C23×C13C22×D411yescharacteristic
153C22×D13—22no—
154C22×D13—21no—
155C22×D13—21no—
156C22×D13C2×C22⋊C412yes—
157C22×D13#13714yes—
158Q8×C13—28no—
159Q8×C13—42no—
160Q8×C13—42no—
161C2×C4×C13—22no—
162C2×C4×C13—24no—
163C2×C4×C13—44no—
164C2×C4×C13—42no—
165C2×C4×C13—42no—
166C2×C4×C13—42no—
167C2×C4×C13C2×C22⋊C412yes—
168C2×C4×C13C2×C22⋊C412yes—
169C2×C4×C13#13512yes—
170C2×C4×C13#13512yes—
171C2×C4×C13C23×C411yescharacteristic
172C2×C4×C13C22×D411yescharacteristic
173C2×C4×C13H(5,𝔽2)12yes—
174C2×C4×C132−1+412yes—
175C2×Dic13—22no—
176C2×Dic13—21no—
177C2×Dic13—21no—
178C2×Dic13—22no—
179C2×Dic13—24no—
180C2×Dic13—42no—
181C2×Dic13—42no—
182C2×Dic13—42no—
183C2×Dic13—42no—
184C2×Dic13—42no—
185C2×Dic13C2×C22⋊C412yes—
186C2×Dic13C2×C22⋊C412yes—
187C2×Dic13C2×C22⋊C412yes—
188C4×D13—28no—
189C4×D13—24no—
190C4×D13—22no—
191C4×D13—22no—
192C4×D13—28no—
193Dic26—48no—
194C8×C13—42no—
195#1055—42no—
196C23×C8—132no—
197#533—138no—
198#533—264no—
199C2×C4⋊Q8—131no—
200C2×C4⋊Q8C2×D1311yescharacteristic
201C2×#125—261no—
202C2×C22⋊Q8—132no—
203C2×C22⋊Q8—261no—
204C2×C4×Q8—132no—
205C2×C4×Q8—261no—
206C2×#117—261no—
207C22×C42—131no—
208C2×C4⋊C8—132no—
209C2×C4⋊C8—131no—
210C2×C4⋊C8—264no—
211C2×C4⋊C8C2×D1311yescharacteristic
212C2×#103—134no—
213C2×#103C2×D1314yes—
214#383—261no—
215#382—132no—
216#381—261no—
217#380—132no—
218C4×C4⋊C4—131no—
219C4×C4⋊C4C2×D1311yescharacteristic
220C4×C22⋊C4—261no—
221#376—261no—
222#340—134no—
223#340—134no—
224C22×C13C22×C22⋊C411yescharacteristic
225C22×C13#53712yes—
226C22×C13C2×#13511yescharacteristic
227C22×C13C2×#13511yescharacteristic
228C22×C13C2×#13712yes—
229C2×D13—22no—
230C2×D13—22no—
231C2×D13—24no—
232C2×D13—24no—
233C2×D13#41914yes—
234C4×C13—22no—
235C4×C13—44no—
236C4×C13—82no—
237C4×C13#41614yes—
238C4×C13#52012yes—
239C4×C13#53511yescharacteristic
240C4×C13#53611yescharacteristic
241Dic13—22no—
242Dic13—22no—
243Dic13—22no—
244Dic13—44no—
245Dic13—82no—
246C22×Q8—261no—
247C22×Q8C22×D1312yes—
248C23×C4—131no—
249C23×C4—131no—
250C23×C4—131no—
251C22×C8—132no—
252C22×C8—264no—
253C22×C8—524no—
254C22×C8C22×D1312yes—
255C4⋊Q8—22no—
256C4⋊Q8—134no—
257C4⋊Q8—262no—
258C4⋊Q8C4×D1314yes—
259#125—268no—
260C22⋊Q8—138no—
261C22⋊Q8—268no—
262C22⋊Q8—264no—
263C4×Q8—138no—
264C4×Q8—268no—
265C4×Q8—264no—
266#117—268no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—132no—
270C2×C4⋊C4—132no—
271C2×C4⋊C4—262no—
272C2×C4⋊C4—262no—
273C2×C4⋊C4—261no—
274C2×C4⋊C4C22×D1312yes—
275C2×C22⋊C4—262no—
276C2×C22⋊C4—262no—
277C2×C42—21no—
278C2×C42—131no—
279C2×C42—131no—
280C2×C42—131no—
281C2×C42—134no—
282C2×C42—134no—
283C2×C42—262no—
284C2×C42—261no—
285C2×C42C22×D1311yescharacteristic
286C4⋊C8—22no—
287C4⋊C8—264no—
288C4⋊C8—262no—
289#103—44no—
290#103—524no—
291#95—21no—
292#95—262no—
293#95—262no—
294#95—262no—
295#95—261no—
296C2×C13#231111yescharacteristic
297C2×C13C2×#41611yescharacteristic
298C2×C13C2×#41911yescharacteristic
299C2×C13#324812yes—
300C2×C13#324812yes—
301D13—24no—
302C24—131no—
303C2×Q8—22no—
304C2×Q8—24no—
305C2×Q8—24no—
306C2×Q8—264no—
307C2×Q8—522no—
308C2×Q8—522no—
309C2×Q8C2×C4×D1314yes—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—131no—
313C22×C4—131no—
314C22×C4—131no—
315C22×C4—134no—
316C22×C4—134no—
317C22×C4—132no—
318C22×C4—132no—
319C22×C4—264no—
320C22×C4—262no—
321C22×C4—262no—
322C22×C4—262no—
323C22×C4—262no—
324C22×C4—262no—
325C22×C4—262no—
326C22×C4D4×D1311yescharacteristic
327C22×C4D4×D1311yescharacteristic
328C22×C4C23×D1311yescharacteristic
329C2×C8—22no—
330C2×C8—24no—
331C2×C8—262no—
332C2×C8—264no—
333C2×C8—528no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—134no—
339C4⋊C4—268no—
340C4⋊C4—268no—
341C4⋊C4—264no—
342C4⋊C4—262no—
343C4⋊C4—262no—
344C4⋊C4—262no—
345C22⋊C4—268no—
346C22⋊C4—524no—
347C42—42no—
348C42—134no—
349C42—134no—
350C42—132no—
351C42—132no—
352C42—268no—
353C42—522no—
354C42C2×C4×D1312yes—
355C42D4×D1312yes—
356C13#2188911yescharacteristic, complemented, Sylow
357C23—132no—
358C23—134no—
359C23—261no—
360C23—261no—
361C23—262no—
362C23C2×D4×D1311yescharacteristic
363Q8—28no—
364Q8—42no—
365Q8—42no—
366Q8—528no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—44no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—132no—
374C2×C4—132no—
375C2×C4—132no—
376C2×C4—268no—
377C2×C4—261no—
378C2×C4—261no—
379C2×C4—262no—
380C2×C4—262no—
381C2×C4—268no—
382C2×C4—264no—
383C2×C4—262no—
384C2×C4—262no—
385C2×C4—264no—
386C2×C4—522no—
387C2×C4—522no—
388C2×C4—522no—
389C2×C4—522no—
390C2×C4—522no—
391C2×C4C22⋊C4×D1312yes—
392C2×C4C22⋊C4×D1312yes—
393C2×C4#8817012yes—
394C2×C4#8817312yes—
395C2×C4C22×C4×D1311yescharacteristic
396C2×C4C2×D4×D1311yescharacteristic
397C2×C4#8825112yes—
398C2×C4#8825712yes—
399C8—42no—
400C8—522no—
401C22—134no—
402C22—262no—
403C22—264no—
404C22—264no—
405C22—262no—
406C22C2×C22⋊C4×D1311yescharacteristic
407C22#1171931312yes—
408C22C2×#8817011yescharacteristic
409C22C2×#8817311yescharacteristic
410C22D13×#13712yes—
411C4—22no—
412C4—44no—
413C4—82no—
414C4—262no—
415C4—262no—
416C4—262no—
417C4—524no—
418C4—1042no—
419C4#1171846514yes—
420C4#1171925112yes—
421C4#1171938011yescharacteristic
422C4#1171942011yescharacteristic
423C2—264no—
424C2#1311742611yescharacteristic
425C2C2×#1171846511yescharacteristic
426C2D13×#41911yescharacteristic
427C2#1312616912yes—
428C2#1312617112yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1981C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1981D13
hypocenterC13#21889
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
4. #13115788C2semidirect
5. #13115787C2semidirect
6. #13115760C2semidirect
8. #13114849C2semidirect
9. C13×#1981C2semidirect
15. #11719433C4semidirect
149. #1981D13semidirect
356. C13#21889semidirect

Maximal subgroups

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

subgroupindex
C2×#117194332
C2×D13×C4⋊C82
#131172322
#131157882
#131157872
#131157602
#131152562
#131148492
C13×#19812
#2188913