Finite Group Databasebeta

← #15936037

Subgroups — #15936037

Order 3328.

672 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117861C211yesmaximal, characteristic
2#13116255C211yesmaximal, characteristic, complemented
3#13116214C211yesmaximal, characteristic, complemented
4#13116039C211yesmaximal, characteristic
5#13116032C211yesmaximal, characteristic
6#13115602C211yesmaximal, characteristic, complemented
7#13115571C211yesmaximal, characteristic, complemented
8#13115451C211yesmaximal, characteristic
9#13115425C211yesmaximal, characteristic, complemented
10#13115421C211yesmaximal, characteristic, complemented
11#13115089C211yesmaximal, characteristic, complemented
12#13115033C211yesmaximal, characteristic
13#13114928C211yesmaximal, characteristic
14#13114669C211yesmaximal, characteristic, complemented
15C13×#2494C211yesmaximal, characteristic
16C2×#88180C2211yescharacteristic
17C2×#88178C2211yescharacteristic
18C2×C4×Dic26C2211yescharacteristic
19C13×#401—21no—
20C13×#397—21no—
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#388—21no—
24C13×#387—21no—
25C13×#382C2211yescharacteristic
26C13×#380C2211yescharacteristic
27C13×#380C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88050C2211yescharacteristic
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40#11718606—21no—
41#11718605—21no—
42C4×C4⋊Dic13C2211yescharacteristic
43#11718590C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×#88043C2211yescharacteristic
47#11718313—21no—
48#11718310—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×Dic26C2311yescharacteristic
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4C2311yescharacteristic
64C2×C13×C4⋊C4C2311yescharacteristic
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C22⋊C4—21no—
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4D411yescharacteristic
70C2×C13×C22⋊C4D411yescharacteristic
71C2×C42×C13—21no—
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76#88180—22no—
77#88180—41no—
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81#88178—22no—
82#88178—22no—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C4×Dic26—22no—
94C4×Dic26—41no—
95C13×#95—21no—
96C13×#95—21no—
97C13×#95—21no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108C22⋊#1055—22no—
109C22⋊#1055—41no—
110#88050—22no—
111#88050—22no—
112#88050—22no—
113#88050—41no—
114#88048—22no—
115#88048—41no—
116#88047—22no—
117#88047—22no—
118C4⋊#1055—22no—
119#88043—41no—
120#27061—131nomaximal, Sylow
121C24×C13C2×D411yescharacteristic
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2411yescharacteristic
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C2×Dic26—21no—
143C2×Dic26—21no—
144C2×Dic26—21no—
145C2×Dic26—21no—
146C2×Dic26—21no—
147C2×Dic26#4112yes—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—42no—
157C13×C4⋊C4—81no—
158C13×C22⋊C4—41no—
159C13×C22⋊C4—41no—
160C13×C22⋊C4—42no—
161C13×C22⋊C4—81no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—81no—
167C22⋊Dic13—24no—
168C22⋊Dic13—42no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13#4112yes—
174C4⋊Dic13#4112yes—
175#6101—24no—
176#6101—42no—
177#6101—42no—
178C4×Dic13—42no—
179C4×Dic13—42no—
180C4×Dic13—42no—
181C2×#1055—21no—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055#4112yes—
193#2494D1311yescharacteristic
194#2362—131no—
195#2074—131no—
196#2066—131no—
197#2036—131no—
198#2035—131no—
199#1949—131no—
200#1943—131no—
201#1924—131no—
202#1921—131no—
203#1920—131no—
204#1863—131no—
205#1854—131no—
206#1825—131no—
207#1763—131no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13C22×D411yescharacteristic
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13H(5,𝔽2)11yescharacteristic
252C2×C4×C132−1+411yescharacteristic
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265Dic26—22no—
266Dic26—22no—
267Dic26—41no—
268Dic26—41no—
269#1055—22no—
270#1055—41no—
271#1055—41no—
272#1055—41no—
273C2×C22⋊Q8—131no—
274C2×C4×Q8—131no—
275C2×#117—131no—
276C2×#107—131no—
277C2×#107—131no—
278C2×#106—131no—
279C2×#106—131no—
280C2×C4⋊C8—131no—
281C2×#103—131no—
282C2×#103—131no—
283C2×#103—131no—
284C2×#103—131no—
285C2×C22⋊C8—131no—
286C2×C22⋊C8—131no—
287C2×#97—131no—
288#401—21no—
289#397—21no—
290#391—131no—
291#389—131no—
292#389C2×D1311yescharacteristic
293#389C2×D1311yescharacteristic
294#388—21no—
295#388—261no—
296#388—261no—
297#387—21no—
298#387—261no—
299#382C2×D1311yescharacteristic
300#380C2×D1311yescharacteristic
301#380C2×D1311yescharacteristic
302C4×C4⋊C4—131no—
303C4×C4⋊C4—261no—
304C4×C4⋊C4C2×D1311yescharacteristic
305C4×C22⋊C4C2×D1311yescharacteristic
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#336—131no—
315#336—131no—
316C22×C13—41no—
317C22×C13—41no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13#52511yescharacteristic
324C22×C13#54611yescharacteristic
325C22×C13#54711yescharacteristic
326C22×C13#57511yescharacteristic
327C22×C13#57511yescharacteristic
328C22×C13#57711yescharacteristic
329C22×C13#57811yescharacteristic
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13—81no—
339C4×C13#52911yescharacteristic
340C4×C13#53911yescharacteristic
341C4×C13#55311yescharacteristic
342C4×C13#55611yescharacteristic
343Dic13—42no—
344Dic13—42no—
345Dic13—42no—
346Dic13—81no—
347C22×Q8—131no—
348C23×C4C22×D1311yescharacteristic
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—131no—
352C22×C8—131no—
353C22⋊Q8—262no—
354C22⋊Q8—262no—
355C4×Q8—262no—
356C4×Q8—521no—
357#117—262no—
358#117—521no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4C22⋊D1311yescharacteristic
376C2×C22⋊C4C22⋊D1311yescharacteristic
377C2×C42—21no—
378C2×C42—261no—
379C2×C42—261no—
380C2×C42—261no—
381C2×C42C22×D1311yescharacteristic
382C2×C42C22×D1311yescharacteristic
383#107—262no—
384#107—262no—
385#106—262no—
386#106—521no—
387C4⋊C8—262no—
388#103—262no—
389#103—262no—
390#103—262no—
391#103—521no—
392C22⋊C8—262no—
393C22⋊C8—521no—
394#97—521no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95C22⋊D1311yescharacteristic
407#95C22⋊D1311yescharacteristic
408C2×C13—81no—
409C2×C13#246611yescharacteristic
410C2×C13#311111yescharacteristic
411C2×C13#312111yescharacteristic
412C2×C13#330711yescharacteristic
413C2×C13#332711yescharacteristic
414C2×C13#334911yescharacteristic
415C2×C13#335011yescharacteristic
416C24C2×C22⋊D1311yescharacteristic
417C2×Q8—132no—
418C2×Q8—261no—
419C2×Q8—261no—
420C2×Q8—261no—
421C2×Q8—261no—
422C2×Q8—261no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4C2×C22⋊D1311yescharacteristic
438C22×C4C2×C22⋊D1311yescharacteristic
439C22×C4C2×C22⋊D1311yescharacteristic
440C22×C4C2×C22⋊D1311yescharacteristic
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C23×D1311yescharacteristic
443C2×C8—132no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—42no—
464C4⋊C4—81no—
465C4⋊C4—132no—
466C4⋊C4—132no—
467C4⋊C4—264no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—522no—
473C4⋊C4—522no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—42no—
477C22⋊C4—81no—
478C22⋊C4—264no—
479C22⋊C4—522no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—81no—
485C42—522no—
486C42—522no—
487C42—522no—
488C13#2706111yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23C22×C22⋊D1311yescharacteristic
497Q8—262no—
498Q8—262no—
499Q8—521no—
500Q8—521no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—262no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4#41×D1311yescharacteristic
545C2×C4#41×D1311yescharacteristic
546C2×C4#41×D1311yescharacteristic
547C2×C4#41×D1311yescharacteristic
548C2×C4#8825611yescharacteristic
549C2×C4#8825711yescharacteristic
550C8—262no—
551C8—521no—
552C8—521no—
553C8—521no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22#1171952711yescharacteristic
562C22#1171952711yescharacteristic
563C22#1171952911yescharacteristic
564C22#1171953311yescharacteristic
565C22#1171953411yescharacteristic
566C22#1171954111yescharacteristic
567C22#1171954311yescharacteristic
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—522no—
578C4—522no—
579C4—522no—
580C4—1041no—
581C4#1171940711yescharacteristic
582C4#1171941111yescharacteristic
583C4#1171941211yescharacteristic
584C4#1171941411yescharacteristic
585C2—81no—
586C2#1311886811yescharacteristic
587C2#1312493911yescharacteristic
588C2#1312505911yescharacteristic
589C2#1312680611yescharacteristic
590C2#1312709811yescharacteristic
591C2#1312736011yescharacteristic
592C2#1312737511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2494C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2494D13
hypocenterC13#27061
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2494

Complements

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

NH ≅ G/Ntype
2. #13116255C2semidirect
3. #13116214C2semidirect
6. #13115602C2semidirect
7. #13115571C2semidirect
9. #13115425C2semidirect
10. #13115421C2semidirect
11. #13115089C2semidirect
14. #13114669C2semidirect
488. C13#27061semidirect

Maximal subgroups

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

subgroupindex
#131178612
#131162552
#131162142
#131160392
#131160322
#131156022
#131155712
#131154512
#131154252
#131154212
#131150892
#131150332
#131149282
#131146692
C13×#24942
#2706113