Finite Group Databasebeta

← #15873134

Subgroups — #15873134

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117332C211yesmaximal, characteristic
2#13115446C211yesmaximal, characteristic
3#13115445C211yesmaximal, characteristic
4#13115444C211yesmaximal, characteristic
5#13115403C211yesmaximal, characteristic, complemented
6#13115400C211yesmaximal, characteristic, complemented
7#13115391C211yesmaximal, characteristic, complemented
8#13115390C211yesmaximal, characteristic, complemented
9#13114987C211yesmaximal, characteristic, complemented
10#13114951C211yesmaximal, characteristic, complemented
11#13114818C211yesmaximal, characteristic
12#13114818C211yesmaximal, characteristic
13#13114696C211yesmaximal, characteristic, complemented
14#13114692C211yesmaximal, characteristic, complemented
15C13×#1924C211yesmaximal, characteristic
16C2×#88180C2211yescharacteristic
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×C22⋊C8C2211yescharacteristic
19C2×C13×C22⋊C8C2211yescharacteristic
20C2×C13×#97C2211yescharacteristic
21C4×C13×C22⋊C4C2211yescharacteristic
22C4×C22⋊Dic13C2211yescharacteristic
23C2×C22⋊#1055C2211yescharacteristic
24C2×C22⋊#1055C2211yescharacteristic
25C2×#88055C2211yescharacteristic
26C2×#88054C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33#11718606C411yescharacteristic
34#11718606C411yescharacteristic
35#11718605C411yescharacteristic
36#11718605C411yescharacteristic
37#11718593C2211yescharacteristic
38C4×#6101C2211yescharacteristic
39C4×#6101C2211yescharacteristic
40C42×Dic13C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718315C411yescharacteristic
44#11718315C411yescharacteristic
45#11718314C411yescharacteristic
46#11718314C411yescharacteristic
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49#11718142C2211yescharacteristic
50#11718142C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×C8×C13C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C2×C13×C22⋊C4C2×C411yescharacteristic
65C2×C13×C22⋊C4C2×C411yescharacteristic
66C2×C42×C13C2311yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C2×C22⋊Dic13C2×C411yescharacteristic
69C2×C22⋊Dic13C2×C411yescharacteristic
70C2×C22⋊Dic13C2×C411yescharacteristic
71C2×C22⋊Dic13C2×C411yescharacteristic
72#88180—22no—
73#88180—22no—
74C2×C4⋊Dic13C2×C411yescharacteristic
75C2×C4⋊Dic13C2×C411yescharacteristic
76C2×#6101C2×C411yescharacteristic
77C2×#6101C2×C411yescharacteristic
78C2×#6101C2×C411yescharacteristic
79C2×#6101C2×C411yescharacteristic
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2×C411yescharacteristic
83C2×C4×Dic13C2×C411yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C2×C4×Dic13C2311yescharacteristic
87C2×C4×Dic13C2311yescharacteristic
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C13×C4⋊C8—41no—
93C13×C22⋊C8—41no—
94C13×C22⋊C8—41no—
95C13×#97—41no—
96C13×#95C2×C411yescharacteristic
97C13×#95C2×C411yescharacteristic
98#88071C2×C411yescharacteristic
99#88071C2×C411yescharacteristic
100#88071C2×C411yescharacteristic
101#88071C2×C411yescharacteristic
102#88071C2×C411yescharacteristic
103#88071C2×C411yescharacteristic
104#88071C2×C411yescharacteristic
105#88071C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108C22⋊#1055—41no—
109C22⋊#1055—41no—
110#88055—41no—
111#88054—22no—
112#88054—22no—
113#88054—22no—
114#88054—22no—
115#88054—41no—
116#88054—41no—
117C8×Dic13—41no—
118C4⋊#1055—41no—
119C4×#1055—41no—
120#21929—131nomaximal, Sylow
121C24×C13C22×C411yescharacteristic
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×C13C22×C411yescharacteristic
129C22×C4×C13C22×C411yescharacteristic
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C22×C411yescharacteristic
132C22×C4×C13C22×C411yescharacteristic
133C22×C4×C13C2411yescharacteristic
134C22×Dic13C22×C411yescharacteristic
135C22×Dic13C22×C411yescharacteristic
136C22×Dic13C22×C411yescharacteristic
137C22×Dic13C22×C411yescharacteristic
138C22×Dic13C22×C411yescharacteristic
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C2×C8×C13—21no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C13×C22⋊C4—22no—
155C13×C22⋊C4—41no—
156C42×C13—21no—
157C42×C13—21no—
158C42×C13—21no—
159C42×C13—21no—
160C22⋊Dic13—22no—
161C22⋊Dic13—22no—
162C22⋊Dic13—22no—
163C22⋊Dic13—41no—
164C4⋊Dic13—22no—
165C4⋊Dic13—22no—
166#6101—22no—
167#6101—22no—
168#6101—41no—
169#6101—41no—
170C4×Dic13—22no—
171C4×Dic13—21no—
172C4×Dic13—21no—
173C4×Dic13—21no—
174C4×Dic13—21no—
175C4×Dic13—21no—
176C4×Dic13—21no—
177C4×Dic13—22no—
178C4×Dic13—41no—
179C4×Dic13—41no—
180C4×Dic13#4112yes—
181C4×Dic13#4112yes—
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—21no—
193C2×#1055—21no—
194#2298—131no—
195#1924—131no—
196#1924D1311yescharacteristic
197#1923—131no—
198#1923—131no—
199#1917—131no—
200#1917—131no—
201#1916—131no—
202#1916—131no—
203#1842—131no—
204#1831—131no—
205#1798—131no—
206#1798—131no—
207#1768—131no—
208#1768—131no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13C23×C411yescharacteristic
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#13112yes—
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13H(5,𝔽2)11yescharacteristic
239C2×C4×C13H(5,𝔽2)11yescharacteristic
240C2×C4×C132−1+411yescharacteristic
241C2×C4×C132−1+411yescharacteristic
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13#11712yes—
264C2×Dic13#11712yes—
265C2×Dic13#13112yes—
266C8×C13—41no—
267C8×C13—41no—
268C8×C13—41no—
269C8×C13—41no—
270#1055—41no—
271#1055—41no—
272#1055—41no—
273#1055—41no—
274C2×#117—131no—
275C2×C4⋊C8—131no—
276C2×C4⋊C8—131no—
277C2×C4⋊C8—131no—
278C2×C4⋊C8—131no—
279C2×C4⋊C8—131no—
280C2×C4⋊C8—131no—
281C2×C4⋊C8—131no—
282C2×C4⋊C8C2×D1311yescharacteristic
283C2×C22⋊C8—131no—
284C2×C22⋊C8—131no—
285C2×C22⋊C8C2×D1311yescharacteristic
286C2×C22⋊C8C2×D1311yescharacteristic
287C2×#97—131no—
288C2×#97C2×D1311yescharacteristic
289C2×C4×C8—131no—
290C2×C4×C8—131no—
291#388—131no—
292#388—131no—
293#388—131no—
294#388—131no—
295#387—131no—
296#387—131no—
297#387—131no—
298#387—131no—
299C4×C4⋊C4—131no—
300C4×C4⋊C4—131no—
301C4×C22⋊C4—131no—
302C4×C22⋊C4C2×D1311yescharacteristic
303#376—131no—
304C43—131no—
305#336—131no—
306#336—131no—
307#336—131no—
308#336—131no—
309#336—131no—
310#336—131no—
311#336—131no—
312#336—131no—
313#336—131no—
314#336—131no—
315#336C2×D1311yescharacteristic
316#336C2×D1311yescharacteristic
317C22×C13—41no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13C2×#11711yescharacteristic
325C22×C13#52011yescharacteristic
326C22×C13#52011yescharacteristic
327C22×C13C2×#13111yescharacteristic
328C22×C13C2×#13111yescharacteristic
329C22×C13#56811yescharacteristic
330C22×C13#56811yescharacteristic
331C4×C13—22no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13#54011yescharacteristic
337C4×C13#54111yescharacteristic
338C4×C13#54211yescharacteristic
339C4×C13#54211yescharacteristic
340Dic13—22no—
341Dic13—22no—
342Dic13—22no—
343Dic13—41no—
344Dic13—41no—
345Dic13—41no—
346Dic13—41no—
347Dic13—41no—
348C23×C4C22×D1311yescharacteristic
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—131no—
352C22×C8—131no—
353C22×C8C22×D1311yescharacteristic
354C22×C8C22×D1311yescharacteristic
355C22×C8C22×D1311yescharacteristic
356C22×C8C22×D1311yescharacteristic
357#117—262no—
358#117—262no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C22⋊C4—131no—
366C2×C22⋊C4—131no—
367C2×C22⋊C4—131no—
368C2×C22⋊C4—131no—
369C2×C22⋊C4C4×D1311yescharacteristic
370C2×C22⋊C4C4×D1311yescharacteristic
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—131no—
375C2×C42—131no—
376C2×C42—131no—
377C2×C42—131no—
378C2×C42—131no—
379C2×C42C22×D1311yescharacteristic
380C2×C42C22×D1311yescharacteristic
381C4⋊C8—41no—
382C4⋊C8—262no—
383C4⋊C8—262no—
384C4⋊C8—262no—
385C4⋊C8—262no—
386C4⋊C8—521no—
387C4⋊C8—521no—
388C4⋊C8—521no—
389C22⋊C8—41no—
390C22⋊C8—41no—
391C22⋊C8—521no—
392C22⋊C8—521no—
393#97—41no—
394#97—521no—
395C4×C8—521no—
396C4×C8—521no—
397#95—131no—
398#95—131no—
399#95—131no—
400#95—131no—
401#95—131no—
402#95—131no—
403#95—131no—
404#95—131no—
405#95—131no—
406#95—131no—
407#95C4×D1311yescharacteristic
408#95C4×D1311yescharacteristic
409C2×C13—81no—
410C2×C13#231411yescharacteristic
411C2×C13#292511yescharacteristic
412C2×C13#292511yescharacteristic
413C2×C13#299211yescharacteristic
414C2×C13#299311yescharacteristic
415C2×C13#299411yescharacteristic
416C2×C13#299511yescharacteristic
417C24C2×C4×D1311yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4C2×C4×D1311yescharacteristic
433C22×C4C2×C4×D1311yescharacteristic
434C22×C4C2×C4×D1311yescharacteristic
435C22×C4C2×C4×D1311yescharacteristic
436C22×C4C2×C4×D1311yescharacteristic
437C22×C4C23×D1311yescharacteristic
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C4⋊C4—262no—
463C4⋊C4—262no—
464C4⋊C4—262no—
465C4⋊C4—262no—
466C4⋊C4—521no—
467C4⋊C4—521no—
468C22⋊C4—22no—
469C22⋊C4—41no—
470C22⋊C4—262no—
471C22⋊C4—262no—
472C22⋊C4—262no—
473C22⋊C4—521no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—132no—
479C42—132no—
480C42—262no—
481C42—262no—
482C42—261no—
483C42—261no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42—261no—
488C42—521no—
489C42—521no—
490C13#2192911yescharacteristic, complemented, Sylow
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23C22×C4×D1311yescharacteristic
499C2×C4—21no—
500C2×C4—21no—
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—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—132no—
518C2×C4—132no—
519C2×C4—132no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4#8816112yes—
542C2×C4#8825111yescharacteristic
543C2×C4#8825111yescharacteristic
544C2×C4#41×D1311yescharacteristic
545C2×C4#41×D1311yescharacteristic
546C2×C4#8825711yescharacteristic
547C2×C4#8825711yescharacteristic
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—521no—
553C8—521no—
554C8—521no—
555C8—521no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22D13×#11711yescharacteristic
564C22#1171925111yescharacteristic
565C22#1171925111yescharacteristic
566C22C2×#8816111yescharacteristic
567C22#1171945011yescharacteristic
568C22D13×#13111yescharacteristic
569C22#1171945511yescharacteristic
570C4—22no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—262no—
576C4—262no—
577C4—262no—
578C4—521no—
579C4—521no—
580C4—521no—
581C4—521no—
582C4—521no—
583C4#1171932011yescharacteristic
584C4#1171936711yescharacteristic
585C4#1171937411yescharacteristic
586C4#1171940611yescharacteristic
587C2—81no—
588C2#1311744011yescharacteristic
589C2#1312349911yescharacteristic
590C2#1312350311yescharacteristic
591C2#1312397111yescharacteristic
592C2#1312398011yescharacteristic
593C2#1312398911yescharacteristic
594C2#1312400711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1924C2
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenter#1924D13
hypocenterC13#21929
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
5. #13115403C2semidirect
6. #13115400C2semidirect
7. #13115391C2semidirect
8. #13115390C2semidirect
9. #13114987C2semidirect
10. #13114951C2semidirect
13. #13114696C2semidirect
14. #13114692C2semidirect
490. C13#21929semidirect

Maximal subgroups

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

subgroupindex
#131173322
#131154462
#131154452
#131154442
#131154032
#131154002
#131153912
#131153902
#131149872
#131149512
#131148182
#131146962
#131146922
C13×#19242
#2192913