Finite Group Databasebeta

← #15889694

Subgroups — #15889694

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118136C211yesmaximal, characteristic
2#13115558C211yesmaximal, characteristic, complemented
3#13115556C211yesmaximal, characteristic, complemented
4#13115552C211yesmaximal, characteristic, complemented
5#13115452C211yesmaximal, characteristic
6#13115446C211yesmaximal, characteristic
7#13115444C211yesmaximal, characteristic
8#13115399C211yesmaximal, characteristic, complemented
9#13115397C211yesmaximal, characteristic, complemented
10#13115391C211yesmaximal, characteristic, complemented
11#13115019C211yesmaximal, characteristic
12#13115019C211yesmaximal, characteristic
13#13114989C211yesmaximal, characteristic, complemented
14#13114980C211yesmaximal, characteristic, complemented
15C13×#1851C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C13×C22⋊C8C2211yescharacteristic
20C4×C13×C22⋊C4C2211yescharacteristic
21C4×C22⋊Dic13C2211yescharacteristic
22C4×C22⋊Dic13C2211yescharacteristic
23C2×C22⋊#1055C2211yescharacteristic
24C2×C22⋊#1055C2211yescharacteristic
25C2×#88055C2211yescharacteristic
26C2×#88055C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33#11718614C411yescharacteristic
34#11718613C411yescharacteristic
35#11718613C411yescharacteristic
36#11718609C411yescharacteristic
37C4×C4⋊Dic13C2211yescharacteristic
38#11718593C2211yescharacteristic
39C4×#6101C2211yescharacteristic
40C4×#6101C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43C13⋊#401C411yescharacteristic
44#11718321C411yescharacteristic
45#11718320C411yescharacteristic
46#11718319C411yescharacteristic
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
60C2×C13×M16—41no—
61C2×C13×M16—41no—
62C2×C13×M16—41no—
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C2×C13×C22⋊C4C2×C411yescharacteristic
68C2×C13×C22⋊C4C2×C411yescharacteristic
69C2×C42×C13C2311yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×C22⋊Dic13C2×C411yescharacteristic
72C2×C22⋊Dic13C2×C411yescharacteristic
73C2×C22⋊Dic13C2×C411yescharacteristic
74C2×C22⋊Dic13C2×C411yescharacteristic
75C2×C4⋊Dic13C2×C411yescharacteristic
76C2×C4⋊Dic13C2×C411yescharacteristic
77C2×#6101C2×C411yescharacteristic
78C2×#6101C2×C411yescharacteristic
79C2×#6101C2×C411yescharacteristic
80C2×#6101C2×C411yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C22×#1055C2311yescharacteristic
86C22×#1055C2311yescharacteristic
87C22×#1055C2311yescharacteristic
88C22×#1055C2311yescharacteristic
89C13×C4⋊C8—41no—
90C13×C4⋊C8—41no—
91C13×C22⋊C8—41no—
92C13×#95C2×C411yescharacteristic
93C13×#95C2×C411yescharacteristic
94#88071C2×C411yescharacteristic
95#88071C2×C411yescharacteristic
96#88071C2×C411yescharacteristic
97#88071C2×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#88055—41no—
112#88054—41no—
113#88054—41no—
114#88054—41no—
115#88054—41no—
116#88054—41no—
117#88054—41no—
118C4⋊#1055—41no—
119C4×#1055—41no—
120#23382—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
142C13×M16—44no—
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—
154C2×C8×C13—21no—
155C13×C22⋊C4—22no—
156C13×C22⋊C4—41no—
157C42×C13—21no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C22⋊Dic13—41no—
162C22⋊Dic13—41no—
163C22⋊Dic13—41no—
164C22⋊Dic13—41no—
165C4⋊Dic13—22no—
166C4⋊Dic13—41no—
167#6101—22no—
168#6101—41no—
169#6101—41no—
170#6101—41no—
171C4×Dic13—21no—
172C4×Dic13—21no—
173C4×Dic13—21no—
174C4×Dic13—21no—
175C4×Dic13—21no—
176C4×Dic13—21no—
177C4×Dic13—21no—
178C4×Dic13—21no—
179C2×#1055—21no—
180C2×#1055—21no—
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—
191#2401—131no—
192#1940—131no—
193#1940—131no—
194#1939—131no—
195#1924—131no—
196#1924—131no—
197#1923—131no—
198#1917—131no—
199#1917—131no—
200#1916—131no—
201#1851—131no—
202#1851—131no—
203#1851D1311yescharacteristic
204#1843—131no—
205#1840—131no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13C23×C411yescharacteristic
214C2×C4×C13—21no—
215C2×C4×C13—21no—
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—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13#13112yes—
233C2×C4×C13H(5,𝔽2)11yescharacteristic
234C2×C4×C13H(5,𝔽2)11yescharacteristic
235C2×C4×C13H(5,𝔽2)11yescharacteristic
236C2×C4×C132−1+411yescharacteristic
237C2×C4×C132−1+411yescharacteristic
238C2×C4×C132−1+411yescharacteristic
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
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—
263C8×C13—41no—
264C8×C13—41no—
265C8×C13—41no—
266C8×C13—41no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271C22×M16C2×D1311yescharacteristic
272C2×C4⋊C8—131no—
273C2×C4⋊C8—131no—
274C2×C4⋊C8—131no—
275C2×C4⋊C8—131no—
276C2×C4⋊C8—131no—
277C2×C4⋊C8—131no—
278C2×C4⋊C8—131no—
279C2×C4⋊C8C2×D1311yescharacteristic
280C2×C4⋊C8C2×D1311yescharacteristic
281C2×C22⋊C8—131no—
282C2×C22⋊C8—131no—
283C2×C22⋊C8C2×D1311yescharacteristic
284C2×#97—131no—
285C2×#97—131no—
286C2×C4×C8—131no—
287#401—131no—
288#400—131no—
289#400—131no—
290#400—131no—
291#397—131no—
292#397—131no—
293#397—131no—
294#396—131no—
295C4×C4⋊C4—131no—
296C4×C4⋊C4—131no—
297C4×C4⋊C4—131no—
298C4×C22⋊C4—131no—
299C4×C22⋊C4—131no—
300C4×C22⋊C4C2×D1311yescharacteristic
301#376—131no—
302#336—131no—
303#336—131no—
304#336—131no—
305#336—131no—
306#336—131no—
307#336—131no—
308#336—131no—
309#336—131no—
310#336—131no—
311#336—131no—
312#336C2×D1311yescharacteristic
313#336C2×D1311yescharacteristic
314C22×C13—41no—
315C22×C13—41no—
316C22×C13—41no—
317C22×C13—41no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13#52011yescharacteristic
322C22×C13#52011yescharacteristic
323C22×C13#52011yescharacteristic
324C22×C13C2×#13111yescharacteristic
325C22×C13#56811yescharacteristic
326C22×C13#56811yescharacteristic
327C22×C13#56811yescharacteristic
328C4×C13—22no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13#56011yescharacteristic
334C4×C13#56311yescharacteristic
335C4×C13#56311yescharacteristic
336C4×C13#56311yescharacteristic
337Dic13—41no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345C23×C4C22×D1311yescharacteristic
346C2×M16—41no—
347C2×M16—41no—
348C2×M16—41no—
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—131no—
352C22×C8—131no—
353C22×C8C22×D1311yescharacteristic
354C22×C8C22×D1311yescharacteristic
355C22×C8C22×D1311yescharacteristic
356C22×C8C22×D1311yescharacteristic
357C2×C4⋊C4—131no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C22⋊C4—131no—
364C2×C22⋊C4—131no—
365C2×C22⋊C4—131no—
366C2×C22⋊C4—131no—
367C2×C22⋊C4C4×D1311yescharacteristic
368C2×C22⋊C4C4×D1311yescharacteristic
369C2×C42—131no—
370C2×C42—131no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42C22×D1311yescharacteristic
374C2×C42C22×D1311yescharacteristic
375C4⋊C8—41no—
376C4⋊C8—41no—
377C4⋊C8—521no—
378C4⋊C8—521no—
379C4⋊C8—521no—
380C4⋊C8—521no—
381C4⋊C8—521no—
382C4⋊C8—521no—
383C4⋊C8—521no—
384C22⋊C8—41no—
385C22⋊C8—521no—
386C22⋊C8—521no—
387#97—521no—
388#97—521no—
389C4×C8—521no—
390#95—131no—
391#95—131no—
392#95—131no—
393#95—131no—
394#95—131no—
395#95—131no—
396#95—131no—
397#95—131no—
398#95—131no—
399#95—131no—
400#95—131no—
401#95—131no—
402#95—131no—
403#95—131no—
404#95C4×D1311yescharacteristic
405#95C4×D1311yescharacteristic
406C2×C13—81no—
407C2×C13#238311yescharacteristic
408C2×C13#299211yescharacteristic
409C2×C13#299311yescharacteristic
410C2×C13#299311yescharacteristic
411C2×C13#299511yescharacteristic
412C2×C13#299511yescharacteristic
413C2×C13#299511yescharacteristic
414C24C2×C4×D1311yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—131no—
422C22×C4—131no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—131no—
429C22×C4C2×C4×D1311yescharacteristic
430C22×C4C2×C4×D1311yescharacteristic
431C22×C4C2×C4×D1311yescharacteristic
432C22×C4C2×C4×D1311yescharacteristic
433C22×C4C2×C4×D1311yescharacteristic
434C22×C4C23×D1311yescharacteristic
435M16—44no—
436C2×C8—21no—
437C2×C8—21no—
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—261no—
449C2×C8—261no—
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—
460C4⋊C4—262no—
461C4⋊C4—262no—
462C4⋊C4—521no—
463C4⋊C4—521no—
464C4⋊C4—521no—
465C4⋊C4—521no—
466C22⋊C4—22no—
467C22⋊C4—41no—
468C22⋊C4—521no—
469C22⋊C4—521no—
470C22⋊C4—521no—
471C22⋊C4—521no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—261no—
477C42—261no—
478C42—261no—
479C42—261no—
480C42—261no—
481C42—261no—
482C42—261no—
483C42—261no—
484C13#2338211yescharacteristic, complemented, Sylow
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23C22×C4×D1311yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
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—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
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#8816112yes—
536C2×C4#8825111yescharacteristic
537C2×C4#8825111yescharacteristic
538C2×C4#8825111yescharacteristic
539C2×C4#8825411yescharacteristic
540C2×C4#8825711yescharacteristic
541C2×C4#8825711yescharacteristic
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—521no—
547C8—521no—
548C8—521no—
549C8—521no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22#1171920911yescharacteristic
558C22#1171925111yescharacteristic
559C22#1171925111yescharacteristic
560C22C2×#8816111yescharacteristic
561C22#1171945011yescharacteristic
562C22#1171945511yescharacteristic
563C22#1171945511yescharacteristic
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—521no—
570C4—521no—
571C4—521no—
572C4—521no—
573C4—521no—
574C4—521no—
575C4—521no—
576C4—521no—
577C4#1171930011yescharacteristic
578C4#1171935111yescharacteristic
579C4#1171935111yescharacteristic
580C4#1171935611yescharacteristic
581C2—81no—
582C2#1311802411yescharacteristic
583C2#1312397611yescharacteristic
584C2#1312398011yescharacteristic
585C2#1312398111yescharacteristic
586C2#1312400011yescharacteristic
587C2#1312400411yescharacteristic
588C2#1312400711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1851C2
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenter#1851D13
hypocenterC13#23382
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
2. #13115558C2semidirect
3. #13115556C2semidirect
4. #13115552C2semidirect
8. #13115399C2semidirect
9. #13115397C2semidirect
10. #13115391C2semidirect
13. #13114989C2semidirect
14. #13114980C2semidirect
484. C13#23382semidirect

Maximal subgroups

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

subgroupindex
#131181362
#131155582
#131155562
#131155522
#131154522
#131154462
#131154442
#131153992
#131153972
#131153912
#131150192
#131149892
#131149802
C13×#18512
#2338213