Finite Group Databasebeta

← #15921088

Subgroups — #15921088

Order 3328.

706 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#13119857C211yesmaximal, characteristic, complemented
2#13117807C211yesmaximal, characteristic
3#13116223C211yesmaximal, characteristic
4#13116209C211yesmaximal, characteristic
5#13115983C211yesmaximal, characteristic
6#13115973C211yesmaximal, characteristic
7#13115791C211yesmaximal, characteristic, complemented
8#13115787C211yesmaximal, characteristic, complemented
9#13115606C211yesmaximal, characteristic, complemented
10#13115429C211yesmaximal, characteristic, complemented
11#13115422C211yesmaximal, characteristic, complemented
12#13114967C211yesmaximal, characteristic, complemented
13#13114847C211yesmaximal, characteristic
14C4×#88061C211yesmaximal, characteristic
15C13×#1939C211yesmaximal, characteristic, complemented
16C2×C4×D52C2211yescharacteristic
17C2×#88124C2211yescharacteristic
18C2×#88123C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C2×#88061C2211yescharacteristic
25C2×#88061C2211yescharacteristic
26C2×#88061C2211yescharacteristic
27C2×#88061C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88057C2211yescharacteristic
30#11718651—21no—
31#11718651—21no—
32#11718645—21no—
33#11718640—21no—
34#11718600C2211yescharacteristic
35#11718600C2211yescharacteristic
36#11718597C2211yescharacteristic
37#11718597C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718327—21no—
44#11718325—21no—
45#11718308—21no—
46#11718307—21no—
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59C22×D52C2311yescharacteristic
60C22×C4×D13—21no—
61C22×Dic26—21no—
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C2×C13×C4⋊C4D411yescharacteristic
67C2×C13×C4⋊C4D411yescharacteristic
68C2×C42×C13C2311yescharacteristic
69C2×C42×C13C2311yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×#6103—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×#6101—21no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C4×D52—22no—
92C4×D52Q814yescomplemented
93#88124—22no—
94#88124—41no—
95#88123—22no—
96#88123—41no—
97C13×C4⋊C8—22no—
98C13×C4⋊C8—41no—
99C13×C4⋊C8—41no—
100C4×C8×C13—22no—
101C13×#95D411yescharacteristic
102C13×#95D411yescharacteristic
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88061—22no—
113#88061—22no—
114#88061—41no—
115#88061—41no—
116#88058—22no—
117#88057—22no—
118#26028—131nomaximal, Sylow
119C23×D13—21no—
120C22×C4×C13C2×D411yescharacteristic
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2411yescharacteristic
127C22×Dic13—21no—
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C2×D52—21no—
135C2×D52—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52C2×Q812yes—
140C2×C4×D13—24no—
141C2×C4×D13—81no—
142C2×C4×D13—81no—
143C2×Dic26—42no—
144C2×Dic26—42no—
145C2×Dic26—81no—
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—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—41no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13C2×Q812yes—
165C42×C13#4112yes—
166#6103—24no—
167#6103—42no—
168#6103—42no—
169#6103—81no—
170#6103—81no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—42no—
183C4⋊Dic13C2×Q812yes—
184C4⋊Dic13#4112yes—
185C4⋊Dic13#4112yes—
186#6101—42no—
187#6101—42no—
188#6101—42no—
189#6101—81no—
190C4×Dic13—81no—
191C4×Dic13—81no—
192C4×Dic13—81no—
193#2550—131no—
194#2357—131no—
195#2067—131no—
196#2065—131no—
197#2025—131no—
198#2023—131no—
199#1989—131no—
200#1988—131no—
201#1949—131no—
202#1939D1311yescharacteristic, complemented
203#1921—131no—
204#1920—131no—
205#1835—131no—
206#1804—131no—
207C4×#102—131no—
208C23×C13C22×D411yescharacteristic
209C22×D13—22no—
210C22×D13—41no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13—41no—
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×C13C22⋊Q812yes—
232C2×C4×C13C22⋊Q812yes—
233C2×C4×C13#13512yes—
234C2×C4×C13C22×Q811yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13H(5,𝔽2)11yescharacteristic
239C2×C4×C132−1+411yescharacteristic
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—41no—
244C2×Dic13—41no—
245C2×Dic13—41no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261D52—22no—
262D52—22no—
263D52—41no—
264D52—41no—
265C4×D13—84no—
266Dic26—84no—
267C8×C13—41no—
268C8×C13—41no—
269C8×C13—41no—
270C8×C13—41no—
271C2×C4⋊Q8—131no—
272C2×#125—131no—
273C2×C4×D4—131no—
274C2×#107—131no—
275C2×#106—131no—
276C2×C4⋊C8C2×D1311yescharacteristic
277C2×C4⋊C8C2×D1311yescharacteristic
278C2×C4⋊C8C2×D1311yescharacteristic
279C2×#102—131no—
280C2×#102—131no—
281C2×#102—131no—
282C2×#102—131no—
283C2×C4×C8C2×D1311yescharacteristic
284#398—261no—
285#395—261no—
286#391—261no—
287#390—131no—
288#390—131no—
289#389—131no—
290#389—131no—
291#389—261no—
292#388—261no—
293#388—261no—
294#382—131no—
295#382—131no—
296#381—261no—
297C4×C4⋊C4—131no—
298C4×C4⋊C4—131no—
299C4×C4⋊C4—131no—
300C4×C4⋊C4C2×D1311yescharacteristic
301C4×C22⋊C4—261no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#336C2×D1311yescharacteristic
313#336C2×D1311yescharacteristic
314C22×C13C2×C22⋊Q811yescharacteristic
315C22×C13#54611yescharacteristic
316C22×C13#54811yescharacteristic
317C22×C13C2×#13511yescharacteristic
318C22×C13#57511yescharacteristic
319C22×C13#57611yescharacteristic
320C22×C13#57711yescharacteristic
321C2×D13—42no—
322C2×D13—42no—
323C2×D13—42no—
324C2×D13—81no—
325C2×D13—81no—
326C2×D13—81no—
327C2×D13—81no—
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—22no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13#53311yescharacteristic
335C4×C13#54411yescharacteristic
336C4×C13#55511yescharacteristic
337C4×C13#55611yescharacteristic
338Dic13—42no—
339Dic13—42no—
340Dic13—42no—
341Dic13—81no—
342Dic13—81no—
343Dic13—81no—
344Dic13—81no—
345C22×Q8—261no—
346C22×D4—131no—
347C23×C4—261no—
348C22×C8C22×D1311yescharacteristic
349C22×C8C22×D1311yescharacteristic
350C22×C8C22×D1311yescharacteristic
351C22×C8C22×D1311yescharacteristic
352C4⋊Q8—262no—
353C4⋊Q8—521no—
354#125—262no—
355#125—521no—
356C4×D4—134no—
357C4×D4—262no—
358C2×C4⋊C4—131no—
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×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4D5211yescharacteristic
371C2×C4⋊C4D5211yescharacteristic
372C2×C22⋊C4—261no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C42—261no—
378C2×C42—261no—
379C2×C42—261no—
380C2×C42C22×D1311yescharacteristic
381C2×C42C22×D1311yescharacteristic
382C2×C42C22×D1311yescharacteristic
383#107—262no—
384#106—262no—
385C4⋊C8—22no—
386C4⋊C8—41no—
387C4⋊C8—41no—
388#102—262no—
389#102—262no—
390#102—521no—
391#102—521no—
392C4×C8—22no—
393#95—261no—
394#95—261no—
395#95—261no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95D5211yescharacteristic
403#95D5211yescharacteristic
404C2×C13#243911yescharacteristic
405C2×C13#307611yescharacteristic
406C2×C13#308111yescharacteristic
407C2×C13#329711yescharacteristic
408C2×C13#332611yescharacteristic
409C2×C13#336511yescharacteristic
410C2×C13#337011yescharacteristic
411D13—82no—
412C24—261no—
413C2×Q8—522no—
414C2×Q8—522no—
415C2×Q8—1041no—
416C2×D4—132no—
417C2×D4—261no—
418C2×D4—261no—
419C2×D4—261no—
420C2×D4—261no—
421C2×D4—261no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—264no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—1041no—
431C22×C4—1041no—
432C22×C4C2×D5211yescharacteristic
433C22×C4C2×D5211yescharacteristic
434C22×C4C2×D5211yescharacteristic
435C22×C4C2×D5211yescharacteristic
436C22×C4C2×D5211yescharacteristic
437C22×C4C2×D5211yescharacteristic
438C22×C4C23×D1311yescharacteristic
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—21no—
451C4⋊C4—22no—
452C4⋊C4—41no—
453C4⋊C4—132no—
454C4⋊C4—132no—
455C4⋊C4—132no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—522no—
468C4⋊C4—522no—
469C4⋊C4—522no—
470C4⋊C4—522no—
471C4⋊C4—1041no—
472C22⋊C4—264no—
473C22⋊C4—522no—
474C22⋊C4—522no—
475C22⋊C4—1041no—
476C22⋊C4—1041no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—1041no—
482C42—1041no—
483C42—1041no—
484C42#612912yes—
485C42Q8×D1312yes—
486C13#2602811yescharacteristic, complemented, Sylow
487C23—262no—
488C23—521no—
489C23—521no—
490C23—521no—
491C23—521no—
492C23—521no—
493C23—521no—
494C23C22×D5211yescharacteristic
495Q8—1044no—
496D4—262no—
497D4—262no—
498D4—521no—
499D4—521no—
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—21no—
514C2×C4—21no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—262no—
518C2×C4—521no—
519C2×C4—521no—
520C2×C4—521no—
521C2×C4—521no—
522C2×C4—521no—
523C2×C4—521no—
524C2×C4—521no—
525C2×C4—521no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—1044no—
537C2×C4#8815112yes—
538C2×C4#8815112yes—
539C2×C4#8815812yes—
540C2×C4C2×#612911yescharacteristic
541C2×C4#8825111yescharacteristic
542C2×C4C2×Q8×D1311yescharacteristic
543C2×C4#8825411yescharacteristic
544C2×C4#41×D1311yescharacteristic
545C2×C4#41×D1311yescharacteristic
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—522no—
551C22—522no—
552C22—522no—
553C22—1041no—
554C22—1041no—
555C22—1041no—
556C22—1041no—
557C22C2×#8815111yescharacteristic
558C22#1171925911yescharacteristic
559C22#1171928111yescharacteristic
560C22C2×#8815811yescharacteristic
561C22#1171945311yescharacteristic
562C22#1171945611yescharacteristic
563C22#1171945711yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—522no—
571C4—522no—
572C4—522no—
573C4—1041no—
574C4—1041no—
575C4—1041no—
576C4—1041no—
577C4#1171932111yescharacteristic
578C4#1171934611yescharacteristic
579C4#1171939311yescharacteristic
580C4#1171943411yescharacteristic
581C2—1042no—
582C2#1311852511yescharacteristic
583C2#1312462611yescharacteristic
584C2#1312466811yescharacteristic
585C2#1312668811yescharacteristic
586C2#1312709111yescharacteristic
587C2#1312753411yescharacteristic
588C2#1312759111yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1939C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#1939D13
hypocenterC13#26028
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. #13119857C2semidirect
7. #13115791C2semidirect
8. #13115787C2semidirect
9. #13115606C2semidirect
10. #13115429C2semidirect
11. #13115422C2semidirect
12. #13114967C2semidirect
15. C13×#1939C2semidirect
92. C4×D52Q8semidirect
202. #1939D13semidirect
486. C13#26028semidirect

Maximal subgroups

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

subgroupindex
#131198572
#131178072
#131162232
#131162092
#131159832
#131159732
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C4×#880612
C13×#19392
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