Finite Group Databasebeta

← #15921966

Subgroups — #15921966

Order 3328.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120070C211yesmaximal, characteristic, complemented
2#13117807C211yesmaximal, characteristic
3#13116363C211yesmaximal, characteristic
4#13116356C211yesmaximal, characteristic
5#13116209C211yesmaximal, characteristic
6#13116209C211yesmaximal, characteristic
7#13115606C211yesmaximal, characteristic, complemented
8#13115606C211yesmaximal, characteristic, complemented
9#13115600C211yesmaximal, characteristic, complemented
10#13115429C211yesmaximal, characteristic, complemented
11#13115408C211yesmaximal, characteristic, complemented
12#13115000C211yesmaximal, characteristic, complemented
13#13114847C211yesmaximal, characteristic
14C4×#88061C211yesmaximal, characteristic
15C13×#1939C211yesmaximal, characteristic, complemented
16C2×C4×D52C2211yescharacteristic
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C2×C4×C8×C13C2211yescharacteristic
21C4×C13×C4⋊C4C2211yescharacteristic
22C2×#88061C2211yescharacteristic
23C2×#88061C2211yescharacteristic
24C2×#88061C2211yescharacteristic
25C2×#88061C2211yescharacteristic
26C2×#88058C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88057C2211yescharacteristic
30C2×#88057C2211yescharacteristic
31C2×#88057C2211yescharacteristic
32#11718651—21no—
33#11718651—21no—
34#11718647—21no—
35#11718645—21no—
36#11718600C2211yescharacteristic
37#11718600C2211yescharacteristic
38#11718597C2211yescharacteristic
39#11718597C2211yescharacteristic
40#11718597C2211yescharacteristic
41#11718596C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44C4×C4⋊Dic13C2211yescharacteristic
45#11718589C2211yescharacteristic
46#11718589C2211yescharacteristic
47#11718327—21no—
48#11718325—21no—
49#11718316—21no—
50#11718315—21no—
51C13×#336C2211yescharacteristic
52C13×#336C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59C22×D52C2311yescharacteristic
60C22×C4×D13—21no—
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C2×C13×C4⋊C4D411yescharacteristic
66C2×C13×C4⋊C4D411yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C2×C42×C13C2311yescharacteristic
69C2×C42×C13C2311yescharacteristic
70C2×#6103—21no—
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13—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×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C4×D52—22no—
90C4×D52Q814yes—
91C13×C4⋊C8—22no—
92C13×C4⋊C8—22no—
93C13×C4⋊C8—22no—
94C4×C8×C13—22no—
95C13×#95D411yescharacteristic
96C13×#95D411yescharacteristic
97#88071—21no—
98#88071—21no—
99#88071—21no—
100#88071—21no—
101#88071—21no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88061—22no—
109#88061—22no—
110#88061—41no—
111#88061—41no—
112#88058—22no—
113#88058—22no—
114#88058—41no—
115#88057—41no—
116#88057—41no—
117#88057—41no—
118#26094—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×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#4112yes—
154C2×C8×C13#4112yes—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—41no—
157C42×C13—21no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13C2×Q812yes—
162C42×C13#4112yes—
163#6103—24no—
164#6103—42no—
165#6103—42no—
166#6103—81no—
167#6103—81no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
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—42no—
182C4⋊Dic13—81no—
183C4⋊Dic13C2×Q812yes—
184#6101—42no—
185#6101—81no—
186C4×Dic13—81no—
187C4×Dic13—81no—
188C4×Dic13—81no—
189#2570—131no—
190#2357—131no—
191#2093—131no—
192#2092—131no—
193#2065—131no—
194#2065—131no—
195#1949—131no—
196#1949—131no—
197#1948—131no—
198#1939D1311yescharacteristic, complemented
199#1921—131no—
200#1918—131no—
201#1846—131no—
202#1804—131no—
203C4×#102—131no—
204C23×C13C22×D411yescharacteristic
205C22×D13—22no—
206C22×D13—41no—
207C22×D13—41no—
208C22×D13—41no—
209C22×D13—41no—
210C22×D13—41no—
211C22×D13—41no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
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×C13C22⋊Q812yes—
228C2×C4×C13C22⋊Q812yes—
229C2×C4×C13#13512yes—
230C2×C4×C13C22×Q811yescharacteristic
231C2×C4×C13C2×#4111yescharacteristic
232C2×C4×C13C2×#4111yescharacteristic
233C2×C4×C13C2×#4111yescharacteristic
234C2×C4×C13H(5,𝔽2)11yescharacteristic
235C2×C4×C132−1+411yescharacteristic
236C2×Dic13—22no—
237C2×Dic13—41no—
238C2×Dic13—41no—
239C2×Dic13—41no—
240C2×Dic13—41no—
241C2×Dic13—41no—
242C2×Dic13—41no—
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—
257D52—22no—
258D52—22no—
259D52—41no—
260D52—41no—
261C4×D13—84no—
262C8×C13—22no—
263C8×C13—22no—
264C8×C13—41no—
265C8×C13—41no—
266C2×C4×D4—131no—
267C2×#107—131no—
268C2×#107—131no—
269C2×#107—131no—
270C2×#106—131no—
271C2×#106—131no—
272C2×#106—131no—
273C2×C4⋊C8C2×D1311yescharacteristic
274C2×C4⋊C8C2×D1311yescharacteristic
275C2×C4⋊C8C2×D1311yescharacteristic
276C2×#102—131no—
277C2×#102—131no—
278C2×#102—131no—
279C2×#102—131no—
280C2×C4×C8C2×D1311yescharacteristic
281#400—261no—
282#398—261no—
283#390—131no—
284#390—131no—
285#389—131no—
286#389—131no—
287#388—261no—
288#388—261no—
289#387—261no—
290#387—261no—
291#384—131no—
292#382—131no—
293#382—131no—
294#382—131no—
295#381—261no—
296C4×C4⋊C4—131no—
297C4×C4⋊C4—131no—
298C4×C4⋊C4—131no—
299C4×C4⋊C4C2×D1311yescharacteristic
300C4×C22⋊C4—261no—
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#336C2×D1311yescharacteristic
308#336C2×D1311yescharacteristic
309C22×C13C2×C22⋊Q811yescharacteristic
310C22×C13#54711yescharacteristic
311C22×C13#55011yescharacteristic
312C22×C13C2×#13511yescharacteristic
313C22×C13#57511yescharacteristic
314C22×C13#57611yescharacteristic
315C22×C13#57711yescharacteristic
316C2×D13—42no—
317C2×D13—42no—
318C2×D13—42no—
319C2×D13—81no—
320C2×D13—81no—
321C2×D13—81no—
322C2×D13—81no—
323C4×C13—22no—
324C4×C13—22no—
325C4×C13—22no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13#53311yescharacteristic
330C4×C13#54411yescharacteristic
331C4×C13#55211yescharacteristic
332C4×C13#55311yescharacteristic
333Dic13—42no—
334Dic13—81no—
335Dic13—81no—
336Dic13—81no—
337Dic13—81no—
338Dic13—81no—
339Dic13—81no—
340C22×D4—131no—
341C23×C4—261no—
342C22×C8C22×D1311yescharacteristic
343C22×C8C22×D1311yescharacteristic
344C22×C8C22×D1311yescharacteristic
345C22×C8C22×D1311yescharacteristic
346C4×D4—134no—
347C4×D4—262no—
348C2×C4⋊C4—131no—
349C2×C4⋊C4—131no—
350C2×C4⋊C4—131no—
351C2×C4⋊C4—131no—
352C2×C4⋊C4—131no—
353C2×C4⋊C4—131no—
354C2×C4⋊C4—131no—
355C2×C4⋊C4—261no—
356C2×C4⋊C4—261no—
357C2×C4⋊C4—261no—
358C2×C4⋊C4—261no—
359C2×C4⋊C4D5211yescharacteristic
360C2×C4⋊C4D5211yescharacteristic
361C2×C22⋊C4—261no—
362C2×C22⋊C4—261no—
363C2×C22⋊C4—261no—
364C2×C22⋊C4—261no—
365C2×C22⋊C4—261no—
366C2×C42—261no—
367C2×C42—261no—
368C2×C42—261no—
369C2×C42C22×D1311yescharacteristic
370C2×C42C22×D1311yescharacteristic
371C2×C42C22×D1311yescharacteristic
372#107—262no—
373#107—262no—
374#107—521no—
375#106—521no—
376#106—521no—
377#106—521no—
378C4⋊C8—22no—
379C4⋊C8—22no—
380C4⋊C8—22no—
381#102—262no—
382#102—262no—
383#102—521no—
384#102—521no—
385C4×C8—22no—
386#95—261no—
387#95—261no—
388#95—261no—
389#95—261no—
390#95—261no—
391#95—261no—
392#95—261no—
393#95—261no—
394#95—261no—
395#95—261no—
396#95—261no—
397#95D5211yescharacteristic
398#95D5211yescharacteristic
399C2×C13#244111yescharacteristic
400C2×C13#307611yescharacteristic
401C2×C13#308111yescharacteristic
402C2×C13#333711yescharacteristic
403C2×C13#335511yescharacteristic
404C2×C13#339611yescharacteristic
405C2×C13#340111yescharacteristic
406D13—82no—
407C24—261no—
408C2×D4—132no—
409C2×D4—261no—
410C2×D4—261no—
411C2×D4—261no—
412C2×D4—261no—
413C2×D4—261no—
414C22×C4—261no—
415C22×C4—264no—
416C22×C4—261no—
417C22×C4—261no—
418C22×C4—261no—
419C22×C4—261no—
420C22×C4—261no—
421C22×C4—261no—
422C22×C4—1041no—
423C22×C4—1041no—
424C22×C4C2×D5211yescharacteristic
425C22×C4C2×D5211yescharacteristic
426C22×C4C2×D5211yescharacteristic
427C22×C4C2×D5211yescharacteristic
428C22×C4C2×D5211yescharacteristic
429C22×C4C2×D5211yescharacteristic
430C22×C4C23×D1311yescharacteristic
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8#612912yes—
442C2×C8#613112yes—
443C4⋊C4—22no—
444C4⋊C4—41no—
445C4⋊C4—132no—
446C4⋊C4—261no—
447C4⋊C4—261no—
448C4⋊C4—261no—
449C4⋊C4—261no—
450C4⋊C4—261no—
451C4⋊C4—261no—
452C4⋊C4—261no—
453C4⋊C4—261no—
454C4⋊C4—261no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—522no—
460C4⋊C4—522no—
461C4⋊C4—1041no—
462C4⋊C4—1041no—
463C22⋊C4—264no—
464C22⋊C4—522no—
465C22⋊C4—522no—
466C22⋊C4—1041no—
467C22⋊C4—1041no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—1041no—
473C42—1041no—
474C42—1041no—
475C42#612912yes—
476C42Q8×D1312yes—
477C13#2609411yescharacteristic, complemented, Sylow
478C23—262no—
479C23—521no—
480C23—521no—
481C23—521no—
482C23—521no—
483C23—521no—
484C23—521no—
485C23C22×D5211yescharacteristic
486D4—262no—
487D4—262no—
488D4—521no—
489D4—521no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
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—262no—
506C2×C4—521no—
507C2×C4—521no—
508C2×C4—521no—
509C2×C4—521no—
510C2×C4—521no—
511C2×C4—521no—
512C2×C4—521no—
513C2×C4—521no—
514C2×C4—521no—
515C2×C4—521no—
516C2×C4—521no—
517C2×C4—521no—
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—1044no—
527C2×C4#8815112yes—
528C2×C4#8815112yes—
529C2×C4#8815812yes—
530C2×C4C2×#612911yescharacteristic
531C2×C4C2×#612911yescharacteristic
532C2×C4C2×Q8×D1311yescharacteristic
533C2×C4C2×#613111yescharacteristic
534C2×C4#8825611yescharacteristic
535C2×C4#8825711yescharacteristic
536C8—22no—
537C8—22no—
538C8—41no—
539C8—41no—
540C22—522no—
541C22—522no—
542C22—522no—
543C22—1041no—
544C22—1041no—
545C22—1041no—
546C22—1041no—
547C22C2×#8815111yescharacteristic
548C22#1171926011yescharacteristic
549C22#1171928211yescharacteristic
550C22C2×#8815811yescharacteristic
551C22#1171945311yescharacteristic
552C22#1171945611yescharacteristic
553C22#1171945711yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—522no—
561C4—1041no—
562C4—1041no—
563C4—1041no—
564C4—1041no—
565C4—1041no—
566C4—1041no—
567C4#1171932311yescharacteristic
568C4#1171934711yescharacteristic
569C4#1171939411yescharacteristic
570C4#1171943311yescharacteristic
571C2—1042no—
572C2#1311854711yescharacteristic
573C2#1312462611yescharacteristic
574C2#1312466811yescharacteristic
575C2#1312721711yescharacteristic
576C2#1312744111yescharacteristic
577C2#1312784911yescharacteristic
578C2#1312790411yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1939C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#1939D13
hypocenterC13#26094
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. #13120070C2semidirect
7. #13115606C2semidirect
8. #13115606C2semidirect
9. #13115600C2semidirect
10. #13115429C2semidirect
11. #13115408C2semidirect
12. #13115000C2semidirect
15. C13×#1939C2semidirect
198. #1939D13semidirect
477. C13#26094semidirect

Maximal subgroups

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

subgroupindex
#131200702
#131178072
#131163632
#131163562
#131162092
#131156062
#131156002
#131154292
#131154082
#131150002
#131148472
C4×#880612
C13×#19392
#2609413