Finite Group Databasebeta

← #15921968

Subgroups — #15921968

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#13120064C211yesmaximal, characteristic, complemented
2#13117809C211yesmaximal, characteristic
3#13116362C211yesmaximal, characteristic
4#13116355C211yesmaximal, characteristic
5#13116208C211yesmaximal, characteristic
6#13116208C211yesmaximal, characteristic
7#13115604C211yesmaximal, characteristic, complemented
8#13115603C211yesmaximal, characteristic, complemented
9#13115598C211yesmaximal, characteristic, complemented
10#13115554C211yesmaximal, characteristic, complemented
11#13115427C211yesmaximal, characteristic, complemented
12#13115406C211yesmaximal, characteristic, complemented
13#13115000C211yesmaximal, characteristic, complemented
14#13114846C211yesmaximal, characteristic
15C4×C13×#102C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C13×#102C2211yescharacteristic
18C2×C13×#102C2211yescharacteristic
19C2×C4×C8×C13C2211yescharacteristic
20C4×C13×C4⋊C4C2211yescharacteristic
21#11718882C2211yescharacteristic
22#11718882C2211yescharacteristic
23C2×#88072C2211yescharacteristic
24C2×#88072C2211yescharacteristic
25#11718872—21no—
26C4×C22⋊Dic13—21no—
27C2×#88058C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88057C2211yescharacteristic
30C2×#88057C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33#11718638C2211yescharacteristic
34#11718637C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37#11718634C2211yescharacteristic
38#11718634C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718612—21no—
42#11718612—21no—
43#11718597C2211yescharacteristic
44#11718597C2211yescharacteristic
45C4×C4⋊Dic13C2211yescharacteristic
46#11718594—21no—
47#11718594—21no—
48C2×C4⋊#1055C2211yescharacteristic
49#11718321—21no—
50#11718318—21no—
51C13×#340C2211yescharacteristic
52C13×#340C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C22×D4×C13C2311yescharacteristic
60C23×C4×C13—21no—
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C4×D4×C13—22no—
64C4×D4×C13Q814yes—
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C22⋊C4—21no—
69C2×C42×C13—21no—
70C2×C42×C13C2311yescharacteristic
71C2×C22⋊Dic13—21no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C4⋊Dic13D411yescharacteristic
76C2×C4⋊Dic13D411yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13C2311yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C13×#102—22no—
92C13×#102—22no—
93C4×C8×C13—22no—
94C13×#95—21no—
95#88072—41no—
96#88072—41no—
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#88071D411yescharacteristic
108#88071D411yescharacteristic
109#88058—22no—
110#88058—22no—
111#88057—41no—
112#88057—41no—
113#88054—22no—
114#88054—22no—
115#88048—41no—
116#88047—41no—
117C4⋊#1055—22no—
118#26094—131nomaximal, Sylow
119C24×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13C2×Q812yes—
126C22×C4×C13—21no—
127C22×C4×C13—24no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—81no—
131C22×C4×C13—81no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2411yescharacteristic
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13C2×D411yescharacteristic
140C22×Dic13C2×D411yescharacteristic
141C22×Dic13C2×D411yescharacteristic
142C22×Dic13C2×D411yescharacteristic
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13#4112yes—
148C2×C8×C13#4112yes—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4C2×Q812yes—
155C13×C22⋊C4—24no—
156C42×C13—81no—
157C42×C13C2×Q812yes—
158C42×C13#4112yes—
159C22⋊Dic13—42no—
160C22⋊Dic13—42no—
161C22⋊Dic13—81no—
162C22⋊Dic13—81no—
163C4⋊Dic13—22no—
164C4⋊Dic13—21no—
165C4⋊Dic13—21no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—41no—
173#6101—42no—
174#6101—42no—
175#6101—81no—
176#6101—81no—
177C4×Dic13—21no—
178C4×Dic13—21no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—81no—
182C4×Dic13—81no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
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#1939—131no—
199#1921—131no—
200#1918—131no—
201#1846—131no—
202#1804—131no—
203C4×#102D1311yescharacteristic
204C23×C13—22no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13C22×D411yescharacteristic
212D4×C13—22no—
213D4×C13—22no—
214D4×C13—41no—
215D4×C13—41no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—22no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—84no—
230C2×C4×C13C22⋊Q812yes—
231C2×C4×C13C22⋊Q812yes—
232C2×C4×C13C22×Q811yescharacteristic
233C2×C4×C13C2×#4111yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×C4×C13H(5,𝔽2)11yescharacteristic
237C2×C4×C132−1+411yescharacteristic
238C2×Dic13—21no—
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—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—
261C2×Dic13#13512yes—
262C8×C13—22no—
263C8×C13—22no—
264#1055—41no—
265#1055—41no—
266C2×C4×D4C2×D1311yescharacteristic
267C2×#107—131no—
268C2×#107—131no—
269C2×#107—131no—
270C2×#106—131no—
271C2×#106—131no—
272C2×#106—131no—
273C2×C4⋊C8—131no—
274C2×C4⋊C8—131no—
275C2×C4⋊C8—131no—
276C2×#102—131no—
277C2×#102—131no—
278C2×#102C2×D1311yescharacteristic
279C2×#102C2×D1311yescharacteristic
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#340C2×D1311yescharacteristic
306#340C2×D1311yescharacteristic
307#336—131no—
308#336—131no—
309C22×C13—42no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—81no—
313C22×C13—81no—
314C22×C13—81no—
315C22×C13—81no—
316C22×C13C2×C22⋊Q811yescharacteristic
317C22×C13#54711yescharacteristic
318C22×C13#55011yescharacteristic
319C22×C13C2×#13511yescharacteristic
320C22×C13#57511yescharacteristic
321C22×C13#57611yescharacteristic
322C22×C13#57711yescharacteristic
323C4×C13—22no—
324C4×C13—22no—
325C4×C13—42no—
326C4×C13—81no—
327C4×C13—81no—
328C4×C13#53311yescharacteristic
329C4×C13#54411yescharacteristic
330C4×C13#55211yescharacteristic
331C4×C13#55311yescharacteristic
332Dic13—22no—
333Dic13—41no—
334Dic13—41no—
335Dic13—41no—
336Dic13—81no—
337Dic13—81no—
338Dic13—81no—
339Dic13—81no—
340C22×D4C22×D1311yescharacteristic
341C23×C4—21no—
342C22×C8—131no—
343C22×C8—131no—
344C22×C8C22×D1311yescharacteristic
345C22×C8C22×D1311yescharacteristic
346C4×D4—22no—
347C4×D4Dic2614yes—
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—261no—
355C2×C4⋊C4—261no—
356C2×C4⋊C4—261no—
357C2×C4⋊C4—261no—
358C2×C4⋊C4C22×D1311yescharacteristic
359C2×C4⋊C4C22×D1311yescharacteristic
360C2×C4⋊C4C22×D1311yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—261no—
363C2×C22⋊C4—261no—
364C2×C22⋊C4—261no—
365C2×C22⋊C4—261no—
366C2×C42—21no—
367C2×C42—131no—
368C2×C42—131no—
369C2×C42—261no—
370C2×C42—261no—
371C2×C42C22×D1311yescharacteristic
372#107—262no—
373#107—262no—
374#107—521no—
375#106—521no—
376#106—521no—
377#106—521no—
378C4⋊C8—262no—
379C4⋊C8—262no—
380C4⋊C8—262no—
381#102—22no—
382#102—22no—
383#102—521no—
384#102—521no—
385C4×C8—22no—
386#95—21no—
387#95—131no—
388#95—131no—
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#95—261no—
398#95—261no—
399C2×C13—82no—
400C2×C13#244111yescharacteristic
401C2×C13#307611yescharacteristic
402C2×C13#308111yescharacteristic
403C2×C13#333711yescharacteristic
404C2×C13#335511yescharacteristic
405C2×C13#339611yescharacteristic
406C2×C13#340111yescharacteristic
407C24—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4C2×Dic2612yes—
414C22×C4—21no—
415C22×C4—24no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—81no—
419C22×C4—81no—
420C22×C4—131no—
421C22×C4—131no—
422C22×C4—131no—
423C22×C4—131no—
424C22×C4—261no—
425C22×C4—261no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4D4×D1311yescharacteristic
429C22×C4D4×D1311yescharacteristic
430C22×C4C23×D1311yescharacteristic
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—261no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8#612712yes—
442C2×C8#612712yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—262no—
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—521no—
458C4⋊C4—522no—
459C4⋊C4—522no—
460C4⋊C4—1041no—
461C4⋊C4—1041no—
462C4⋊C4C2×Dic2612yes—
463C22⋊C4—24no—
464C22⋊C4—522no—
465C22⋊C4—522no—
466C22⋊C4—1041no—
467C22⋊C4—1041no—
468C42—81no—
469C42—261no—
470C42—261no—
471C42—261no—
472C42—261no—
473C42—1041no—
474C42—1041no—
475C42C2×Dic2612yes—
476C42#612912yes—
477C13#2609411yescharacteristic, complemented, Sylow
478C23—22no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23C2×D4×D1311yescharacteristic
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—84no—
504C2×C4—132no—
505C2×C4—261no—
506C2×C4—261no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
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—521no—
527C2×C4—521no—
528C2×C4#8813212yes—
529C2×C4#8813212yes—
530C2×C4C22×Dic2611yescharacteristic
531C2×C4C2×#612711yescharacteristic
532C2×C4C2×#612711yescharacteristic
533C2×C4C2×#612911yescharacteristic
534C2×C4#8825611yescharacteristic
535C2×C4#8825711yescharacteristic
536C8—22no—
537C8—22no—
538C8—521no—
539C8—521no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C2×#8813211yescharacteristic
548C22#1171925611yescharacteristic
549C22#1171925811yescharacteristic
550C22#1171946211yescharacteristic
551C22#1171946711yescharacteristic
552C22D13×#13511yescharacteristic
553C22#1171947311yescharacteristic
554C4—22no—
555C4—22no—
556C4—42no—
557C4—81no—
558C4—81no—
559C4—262no—
560C4—521no—
561C4—521no—
562C4—521no—
563C4—1041no—
564C4—1041no—
565C4—1041no—
566C4—1041no—
567C4#1171917511yescharacteristic
568C4#1171922411yescharacteristic
569C4#1171924611yescharacteristic
570C4#1171927011yescharacteristic
571C2—82no—
572C2#1311854911yescharacteristic
573C2#1312462011yescharacteristic
574C2#1312466311yescharacteristic
575C2#1312722011yescharacteristic
576C2#1312744311yescharacteristic
577C2#1312784811yescharacteristic
578C2#1312789811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC4×C13×#102C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenterC4×#102D13
hypocenterC13#26094
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #13120064C2semidirect
7. #13115604C2semidirect
8. #13115603C2semidirect
9. #13115598C2semidirect
10. #13115554C2semidirect
11. #13115427C2semidirect
12. #13115406C2semidirect
13. #13115000C2semidirect
477. C13#26094semidirect

Maximal subgroups

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

subgroupindex
#131200642
#131178092
#131163622
#131163552
#131162082
#131156042
#131156032
#131155982
#131155542
#131154272
#131154062
#131150002
#131148462
C4×C13×#1022
#2609413