Finite Group Databasebeta

← #15921992

Subgroups — #15921992

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#13116369C211yesmaximal, characteristic
3#13116357C211yesmaximal, characteristic
4#13116224C211yesmaximal, characteristic
5#13116224C211yesmaximal, characteristic
6#13115604C211yesmaximal, characteristic, complemented
7#13115602C211yesmaximal, characteristic, complemented
8#13115594C211yesmaximal, characteristic, complemented
9#13115555C211yesmaximal, characteristic, complemented
10#13115421C211yesmaximal, characteristic, complemented
11#13115414C211yesmaximal, characteristic, complemented
12#13114998C211yesmaximal, characteristic, complemented
13#13114846C211yesmaximal, characteristic
14C4×#88072C211yesmaximal, characteristic
15C13×#2357C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C13×#390C2211yescharacteristic
18C13×#390C2211yescharacteristic
19C13×#388—21no—
20C13×#388—21no—
21C13×#382C2211yescharacteristic
22C13×#381—21no—
23C4×C13×C4⋊C4C2211yescharacteristic
24C4×C13×C4⋊C4C2211yescharacteristic
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C22⋊C4—21no—
27C2×#88072C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31#11718647—21no—
32#11718645—21no—
33C2×#88048C2211yescharacteristic
34C2×#88048C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39#11718597C2211yescharacteristic
40#11718597C2211yescharacteristic
41#11718596C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718589C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49#11718316—21no—
50#11718315—21no—
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D4×C13C2311yescharacteristic
60C23×C4×C13—21no—
61C4×D4×C13—22no—
62C4×D4×C13Q814yes—
63C2×C13×C4⋊C4D411yescharacteristic
64C2×C13×C4⋊C4D411yescharacteristic
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—21no—
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C42×C13—21no—
74C2×C42×C13—21no—
75C2×C42×C13C2311yescharacteristic
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×#6101—21no—
85C2×#6101—21no—
86C2×C4×Dic13—21no—
87C22×#1055C2311yescharacteristic
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C13×#95—21no—
92C13×#95—21no—
93C13×#95—21no—
94C13×#95—21no—
95C13×#95D411yescharacteristic
96C13×#95D411yescharacteristic
97#88072—22no—
98#88072—22no—
99#88072—41no—
100#88072—41no—
101#88071—21no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88048—22no—
109#88048—22no—
110#88048—41no—
111#88047—41no—
112#88047—41no—
113#88047—41no—
114C4⋊#1055—22no—
115C4⋊#1055—22no—
116C4⋊#1055—22no—
117C4×#1055—22no—
118#26096—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×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2411yescharacteristic
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C13×C4⋊C4—22no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—41no—
150C13×C4⋊C4C2×Q812yes—
151C13×C22⋊C4—24no—
152C13×C22⋊C4—42no—
153C13×C22⋊C4—42no—
154C13×C22⋊C4—81no—
155C13×C22⋊C4—81no—
156C42×C13—21no—
157C42×C13—21no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—81no—
161C42×C13—81no—
162C42×C13C2×Q812yes—
163C42×C13#4112yes—
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—42no—
173C4⋊Dic13—81no—
174#6101—42no—
175#6101—81no—
176C4×Dic13—81no—
177C2×#1055—21no—
178C2×#1055—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#4112yes—
188C2×#1055#4112yes—
189#2570—131no—
190#2357D1311yescharacteristic
191#2094—131no—
192#2092—131no—
193#2067—131no—
194#2067—131no—
195#1949—131no—
196#1949—131no—
197#1947—131no—
198#1939—131no—
199#1920—131no—
200#1919—131no—
201#1846—131no—
202#1804—131no—
203C4×#102—131no—
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—21no—
221C2×C4×C13—21no—
222C2×C4×C13—22no—
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—21no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—84no—
241C2×C4×C13C22⋊Q812yes—
242C2×C4×C13C22⋊Q812yes—
243C2×C4×C13#13512yes—
244C2×C4×C13C22×Q811yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13H(5,𝔽2)11yescharacteristic
249C2×C4×C132−1+411yescharacteristic
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—41no—
262#1055—22no—
263#1055—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×#102—131no—
279C2×#102—131no—
280C2×C4×C8—131no—
281#400—261no—
282#398—261no—
283#390C2×D1311yescharacteristic
284#390C2×D1311yescharacteristic
285#389—131no—
286#389—131no—
287#388—21no—
288#388—21no—
289#387—261no—
290#387—261no—
291#384—131no—
292#382—131no—
293#382—131no—
294#382C2×D1311yescharacteristic
295#381—21no—
296C4×C4⋊C4—131no—
297C4×C4⋊C4C2×D1311yescharacteristic
298C4×C4⋊C4C2×D1311yescharacteristic
299C4×C4⋊C4C2×D1311yescharacteristic
300C4×C22⋊C4—21no—
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
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—22no—
326C4×C13—42no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13—81no—
331C4×C13—81no—
332C4×C13#53311yescharacteristic
333C4×C13#54411yescharacteristic
334C4×C13#55211yescharacteristic
335C4×C13#55311yescharacteristic
336Dic13—81no—
337Dic13—81no—
338Dic13—81no—
339Dic13—81no—
340C22×D4C22×D1311yescharacteristic
341C23×C4—21no—
342C22×C8—131no—
343C22×C8—131no—
344C22×C8—131no—
345C22×C8—131no—
346C4×D4—22no—
347C4×D4Dic2614yes—
348C2×C4⋊C4—131no—
349C2×C4⋊C4—131no—
350C2×C4⋊C4—131no—
351C2×C4⋊C4—131no—
352C2×C4⋊C4—261no—
353C2×C4⋊C4—261no—
354C2×C4⋊C4—261no—
355C2×C4⋊C4—261no—
356C2×C4⋊C4C22⋊D1311yescharacteristic
357C2×C4⋊C4C22⋊D1311yescharacteristic
358C2×C4⋊C4C22×D1311yescharacteristic
359C2×C4⋊C4C22×D1311yescharacteristic
360C2×C4⋊C4C22×D1311yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—261no—
369C2×C42C22×D1311yescharacteristic
370C2×C42C22×D1311yescharacteristic
371C2×C42C22×D1311yescharacteristic
372#107—521no—
373#107—521no—
374#107—521no—
375#106—262no—
376#106—262no—
377#106—521no—
378C4⋊C8—262no—
379C4⋊C8—262no—
380C4⋊C8—262no—
381#102—262no—
382#102—262no—
383#102—521no—
384#102—521no—
385C4×C8—262no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—261no—
391#95—261no—
392#95—261no—
393#95—261no—
394#95—261no—
395#95—261no—
396#95—261no—
397#95C22⋊D1311yescharacteristic
398#95C22⋊D1311yescharacteristic
399C2×C13—82no—
400C2×C13#244111yescharacteristic
401C2×C13#307611yescharacteristic
402C2×C13#308111yescharacteristic
403C2×C13#333911yescharacteristic
404C2×C13#335111yescharacteristic
405C2×C13#339411yescharacteristic
406C2×C13#340311yescharacteristic
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—261no—
421C22×C4—261no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4C2×C22⋊D1311yescharacteristic
425C22×C4C2×C22⋊D1311yescharacteristic
426C22×C4C2×C22⋊D1311yescharacteristic
427C22×C4C2×C22⋊D1311yescharacteristic
428C22×C4C2×C22⋊D1311yescharacteristic
429C22×C4C2×C22⋊D1311yescharacteristic
430C22×C4C23×D1311yescharacteristic
431C2×C8—132no—
432C2×C8—132no—
433C2×C8—261no—
434C2×C8—261no—
435C2×C8—261no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8—261no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—41no—
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—522no—
459C4⋊C4—522no—
460C4⋊C4—1041no—
461C4⋊C4—1041no—
462C4⋊C4C2×Dic2612yes—
463C22⋊C4—24no—
464C22⋊C4—42no—
465C22⋊C4—42no—
466C22⋊C4—81no—
467C22⋊C4—81no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—81no—
473C42—81no—
474C42—1041no—
475C42C2×Dic2612yes—
476C42#612712yes—
477C13#2609611yescharacteristic, complemented, Sylow
478C23—22no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23C22×C22⋊D1311yescharacteristic
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
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—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—84no—
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—521no—
527C2×C4#8817812yes—
528C2×C4#8817812yes—
529C2×C4#8820412yes—
530C2×C4C22×Dic2611yescharacteristic
531C2×C4C2×#612711yescharacteristic
532C2×C4#41×D1311yescharacteristic
533C2×C4#41×D1311yescharacteristic
534C2×C4#8825611yescharacteristic
535C2×C4#8825711yescharacteristic
536C8—262no—
537C8—262no—
538C8—521no—
539C8—521no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C2×#8817811yescharacteristic
548C22C2×#8820411yescharacteristic
549C22#1171952711yescharacteristic
550C22#1171952911yescharacteristic
551C22#1171953911yescharacteristic
552C22#1171954011yescharacteristic
553C22#1171954111yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—42no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—1041no—
564C4—1041no—
565C4—1041no—
566C4—1041no—
567C4#1171922211yescharacteristic
568C4#1171922411yescharacteristic
569C4#1171923411yescharacteristic
570C4#1171923511yescharacteristic
571C2—82no—
572C2#1311854311yescharacteristic
573C2#1312462411yescharacteristic
574C2#1312466711yescharacteristic
575C2#1312723211yescharacteristic
576C2#1312739011yescharacteristic
577C2#1312782811yescharacteristic
578C2#1312792011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2357C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2357D13
hypocenterC13#26096
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
1. #13120070C2semidirect
6. #13115604C2semidirect
7. #13115602C2semidirect
8. #13115594C2semidirect
9. #13115555C2semidirect
10. #13115421C2semidirect
11. #13115414C2semidirect
12. #13114998C2semidirect
477. C13#26096semidirect

Maximal subgroups

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

subgroupindex
#131200702
#131163692
#131163572
#131162242
#131156042
#131156022
#131155942
#131155552
#131154212
#131154142
#131149982
#131148462
C4×#880722
C13×#23572
#2609613