Finite Group Databasebeta

← #15922024

Subgroups — #15922024

Order 3328.

708 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117783C211yesmaximal, characteristic
2#13116365C211yesmaximal, characteristic
3#13116360C211yesmaximal, characteristic
4#13116221C211yesmaximal, characteristic
5#13116207C211yesmaximal, characteristic
6#13115602C211yesmaximal, characteristic, complemented
7#13115594C211yesmaximal, characteristic, complemented
8#13115592C211yesmaximal, characteristic, complemented
9#13115560C211yesmaximal, characteristic, complemented
10#13115425C211yesmaximal, characteristic, complemented
11#13115418C211yesmaximal, characteristic, complemented
12#13115005C211yesmaximal, characteristic, complemented
13#13114843C211yesmaximal, characteristic
14#13114664C211yesmaximal, characteristic
15C13×#2570C211yesmaximal, characteristic, complemented
16C2×#88146—21no—
17C2×C4×D52C2211yescharacteristic
18C13×#400—21no—
19C13×#398—21no—
20C13×#389C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#387—21no—
23C13×#387—21no—
24C13×#384C2211yescharacteristic
25C13×#382C2211yescharacteristic
26C13×#382C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29#11718648—21no—
30C2×#88049C2211yescharacteristic
31C2×#88049C2211yescharacteristic
32C2×#88049C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88048C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40#11718600C2211yescharacteristic
41#11718600C2211yescharacteristic
42#11718596C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44C4×C4⋊Dic13C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49#11718331—21no—
50#11718331—21no—
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D52C2311yescharacteristic
60C22×C4×D13—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4D411yescharacteristic
66C2×C13×C4⋊C4D411yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C42×C13—21no—
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×#6103—21no—
76C2×#6103—21no—
77C2×#6103—21no—
78C2×#6103—21no—
79C2×#6103—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C22×#1055C2311yescharacteristic
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91#88146—44no—
92C4×D52—22no—
93C4×D52Q814yes—
94C13×#95—21no—
95C13×#95—21no—
96C13×#95—21no—
97C13×#95—21no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95D411yescharacteristic
102C13×#95D411yescharacteristic
103#88071—21no—
104#88071—21no—
105#88049—22no—
106#88049—22no—
107#88049—41no—
108#88049—41no—
109#88048—22no—
110#88048—41no—
111#88047—22no—
112#88047—41no—
113#88047—41no—
114#88047—41no—
115C4⋊#1055—22no—
116C4⋊#1055—22no—
117C4⋊#1055—22no—
118#88043—22no—
119#26098—131nomaximal, Sylow
120C23×D13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2411yescharacteristic
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C2×D52—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52C2×Q812yes—
141C2×C4×D13—24no—
142C2×C4×D13—42no—
143C2×C4×D13—42no—
144C13×C4⋊C4—22no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—41no—
154C13×C4⋊C4—42no—
155C13×C4⋊C4—42no—
156C13×C4⋊C4—81no—
157C13×C4⋊C4—81no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—81no—
163C42×C13C2×Q812yes—
164C42×C13#4112yes—
165#6103—24no—
166#6103—42no—
167#6103—42no—
168#6103—81no—
169#6103—81no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—42no—
176C4⋊Dic13—81no—
177C4⋊Dic13C2×Q812yes—
178C4×Dic13—42no—
179C4×Dic13—42no—
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#4112yes—
191C2×#1055#4112yes—
192#2570D1311yescharacteristic, complemented
193#2354—131no—
194#2093—131no—
195#2092—131no—
196#2067—131no—
197#2065—131no—
198#1949—131no—
199#1947—131no—
200#1947—131no—
201#1940—131no—
202#1921—131no—
203#1920—131no—
204#1847—131no—
205#1804—131no—
206#1762—131no—
207C23×C13C22×D411yescharacteristic
208C22×D13—22no—
209C22×D13—41no—
210C22×D13—41no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
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—21no—
229C2×C4×C13—21no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
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—41no—
241C2×C4×C13—41no—
242C2×C4×C13C22⋊Q812yes—
243C2×C4×C13C22⋊Q812yes—
244C2×C4×C13AGL(1,ℤ/8)12yes—
245C2×C4×C13C22×Q811yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13H(5,𝔽2)11yescharacteristic
250C2×C4×C132−1+411yescharacteristic
251C2×Dic13—22no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260D52—22no—
261D52—22no—
262D52—41no—
263D52—41no—
264C4×D13—48no—
265#1055—22no—
266#1055—22no—
267#1055—41no—
268#1055—41no—
269C2×C4×D4—131no—
270C2×#117—261no—
271C2×#107—131no—
272C2×#107—131no—
273C2×#107—131no—
274C2×#107—131no—
275C2×#106—131no—
276C2×#106—131no—
277C2×C4⋊C8—131no—
278C2×C4⋊C8—131no—
279C2×C4⋊C8—131no—
280C2×#102—131no—
281C2×#102—131no—
282C2×#102—131no—
283C2×#102—131no—
284C2×#97—131no—
285#400—21no—
286#398—21no—
287#390—131no—
288#390—131no—
289#389C2×D1311yescharacteristic
290#389C2×D1311yescharacteristic
291#388—261no—
292#388—261no—
293#387—21no—
294#387—21no—
295#384—131no—
296#384C2×D1311yescharacteristic
297#382C2×D1311yescharacteristic
298#382C2×D1311yescharacteristic
299#380—261no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4C2×D1311yescharacteristic
303C4×C4⋊C4C2×D1311yescharacteristic
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#336—131no—
311#336—131no—
312C22×C13C2×C22⋊Q811yescharacteristic
313C22×C13#54711yescharacteristic
314C22×C13#55011yescharacteristic
315C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
316C22×C13#57511yescharacteristic
317C22×C13#57611yescharacteristic
318C22×C13#57811yescharacteristic
319C2×D13—42no—
320C2×D13—42no—
321C2×D13—42no—
322C2×D13—81no—
323C2×D13—81no—
324C2×D13—81no—
325C2×D13—81no—
326C4×C13—22no—
327C4×C13—22no—
328C4×C13—22no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—81no—
333C4×C13—81no—
334C4×C13—81no—
335C4×C13—81no—
336C4×C13#53311yescharacteristic
337C4×C13#54411yescharacteristic
338C4×C13#55211yescharacteristic
339C4×C13#55311yescharacteristic
340Dic13—42no—
341Dic13—81no—
342Dic13—81no—
343C22×D4—131no—
344C23×C4—261no—
345C22×C8—131no—
346C22×C8—131no—
347C22×C8—131no—
348C22×C8—131no—
349C4×D4—134no—
350C4×D4—262no—
351#117—524no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—131no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—261no—
360C2×C4⋊C4—261no—
361C2×C4⋊C4C22⋊D1311yescharacteristic
362C2×C4⋊C4C22⋊D1311yescharacteristic
363C2×C4⋊C4C22×D1311yescharacteristic
364C2×C4⋊C4C22×D1311yescharacteristic
365C2×C4⋊C4C22×D1311yescharacteristic
366C2×C4⋊C4C22×D1311yescharacteristic
367C2×C22⋊C4—261no—
368C2×C22⋊C4—261no—
369C2×C22⋊C4—261no—
370C2×C22⋊C4—261no—
371C2×C22⋊C4—261no—
372C2×C42—21no—
373C2×C42—261no—
374C2×C42—261no—
375C2×C42C22×D1311yescharacteristic
376C2×C42C22×D1311yescharacteristic
377C2×C42C22×D1311yescharacteristic
378#107—262no—
379#107—521no—
380#107—521no—
381#107—521no—
382#106—262no—
383#106—521no—
384C4⋊C8—262no—
385C4⋊C8—262no—
386C4⋊C8—262no—
387#102—262no—
388#102—262no—
389#102—521no—
390#102—521no—
391#97—262no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—261no—
400#95—261no—
401#95C22⋊D1311yescharacteristic
402#95C22⋊D1311yescharacteristic
403C2×C13#244111yescharacteristic
404C2×C13#307711yescharacteristic
405C2×C13#308311yescharacteristic
406C2×C13#334311yescharacteristic
407C2×C13#334711yescharacteristic
408C2×C13#339911yescharacteristic
409C2×C13#340211yescharacteristic
410D13—82no—
411C24—261no—
412C2×D4—132no—
413C2×D4—261no—
414C2×D4—261no—
415C2×D4—261no—
416C2×D4—261no—
417C2×D4—261no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—261no—
423C22×C4—264no—
424C22×C4—261no—
425C22×C4—261no—
426C22×C4—522no—
427C22×C4—522no—
428C22×C4C2×C22⋊D1311yescharacteristic
429C22×C4C2×C22⋊D1311yescharacteristic
430C22×C4C2×C22⋊D1311yescharacteristic
431C22×C4C2×C22⋊D1311yescharacteristic
432C22×C4C2×C22⋊D1311yescharacteristic
433C22×C4C2×C22⋊D1311yescharacteristic
434C22×C4C23×D1311yescharacteristic
435C2×C8—132no—
436C2×C8—132no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—41no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—81no—
460C4⋊C4—81no—
461C4⋊C4—132no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—522no—
468C4⋊C4—1041no—
469C22⋊C4—264no—
470C22⋊C4—522no—
471C22⋊C4—522no—
472C22⋊C4—1041no—
473C22⋊C4—1041no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—81no—
479C42—522no—
480C42—522no—
481C42Q8×D1312yes—
482C42#613112yes—
483C13#2609811yescharacteristic, complemented, Sylow
484C23—262no—
485C23—521no—
486C23—521no—
487C23—521no—
488C23—521no—
489C23—521no—
490C23—521no—
491C23C22×C22⋊D1311yescharacteristic
492D4—262no—
493D4—262no—
494D4—521no—
495D4—521no—
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—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—262no—
524C2×C4—528no—
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#8820012yes—
534C2×C4#8820012yes—
535C2×C4#8820312yes—
536C2×C4C2×Q8×D1311yescharacteristic
537C2×C4C2×#613111yescharacteristic
538C2×C4#41×D1311yescharacteristic
539C2×C4#41×D1311yescharacteristic
540C2×C4#8825611yescharacteristic
541C2×C4#8825711yescharacteristic
542C8—262no—
543C8—262no—
544C8—521no—
545C8—521no—
546C22—522no—
547C22—522no—
548C22—522no—
549C22—1041no—
550C22—1041no—
551C22—1041no—
552C22—1041no—
553C22C2×#8820011yescharacteristic
554C22C2×#8820311yescharacteristic
555C22#1171952711yescharacteristic
556C22#1171952911yescharacteristic
557C22#1171953911yescharacteristic
558C22#1171954011yescharacteristic
559C22#1171954311yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—522no—
571C4—1041no—
572C4—1041no—
573C4#1171939311yescharacteristic
574C4#1171939411yescharacteristic
575C4#1171939911yescharacteristic
576C4#1171940011yescharacteristic
577C2—1042no—
578C2#1311854511yescharacteristic
579C2#1312462911yescharacteristic
580C2#1312468311yescharacteristic
581C2#1312727611yescharacteristic
582C2#1312733011yescharacteristic
583C2#1312787411yescharacteristic
584C2#1312791111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2570C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2570D13
hypocenterC13#26098
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2570

Complements

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

NH ≅ G/Ntype
6. #13115602C2semidirect
7. #13115594C2semidirect
8. #13115592C2semidirect
9. #13115560C2semidirect
10. #13115425C2semidirect
11. #13115418C2semidirect
12. #13115005C2semidirect
15. C13×#2570C2semidirect
192. #2570D13semidirect
483. C13#26098semidirect

Maximal subgroups

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

subgroupindex
#131177832
#131163652
#131163602
#131162212
#131162072
#131156022
#131155942
#131155922
#131155602
#131154252
#131154182
#131150052
#131148432
#131146642
C13×#25702
#2609813