Finite Group Databasebeta

← #15922021

Subgroups — #15922021

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#13120066C211yesmaximal, characteristic, complemented
2#13117784C211yesmaximal, characteristic
3#13116359C211yesmaximal, characteristic
4#13116220C211yesmaximal, characteristic
5#13116210C211yesmaximal, characteristic
6#13115601C211yesmaximal, characteristic, complemented
7#13115592C211yesmaximal, characteristic, complemented
8#13115591C211yesmaximal, characteristic, complemented
9#13115558C211yesmaximal, characteristic, complemented
10#13115430C211yesmaximal, characteristic, complemented
11#13115422C211yesmaximal, characteristic, complemented
12#13115003C211yesmaximal, characteristic, complemented
13#13114844C211yesmaximal, characteristic
14#13114663C211yesmaximal, characteristic
15C13×#2093C211yesmaximal, characteristic
16C2×D4×Dic13C2211yescharacteristic
17C2×#88131—21no—
18C2×C13×#107C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#102C2211yescharacteristic
21C2×C13×#102C2211yescharacteristic
22C13×#390C2211yescharacteristic
23C13×#384C2211yescharacteristic
24#11718882C2211yescharacteristic
25C2×#88072C2211yescharacteristic
26C2×#88072C2211yescharacteristic
27C2×#88057C2211yescharacteristic
28C2×#88055C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31#11718646C2211yescharacteristic
32#11718644—21no—
33#11718643—21no—
34#11718642—21no—
35#11718639—21no—
36#11718638C2211yescharacteristic
37#11718638C2211yescharacteristic
38#11718637C2211yescharacteristic
39C4⋊C4×Dic13C2211yescharacteristic
40C4⋊C4×Dic13C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718606—21no—
45#11718605—21no—
46#11718603—21no—
47C4×C4⋊Dic13C2211yescharacteristic
48C4×#6101C2211yescharacteristic
49#11718589C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51C13×#336C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C22×D4×C13C2311yescharacteristic
60C23×Dic13—21no—
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C42×C13C2311yescharacteristic
71C2×C22⋊Dic13—21no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74D4×Dic13—22no—
75D4×Dic13Q814yes—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101D411yescharacteristic
85C2×#6101D411yescharacteristic
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13C2311yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93#88131—44no—
94C13×#107—22no—
95C13×#107—41no—
96C13×#102—22no—
97C13×#102—41no—
98#88072—22no—
99#88072—41no—
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#88071—21no—
109#88071D411yescharacteristic
110#88071D411yescharacteristic
111#88057—22no—
112#88055—22no—
113#88054—22no—
114#88054—22no—
115#88048—41no—
116#88047—41no—
117#88047—41no—
118C4⋊#1055—22no—
119#26098—131nomaximal, Sylow
120C24×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13C2×Q812yes—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2411yescharacteristic
133C22×Dic13—21no—
134C22×Dic13—24no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—42no—
139C22×Dic13—42no—
140C22×Dic13C2×D411yescharacteristic
141C22×Dic13C2×D411yescharacteristic
142C22×Dic13C2×D411yescharacteristic
143C22×Dic13C2×D411yescharacteristic
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13#4112yes—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—42no—
157C13×C4⋊C4—81no—
158C13×C22⋊C4—42no—
159C13×C22⋊C4—81no—
160C42×C13—21no—
161C42×C13—21no—
162C22⋊Dic13—24no—
163C22⋊Dic13—42no—
164C22⋊Dic13—81no—
165C4⋊Dic13—21no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—81no—
173C4⋊Dic13C2×Q812yes—
174#6101—22no—
175#6101—41no—
176#6101—42no—
177#6101—42no—
178#6101—81no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—42no—
182C4×Dic13—42no—
183C4×Dic13—81no—
184C4×Dic13C2×Q812yes—
185C4×Dic13#4112yes—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055#4112yes—
192#2570—131no—
193#2354—131no—
194#2093D1311yescharacteristic
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×C13—22no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—41no—
214C23×C13C22×D411yescharacteristic
215D4×C13—22no—
216D4×C13—22no—
217D4×C13—41no—
218D4×C13—41no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13AGL(1,ℤ/8)12yes—
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—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—22no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—48no—
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—
262C2×Dic13—41no—
263C2×Dic13C22⋊Q812yes—
264C2×Dic13C22⋊Q812yes—
265C8×C13—22no—
266C8×C13—41no—
267#1055—22no—
268#1055—41no—
269C2×C4×D4—131no—
270C2×#117—261no—
271C2×#107—131no—
272C2×#107—131no—
273C2×#107C2×D1311yescharacteristic
274C2×#107C2×D1311yescharacteristic
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×#102C2×D1311yescharacteristic
283C2×#102C2×D1311yescharacteristic
284C2×#97—131no—
285#400—261no—
286#398—261no—
287#390—131no—
288#390C2×D1311yescharacteristic
289#389—131no—
290#389—131no—
291#388—261no—
292#388—261no—
293#387—261no—
294#387—261no—
295#384—131no—
296#384C2×D1311yescharacteristic
297#382—131no—
298#382—131no—
299#380—261no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4—131no—
303C4×C4⋊C4—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#336—131no—
311#336C2×D1311yescharacteristic
312C22×C13—42no—
313C22×C13—42no—
314C22×C13—42no—
315C22×C13—81no—
316C22×C13—81no—
317C22×C13—81no—
318C22×C13—81no—
319C22×C13C2×C22⋊Q811yescharacteristic
320C22×C13#54711yescharacteristic
321C22×C13#55011yescharacteristic
322C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
323C22×C13#57511yescharacteristic
324C22×C13#57611yescharacteristic
325C22×C13#57811yescharacteristic
326C4×C13—22no—
327C4×C13—41no—
328C4×C13—81no—
329C4×C13—81no—
330C4×C13—81no—
331C4×C13#53311yescharacteristic
332C4×C13#54411yescharacteristic
333C4×C13#55211yescharacteristic
334C4×C13#55311yescharacteristic
335Dic13—22no—
336Dic13—22no—
337Dic13—42no—
338Dic13—41no—
339Dic13—41no—
340Dic13—81no—
341Dic13—81no—
342Dic13—81no—
343C22×D4C22×D1311yescharacteristic
344C23×C4—261no—
345C22×C8—131no—
346C22×C8—131no—
347C22×C8C22×D1311yescharacteristic
348C22×C8C22×D1311yescharacteristic
349C4×D4—134no—
350C4×D4—262no—
351#117—524no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—131no—
355C2×C4⋊C4—131no—
356C2×C4⋊C4—131no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—261no—
361C2×C4⋊C4—261no—
362C2×C4⋊C4—261no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4C22×D1311yescharacteristic
365C2×C4⋊C4C22×D1311yescharacteristic
366C2×C4⋊C4C22×D1311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—261no—
370C2×C22⋊C4—261no—
371C2×C22⋊C4—261no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—261no—
375C2×C42—261no—
376C2×C42—261no—
377C2×C42C22×D1311yescharacteristic
378#107—22no—
379#107—41no—
380#107—521no—
381#107—521no—
382#106—262no—
383#106—521no—
384C4⋊C8—262no—
385C4⋊C8—262no—
386C4⋊C8—262no—
387#102—22no—
388#102—41no—
389#102—262no—
390#102—521no—
391#97—262no—
392#95—131no—
393#95—131no—
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#95—261no—
403C2×C13—82no—
404C2×C13#244111yescharacteristic
405C2×C13#307711yescharacteristic
406C2×C13#308311yescharacteristic
407C2×C13#334311yescharacteristic
408C2×C13#334711yescharacteristic
409C2×C13#339911yescharacteristic
410C2×C13#340211yescharacteristic
411C24—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4Q8×D1312yes—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—131no—
422C22×C4—131no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—264no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—522no—
431C22×C4—522no—
432C22×C4D4×D1311yescharacteristic
433C22×C4D4×D1311yescharacteristic
434C22×C4C23×D1311yescharacteristic
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—132no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8#612912yes—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—42no—
454C4⋊C4—81no—
455C4⋊C4—132no—
456C4⋊C4—262no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—521no—
465C4⋊C4—522no—
466C4⋊C4—522no—
467C4⋊C4—1041no—
468C4⋊C4—1041no—
469C22⋊C4—42no—
470C22⋊C4—81no—
471C22⋊C4—264no—
472C22⋊C4—522no—
473C22⋊C4—1041no—
474C42—21no—
475C42—21no—
476C42—132no—
477C42—132no—
478C42—261no—
479C42—261no—
480C42—522no—
481C42—522no—
482C42—1041no—
483C13#2609811yescharacteristic, complemented, Sylow
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C2×D4×D1311yescharacteristic
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—132no—
511C2×C4—132no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—262no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—528no—
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#8816512yes—
536C2×C4C2×#612911yescharacteristic
537C2×C4#8825111yescharacteristic
538C2×C4C2×Q8×D1311yescharacteristic
539C2×C4#41×D1311yescharacteristic
540C2×C4#41×D1311yescharacteristic
541C2×C4#8825711yescharacteristic
542C8—22no—
543C8—41no—
544C8—262no—
545C8—521no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22D13×C22⋊Q811yescharacteristic
554C22#1171936011yescharacteristic
555C22#1171942311yescharacteristic
556C22C2×#8816511yescharacteristic
557C22#1171946211yescharacteristic
558C22#1171948211yescharacteristic
559C22#1171948411yescharacteristic
560C4—22no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—262no—
566C4—262no—
567C4—522no—
568C4—521no—
569C4—521no—
570C4—1041no—
571C4—1041no—
572C4—1041no—
573C4#1171932711yescharacteristic
574C4#1171932811yescharacteristic
575C4#1171935511yescharacteristic
576C4#1171936611yescharacteristic
577C2—82no—
578C2#1311854211yescharacteristic
579C2#1312462811yescharacteristic
580C2#1312468211yescharacteristic
581C2#1312728011yescharacteristic
582C2#1312733911yescharacteristic
583C2#1312788311yescharacteristic
584C2#1312791211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2093C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2093D13
hypocenterC13#26098
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
1. #13120066C2semidirect
6. #13115601C2semidirect
7. #13115592C2semidirect
8. #13115591C2semidirect
9. #13115558C2semidirect
10. #13115430C2semidirect
11. #13115422C2semidirect
12. #13115003C2semidirect
483. C13#26098semidirect

Maximal subgroups

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

subgroupindex
#131200662
#131177842
#131163592
#131162202
#131162102
#131156012
#131155922
#131155912
#131155582
#131154302
#131154222
#131150032
#131148442
#131146632
C13×#20932
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