Finite Group Databasebeta

← #15880607

Subgroups — #15880607

Order 3328.

766 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
1C2×#11718541C211yesmaximal, characteristic
2#13117725C211yesmaximal, characteristic
3#13117720C211yesmaximal, characteristic
4#13115578C211yesmaximal, characteristic, complemented
5#13115576C211yesmaximal, characteristic, complemented
6#13115429C211yesmaximal, characteristic, complemented
7#13115427C211yesmaximal, characteristic, complemented
8#13115409C211yesmaximal, characteristic, complemented
9#13114930C211yesmaximal, characteristic
10#13114930C211yesmaximal, characteristic
11#13114864C211yesmaximal, characteristic
12#13114734C211yesmaximal, characteristic, complemented
13#13114732C211yesmaximal, characteristic, complemented
14#13114611C211yesmaximal, characteristic
15C13×#1918C211yesmaximal, characteristic, complemented
16C22×C8×D13C2211yescharacteristic
17C2×#88146C2211yescharacteristic
18C2×#88146C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C13×#389C2211yescharacteristic
21C4×C13×C4⋊C4C2211yescharacteristic
22C2×#88060C2211yescharacteristic
23C2×#88058C2211yescharacteristic
24C2×#88055C2211yescharacteristic
25#11718651—21no—
26#11718648C2211yescharacteristic
27#11718648C2211yescharacteristic
28#11718646C2211yescharacteristic
29#11718638—21no—
30C4⋊C4×Dic13C2211yescharacteristic
31C4⋊C4×Dic13C2211yescharacteristic
32#11718634C2211yescharacteristic
33C2×#88048C2211yescharacteristic
34C2×#88048C2211yescharacteristic
35C2×#88047C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37#11718601—21no—
38C4×#6103C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40C4×#6101—21no—
41#11718589C2211yescharacteristic
42C2×#88043C2211yescharacteristic
43#11718541C418yescomplemented
44#11718331—21no—
45#11718330—21no—
46#11718312—21no—
47#11718309—21no—
48C13×#340C2211yescharacteristic
49C13×#340C2211yescharacteristic
50C13×#340C2211yescharacteristic
51C13×#336C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×C4×D13C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4C2311yescharacteristic
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C42×C13—21no—
69C2×C42×C13C2311yescharacteristic
70C2×#6103—21no—
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103D411yescharacteristic
75C2×#6103D411yescharacteristic
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×#6101—21no—
82C2×#6101—21no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C2×C8×D13—22no—
92C2×C8×D13—22no—
93C2×C8×D13C2×C414yes—
94#88146—22no—
95#88146—22no—
96#88146C2×C414yes—
97#88146C2×C414yes—
98C13×#107C2×C414yes—
99C13×#95—21no—
100C13×#95—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#88060—22no—
112#88058C2×C414yes—
113#88055—22no—
114#88048C2×C414yes—
115#88048C2×C414yes—
116#88047—22no—
117#88047—22no—
118#88043—22no—
119#22616—131nomaximal, Sylow
120C23×D13C2×D411yescharacteristic
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×C13C2411yescharacteristic
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13C2×D411yescharacteristic
133C22×Dic13C2×D411yescharacteristic
134C22×Dic13C2×D411yescharacteristic
135C2×C4×D13—21no—
136C2×C4×D13—21no—
137C2×C4×D13—21no—
138C2×C4×D13—21no—
139C2×C4×D13C22×C412yes—
140C2×C4×D13#4112yes—
141C2×C8×C13—21no—
142C2×C8×C13—21no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13C22×C412yes—
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—81no—
154C13×C4⋊C4C22×C412yes—
155C13×C4⋊C4C22×C412yes—
156C42×C13—21no—
157C42×C13—21no—
158C42×C13—81no—
159#6103—24no—
160#6103—24no—
161#6103—41no—
162#6103—41no—
163#6103—81no—
164#6103—81no—
165C4⋊Dic13—21no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—81no—
172C4⋊Dic13C22×C412yes—
173C4⋊Dic13C22×C412yes—
174#6101—42no—
175#6101—42no—
176C4×Dic13—21no—
177C4×Dic13—21no—
178C4×Dic13—24no—
179C4×Dic13—24no—
180C4×Dic13—42no—
181C4×Dic13—42no—
182C4×Dic13—81no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055C22×C412yes—
187C2×#1055#4112yes—
188C2×#1055#4112yes—
189C8×D13—28no—
190C2×#427—131no—
191#2347—131no—
192#2346—131no—
193#1944—131no—
194#1944—131no—
195#1921—131no—
196#1921—131no—
197#1918—131no—
198#1918D1311yescharacteristic, complemented
199#1825—131no—
200#1825—131no—
201#1808—131no—
202#1776—131no—
203#1776—131no—
204#1752—131no—
205C23×C13C22×D411yescharacteristic
206C22×D13—21no—
207C22×D13—21no—
208C22×D13—21no—
209C22×D13—21no—
210C22×D13—21no—
211C22×D13—21no—
212C22×D13C4×D412yes—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
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—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—41no—
230C2×C4×C13—41no—
231C2×C4×C13C23×C411yescharacteristic
232C2×C4×C13C2×#4111yescharacteristic
233C2×C4×C13C2×#4111yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C132−1+411yescharacteristic
236C2×C4×C132−1+411yescharacteristic
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
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—
257C2×Dic13C4×D412yes—
258C4×D13—22no—
259C4×D13—22no—
260C4×D13—22no—
261C4×D13—22no—
262C8×C13—22no—
263C8×C13—41no—
264#1055—41no—
265#1055#11714yes—
266C23×C8—131no—
267C2×#117—131no—
268C2×#117—131no—
269#427—138no—
270C2×#107—131no—
271C2×#107—131no—
272C2×#107—131no—
273C2×#107C2×D1311yescharacteristic
274C2×#106—131no—
275C2×#106—131no—
276C2×C22⋊C8—131no—
277C2×#97—131no—
278C2×#97—131no—
279#389—131no—
280#389—131no—
281#389—131no—
282#389C2×D1311yescharacteristic
283#388—261no—
284#388—261no—
285#388—261no—
286#388—261no—
287#383—261no—
288#382—261no—
289#380—131no—
290#380—131no—
291C4×C4⋊C4—131no—
292C4×C4⋊C4—131no—
293C4×C4⋊C4—131no—
294C4×C4⋊C4—261no—
295C4×C4⋊C4C2×D1311yescharacteristic
296C4×C22⋊C4—131no—
297#376—261no—
298#340—131no—
299#340—131no—
300#340—131no—
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340C2×D1311yescharacteristic
306#340C2×D1311yescharacteristic
307#340C2×D1311yescharacteristic
308#336—131no—
309#336C2×D1311yescharacteristic
310C22×C13C2×C4×D411yescharacteristic
311C22×C13#54711yescharacteristic
312C22×C13#54711yescharacteristic
313C22×C13#57511yescharacteristic
314C22×C13#57511yescharacteristic
315C22×C13#57611yescharacteristic
316C22×C13#57811yescharacteristic
317C2×D13—22no—
318C2×D13—22no—
319C2×D13—22no—
320C2×D13—41no—
321C2×D13—41no—
322C2×D13—41no—
323C2×D13—41no—
324C4×C13—41no—
325C4×C13—41no—
326C4×C13—42no—
327C4×C13—42no—
328C4×C13—81no—
329C4×C13—81no—
330C4×C13C2×#11711yescharacteristic
331C4×C13#51911yescharacteristic
332C4×C13#55211yescharacteristic
333C4×C13#55211yescharacteristic
334Dic13—22no—
335Dic13—41no—
336Dic13—41no—
337Dic13—42no—
338Dic13—42no—
339Dic13—81no—
340Dic13—81no—
341C23×C4—131no—
342C22×C8—131no—
343C22×C8—134no—
344C22×C8—131no—
345C22×C8—262no—
346C22×C8—262no—
347C22×C8C22×D1311yescharacteristic
348C22×C8C22×D1311yescharacteristic
349#117—134no—
350#117—134no—
351#117—262no—
352#117—262no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—131no—
355C2×C4⋊C4—131no—
356C2×C4⋊C4—131no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—261no—
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×C22⋊C4—131no—
366C2×C22⋊C4—131no—
367C2×C22⋊C4—261no—
368C2×C22⋊C4—261no—
369C2×C22⋊C4—261no—
370C2×C22⋊C4—261no—
371C2×C42—21no—
372C2×C42—131no—
373C2×C42—261no—
374C2×C42—261no—
375C2×C42—261no—
376C2×C42—261no—
377C2×C42—261no—
378C2×C42C22×D1311yescharacteristic
379#107—134no—
380#107—262no—
381#107—262no—
382#107C4×D1314yes—
383#106—134no—
384#106—134no—
385C22⋊C8—262no—
386#97—262no—
387#97—262no—
388#95—21no—
389#95—21no—
390#95—131no—
391#95—131no—
392#95—261no—
393#95—261no—
394#95—261no—
395#95—261no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95—261no—
400C2×C13#234411yescharacteristic
401C2×C13#294311yescharacteristic
402C2×C13#295111yescharacteristic
403C2×C13#334711yescharacteristic
404C2×C13#334711yescharacteristic
405C2×C13#334911yescharacteristic
406C2×C13#334911yescharacteristic
407D13—42no—
408C24—131no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—131no—
414C22×C4—132no—
415C22×C4—132no—
416C22×C4—131no—
417C22×C4—131no—
418C22×C4—261no—
419C22×C4—261no—
420C22×C4—261no—
421C22×C4—261no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—261no—
426C22×C4D4×D1311yescharacteristic
427C22×C4D4×D1311yescharacteristic
428C22×C4C23×D1311yescharacteristic
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—132no—
435C2×C8—132no—
436C2×C8—132no—
437C2×C8—268no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8C2×C4×D1312yes—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—81no—
449C4⋊C4—132no—
450C4⋊C4—132no—
451C4⋊C4—261no—
452C4⋊C4—261no—
453C4⋊C4—261no—
454C4⋊C4—261no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—522no—
458C4⋊C4—522no—
459C4⋊C4—1041no—
460C4⋊C4C2×C4×D1312yes—
461C4⋊C4C2×C4×D1312yes—
462C22⋊C4—264no—
463C22⋊C4—264no—
464C22⋊C4—521no—
465C22⋊C4—521no—
466C22⋊C4—1041no—
467C22⋊C4—1041no—
468C42—21no—
469C42—21no—
470C42—81no—
471C42—264no—
472C42—264no—
473C42—261no—
474C42—261no—
475C42—522no—
476C42—522no—
477C42—1041no—
478C13#2261611yescharacteristic, complemented, Sylow
479C23—132no—
480C23—261no—
481C23—261no—
482C23—261no—
483C23—261no—
484C23—261no—
485C23—261no—
486C23C2×D4×D1311yescharacteristic
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—21no—
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—41no—
504C2×C4—41no—
505C2×C4—132no—
506C2×C4—261no—
507C2×C4—261no—
508C2×C4—262no—
509C2×C4—262no—
510C2×C4—262no—
511C2×C4—262no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—262no—
517C2×C4—262no—
518C2×C4—261no—
519C2×C4—261no—
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—521no—
529C2×C4—521no—
530C2×C4C22×C4×D1311yescharacteristic
531C2×C4#8825411yescharacteristic
532C2×C4#41×D1311yescharacteristic
533C2×C4#41×D1311yescharacteristic
534C2×C4#41×D1311yescharacteristic
535C2×C4#8825711yescharacteristic
536C8—22no—
537C8—41no—
538C8—134no—
539C8—521no—
540C22—262no—
541C22—262no—
542C22—262no—
543C22—521no—
544C22—521no—
545C22—521no—
546C22—521no—
547C22C4×D4×D1311yescharacteristic
548C22#1171933611yescharacteristic
549C22#1171936011yescharacteristic
550C22#1171946211yescharacteristic
551C22#1171947611yescharacteristic
552C22#1171948211yescharacteristic
553C22#1171948211yescharacteristic
554C4—42no—
555C4—42no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—262no—
561C4—522no—
562C4—522no—
563C4—521no—
564C4—521no—
565C4—1041no—
566C4—1041no—
567C4D13×#11711yescharacteristic
568C4#1171927711yescharacteristic
569C4#1171939811yescharacteristic
570C4#1171941311yescharacteristic
571C2—522no—
572C2#1311770211yescharacteristic
573C2#1312363511yescharacteristic
574C2#1312370611yescharacteristic
575C2#1312733911yescharacteristic
576C2#1312734311yescharacteristic
577C2#1312736911yescharacteristic
578C2#1312737311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1918C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1918D13
hypocenterC13#22616
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
4. #13115578C2semidirect
5. #13115576C2semidirect
6. #13115429C2semidirect
7. #13115427C2semidirect
8. #13115409C2semidirect
12. #13114734C2semidirect
13. #13114732C2semidirect
15. C13×#1918C2semidirect
43. #11718541C4semidirect
198. #1918D13semidirect
478. C13#22616semidirect

Maximal subgroups

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

subgroupindex
C2×#117185412
#131177252
#131177202
#131155782
#131155762
#131154292
#131154272
#131154092
#131149302
#131148642
#131147342
#131147322
#131146112
C13×#19182
#2261613