Finite Group Databasebeta

← #15880647

Subgroups — #15880647

Order 3328.

782 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
1C2×#11718782C211yesmaximal, characteristic
2#13117719C211yesmaximal, characteristic
3#13117711C211yesmaximal, characteristic
4#13115574C211yesmaximal, characteristic, complemented
5#13115569C211yesmaximal, characteristic, complemented
6#13115429C211yesmaximal, characteristic, complemented
7#13115422C211yesmaximal, characteristic, complemented
8#13115415C211yesmaximal, characteristic, complemented
9#13115408C211yesmaximal, characteristic, complemented
10#13114932C211yesmaximal, characteristic
11#13114923C211yesmaximal, characteristic
12#13114869C211yesmaximal, characteristic
13#13114733C211yesmaximal, characteristic, complemented
14C4×#88057C211yesmaximal, characteristic, complemented
15C13×#1753C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C2×C13×C22⋊C8C2211yescharacteristic
20C2×C13×#97C2211yescharacteristic
21C2×C4×C8×C13C2211yescharacteristic
22C4×C13×C22⋊C4C2211yescharacteristic
23#11718873C2211yescharacteristic
24#11718873C2211yescharacteristic
25#11718782C418yescomplemented
26C2×#88058C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88057C2211yescharacteristic
30C2×#88057C2211yescharacteristic
31C2×#88057C2211yescharacteristic
32#11718605—21no—
33#11718605—21no—
34#11718603—21no—
35C22⋊C4×Dic13—21no—
36C4×C4⋊Dic13C2211yescharacteristic
37C4×C4⋊Dic13C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718589C2211yescharacteristic
44#11718315—21no—
45#11718315—21no—
46#11718311—21no—
47#11718309—21no—
48C13×#336C2211yescharacteristic
49C13×#336C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C2×C13×M16—22no—
63C2×C13×M16—22no—
64C2×C13×M16C2×C414yes—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C2×C13×C22⋊C4D411yescharacteristic
70C2×C13×C22⋊C4D411yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76#88180—22no—
77#88180C2×C414yes—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13C2×C414yes—
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C13×C22⋊C8—22no—
99C13×#97—22no—
100C4×C8×C13—22no—
101C13×#95D411yescharacteristic
102C13×#95D411yescharacteristic
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88058—22no—
114#88058C2×C414yes—
115#88058C2×C414yes—
116#88057—22no—
117#88057C2×C414yes—
118#88057C2×C414yes—
119#22621—131nomaximal, Sylow
120C24×C13C2×D411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13C22×C412yes—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13#4112yes—
132C22×C4×C13C2411yescharacteristic
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—24no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—81no—
143C22×Dic13—81no—
144C13×M16—28no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13C22×C412yes—
154C2×C8×C13C22×C412yes—
155C2×C8×C13#4112yes—
156C2×C8×C13#4112yes—
157C13×C22⋊C4—22no—
158C13×C22⋊C4—41no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—21no—
163C22⋊Dic13—24no—
164C22⋊Dic13—42no—
165C22⋊Dic13—81no—
166C4⋊Dic13—24no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13C22×C412yes—
180C4⋊Dic13C22×C412yes—
181C4⋊Dic13C22×C412yes—
182C4⋊Dic13C22×C412yes—
183#6101—81no—
184#6101—81no—
185#6101—81no—
186#6101—81no—
187C4×Dic13—24no—
188C4×Dic13—42no—
189C4×Dic13—42no—
190C4×Dic13—81no—
191C4×Dic13—81no—
192C2×#428—131no—
193#2346—131no—
194#2345—131no—
195#1943—131no—
196#1942—131no—
197#1921—131no—
198#1920—131no—
199#1919—131no—
200#1918—131no—
201#1825—131no—
202#1823—131no—
203#1809—131no—
204#1776—131no—
205C4×#106—131no—
206#1753D1311yescharacteristic
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13C4×D412yes—
214C23×C13C22×D411yescharacteristic
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
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×C13C4×D412yes—
233C2×C4×C13#13712yes—
234C2×C4×C13C23×C411yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C132−1+411yescharacteristic
239C2×C4×C132−1+411yescharacteristic
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—41no—
245C2×Dic13—41no—
246C2×Dic13—41no—
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×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—84no—
265C8×C13—22no—
266C8×C13—41no—
267C8×C13—41no—
268C8×C13#11714yes—
269C22×M16C2×D1311yescharacteristic
270C2×#117—131no—
271C22×C4⋊C4—131no—
272#428—138no—
273C2×#107—131no—
274C2×#107—131no—
275C2×#107—131no—
276C2×#106—131no—
277C2×#106—131no—
278C2×#106—131no—
279C2×C22⋊C8C2×D1311yescharacteristic
280C2×#97C2×D1311yescharacteristic
281C2×C4×C8C2×D1311yescharacteristic
282#389—131no—
283#389—131no—
284#389—131no—
285#389—131no—
286#388—261no—
287#388—261no—
288#387—261no—
289#387—261no—
290#382—261no—
291#380—131no—
292#380—131no—
293#380—261no—
294C4×C4⋊C4—131no—
295C4×C4⋊C4—131no—
296C4×C4⋊C4—131no—
297C4×C4⋊C4—131no—
298C4×C22⋊C4—261no—
299C4×C22⋊C4C2×D1311yescharacteristic
300#376—261no—
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#336C2×D1311yescharacteristic
312#336C2×D1311yescharacteristic
313C22×C13—22no—
314C22×C13—22no—
315C22×C13—22no—
316C22×C13—41no—
317C22×C13—41no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13C2×C4×D411yescharacteristic
321C22×C13#54711yescharacteristic
322C22×C13#54711yescharacteristic
323C22×C13C2×#13711yescharacteristic
324C22×C13#57511yescharacteristic
325C22×C13#57611yescharacteristic
326C22×C13#57711yescharacteristic
327C4×C13—22no—
328C4×C13—22no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13C2×#11711yescharacteristic
333C4×C13#51911yescharacteristic
334C4×C13#55211yescharacteristic
335C4×C13#55211yescharacteristic
336Dic13—42no—
337Dic13—42no—
338Dic13—42no—
339Dic13—42no—
340Dic13—81no—
341Dic13—81no—
342Dic13—81no—
343Dic13—81no—
344C23×C4—261no—
345C23×C4C22×D1311yescharacteristic
346C2×M16—22no—
347C2×M16—22no—
348C2×M16C4×D1314yes—
349C22×C8C22×D1311yescharacteristic
350C22×C8C22×D1311yescharacteristic
351C22×C8C22×D1311yescharacteristic
352C22×C8C22×D1311yescharacteristic
353#117—134no—
354#117—262no—
355C2×C4⋊C4—134no—
356C2×C4⋊C4—131no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—262no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C22⋊C4—261no—
371C2×C22⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C22⋊C4D5211yescharacteristic
374C2×C22⋊C4D5211yescharacteristic
375C2×C42—261no—
376C2×C42—261no—
377C2×C42—261no—
378C2×C42—261no—
379C2×C42—261no—
380C2×C42C22×D1311yescharacteristic
381C2×C42C22×D1311yescharacteristic
382#107—134no—
383#107—134no—
384#107—262no—
385#106—134no—
386#106—134no—
387#106—262no—
388C22⋊C8—22no—
389#97—22no—
390C4×C8—22no—
391#95—261no—
392#95—261no—
393#95—261no—
394#95—261no—
395#95—261no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95D5211yescharacteristic
402#95D5211yescharacteristic
403C2×C13—42no—
404C2×C13#234411yescharacteristic
405C2×C13C4×#13711yescharacteristic
406C2×C13#294611yescharacteristic
407C2×C13#334411yescharacteristic
408C2×C13#334711yescharacteristic
409C2×C13#335111yescharacteristic
410C2×C13#335711yescharacteristic
411C24C2×D5211yescharacteristic
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—261no—
417C22×C4—261no—
418C22×C4—261no—
419C22×C4—261no—
420C22×C4—264no—
421C22×C4—261no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—1041no—
426C22×C4—1041no—
427C22×C4C2×C4×D1312yes—
428C22×C4C2×D5211yescharacteristic
429C22×C4C2×D5211yescharacteristic
430C22×C4C2×D5211yescharacteristic
431C22×C4C2×D5211yescharacteristic
432C22×C4C2×D5211yescharacteristic
433C22×C4#612712yes—
434C22×C4C23×D1311yescharacteristic
435M16—28no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8C2×C4×D1312yes—
445C2×C8C2×C4×D1312yes—
446C2×C8#612912yes—
447C2×C8#612912yes—
448C4⋊C4—132no—
449C4⋊C4—132no—
450C4⋊C4—132no—
451C4⋊C4—132no—
452C4⋊C4—264no—
453C4⋊C4—261no—
454C4⋊C4—261no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—1041no—
466C4⋊C4—1041no—
467C4⋊C4—1041no—
468C4⋊C4—1041no—
469C22⋊C4—22no—
470C22⋊C4—41no—
471C22⋊C4—264no—
472C22⋊C4—522no—
473C22⋊C4—1041no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—264no—
479C42—522no—
480C42—522no—
481C42—1041no—
482C42—1041no—
483C13#2262111yescharacteristic, complemented, Sylow
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23C4×D5212yes—
491C23C22×D5211yescharacteristic
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
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—262no—
510C2×C4—262no—
511C2×C4—262no—
512C2×C4—262no—
513C2×C4—521no—
514C2×C4—521no—
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—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—1044no—
534C2×C4C4×D5212yes—
535C2×C4#8816312yes—
536C2×C4C22×C4×D1311yescharacteristic
537C2×C4C2×#612711yescharacteristic
538C2×C4C2×#612911yescharacteristic
539C2×C4C2×#612911yescharacteristic
540C2×C4#8825711yescharacteristic
541C2×C4#8825711yescharacteristic
542C8—22no—
543C8—41no—
544C8—41no—
545C8#8813114yes—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22C2×C4×D5211yescharacteristic
554C22#1171926011yescharacteristic
555C22#1171926011yescharacteristic
556C22C2×#8816311yescharacteristic
557C22#1171945311yescharacteristic
558C22#1171945611yescharacteristic
559C22#1171945711yescharacteristic
560C4—22no—
561C4—22no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—522no—
566C4—522no—
567C4—522no—
568C4—522no—
569C4—1041no—
570C4—1041no—
571C4—1041no—
572C4—1041no—
573C4C2×#8813111yescharacteristic
574C4#1171922111yescharacteristic
575C4#1171924611yescharacteristic
576C4#1171924611yescharacteristic
577C2—42no—
578C2#1311770311yescharacteristic
579C2C4×#8816311yescharacteristic
580C2#1312367011yescharacteristic
581C2#1312729311yescharacteristic
582C2#1312733811yescharacteristic
583C2#1312739811yescharacteristic
584C2#1312746311yescharacteristic
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1753C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#1753D13
hypocenterC13#22621
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
4. #13115574C2semidirect
5. #13115569C2semidirect
6. #13115429C2semidirect
7. #13115422C2semidirect
8. #13115415C2semidirect
9. #13115408C2semidirect
13. #13114733C2semidirect
14. C4×#88057C2semidirect
25. #11718782C4semidirect
483. C13#22621semidirect

Maximal subgroups

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

subgroupindex
C2×#117187822
#131177192
#131177112
#131155742
#131155692
#131154292
#131154222
#131154152
#131154082
#131149322
#131149232
#131148692
#131147332
C4×#880572
C13×#17532
#2262113