Finite Group Databasebeta

← #15880662

Subgroups — #15880662

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718782C211yesmaximal, characteristic
2#13117727C211yesmaximal, characteristic
3#13117703C211yesmaximal, 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#13114927C211yesmaximal, characteristic
12#13114869C211yesmaximal, characteristic
13#13114733C211yesmaximal, characteristic, complemented
14C4×#88057C211yesmaximal, characteristic, complemented
15C13×#1753C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C2×#88131—21no—
20C2×C13×C22⋊C8C2211yescharacteristic
21C2×C13×#97C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C4×C13×C22⋊C4C2211yescharacteristic
24#11718873C2211yescharacteristic
25#11718873C2211yescharacteristic
26#11718782C418yescomplemented
27C2×#88058C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88058C2211yescharacteristic
30C2×#88057C2211yescharacteristic
31C2×#88057C2211yescharacteristic
32C2×#88057C2211yescharacteristic
33#11718606—21no—
34#11718606—21no—
35#11718604—21no—
36C4×C4⋊Dic13C2211yescharacteristic
37C4×C4⋊Dic13C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718589C2211yescharacteristic
44#11718314—21no—
45#11718314—21no—
46#11718312—21no—
47#11718310—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—
98#88131—44no—
99C13×C22⋊C8—22no—
100C13×#97—22no—
101C4×C8×C13—22no—
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
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#88071—21no—
114#88058—22no—
115#88058C2×C414yes—
116#88058C2×C414yes—
117#88057—22no—
118#88057C2×C414yes—
119#88057C2×C414yes—
120#22622—131nomaximal, Sylow
121C24×C13C2×D411yescharacteristic
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13C22×C412yes—
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13#4112yes—
133C22×C4×C13C2411yescharacteristic
134C22×Dic13—24no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—42no—
144C22×Dic13—42no—
145C13×M16—28no—
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×C13—21no—
154C2×C8×C13C22×C412yes—
155C2×C8×C13C22×C412yes—
156C2×C8×C13#4112yes—
157C2×C8×C13#4112yes—
158C13×C22⋊C4—22no—
159C13×C22⋊C4—41no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—21no—
164C22⋊Dic13—24no—
165C22⋊Dic13—42no—
166C22⋊Dic13—81no—
167C4⋊Dic13—24no—
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⋊Dic13—21no—
180C4⋊Dic13C22×C412yes—
181C4⋊Dic13C22×C412yes—
182C4⋊Dic13C22×C412yes—
183C4⋊Dic13C22×C412yes—
184#6101—42no—
185#6101—42no—
186#6101—42no—
187#6101—42no—
188C4×Dic13—24no—
189C4×Dic13—42no—
190C4×Dic13—42no—
191C4×Dic13—81no—
192C4×Dic13—81no—
193C2×#428—131no—
194#2347—131no—
195#2344—131no—
196#1943—131no—
197#1942—131no—
198#1921—131no—
199#1920—131no—
200#1919—131no—
201#1918—131no—
202#1825—131no—
203#1824—131no—
204#1809—131no—
205#1776—131no—
206C4×#106—131no—
207#1753D1311yescharacteristic
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13C4×D412yes—
215C23×C13C22×D411yescharacteristic
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
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—21no—
233C2×C4×C13C4×D412yes—
234C2×C4×C13AGL(1,ℤ/8)12yes—
235C2×C4×C13C23×C411yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C132−1+411yescharacteristic
240C2×C4×C132−1+411yescharacteristic
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—48no—
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—41no—
265C2×Dic13—41no—
266C8×C13—22no—
267C8×C13—41no—
268C8×C13—41no—
269C8×C13#11714yescomplemented
270C22×M16C2×D1311yescharacteristic
271C2×#117—131no—
272C2×#117—261no—
273C22×C4⋊C4—131no—
274#428—138no—
275C2×#107—131no—
276C2×#107—131no—
277C2×#107—131no—
278C2×#106—131no—
279C2×#106—131no—
280C2×#106—131no—
281C2×C22⋊C8C2×D1311yescharacteristic
282C2×#97C2×D1311yescharacteristic
283C2×C4×C8C2×D1311yescharacteristic
284#389—131no—
285#389—131no—
286#389—131no—
287#389—131no—
288#388—261no—
289#388—261no—
290#387—261no—
291#387—261no—
292#383—261no—
293#381—261no—
294#380—131no—
295#380—131no—
296C4×C4⋊C4—131no—
297C4×C4⋊C4—131no—
298C4×C4⋊C4—131no—
299C4×C4⋊C4—131no—
300C4×C4⋊C4—261no—
301C4×C22⋊C4C2×D1311yescharacteristic
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#340—131no—
312#336C2×D1311yescharacteristic
313#336C2×D1311yescharacteristic
314C22×C13—22no—
315C22×C13—22no—
316C22×C13—22no—
317C22×C13—41no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13C2×C4×D411yescharacteristic
322C22×C13#54711yescharacteristic
323C22×C13#54711yescharacteristic
324C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C13#57511yescharacteristic
326C22×C13#57711yescharacteristic
327C22×C13#57811yescharacteristic
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13C2×#11711yescharacteristic
334C4×C13#51911yescharacteristic
335C4×C13#55211yescharacteristic
336C4×C13#55211yescharacteristic
337Dic13—42no—
338Dic13—42no—
339Dic13—42no—
340Dic13—42no—
341Dic13—81no—
342Dic13—81no—
343Dic13—81no—
344Dic13—81no—
345C23×C4—261no—
346C23×C4C22×D1311yescharacteristic
347C2×M16—22no—
348C2×M16—22no—
349C2×M16C4×D1314yes—
350C22×C8C22×D1311yescharacteristic
351C22×C8C22×D1311yescharacteristic
352C22×C8C22×D1311yescharacteristic
353C22×C8C22×D1311yescharacteristic
354#117—134no—
355#117—262no—
356#117—524no—
357C2×C4⋊C4—134no—
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—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4D5211yescharacteristic
376C2×C22⋊C4D5211yescharacteristic
377C2×C42—261no—
378C2×C42—261no—
379C2×C42—261no—
380C2×C42—261no—
381C2×C42—261no—
382C2×C42C22×D1311yescharacteristic
383C2×C42C22×D1311yescharacteristic
384#107—134no—
385#107—134no—
386#107—262no—
387#106—134no—
388#106—134no—
389#106—262no—
390C22⋊C8—22no—
391#97—22no—
392C4×C8—22no—
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#95—261no—
402#95—261no—
403#95D5211yescharacteristic
404#95D5211yescharacteristic
405C2×C13—42no—
406C2×C13#234411yescharacteristic
407C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
408C2×C13#294711yescharacteristic
409C2×C13#334511yescharacteristic
410C2×C13#334911yescharacteristic
411C2×C13#335111yescharacteristic
412C2×C13#335311yescharacteristic
413C24C2×D5211yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—264no—
419C22×C4—261no—
420C22×C4—261no—
421C22×C4—261no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—261no—
426C22×C4—261no—
427C22×C4—522no—
428C22×C4—522no—
429C22×C4C2×C4×D1312yes—
430C22×C4C2×D5211yescharacteristic
431C22×C4C2×D5211yescharacteristic
432C22×C4C2×D5211yescharacteristic
433C22×C4C2×D5211yescharacteristic
434C22×C4C2×D5211yescharacteristic
435C22×C4#612712yes—
436C22×C4C23×D1311yescharacteristic
437M16—28no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8C2×C4×D1312yes—
447C2×C8C2×C4×D1312yes—
448C2×C8#612912yes—
449C2×C8#612912yes—
450C4⋊C4—132no—
451C4⋊C4—132no—
452C4⋊C4—132no—
453C4⋊C4—132no—
454C4⋊C4—264no—
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—261no—
466C4⋊C4—261no—
467C4⋊C4—522no—
468C4⋊C4—522no—
469C4⋊C4—522no—
470C4⋊C4—522no—
471C22⋊C4—22no—
472C22⋊C4—41no—
473C22⋊C4—264no—
474C22⋊C4—522no—
475C22⋊C4—1041no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—264no—
481C42—522no—
482C42—522no—
483C42—1041no—
484C42—1041no—
485C13#2262211yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23C4×D5212yes—
493C23C22×D5211yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
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—262no—
512C2×C4—262no—
513C2×C4—262no—
514C2×C4—262no—
515C2×C4—528no—
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—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4C4×D5212yes—
537C2×C4#8816212yes—
538C2×C4C22×C4×D1311yescharacteristic
539C2×C4C2×#612711yescharacteristic
540C2×C4C2×#612911yescharacteristic
541C2×C4C2×#612911yescharacteristic
542C2×C4#8825711yescharacteristic
543C2×C4#8825711yescharacteristic
544C8—22no—
545C8—41no—
546C8—41no—
547C8#8813114yescomplemented
548C22—22no—
549C22—22no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22C2×C4×D5211yescharacteristic
556C22#1171926011yescharacteristic
557C22#1171926011yescharacteristic
558C22C2×#8816211yescharacteristic
559C22#1171945311yescharacteristic
560C22#1171945611yescharacteristic
561C22#1171945811yescharacteristic
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—522no—
568C4—522no—
569C4—522no—
570C4—522no—
571C4—1041no—
572C4—1041no—
573C4—1041no—
574C4—1041no—
575C4C2×#8813111yescharacteristic
576C4#1171922111yescharacteristic
577C4#1171924611yescharacteristic
578C4#1171924611yescharacteristic
579C2—42no—
580C2#1311770311yescharacteristic
581C2C4×#8816211yescharacteristic
582C2#1312368111yescharacteristic
583C2#1312730811yescharacteristic
584C2#1312736811yescharacteristic
585C2#1312739811yescharacteristic
586C2#1312742111yescharacteristic
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#22622
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
26. #11718782C4semidirect
269. C8×C13#117semidirect
485. C13#22622semidirect
547. C8#88131semidirect

Maximal subgroups

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

subgroupindex
C2×#117187822
#131177272
#131177032
#131155742
#131155692
#131154292
#131154222
#131154152
#131154082
#131149322
#131149272
#131148692
#131147332
C4×#880572
C13×#17532
#2262213