Finite Group Databasebeta

← #15875162

Subgroups — #15875162

Order 3328.

732 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×#11718670C211yesmaximal, characteristic
2#13117575C211yesmaximal, characteristic, complemented
3#13117479C211yesmaximal, characteristic
4#13115791C211yesmaximal, characteristic, complemented
5#13115592C211yesmaximal, characteristic, complemented
6#13115578C211yesmaximal, characteristic, complemented
7#13115568C211yesmaximal, characteristic, complemented
8#13115530C211yesmaximal, characteristic
9#13115516C211yesmaximal, characteristic
10#13115459C211yesmaximal, characteristic
11#13115459C211yesmaximal, characteristic
12#13115431C211yesmaximal, characteristic, complemented
13#13115417C211yesmaximal, characteristic, complemented
14#13114695C211yesmaximal, characteristic, complemented
15C13×#1802C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×#88124C2211yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C13×#102C2211yescharacteristic
20C2×C13×#102C2211yescharacteristic
21C13×#384C2211yescharacteristic
22#11718882C2211yescharacteristic
23#11718882C2211yescharacteristic
24C2×#88072C2211yescharacteristic
25C2×#88072C2211yescharacteristic
26#11718873—21no—
27#11718872—21no—
28C2×#88055C2211yescharacteristic
29C2×C8×Dic13C2211yescharacteristic
30#11718670C418yescomplemented
31#11718646C2211yescharacteristic
32#11718646C2211yescharacteristic
33#11718639—21no—
34#11718639—21no—
35C4⋊C4×Dic13C2211yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37#11718634C2211yescharacteristic
38#11718634C2211yescharacteristic
39#11718633—21no—
40#11718633—21no—
41C2×#88048C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718612—21no—
46#11718612—21no—
47C4×C4⋊Dic13C2211yescharacteristic
48#11718593C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C4×D4×C13—22no—
65C4×D4×C13C2×C414yes—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C22⋊C4—21no—
72C2×C42×C13C2311yescharacteristic
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13C2311yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94#88124—22no—
95#88124C2×C414yes—
96C13×C4⋊C8—22no—
97C13×#102—41no—
98C13×#102—41no—
99#88072C2×C414yes—
100#88072C2×C414yes—
101#88071—21no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071D411yescharacteristic
109#88071D411yescharacteristic
110#88071D411yescharacteristic
111#88071D411yescharacteristic
112#88055—41no—
113C8×Dic13—41no—
114#88048C2×C414yes—
115#88047—41no—
116#88047—41no—
117#88047C2×C414yes—
118C4⋊#1055C2×C414yes—
119#22126—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×C13C22×C412yes—
127C22×C4×C13—21no—
128C22×C4×C13—24no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—81no—
132C22×C4×C13—81no—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2411yescharacteristic
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
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—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—81no—
156C13×C4⋊C4—81no—
157C13×C4⋊C4C22×C412yes—
158C13×C22⋊C4—24no—
159C42×C13C22×C412yes—
160C42×C13#4112yes—
161C22⋊Dic13—81no—
162C22⋊Dic13—81no—
163C22⋊Dic13—81no—
164C22⋊Dic13—81no—
165C4⋊Dic13—21no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—81no—
172C4⋊Dic13—81no—
173C4⋊Dic13C22×C412yes—
174C4⋊Dic13C22×C412yes—
175#6101—24no—
176#6101—24no—
177#6101—81no—
178#6101—81no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—21no—
182C4×Dic13—21no—
183C4×Dic13—81no—
184C4×Dic13—81no—
185C4×Dic13—81no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055C22×C412yes—
191C2×#1055C22×C412yes—
192C2×#478—131no—
193#2330—131no—
194#2319—131no—
195#1989—131no—
196#1947—131no—
197#1944—131no—
198#1942—131no—
199#1936—131no—
200#1934—131no—
201#1925—131no—
202#1925—131no—
203#1921—131no—
204#1919—131no—
205#1802D1311yescharacteristic
206#1768—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—22no—
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—84no—
233C2×C4×C13C4×D412yes—
234C2×C4×C13C4×D412yes—
235C2×C4×C13C23×C411yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13H(5,𝔽2)11yescharacteristic
238C2×C4×C132−1+411yescharacteristic
239C2×C4×C132−1+411yescharacteristic
240C2×C4×C132−1+411yescharacteristic
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
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—
265C8×C13—41no—
266C8×C13—41no—
267#1055—22no—
268#1055—22no—
269C2×#125—131no—
270C2×C4×D4C2×D1311yescharacteristic
271#478—138no—
272C2×#107—131no—
273C2×#107—131no—
274C2×#107—131no—
275C2×#106—131no—
276C2×C4⋊C8—131no—
277C2×C4⋊C8C2×D1311yescharacteristic
278C2×#102—131no—
279C2×#102—131no—
280C2×#102C2×D1311yescharacteristic
281C2×#102C2×D1311yescharacteristic
282C2×#97—131no—
283C2×C4×C8—131no—
284#390—131no—
285#390—131no—
286#389—131no—
287#389—131no—
288#389—131no—
289#389—131no—
290#389—261no—
291#389—261no—
292#388—261no—
293#388—261no—
294#387—261no—
295#387—261no—
296#384C2×D1311yescharacteristic
297#381—261no—
298#380—261no—
299C4×C4⋊C4—131no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
302#376—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340C2×D1311yescharacteristic
310#340C2×D1311yescharacteristic
311#336—131no—
312#336—131no—
313C22×C13—42no—
314C22×C13—42no—
315C22×C13—42no—
316C22×C13—81no—
317C22×C13—81no—
318C22×C13—81no—
319C22×C13—81no—
320C22×C13C2×C4×D411yescharacteristic
321C22×C13#53611yescharacteristic
322C22×C13#53711yescharacteristic
323C22×C13#57611yescharacteristic
324C22×C13#57611yescharacteristic
325C22×C13#57711yescharacteristic
326C22×C13#57811yescharacteristic
327C4×C13—22no—
328C4×C13—22no—
329C4×C13—42no—
330C4×C13—81no—
331C4×C13—81no—
332C4×C13#51911yescharacteristic
333C4×C13#52011yescharacteristic
334C4×C13#54111yescharacteristic
335C4×C13#54211yescharacteristic
336Dic13—42no—
337Dic13—42no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—81no—
343Dic13—81no—
344C22×D4C22×D1311yescharacteristic
345C23×C4—21no—
346C22×C8—131no—
347C22×C8—131no—
348C22×C8C22×D1311yescharacteristic
349C22×C8C22×D1311yescharacteristic
350#125—134no—
351#125—262no—
352C4×D4—22no—
353C4×D4C4×D1314yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
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⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4C22×D1311yescharacteristic
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—261no—
371C2×C22⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C22⋊C4—261no—
374C2×C42—131no—
375C2×C42—131no—
376C2×C42—261no—
377C2×C42—261no—
378C2×C42—261no—
379C2×C42C22×D1311yescharacteristic
380#107—134no—
381#107—521no—
382#107—521no—
383#106—134no—
384C4⋊C8—22no—
385C4⋊C8—134no—
386#102—41no—
387#102—41no—
388#102—134no—
389#102—134no—
390#97—521no—
391C4×C8—521no—
392#95—131no—
393#95—131no—
394#95—131no—
395#95—131no—
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#232311yescharacteristic
405C2×C13#294611yescharacteristic
406C2×C13#295111yescharacteristic
407C2×C13#324111yescharacteristic
408C2×C13#324311yescharacteristic
409C2×C13#325811yescharacteristic
410C2×C13#325911yescharacteristic
411C24—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4C2×C4×D1312yes—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—81no—
423C22×C4—81no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—261no—
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—21no—
441C2×C8—132no—
442C2×C8—132no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—81no—
453C4⋊C4—81no—
454C4⋊C4—132no—
455C4⋊C4—132no—
456C4⋊C4—264no—
457C4⋊C4—264no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—1041no—
465C4⋊C4—1041no—
466C4⋊C4—1041no—
467C4⋊C4—1041no—
468C4⋊C4C2×C4×D1312yes—
469C22⋊C4—24no—
470C22⋊C4—1041no—
471C22⋊C4—1041no—
472C22⋊C4—1041no—
473C22⋊C4—1041no—
474C42—261no—
475C42—261no—
476C42—261no—
477C42—261no—
478C42—1041no—
479C42—1041no—
480C42—1041no—
481C42C2×C4×D1312yes—
482C42#612912yes—
483C13#2212611yescharacteristic, 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—22no—
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—84no—
510C2×C4—262no—
511C2×C4—262no—
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—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
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#8813512yes—
535C2×C4#8813512yes—
536C2×C4C22×C4×D1311yescharacteristic
537C2×C4C2×#612911yescharacteristic
538C2×C4#8825111yescharacteristic
539C2×C4#8825411yescharacteristic
540C2×C4#8825711yescharacteristic
541C2×C4#8825711yescharacteristic
542C8—41no—
543C8—41no—
544C8—262no—
545C8—262no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×#8813511yescharacteristic
554C22#1171931311yescharacteristic
555C22#1171933311yescharacteristic
556C22#1171946211yescharacteristic
557C22#1171946711yescharacteristic
558C22#1171947911yescharacteristic
559C22#1171948411yescharacteristic
560C4—22no—
561C4—22no—
562C4—42no—
563C4—81no—
564C4—81no—
565C4—522no—
566C4—521no—
567C4—522no—
568C4—521no—
569C4—521no—
570C4—521no—
571C4—1041no—
572C4—1041no—
573C4#1171920911yescharacteristic
574C4#1171922111yescharacteristic
575C4#1171930811yescharacteristic
576C4#1171933011yescharacteristic
577C2—82no—
578C2#1311751411yescharacteristic
579C2#1312366211yescharacteristic
580C2#1312370711yescharacteristic
581C2#1312608811yescharacteristic
582C2#1312611611yescharacteristic
583C2#1312625811yescharacteristic
584C2#1312627311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1802C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#1802D13
hypocenterC13#22126
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. #13117575C2semidirect
4. #13115791C2semidirect
5. #13115592C2semidirect
6. #13115578C2semidirect
7. #13115568C2semidirect
12. #13115431C2semidirect
13. #13115417C2semidirect
14. #13114695C2semidirect
30. #11718670C4semidirect
483. C13#22126semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
#131175752
#131174792
#131157912
#131155922
#131155782
#131155682
#131155302
#131155162
#131154592
#131154312
#131154172
#131146952
C13×#18022
#2212613