Finite Group Databasebeta

← #15863360

Subgroups — #15863360

Order 3328.

1070 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718542C211yesmaximal, characteristic
2C2×#11718522C211yesmaximal, characteristic
3C2×#11718541C211yesmaximal, characteristic
4C2×D13×#106C211yesmaximal, characteristic
5C2×#11718369C211yesmaximal, characteristic
6#13117461C211yesmaximal, characteristic
7#13117457C211yesmaximal, characteristic
8#13115004C211yesmaximal, characteristic, complemented
9#13115003C211yesmaximal, characteristic, complemented
10#13115001C211yesmaximal, characteristic, complemented
11#13114999C211yesmaximal, characteristic, complemented
12#13114998C211yesmaximal, characteristic, complemented
13#13114992C211yesmaximal, characteristic, complemented
14#13114991C211yesmaximal, characteristic, complemented
15C13×#1847C211yesmaximal, characteristic, complemented
16C22×#6094C2211yescharacteristic
17C22×C8×D13C2211yescharacteristic
18C2×#88146C2211yescharacteristic
19C2×#88146C2211yescharacteristic
20C2×C4⋊C4×D13C2211yescharacteristic
21C2×C4⋊C4×D13C2211yescharacteristic
22C2×#88126C2211yescharacteristic
23C2×C13×#107C2211yescharacteristic
24C2×C13×#107C2211yescharacteristic
25C2×C13×#106C2211yescharacteristic
26C2×C13×#106C2211yescharacteristic
27C2×C13×#97C2211yescharacteristic
28C13×#384C2211yescharacteristic
29C13×#382C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31C2×#88058C2211yescharacteristic
32C2×#88057C2211yescharacteristic
33C2×#88057C2211yescharacteristic
34C2×#88055C2211yescharacteristic
35C2×C8×Dic13C2211yescharacteristic
36#11718650—22no—
37#11718638C2211yescharacteristic
38#11718638C2211yescharacteristic
39#11718637C2211yescharacteristic
40#11718637C2211yescharacteristic
41#11718633—22no—
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46C2×#88048C2211yescharacteristic
47C2×#88048C2211yescharacteristic
48C2×#88047C2211yescharacteristic
49C2×#88047C2211yescharacteristic
50#11718597C2211yescharacteristic
51#11718596C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718542—24no—
54#11718541—24no—
55#11718522—24no—
56D13×#106—24no—
57#11718369C418yescomplemented
58#11718329—22no—
59#11718308—22no—
60C22×C4×D13—21no—
61C22×C4×D13—21no—
62C22×C4×D13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103D412yes—
74C2×C4⋊Dic13—22no—
75C2×C4⋊Dic13C2311yescharacteristic
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×#6101—21no—
80C2×#6101—21no—
81C2×#6101—22no—
82C2×#6101—22no—
83C2×#6101D412yes—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13C2311yescharacteristic
87C22×#1055C2311yescharacteristic
88C22×#1055C2311yescharacteristic
89C2×#6094C2×C414yes—
90C2×#6094D414yes—
91C2×#6094Q814yes—
92C2×C8×D13C2×C414yes—
93C2×C8×D13D414yes—
94C2×C8×D13Q814yes—
95#88146—22no—
96#88146—22no—
97#88146—22no—
98#88146—22no—
99C4⋊C4×D13—22no—
100C4⋊C4×D13—22no—
101C4⋊C4×D13—22no—
102C4⋊C4×D13—22no—
103#88126C2×C414yes—
104#88126Q814yes—
105C13×#107—22no—
106C13×#107—22no—
107C13×#106—22no—
108C13×#106—22no—
109C13×#97C2×C414yescomplemented
110C13×#95—22no—
111#88071—22no—
112#88071—22no—
113#88071—22no—
114#88058—22no—
115#88058—22no—
116#88057—22no—
117#88057—22no—
118#88055C2×C414yescomplemented
119C8×Dic13C2×C414yescomplemented
120#88048—22no—
121#88048—22no—
122#88048—22no—
123#88048—22no—
124#88048—22no—
125#88048—22no—
126#88047—22no—
127#88047—22no—
128C4×#1055C2×C414yescomplemented
129#20802—131nomaximal, Sylow
130C23×D13C2×D411yescharacteristic
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13C2×D412yes—
136C22×C4×C13C2411yescharacteristic
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13C2×D412yes—
142C22×Dic13C2×D411yescharacteristic
143C2×C4×D13—42no—
144C2×C4×D13—42no—
145C2×C4×D13—82no—
146C2×C4×D13—82no—
147C2×C4×D13C22×C412yes—
148C2×C4×D13C2×D412yes—
149C2×C4×D13C2×D412yes—
150C2×C4×D13C2×Q812yes—
151C2×C4×D13C2×Q812yes—
152C2×C4×D13C2×Q812yes—
153C2×C8×C13C22×C412yes—
154C2×C8×C13C22×C412yes—
155C2×C8×C13C2×D412yes—
156C2×C8×C13C2×D412yes—
157C2×C8×C13C2×Q812yes—
158C2×C8×C13C2×Q812yes—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—82no—
168C42×C13C22×C412yes—
169C42×C13C2×Q812yes—
170#6103—42no—
171#6103—42no—
172#6103C4⋊C418yes—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—82no—
182#6101—42no—
183#6101—42no—
184#6101—82no—
185#6101—82no—
186#6101C4⋊C418yes—
187C4×Dic13—42no—
188C4×Dic13—42no—
189C4×Dic13C22×C412yes—
190C4×Dic13C2×Q812yes—
191C2×#1055C22×C412yes—
192C2×#1055C22×C412yes—
193C2×#1055C2×D412yes—
194C2×#1055C2×D412yes—
195C2×#1055C2×Q812yes—
196C2×#1055C2×Q812yes—
197#6094C4⋊C4116yescomplemented
198C8×D13C4⋊C4116yescomplemented
199C2×#428—131no—
200C2×#428—131no—
201C2×#427—131no—
202C22×#106—131no—
203C2×#405—131no—
204#2317—131no—
205#2317—131no—
206#1847—131no—
207#1847—131no—
208#1847—131no—
209#1847D1311yescharacteristic, complemented
210#1846—131no—
211#1846—131no—
212#1844—131no—
213#1844—131no—
214C23×C13C22×D411yescharacteristic
215C22×D13—22no—
216C22×D13—22no—
217C22×D13C2×C4⋊C412yes—
218C22×D13#12712yes—
219C22×D13C4⋊Q812yes—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13C2×C4⋊C414yes—
231C2×C4×C13C23×C411yescharacteristic
232C2×C4×C13C22×D411yescharacteristic
233C2×C4×C13C22×D411yescharacteristic
234C2×C4×C13C22×Q811yescharacteristic
235C2×C4×C13C22×Q811yescharacteristic
236C2×C4×C13C22×Q811yescharacteristic
237C2×Dic13—22no—
238C2×Dic13—22no—
239C2×Dic13—41no—
240C2×Dic13—41no—
241C2×Dic13—41no—
242C2×Dic13—41no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13C2×C4⋊C414yes—
248C2×Dic13C2×C4⋊C412yes—
249C2×Dic13#12712yes—
250C2×Dic13C4⋊Q812yes—
251C4×D13—84no—
252C4×D13—84no—
253C4×D13C2×C4⋊C414yes—
254C4×D13C2×C4⋊C414yes—
255C4×D13C4⋊Q814yes—
256C4×D13C4⋊Q814yes—
257C8×C13C2×C4⋊C414yes—
258C8×C13C2×C4⋊C414yes—
259#1055C2×C4⋊C414yes—
260#1055C2×C4⋊C414yes—
261C22×M16—131no—
262C23×C8—131no—
263C2×#117—131no—
264C2×#117—131no—
265C2×#117—131no—
266C22×C4⋊C4—131no—
267C22×C4⋊C4—131no—
268#428—264no—
269#428—264no—
270#427—264no—
271C2×#107—131no—
272C2×#107—131no—
273C2×#107—131no—
274C2×#107—131no—
275C2×#107C2×D1311yescharacteristic
276C2×#107C2×D1311yescharacteristic
277C2×#106—131no—
278C2×#106—131no—
279C2×#106—131no—
280C2×#106—131no—
281C2×#106—131no—
282C2×#106—131no—
283C2×#106—131no—
284C2×#106—131no—
285C2×#106—264no—
286C2×#106C2×D1311yescharacteristic
287C2×#106C2×D1311yescharacteristic
288#405—138no—
289C2×#97—131no—
290C2×#97C2×D1311yescharacteristic
291C2×C4×C8—131no—
292C2×C4×C8—131no—
293#389—262no—
294#389—262no—
295#385—262no—
296#385—262no—
297#384—131no—
298#384—131no—
299#384—131no—
300#384C2×D1311yescharacteristic
301#382—131no—
302#382—131no—
303#382—131no—
304#382C2×D1311yescharacteristic
305C22×C13C22×C4⋊C411yescharacteristic
306C22×C13C2×#12711yescharacteristic
307C22×C13C2×C4⋊Q811yescharacteristic
308C22×C13#57712yes—
309C22×C13#57712yes—
310C2×D13—22no—
311C2×D13—22no—
312C2×D13—24no—
313C2×D13—24no—
314C2×D13#38414yes—
315C4×C13—24no—
316C4×C13—81no—
317C4×C13—81no—
318C4×C13—81no—
319C4×C13—81no—
320C4×C13C22×C4⋊C411yescharacteristic
321C4×C13C22×C4⋊C411yescharacteristic
322C4×C13C2×C4⋊Q811yescharacteristic
323C4×C13C2×C4⋊Q811yescharacteristic
324Dic13—24no—
325Dic13—81no—
326Dic13—81no—
327Dic13—81no—
328Dic13—81no—
329Dic13#38414yes—
330C23×C4—131no—
331C23×C4—261no—
332C23×C4—261no—
333C2×M16—134no—
334C2×M16—134no—
335C2×M16—134no—
336C22×C8—131no—
337C22×C8—131no—
338C22×C8—134no—
339C22×C8—134no—
340C22×C8—134no—
341C22×C8C22×D1311yescharacteristic
342C22×C8C22×D1311yescharacteristic
343#117—134no—
344#117—134no—
345#117—262no—
346#117—262no—
347#117—262no—
348#117—262no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—132no—
351C2×C4⋊C4—131no—
352C2×C4⋊C4—131no—
353C2×C4⋊C4—131no—
354C2×C4⋊C4—131no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4—262no—
357C2×C4⋊C4—262no—
358C2×C4⋊C4—262no—
359C2×C4⋊C4—261no—
360C2×C4⋊C4—261no—
361C2×C4⋊C4—262no—
362C2×C4⋊C4—262no—
363C2×C4⋊C4—262no—
364C2×C4⋊C4C22×D1311yescharacteristic
365C2×C4⋊C4C22×D1311yescharacteristic
366C2×C4⋊C4C22×D1311yescharacteristic
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C22⋊C4—132no—
369C2×C22⋊C4—261no—
370C2×C22⋊C4—261no—
371C2×C42—131no—
372C2×C42—261no—
373C2×C42—261no—
374C2×C42C22×D1311yescharacteristic
375#107—22no—
376#107—22no—
377#107—262no—
378#107—262no—
379#107—262no—
380#107—262no—
381#106—22no—
382#106—22no—
383#106—262no—
384#106—262no—
385#106—262no—
386#106—262no—
387#106—262no—
388#106—262no—
389#106—262no—
390#106—262no—
391#97—134no—
392#97C4×D1314yescomplemented
393C4×C8—134no—
394C4×C8—134no—
395#95—22no—
396#95—262no—
397#95—262no—
398#95—262no—
399C2×C13C2×#38411yescharacteristic
400C2×C13#291212yes—
401C2×C13#315411yescharacteristic
402C2×C13#315411yescharacteristic
403C2×C13#316312yes—
404D13—24no—
405C24—131no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—131no—
411C22×C4—132no—
412C22×C4—132no—
413C22×C4—132no—
414C22×C4—132no—
415C22×C4—132no—
416C22×C4—132no—
417C22×C4—132no—
418C22×C4—261no—
419C22×C4—261no—
420C22×C4—261no—
421C22×C4—261no—
422C22×C4—522no—
423C22×C4—522no—
424C22×C4—1042no—
425C22×C4—1042no—
426C22×C4D4×D1312yes—
427C22×C4C23×D1311yescharacteristic
428M16—1316no—
429C2×C8—132no—
430C2×C8—132no—
431C2×C8—132no—
432C2×C8—132no—
433C2×C8—132no—
434C2×C8—132no—
435C2×C8—1316no—
436C2×C8C2×C4×D1312yes—
437C2×C8C2×C4×D1312yes—
438C2×C8D4×D1312yes—
439C2×C8D4×D1312yes—
440C2×C8Q8×D1312yes—
441C2×C8Q8×D1312yes—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—82no—
451C4⋊C4—138no—
452C4⋊C4—261no—
453C4⋊C4—261no—
454C4⋊C4—261no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—522no—
461C4⋊C4—522no—
462C4⋊C4—1042no—
463C4⋊C4—1042no—
464C4⋊C4—1042no—
465C22⋊C4—138no—
466C22⋊C4—522no—
467C22⋊C4—522no—
468C42—132no—
469C42—132no—
470C42—522no—
471C42—522no—
472C42C2×C4×D1312yes—
473C42Q8×D1312yes—
474C13#2080211yescharacteristic, complemented, Sylow
475C23—132no—
476C23—132no—
477C23—132no—
478C23—262no—
479C23—262no—
480C23C2×D4×D1311yescharacteristic
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—132no—
492C2×C4—132no—
493C2×C4—132no—
494C2×C4—134no—
495C2×C4—134no—
496C2×C4—134no—
497C2×C4—134no—
498C2×C4—134no—
499C2×C4—262no—
500C2×C4—262no—
501C2×C4—522no—
502C2×C4—522no—
503C2×C4—522no—
504C2×C4—522no—
505C2×C4—521no—
506C2×C4—521no—
507C2×C4—521no—
508C2×C4—521no—
509C2×C4—1044no—
510C2×C4—1044no—
511C2×C4C4⋊C4×D1314yes—
512C2×C4C22×C4×D1311yescharacteristic
513C2×C4C2×D4×D1311yescharacteristic
514C2×C4C2×D4×D1311yescharacteristic
515C2×C4C2×Q8×D1311yescharacteristic
516C2×C4C2×Q8×D1311yescharacteristic
517C2×C4C2×Q8×D1311yescharacteristic
518C8—134no—
519C8—134no—
520C8C4⋊C4×D1314yes—
521C8C4⋊C4×D1314yes—
522C22—134no—
523C22—264no—
524C22—262no—
525C22—262no—
526C22—264no—
527C22C2×C4⋊C4×D1311yescharacteristic
528C22D13×#12711yescharacteristic
529C22D13×C4⋊Q811yescharacteristic
530C22#1171948012yes—
531C22#1171948312yes—
532C4—24no—
533C4—81no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4—134no—
538C4—264no—
539C4—1041no—
540C4—1041no—
541C4—1041no—
542C4—1041no—
543C4C2×C4⋊C4×D1311yescharacteristic
544C4C2×C4⋊C4×D1311yescharacteristic
545C4D13×C4⋊Q811yescharacteristic
546C4D13×C4⋊Q811yescharacteristic
547C2—264no—
548C2D13×#38411yescharacteristic
549C2#1312343012yes—
550C2#1312530911yescharacteristic
551C2#1312531111yescharacteristic
552C2#1312536312yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1847C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1847D13
hypocenterC13#20802
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
8. #13115004C2semidirect
9. #13115003C2semidirect
10. #13115001C2semidirect
11. #13114999C2semidirect
12. #13114998C2semidirect
13. #13114992C2semidirect
14. #13114991C2semidirect
15. C13×#1847C2semidirect
57. #11718369C4semidirect
109. C13×#97C2×C4semidirect
118. #88055C2×C4semidirect
119. C8×Dic13C2×C4semidirect
128. C4×#1055C2×C4semidirect
197. #6094C4⋊C4semidirect
198. C8×D13C4⋊C4semidirect
209. #1847D13semidirect
392. #97C4×D13semidirect
474. C13#20802semidirect

Maximal subgroups

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

subgroupindex
C2×#117185422
C2×#117185222
C2×#117185412
C2×D13×#1062
C2×#117183692
#131174612
#131174572
#131150042
#131150032
#131150012
#131149992
#131149982
#131149922
#131149912
C13×#18472
#2080213