Finite Group Databasebeta

← #15920993

Subgroups — #15920993

Order 3328.

696 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118561C211yesmaximal, characteristic
2#13117723C211yesmaximal, characteristic
3#13116408C211yesmaximal, characteristic, complemented
4#13116339C211yesmaximal, characteristic, complemented
5#13116335C211yesmaximal, characteristic, complemented
6#13116172C211yesmaximal, characteristic, complemented
7#13115792C211yesmaximal, characteristic, complemented
8#13115601C211yesmaximal, characteristic, complemented
9#13115416C211yesmaximal, characteristic, complemented
10#13115412C211yesmaximal, characteristic, complemented
11#13115028C211yesmaximal, characteristic
12#13115019C211yesmaximal, characteristic
13#13114928C211yesmaximal, characteristic
14#13114556C211yesmaximal, characteristic
15C13×#1809C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C2×#88144C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C13×#380C2211yescharacteristic
23C13×#380C2211yescharacteristic
24C4×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊#1055C2211yescharacteristic
26C2×#88054C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28#11718646C2211yescharacteristic
29#11718638C2211yescharacteristic
30C4⋊C4×Dic13C2211yescharacteristic
31C4⋊C4×Dic13C2211yescharacteristic
32#11718634C2211yescharacteristic
33#11718634C2211yescharacteristic
34#11718634C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37#11718611—21no—
38#11718606—21no—
39#11718606—21no—
40#11718603—21no—
41#11718322—21no—
42#11718321—21no—
43#11718311—21no—
44#11718309—21no—
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47#11718143C2211yescharacteristic
48#11718143C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13—21no—
61C2×C13×M16—22no—
62C2×C13×M16—22no—
63C2×C13×M16—41no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C22⋊C4—21no—
71C2×C13×C22⋊C4—21no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13D411yescharacteristic
74C2×C22⋊Dic13D411yescharacteristic
75#88180—22no—
76#88180Q814yes—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—41no—
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97#88144—22no—
98#88144—41no—
99C13×#107—41no—
100C13×#106—22no—
101C13×#95—21no—
102C13×#95—21no—
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#88071D411yescharacteristic
112#88071D411yescharacteristic
113C22⋊#1055—22no—
114#88054—22no—
115#88054—41no—
116#88048—22no—
117#88048—41no—
118#26019—131nomaximal, Sylow
119C24×C13C2×D411yescharacteristic
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×Q812yes—
130C22×C4×C13#4112yes—
131C22×C4×C13C2411yescharacteristic
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—42no—
137C22×Dic13—42no—
138C22×Dic13—81no—
139C22×Dic13C2×D411yescharacteristic
140C22×Dic13C2×D411yescharacteristic
141C22×Dic13C2×D411yescharacteristic
142C22×Dic13C2×D411yescharacteristic
143C13×M16—44no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13#4112yes—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C22⋊C4—42no—
159C13×C22⋊C4—81no—
160C22⋊Dic13—24no—
161C22⋊Dic13—41no—
162C22⋊Dic13—41no—
163C4⋊Dic13—21no—
164C4⋊Dic13—21no—
165C4⋊Dic13—21no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—42no—
169C4⋊Dic13—42no—
170C4⋊Dic13—81no—
171C4⋊Dic13C2×Q812yes—
172C4⋊Dic13C2×Q812yes—
173C4⋊Dic13#4112yes—
174#6101—42no—
175#6101—81no—
176#6101—81no—
177#6101—81no—
178C4×Dic13—24no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—21no—
182C4×Dic13—21no—
183C4×Dic13—42no—
184C4×Dic13—42no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191#2442—131no—
192#2346—131no—
193#2101—131no—
194#2088—131no—
195#2088—131no—
196#2059—131no—
197#1989—131no—
198#1949—131no—
199#1919—131no—
200#1919—131no—
201#1853—131no—
202#1851—131no—
203#1825—131no—
204#1809D1311yescharacteristic
205#1736—131no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13C22⋊Q812yes—
213C23×C13C22×D411yescharacteristic
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—41no—
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×C13—41no—
232C2×C4×C13C22⋊Q812yes—
233C2×C4×C13C22×Q811yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13H(5,𝔽2)11yescharacteristic
238C2×C4×C132−1+411yescharacteristic
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—22no—
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—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—84no—
264C8×C13—22no—
265C8×C13—41no—
266#1055—41no—
267#1055—41no—
268C22×M16C2×D1311yescharacteristic
269C2×#125—131no—
270C2×#117—131no—
271C22×C4⋊C4—131no—
272C2×#107C2×D1311yescharacteristic
273C2×#106—131no—
274C2×#106—131no—
275C2×#106C2×D1311yescharacteristic
276C2×C4⋊C8—131no—
277C2×C4⋊C8—131no—
278C2×C22⋊C8—131no—
279#400—261no—
280#398—261no—
281#389—131no—
282#389—131no—
283#389—131no—
284#389—131no—
285#388—261no—
286#388—261no—
287#385—261no—
288#382—131no—
289#382—261no—
290#380—261no—
291#380C2×D1311yescharacteristic
292#380C2×D1311yescharacteristic
293C4×C4⋊C4—131no—
294C4×C4⋊C4—131no—
295C4×C22⋊C4—131no—
296#376—261no—
297#340—131no—
298#340—131no—
299#340—131no—
300#340—131no—
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340C2×D1311yescharacteristic
308#340C2×D1311yescharacteristic
309#336—131no—
310#336—131no—
311C22×C13—22no—
312C22×C13—22no—
313C22×C13—22no—
314C22×C13—41no—
315C22×C13—41no—
316C22×C13—41no—
317C22×C13—41no—
318C22×C13C2×C22⋊Q811yescharacteristic
319C22×C13#54611yescharacteristic
320C22×C13#54711yescharacteristic
321C22×C13#57511yescharacteristic
322C22×C13#57511yescharacteristic
323C22×C13#57711yescharacteristic
324C22×C13#57711yescharacteristic
325C4×C13—22no—
326C4×C13—81no—
327C4×C13—81no—
328C4×C13—81no—
329C4×C13—81no—
330C4×C13#53311yescharacteristic
331C4×C13#54411yescharacteristic
332C4×C13#55111yescharacteristic
333C4×C13#55211yescharacteristic
334Dic13—42no—
335Dic13—42no—
336Dic13—41no—
337Dic13—41no—
338Dic13—41no—
339Dic13—41no—
340Dic13—42no—
341Dic13—81no—
342C23×C4—261no—
343C23×C4C22×D1311yescharacteristic
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—41no—
347C22×C8—131no—
348C22×C8—131no—
349C22×C8C22×D1311yescharacteristic
350C22×C8C22×D1311yescharacteristic
351#125—262no—
352#125—521no—
353#117—134no—
354#117—262no—
355C2×C4⋊C4—131no—
356C2×C4⋊C4—131no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—262no—
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⋊C4—261no—
367C2×C4⋊C4—521no—
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C4⋊C4C22×D1311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—131no—
375C2×C22⋊C4—131no—
376C2×C22⋊C4—261no—
377C2×C42—131no—
378C2×C42—131no—
379C2×C42—261no—
380C2×C42—261no—
381C2×C42—261no—
382#107—41no—
383#106—22no—
384#106—262no—
385#106—521no—
386C4⋊C8—262no—
387C4⋊C8—521no—
388C22⋊C8—262no—
389#95—21no—
390#95—21no—
391#95—131no—
392#95—131no—
393#95—261no—
394#95—261no—
395#95—261no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95—261no—
400#95—261no—
401C2×C13—42no—
402C2×C13#243811yescharacteristic
403C2×C13#308011yescharacteristic
404C2×C13#308411yescharacteristic
405C2×C13#332111yescharacteristic
406C2×C13#332311yescharacteristic
407C2×C13#334811yescharacteristic
408C2×C13#335111yescharacteristic
409C24D4×D1311yescharacteristic
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—131no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—131no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—261no—
426C22×C4—522no—
427C22×C4—522no—
428C22×C4—1041no—
429C22×C4#612712yes—
430C22×C4D4×D1311yescharacteristic
431C22×C4Q8×D1312yes—
432C22×C4C23×D1311yescharacteristic
433M16—44no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8#612912yes—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—132no—
455C4⋊C4—132no—
456C4⋊C4—132no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—522no—
463C4⋊C4—522no—
464C4⋊C4—522no—
465C4⋊C4—1041no—
466C4⋊C4—1041no—
467C4⋊C4—1041no—
468C4⋊C4—1041no—
469C22⋊C4—42no—
470C22⋊C4—81no—
471C22⋊C4—264no—
472C22⋊C4—521no—
473C22⋊C4—521no—
474C42—264no—
475C42—261no—
476C42—261no—
477C42—261no—
478C42—261no—
479C42—522no—
480C42—522no—
481C13#2601911yescharacteristic, complemented, Sylow
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23#8815012yes—
489C23C2×D4×D1311yescharacteristic
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
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—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—262no—
509C2×C4—262no—
510C2×C4—261no—
511C2×C4—261no—
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—262no—
521C2×C4—261no—
522C2×C4—261no—
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—1044no—
533C2×C4#8815012yes—
534C2×C4C2×#612711yescharacteristic
535C2×C4C2×#612911yescharacteristic
536C2×C4#8825111yescharacteristic
537C2×C4C2×Q8×D1311yescharacteristic
538C2×C4#41×D1311yescharacteristic
539C2×C4#8825711yescharacteristic
540C8—22no—
541C8—41no—
542C8—521no—
543C8—521no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22C2×#8815011yescharacteristic
552C22#1171931511yescharacteristic
553C22#1171931611yescharacteristic
554C22#1171947811yescharacteristic
555C22#1171948011yescharacteristic
556C22#1171948211yescharacteristic
557C22#1171948311yescharacteristic
558C4—22no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—522no—
564C4—522no—
565C4—521no—
566C4—521no—
567C4—522no—
568C4—521no—
569C4—521no—
570C4—1041no—
571C4#1171920011yescharacteristic
572C4#1171923611yescharacteristic
573C4#1171932711yescharacteristic
574C4#1171932811yescharacteristic
575C2—42no—
576C2#1311851811yescharacteristic
577C2#1312465711yescharacteristic
578C2#1312469711yescharacteristic
579C2#1312701711yescharacteristic
580C2#1312705811yescharacteristic
581C2#1312734611yescharacteristic
582C2#1312739111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1809C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1809D13
hypocenterC13#26019
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
3. #13116408C2semidirect
4. #13116339C2semidirect
5. #13116335C2semidirect
6. #13116172C2semidirect
7. #13115792C2semidirect
8. #13115601C2semidirect
9. #13115416C2semidirect
10. #13115412C2semidirect
481. C13#26019semidirect

Maximal subgroups

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

subgroupindex
#131185612
#131177232
#131164082
#131163392
#131163352
#131161722
#131157922
#131156012
#131154162
#131154122
#131150282
#131150192
#131149282
#131145562
C13×#18092
#2601913