Finite Group Databasebeta

← #15920683

Subgroups — #15920683

Order 3328.

694 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117727C211yesmaximal, characteristic
2#13116393C211yesmaximal, characteristic, complemented
3#13116338C211yesmaximal, characteristic, complemented
4#13116337C211yesmaximal, characteristic, complemented
5#13116171C211yesmaximal, characteristic, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115597C211yesmaximal, characteristic, complemented
8#13115425C211yesmaximal, characteristic, complemented
9#13115418C211yesmaximal, characteristic, complemented
10#13115035C211yesmaximal, characteristic
11#13115016C211yesmaximal, characteristic
12#13114928C211yesmaximal, characteristic
13#13114859C211yesmaximal, characteristic
14#13114552C211yesmaximal, characteristic
15C13×#2441C211yesmaximal, characteristic
16C2×C13×#125C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19C23×#1055C2211yescharacteristic
20C13×#399—21no—
21C13×#396—21no—
22C13×#389—21no—
23C13×#389C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#387—21no—
26C13×#384C2211yescharacteristic
27C13×#380C2211yescharacteristic
28C4×C13×C22⋊C4C2211yescharacteristic
29#11718873C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×#88048C2211yescharacteristic
32C2×#88048C2211yescharacteristic
33C2×#88048C2211yescharacteristic
34C2×#88047C2211yescharacteristic
35#11718606—21no—
36#11718606—21no—
37C4×C4⋊Dic13C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43#11718312—21no—
44#11718310—21no—
45#11718121C2211yescharacteristic
46#11718121C2211yescharacteristic
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C13×#125—22no—
61C13×#125—41no—
62C13×#117—22no—
63C13×#117—41no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4D411yescharacteristic
77C2×C13×C22⋊C4D411yescharacteristic
78C2×C42×C13—21no—
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83#88180—22no—
84#88180Q814yes—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×#6101—21no—
90C2×#6101—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C22×#1055—22no—
95C22×#1055—22no—
96C22×#1055—41no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95D411yescharacteristic
105C13×#95D411yescharacteristic
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111C22⋊#1055—22no—
112#88048—22no—
113#88048—41no—
114#88048—41no—
115#88047—22no—
116C4⋊#1055—22no—
117C4⋊#1055—41no—
118#25999—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×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×Q812yes—
134C22×C4×C13#4112yes—
135C22×C4×C13C2411yescharacteristic
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—42no—
148C13×C4⋊C4—42no—
149C13×C4⋊C4—42no—
150C13×C4⋊C4—42no—
151C13×C4⋊C4—81no—
152C13×C4⋊C4—81no—
153C13×C4⋊C4#4112yes—
154C13×C22⋊C4—22no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—42no—
157C13×C22⋊C4—81no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—42no—
163C22⋊Dic13—24no—
164C22⋊Dic13—81no—
165C4⋊Dic13—21no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13C2×Q812yes—
172C4⋊Dic13C2×Q812yes—
173#6101—42no—
174#6101—42no—
175C4×Dic13—24no—
176C4×Dic13—81no—
177C4×Dic13—81no—
178C2×#1055—21no—
179C2×#1055—21no—
180C2×#1055—21no—
181C2×#1055—21no—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—44no—
190C2×#1055#4112yes—
191#2441D1311yescharacteristic
192#2347—131no—
193#2099—131no—
194#2088—131no—
195#2088—131no—
196#2059—131no—
197#1989—131no—
198#1948—131no—
199#1921—131no—
200#1920—131no—
201#1854—131no—
202#1850—131no—
203#1825—131no—
204#1807—131no—
205#1735—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—21no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
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—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13C22⋊Q812yes—
244C2×C4×C13#13512yes—
245C2×C4×C13C22×Q811yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13H(5,𝔽2)11yescharacteristic
250C2×C4×C132−1+411yescharacteristic
251C2×Dic13—22no—
252C2×Dic13—22no—
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—
263#1055—22no—
264#1055—41no—
265#1055—41no—
266#1055—41no—
267C23×C8—131no—
268C2×#125C2×D1311yescharacteristic
269C2×#117—131no—
270C2×#117C2×D1311yescharacteristic
271C2×#107—131no—
272C2×#106—131no—
273C2×#106—131no—
274C2×#106—131no—
275C2×C4⋊C8—131no—
276C2×C4⋊C8—131no—
277C2×C22⋊C8—131no—
278#399—21no—
279#396—21no—
280#389—21no—
281#389—131no—
282#389—131no—
283#389C2×D1311yescharacteristic
284#389C2×D1311yescharacteristic
285#388—261no—
286#388—261no—
287#387—21no—
288#384C2×D1311yescharacteristic
289#383—261no—
290#380—131no—
291#380C2×D1311yescharacteristic
292C4×C4⋊C4—131no—
293C4×C4⋊C4—131no—
294C4×C4⋊C4—261no—
295C4×C22⋊C4C2×D1311yescharacteristic
296#340—131no—
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#340—131no—
308#336—131no—
309#336—131no—
310C22×C13—22no—
311C22×C13—22no—
312C22×C13—22no—
313C22×C13—41no—
314C22×C13—41no—
315C22×C13—41no—
316C22×C13—41no—
317C22×C13C2×C22⋊Q811yescharacteristic
318C22×C13#54611yescharacteristic
319C22×C13#54711yescharacteristic
320C22×C13C2×#13511yescharacteristic
321C22×C13#57511yescharacteristic
322C22×C13#57711yescharacteristic
323C22×C13#57711yescharacteristic
324C4×C13—22no—
325C4×C13—22no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13—42no—
330C4×C13—81no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13#53311yescharacteristic
334C4×C13#54411yescharacteristic
335C4×C13#55111yescharacteristic
336C4×C13#55211yescharacteristic
337Dic13—42no—
338Dic13—42no—
339Dic13—81no—
340Dic13—81no—
341C23×C4C22×D1311yescharacteristic
342C22×C8—131no—
343C22×C8—131no—
344C22×C8—131no—
345C22×C8—131no—
346C22×C8—262no—
347C22×C8—262no—
348C22×C8—521no—
349#125—22no—
350#125—41no—
351#117—22no—
352#117—41no—
353#117—134no—
354#117—262no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4C22⋊D1311yescharacteristic
376C2×C22⋊C4C22⋊D1311yescharacteristic
377C2×C42—21no—
378C2×C42—261no—
379C2×C42—261no—
380C2×C42—261no—
381C2×C42C22×D1311yescharacteristic
382C2×C42C22×D1311yescharacteristic
383#107—262no—
384#106—262no—
385#106—521no—
386#106—521no—
387C4⋊C8—262no—
388C4⋊C8—521no—
389C22⋊C8—262no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—261no—
394#95—261no—
395#95—261no—
396#95—261no—
397#95—261no—
398#95C22⋊D1311yescharacteristic
399#95C22⋊D1311yescharacteristic
400C2×C13—42no—
401C2×C13#243811yescharacteristic
402C2×C13#307611yescharacteristic
403C2×C13#308411yescharacteristic
404C2×C13#330411yescharacteristic
405C2×C13#330711yescharacteristic
406C2×C13#333711yescharacteristic
407C2×C13#335011yescharacteristic
408C24C2×C22⋊D1311yescharacteristic
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—261no—
418C22×C4—261no—
419C22×C4—261no—
420C22×C4—261no—
421C22×C4Q8×D1312yes—
422C22×C4#613112yes—
423C22×C4C2×C22⋊D1311yescharacteristic
424C22×C4C2×C22⋊D1311yescharacteristic
425C22×C4C2×C22⋊D1311yescharacteristic
426C22×C4C2×C22⋊D1311yescharacteristic
427C22×C4C2×C22⋊D1311yescharacteristic
428C22×C4C23×D1311yescharacteristic
429C2×C8—132no—
430C2×C8—261no—
431C2×C8—261no—
432C2×C8—261no—
433C2×C8—261no—
434C2×C8—261no—
435C2×C8—261no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—524no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—42no—
450C4⋊C4—42no—
451C4⋊C4—42no—
452C4⋊C4—42no—
453C4⋊C4—81no—
454C4⋊C4—81no—
455C4⋊C4—132no—
456C4⋊C4—132no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—522no—
464C4⋊C4—522no—
465C4⋊C4#612912yes—
466C22⋊C4—22no—
467C22⋊C4—41no—
468C22⋊C4—42no—
469C22⋊C4—81no—
470C22⋊C4—264no—
471C22⋊C4—1041no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—42no—
477C42—264no—
478C42—1041no—
479C42—1041no—
480C13#2599911yescharacteristic, complemented, Sylow
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23#8820012yes—
488C23C22×C22⋊D1311yescharacteristic
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
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—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—262no—
519C2×C4—262no—
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#8820012yes—
531C2×C4#8820412yes—
532C2×C4C2×#612911yescharacteristic
533C2×C4#8825111yescharacteristic
534C2×C4C2×Q8×D1311yescharacteristic
535C2×C4C2×#613111yescharacteristic
536C2×C4#41×D1311yescharacteristic
537C2×C4#8825711yescharacteristic
538C8—262no—
539C8—521no—
540C8—521no—
541C8—521no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22#1171951111yescharacteristic
550C22C2×#8820011yescharacteristic
551C22C2×#8820411yescharacteristic
552C22#1171952711yescharacteristic
553C22#1171952911yescharacteristic
554C22#1171954111yescharacteristic
555C22#1171954211yescharacteristic
556C4—22no—
557C4—22no—
558C4—41no—
559C4—41no—
560C4—42no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—522no—
566C4—522no—
567C4—1041no—
568C4—1041no—
569C4#1171932711yescharacteristic
570C4#1171932811yescharacteristic
571C4#1171934211yescharacteristic
572C4#1171934711yescharacteristic
573C2—42no—
574C2#1311850811yescharacteristic
575C2#1312461811yescharacteristic
576C2#1312469411yescharacteristic
577C2#1312677511yescharacteristic
578C2#1312681211yescharacteristic
579C2#1312721511yescharacteristic
580C2#1312737511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2441C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2441D13
hypocenterC13#25999
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2441

Complements

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

NH ≅ G/Ntype
2. #13116393C2semidirect
3. #13116338C2semidirect
4. #13116337C2semidirect
5. #13116171C2semidirect
6. #13115794C2semidirect
7. #13115597C2semidirect
8. #13115425C2semidirect
9. #13115418C2semidirect
480. C13#25999semidirect

Maximal subgroups

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

subgroupindex
#131177272
#131163932
#131163382
#131163372
#131161712
#131157942
#131155972
#131154252
#131154182
#131150352
#131150162
#131149282
#131148592
#131145522
C13×#24412
#2599913