Finite Group Databasebeta

← #15926569

Subgroups — #15926569

Order 3328.

746 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118527C211yesmaximal, characteristic
2#13116404C211yesmaximal, characteristic, complemented
3#13116338C211yesmaximal, characteristic, complemented
4#13116217C211yesmaximal, characteristic, complemented
5#13115977C211yesmaximal, characteristic, complemented
6#13115784C211yesmaximal, characteristic, complemented
7#13115407C211yesmaximal, characteristic, complemented
8#13115260C211yesmaximal, characteristic
9#13115149C211yesmaximal, characteristic
10#13115090C211yesmaximal, characteristic, complemented
11#13115035C211yesmaximal, characteristic
12#13115016C211yesmaximal, characteristic
13#13114851C211yesmaximal, characteristic, complemented
14#13114552C211yesmaximal, characteristic
15C13×#2362C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C13×#391C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#388—21no—
25C13×#388—21no—
26C13×#387—21no—
27C4×C13×C4⋊C4—21no—
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34#11718873C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38#11718609—21no—
39#11718608—21no—
40#11718597C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45#11718316—21no—
46#11718307—21no—
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C22×Dic26—21no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8Q814yescomplemented
64C4×Q8×C13—22no—
65C4×Q8×C13—41no—
66C13×#117—22no—
67C13×#117—41no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
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×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C22⋊Dic13—21no—
84C2×C22⋊Dic13—21no—
85#88180—22no—
86#88180—41no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×#6101—21no—
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C22×#1055—22no—
96C22×#1055—41no—
97C22×#1055—41no—
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102#88123—22no—
103#88123—41no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95D411yescharacteristic
109C13×#95D411yescharacteristic
110#88075—22no—
111#88075—41no—
112#88075—41no—
113#88075—41no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119C22⋊#1055—22no—
120#88048—41no—
121#88047—22no—
122C4⋊#1055—41no—
123C4⋊#1055—41no—
124#26415—131nomaximal, Sylow
125C24×C13C2×D411yescharacteristic
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13C2×Q812yes—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×Q812yes—
146C22×C4×C13#4112yes—
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C2×Dic26—42no—
153C2×Dic26—42no—
154C2×Dic26—81no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4—42no—
162C13×C4⋊C4C2×Q812yes—
163C13×C4⋊C4#4112yes—
164C13×C22⋊C4—24no—
165C13×C22⋊C4—22no—
166C13×C22⋊C4—41no—
167C13×C22⋊C4—42no—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—42no—
173C42×C13—42no—
174C42×C13—42no—
175C22⋊Dic13—42no—
176C22⋊Dic13—81no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—42no—
185C4⋊Dic13#4112yes—
186#6101—42no—
187#6101—81no—
188C4×Dic13—42no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—44no—
202#2439—131no—
203#2362D1311yescharacteristic
204#2101—131no—
205#2088—131no—
206#2066—131no—
207#2024—131no—
208#1987—131no—
209#1918—131no—
210#1892—131no—
211#1873—131no—
212#1863—131no—
213#1854—131no—
214#1850—131no—
215#1805—131no—
216#1735—131no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13C22⋊Q812yes—
224C23×C13C22×D411yescharacteristic
225Q8×C13—22no—
226Q8×C13—22no—
227Q8×C13—41no—
228Q8×C13—41no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—22no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13C22⋊Q812yes—
259C2×C4×C13#13512yes—
260C2×C4×C13C22×Q811yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13H(5,𝔽2)11yescharacteristic
265C2×C4×C13H(5,𝔽2)11yescharacteristic
266C2×Dic13—22no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278Dic26—84no—
279#1055—41no—
280#1055—41no—
281#1055—41no—
282#1055—41no—
283C23×C8—131no—
284C2×C4⋊Q8—131no—
285C2×C22⋊Q8C2×D1311yescharacteristic
286C2×C4×Q8C2×D1311yescharacteristic
287C2×#117—131no—
288C2×#117C2×D1311yescharacteristic
289C2×#107—131no—
290C2×#106—131no—
291C2×C4⋊C8—131no—
292C2×C4⋊C8—131no—
293C2×#103—131no—
294C2×#103—131no—
295C2×#103—131no—
296C2×#103—131no—
297C2×C22⋊C8—131no—
298#396—261no—
299#393—261no—
300#391—261no—
301#391C2×D1311yescharacteristic
302#389—131no—
303#389—131no—
304#389C2×D1311yescharacteristic
305#388—21no—
306#388—21no—
307#387—21no—
308#387—261no—
309#382—131no—
310#380—131no—
311C4×C4⋊C4—21no—
312C4×C4⋊C4C2×D1311yescharacteristic
313C4×C22⋊C4C2×D1311yescharacteristic
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#336—131no—
325#336—131no—
326C22×C13—22no—
327C22×C13—22no—
328C22×C13—22no—
329C22×C13—41no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13C2×C22⋊Q811yescharacteristic
334C22×C13#54611yescharacteristic
335C22×C13#54611yescharacteristic
336C22×C13C2×#13511yescharacteristic
337C22×C13#57511yescharacteristic
338C22×C13#57711yescharacteristic
339C22×C13#57811yescharacteristic
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—42no—
343C4×C13—42no—
344C4×C13—41no—
345C4×C13—42no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13—81no—
349C4×C13#52911yescharacteristic
350C4×C13#53811yescharacteristic
351C4×C13#55411yescharacteristic
352C4×C13#55411yescharacteristic
353Dic13—42no—
354Dic13—81no—
355Dic13—81no—
356Dic13—81no—
357C22×Q8—261no—
358C22×Q8C22×D1311yescharacteristic
359C23×C4C22×D1311yescharacteristic
360C22×C8—131no—
361C22×C8—131no—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8—262no—
365C22×C8—521no—
366C22×C8—521no—
367C4⋊Q8—262no—
368C4⋊Q8—521no—
369C22⋊Q8—22no—
370C22⋊Q8Dic2614yescomplemented
371C4×Q8—22no—
372C4×Q8—41no—
373#117—22no—
374#117—41no—
375#117—262no—
376#117—521no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C4⋊C4C22×D1311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4C22⋊D1311yescharacteristic
395C2×C22⋊C4C22⋊D1311yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—261no—
400C2×C42C22×D1311yescharacteristic
401C2×C42C22×D1311yescharacteristic
402#107—262no—
403#106—521no—
404C4⋊C8—521no—
405C4⋊C8—521no—
406#103—262no—
407#103—521no—
408#103—521no—
409#103—521no—
410C22⋊C8—262no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95C22⋊D1311yescharacteristic
421#95C22⋊D1311yescharacteristic
422C2×C13—42no—
423C2×C13#245011yescharacteristic
424C2×C13#307611yescharacteristic
425C2×C13#308211yescharacteristic
426C2×C13#330011yescharacteristic
427C2×C13#330311yescharacteristic
428C2×C13#331111yescharacteristic
429C2×C13#331311yescharacteristic
430C24C2×C22⋊D1311yescharacteristic
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—522no—
437C2×Q8—522no—
438C2×Q8—1041no—
439C2×Q8C2×Dic2612yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4C2×Dic2612yes—
453C22×C4#612712yes—
454C22×C4C2×C22⋊D1311yescharacteristic
455C22×C4C2×C22⋊D1311yescharacteristic
456C22×C4C2×C22⋊D1311yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C23×D1311yescharacteristic
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—524no—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—132no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—522no—
489C4⋊C4—522no—
490C4⋊C4—1041no—
491C4⋊C4C2×Dic2612yes—
492C4⋊C4#612912yes—
493C22⋊C4—24no—
494C22⋊C4—22no—
495C22⋊C4—41no—
496C22⋊C4—42no—
497C22⋊C4—522no—
498C22⋊C4—1041no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—42no—
504C42—42no—
505C42—42no—
506C42—522no—
507C13#2641511yescharacteristic, complemented, Sylow
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23#8817812yes—
515C23C22×C22⋊D1311yescharacteristic
516Q8—22no—
517Q8—22no—
518Q8—41no—
519Q8—41no—
520Q8—1044no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—262no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4#8817812yes—
563C2×C4#8820412yes—
564C2×C4C22×Dic2611yescharacteristic
565C2×C4C2×#612711yescharacteristic
566C2×C4C2×#612911yescharacteristic
567C2×C4#8825111yescharacteristic
568C2×C4#41×D1311yescharacteristic
569C2×C4#8825611yescharacteristic
570C8—521no—
571C8—521no—
572C8—521no—
573C8—521no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22C2×#8817811yescharacteristic
582C22#1171951111yescharacteristic
583C22C2×#8820411yescharacteristic
584C22#1171952711yescharacteristic
585C22#1171953411yescharacteristic
586C22#1171954211yescharacteristic
587C22#1171954311yescharacteristic
588C4—22no—
589C4—22no—
590C4—42no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—522no—
598C4—1041no—
599C4—1041no—
600C4—1041no—
601C4#1171924311yescharacteristic
602C4#1171924411yescharacteristic
603C4#1171924811yescharacteristic
604C4#1171926511yescharacteristic
605C2—42no—
606C2#1311865411yescharacteristic
607C2#1312462411yescharacteristic
608C2#1312467811yescharacteristic
609C2#1312671711yescharacteristic
610C2#1312676411yescharacteristic
611C2#1312686611yescharacteristic
612C2#1312690211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2362C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2362D13
hypocenterC13#26415
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. #13116404C2semidirect
3. #13116338C2semidirect
4. #13116217C2semidirect
5. #13115977C2semidirect
6. #13115784C2semidirect
7. #13115407C2semidirect
10. #13115090C2semidirect
13. #13114851C2semidirect
63. C13×C22⋊Q8Q8semidirect
370. C22⋊Q8Dic26semidirect
507. C13#26415semidirect

Maximal subgroups

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

subgroupindex
#131185272
#131164042
#131163382
#131162172
#131159772
#131157842
#131154072
#131152602
#131151492
#131150902
#131150352
#131150162
#131148512
#131145522
C13×#23622
#2641513