Finite Group Databasebeta

← #15791108

Subgroups — #15791108

Order 3328.

1506 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718605C212yesmaximal
2C2×#11718873C211yesmaximal, characteristic
3#13113094C212yesmaximal, complemented
4#13113088C212yesmaximal, complemented
5#13113083C212yesmaximal
6#13113070C212yesmaximal, complemented
7#13113062C212yesmaximal, complemented
8#13113059C211yesmaximal, characteristic
9C13×C22⋊#95C211yesmaximal, characteristic
10C24×C4×C13C2211yescharacteristic
11C22×C13×C22⋊C4C2212yes—
12C22×C22⋊Dic13C2212yes—
13C22×C22⋊Dic13C2211yescharacteristic
14C22×C22⋊Dic13C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×#6101C2212yes—
18C22×C4×Dic13C2212yes—
19C2×C13×#95C2212yes—
20C2×C13×#95C2211yescharacteristic
21C2×C13×#95C2211yescharacteristic
22#11718873C418yescomplemented
23C2×#88071C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32#11718605—28no—
33C25×C13C2311yescharacteristic
34C23×C4×C13—24no—
35C23×C4×C13—42no—
36C23×C4×C13—41no—
37C23×C4×C13—41no—
38C23×C4×C13C2×C414yes—
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×Dic13C2312yes—
44C23×Dic13C2312yes—
45C23×Dic13C2312yes—
46C23×Dic13C2312yes—
47C2×C13×C22⋊C4—24no—
48C2×C13×C22⋊C4—24no—
49C2×C13×C22⋊C4—42no—
50C2×C22⋊Dic13—24no—
51C2×C22⋊Dic13—24no—
52C2×C22⋊Dic13—22no—
53C2×C22⋊Dic13—41no—
54C2×C22⋊Dic13—41no—
55C2×C22⋊Dic13—41no—
56C2×C22⋊Dic13—41no—
57C2×C22⋊Dic13C2×C418yes—
58C2×C22⋊Dic13D414yes—
59C2×C4⋊Dic13—41no—
60C2×C4⋊Dic13—42no—
61C2×C4⋊Dic13—41no—
62C2×C4⋊Dic13C2×C414yes—
63C2×C4⋊Dic13C2×C414yes—
64C2×#6101—24no—
65C2×#6101—42no—
66C2×#6101—42no—
67C2×C4×Dic13—24no—
68C2×C4×Dic13—24no—
69C2×C4×Dic13—42no—
70C13×#95—24no—
71C13×#95—41no—
72C13×#95—41no—
73#88071—24no—
74#88071—24no—
75#88071—24no—
76#88071—24no—
77#88071—42no—
78#88071—42no—
79#88071—42no—
80#88071—42no—
81#88071C2×C418yes—
82#14422—131nomaximal, Sylow
83C24×C13—22no—
84C24×C13—22no—
85C24×C13—21no—
86C24×C13—21no—
87C24×C13—21no—
88C24×C13—22no—
89C24×C13—22no—
90C24×C13—21no—
91C24×C13C22×C412yes—
92C24×C13C2×D412yes—
93C24×C13#4112yes—
94C24×C13C2411yescharacteristic
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—28no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—44no—
117C22×C4×C13—44no—
118C22×C4×C13—48no—
119C22×C4×C13—48no—
120C22×C4×C13C22×C412yes—
121C22×C4×C13C22×C412yes—
122C22×C4×C13#4114yes—
123C22×C4×C13#4114yes—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13C22×C414yes—
150C22×Dic13C22×C414yes—
151C22×Dic13C2×D414yes—
152C13×C22⋊C4—48no—
153C22⋊Dic13—216no—
154C22⋊Dic13—44no—
155C22⋊Dic13—44no—
156C4⋊Dic13—44no—
157C4⋊Dic13—44no—
158#6101—48no—
159C4×Dic13—48no—
160C2×#388—132no—
161C2×#380—131no—
162#1442—132no—
163#1441—132no—
164#1440—132no—
165#1436—132no—
166#1434—132no—
167C22⋊#95—131no—
168C22⋊#95D1311yescharacteristic
169C23×C13—22no—
170C23×C13—22no—
171C23×C13—22no—
172C23×C13—22no—
173C23×C13—22no—
174C23×C13—22no—
175C23×C13—22no—
176C23×C13—22no—
177C23×C13—22no—
178C23×C13—22no—
179C23×C13—24no—
180C23×C13—24no—
181C23×C13—24no—
182C23×C13—24no—
183C23×C13—42no—
184C23×C13—42no—
185C23×C13—42no—
186C23×C13—42no—
187C23×C13—42no—
188C23×C13—42no—
189C23×C13—42no—
190C23×C13—42no—
191C23×C13C4×D414yes—
192C23×C13C23×C411yescharacteristic
193C23×C13C22×D411yescharacteristic
194C23×C13C2×#4112yes—
195C23×C13C2×#4111yescharacteristic
196C23×C13C2×#4112yes—
197C23×C13H(5,𝔽2)11yescharacteristic
198C23×C13H(5,𝔽2)11yescharacteristic
199C23×C13H(5,𝔽2)12yes—
200C23×C13H(5,𝔽2)11yescharacteristic
201C23×C132−1+412yes—
202C23×C132−1+411yescharacteristic
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—24no—
206C2×C4×C13—24no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—416no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13#11714yes—
228C2×Dic13—24no—
229C2×Dic13—24no—
230C2×Dic13—24no—
231C2×Dic13—24no—
232C2×Dic13—24no—
233C2×Dic13—24no—
234C2×Dic13—24no—
235C2×Dic13—24no—
236C2×Dic13—24no—
237C2×Dic13—42no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C24×C4C2×D1311yescharacteristic
257C22×C4⋊C4—131no—
258C22×C4⋊C4—131no—
259C22×C4⋊C4—132no—
260C22×C22⋊C4—132no—
261C22×C22⋊C4—131no—
262C22×C22⋊C4—131no—
263C22×C22⋊C4C2×D1312yes—
264C22×C42—132no—
265#388—268no—
266#380—138no—
267C2×#95—132no—
268C2×#95—132no—
269C2×#95—132no—
270C2×#95—132no—
271C2×#95—132no—
272C2×#95—132no—
273C2×#95—132no—
274C2×#95—132no—
275C2×#95—132no—
276C2×#95C2×D1312yes—
277C2×#95C2×D1311yescharacteristic
278C2×#95C2×D1311yescharacteristic
279C22×C13—24no—
280C22×C13—24no—
281C22×C13—24no—
282C22×C13—42no—
283C22×C13—42no—
284C22×C13—42no—
285C22×C13—42no—
286C22×C13—44no—
287C22×C13—44no—
288C22×C13—44no—
289C22×C13—44no—
290C22×C13C2×#11711yescharacteristic
291C22×C13C2×C4×D411yescharacteristic
292C22×C13C4×#4111yescharacteristic
293C22×C13#51811yescharacteristic
294C22×C13#51811yescharacteristic
295C22×C13#51911yescharacteristic
296C22×C13#52011yescharacteristic
297C22×C13#53411yescharacteristic
298C22×C13#53711yescharacteristic
299C22×C13#53812yes—
300C22×C13#53812yes—
301C22×C13#53811yescharacteristic
302C22×C13#53912yes—
303C22×C13#53911yescharacteristic
304C22×C13#54212yes—
305C22×C13#54612yes—
306C22×C13#54712yes—
307C22×C13#55212yes—
308C22×C13#55212yes—
309C22×C13#55312yes—
310C22×C13#55512yes—
311C22×C13#56212yes—
312C22×C13#56312yes—
313C4×C13—24no—
314C4×C13—42no—
315C4×C13—44no—
316C4×C13—82no—
317Dic13—44no—
318Dic13—44no—
319Dic13—44no—
320Dic13—82no—
321C25C22×D1311yescharacteristic
322C23×C4—24no—
323C23×C4—41no—
324C23×C4—41no—
325C23×C4—42no—
326C23×C4—132no—
327C23×C4—132no—
328C23×C4—132no—
329C23×C4—132no—
330C23×C4C4×D1314yes—
331C23×C4C22×D1312yes—
332C23×C4C22×D1311yescharacteristic
333C23×C4C22×D1312yes—
334C23×C4C22×D1311yescharacteristic
335C2×C4⋊C4—134no—
336C2×C4⋊C4—134no—
337C2×C4⋊C4—264no—
338C2×C4⋊C4—522no—
339C2×C4⋊C4—522no—
340C2×C4⋊C4—521no—
341C2×C4⋊C4—522no—
342C2×C4⋊C4—521no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—138no—
347C2×C22⋊C4—134no—
348C2×C22⋊C4—264no—
349C2×C22⋊C4—264no—
350C2×C22⋊C4—262no—
351C2×C22⋊C4—521no—
352C2×C22⋊C4—521no—
353C2×C22⋊C4—521no—
354C2×C22⋊C4—521no—
355C2×C42—264no—
356C2×C42—264no—
357C2×C42—522no—
358#95—24no—
359#95—41no—
360#95—41no—
361#95—138no—
362#95—264no—
363#95—264no—
364#95—264no—
365#95—264no—
366#95—522no—
367#95—522no—
368#95—522no—
369#95—522no—
370C2×C13—44no—
371C2×C13#231211yescharacteristic
372C2×C13#232511yescharacteristic
373C2×C13#233211yescharacteristic
374C2×C13#234411yescharacteristic
375C2×C13#234611yescharacteristic
376C2×C13#236411yescharacteristic
377C2×C13#237811yescharacteristic
378C2×C13#268612yes—
379C2×C13#269512yes—
380C2×C13#277012yes—
381C2×C13#278112yes—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—22no—
389C24—21no—
390C24C2×C4×D1312yes—
391C24D4×D1312yes—
392C24#613112yes—
393C24C23×D1311yescharacteristic
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—28no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—48no—
418C22×C4—48no—
419C22×C4—134no—
420C22×C4—134no—
421C22×C4—134no—
422C22×C4—262no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4C2×C4×D1312yes—
448C22×C4C2×C4×D1312yes—
449C22×C4#612714yes—
450C22×C4#612914yes—
451C4⋊C4—524no—
452C4⋊C4—524no—
453C4⋊C4—528no—
454C22⋊C4—48no—
455C22⋊C4—2616no—
456C22⋊C4—524no—
457C22⋊C4—524no—
458C42—528no—
459C13#1442211yescharacteristic, complemented, Sylow
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—24no—
465C23—24no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—24no—
471C23—24no—
472C23—22no—
473C23—22no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23#8814714yes—
483C23C22×C4×D1311yescharacteristic
484C23C2×#612712yes—
485C23C2×D4×D1311yescharacteristic
486C23C2×#612912yes—
487C23#8825112yes—
488C23#8825111yescharacteristic
489C23#8825111yescharacteristic
490C23C2×#613111yescharacteristic
491C23#8825611yescharacteristic
492C23#8825712yes—
493C23#8825711yescharacteristic
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—416no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—264no—
519C2×C4—264no—
520C2×C4—264no—
521C2×C4—264no—
522C2×C4—264no—
523C2×C4—264no—
524C2×C4—264no—
525C2×C4—264no—
526C2×C4—264no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—522no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—522no—
540C2×C4—522no—
541C2×C4—522no—
542C2×C4—522no—
543C2×C4—522no—
544C2×C4—522no—
545C2×C4—522no—
546C2×C4#8813114yes—
547C22—24no—
548C22—24no—
549C22—24no—
550C22—42no—
551C22—44no—
552C22—42no—
553C22—44no—
554C22—42no—
555C22—44no—
556C22—44no—
557C22—42no—
558C22C4×#612711yescharacteristic
559C22C2×#8813111yescharacteristic
560C22#1171919111yescharacteristic
561C22#1171919111yescharacteristic
562C22#1171919512yes—
563C22C2×#8814711yescharacteristic
564C22#1171921912yes—
565C22#1171922111yescharacteristic
566C22#1171922811yescharacteristic
567C22#1171924612yes—
568C22#1171926612yes—
569C22#1171926812yes—
570C22#1171926912yes—
571C22#1171929812yes—
572C22#1171929812yes—
573C22#1171930211yescharacteristic
574C22#1171931011yescharacteristic
575C22#1171931612yes—
576C22#1171934712yes—
577C22#1171934911yescharacteristic
578C22#1171935011yescharacteristic
579C22#1171935612yes—
580C22#1171937212yes—
581C4—24no—
582C4—44no—
583C4—42no—
584C4—82no—
585C4—524no—
586C4—524no—
587C4—524no—
588C4—1042no—
589C2—44no—
590C2#1311743211yescharacteristic
591C2#1311753611yescharacteristic
592C2#1311759211yescharacteristic
593C2#1311770711yescharacteristic
594C2#1311771911yescharacteristic
595C2#1311788311yescharacteristic
596C2#1311800411yescharacteristic
597C2#1312123712yes—
598C2#1312136612yes—
599C2#1312233812yes—
600C2#1312249312yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C22⋊#95C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22⋊#95D13
hypocenterC13#14422
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. #13113094C2semidirect
4. #13113088C2semidirect
6. #13113070C2semidirect
7. #13113062C2semidirect
22. #11718873C4semidirect
459. C13#14422semidirect

Maximal subgroups

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

subgroupindex
C2×#117186052
C2×#117188732
#131130942
#131130882
#131130832
#131130702
#131130622
#131130592
C13×C22⋊#952
#1442213