Finite Group Databasebeta

← #15784761

Subgroups — #15784761

Order 3328.

1574 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
1C2×#11718644C211yesmaximal, characteristic
2C2×C4⋊C4×Dic13C211yesmaximal, characteristic
3C2×C4⋊C4×Dic13C211yesmaximal, characteristic
4C2×#11718310C212yesmaximal
5#13113105C211yesmaximal, characteristic
6#13113099C211yesmaximal, characteristic
7#13113094C212yesmaximal
8#13113090C212yesmaximal
9#95×Dic13C212yesmaximal
10#95×Dic13C211yesmaximal, characteristic
11C13×#1441C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic13C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101C2212yes—
17C22×#6101C2212yes—
18C22×C4×Dic13C2211yescharacteristic
19C22×C4×Dic13C2212yes—
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2212yes—
23C2×C13×#95C2212yes—
24C2×C13×#95C2212yes—
25C2×C13×#95C2211yescharacteristic
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35#11718644C418yescomplemented
36C4⋊C4×Dic13—24no—
37C4⋊C4×Dic13—24no—
38#11718310—28no—
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×Dic13C2312yes—
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4C2×C414yes—
55C2×C4⋊Dic13—22no—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—22no—
60C2×C4⋊Dic13C2×C414yes—
61C2×#6101—24no—
62C2×#6101—24no—
63C2×#6101—24no—
64C2×#6101—24no—
65C2×#6101—24no—
66C2×#6101C2×C418yes—
67C2×C4×Dic13—24no—
68C2×C4×Dic13—22no—
69C2×C4×Dic13—22no—
70C2×C4×Dic13—24no—
71C2×C4×Dic13—24no—
72C2×C4×Dic13—24no—
73C2×C4×Dic13—24no—
74C2×C4×Dic13—22no—
75C2×C4×Dic13—24no—
76C2×C4×Dic13—24no—
77C2×C4×Dic13D414yes—
78C2×C4×Dic13D414yes—
79C2×C4×Dic13Q818yes—
80C13×#95—24no—
81C13×#95—24no—
82C13×#95—22no—
83#88071—22no—
84#88071—24no—
85#88071—22no—
86#88071—24no—
87#88071—24no—
88#88071—24no—
89#88071—24no—
90#88071C2×C418yes—
91#88071C2×C414yes—
92C4×#398—131nomaximal, Sylow
93C24×C13C2411yescharacteristic
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—21no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13C22×C412yes—
117C22×C4×C13C22×C412yes—
118C22×C4×C13C22×C412yes—
119C22×C4×C13C2×D412yes—
120C22×C4×C13C2×D412yes—
121C22×C4×C13C2×Q814yes—
122C22×C4×C13#4114yes—
123C22×C4×C13#4112yes—
124C22×C4×C13#4112yes—
125C22×Dic13—22no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—21no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—21no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—21no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13C22×C414yes—
148C22×Dic13C22×C414yes—
149C22×Dic13C2×D412yes—
150C22×Dic13C2×D412yes—
151C22×Dic13C2×D412yes—
152C22×Dic13C2×D412yes—
153C22×Dic13C2×Q814yes—
154C22×Dic13C2×Q814yes—
155C22×Dic13#4112yes—
156C22×Dic13#4114yes—
157C22×Dic13#4112yes—
158C22×Dic13#4114yes—
159C13×C4⋊C4—28no—
160C13×C4⋊C4—28no—
161C4⋊Dic13—28no—
162C4⋊Dic13—28no—
163#6101—216no—
164#6101—216no—
165C4×Dic13—28no—
166C4×Dic13—216no—
167C4×Dic13—28no—
168C4×Dic13—48no—
169C4×Dic13—44no—
170C2×#398—131no—
171C2×C4×C4⋊C4—132no—
172C2×C4×C4⋊C4—131no—
173C2×C4×C4⋊C4—131no—
174#1445—131no—
175#1444—131no—
176#1442—132no—
177#1441—132no—
178#1441D1311yescharacteristic
179C4×#95—132no—
180C4×#95—131no—
181C23×C13C23×C411yescharacteristic
182C23×C13C22×D411yescharacteristic
183C23×C13C22×D411yescharacteristic
184C23×C13C22×Q812yes—
185C23×C13C2×#4111yescharacteristic
186C23×C13C2×#4111yescharacteristic
187C23×C13C2×#4112yes—
188C23×C13C2×#4111yescharacteristic
189C23×C13C2×#4112yes—
190C23×C13C2×#4112yes—
191C23×C13C2×#4111yescharacteristic
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—24no—
195C2×C4×C13—22no—
196C2×C4×C13—22no—
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—24no—
201C2×C4×C13—22no—
202C2×C4×C13—22no—
203C2×C4×C13—24no—
204C2×C4×C13—24no—
205C2×C4×C13—24no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—24no—
209C2×C4×C13—24no—
210C2×C4×C13—42no—
211C2×C4×C13—41no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
214C2×C4×C13—41no—
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×C13C4×D414yes—
222C2×C4×C13C4×D414yes—
223C2×Dic13—24no—
224C2×Dic13—24no—
225C2×Dic13—24no—
226C2×Dic13—24no—
227C2×Dic13—24no—
228C2×Dic13—24no—
229C2×Dic13—24no—
230C2×Dic13—24no—
231C2×Dic13—24no—
232C2×Dic13—22no—
233C2×Dic13—22no—
234C2×Dic13—24no—
235C2×Dic13—22no—
236C2×Dic13—22no—
237C2×Dic13—24no—
238C2×Dic13—22no—
239C2×Dic13—42no—
240C2×Dic13—41no—
241C2×Dic13—41no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—42no—
251C2×Dic13C4×Q818yes—
252C2×Dic13#12114yes—
253C2×Dic13C22⋊Q818yes—
254C2×Dic13#12314yes—
255C2×Dic13#12518yes—
256C2×Dic13C4⋊Q814yes—
257C22×C4⋊C4—132no—
258C22×C4⋊C4—131no—
259C22×C4⋊C4—132no—
260C22×C4⋊C4—131no—
261C22×C4⋊C4C2×D1311yescharacteristic
262C22×C4⋊C4C2×D1311yescharacteristic
263C22×C42—132no—
264C22×C42—131no—
265C22×C42—131no—
266C22×C42—131no—
267C22×C42—132no—
268#398—138no—
269C4×C4⋊C4—268no—
270C4×C4⋊C4—264no—
271C4×C4⋊C4—264no—
272C2×#95—132no—
273C2×#95—131no—
274C2×#95—132no—
275C2×#95—132no—
276C2×#95—132no—
277C2×#95—132no—
278C2×#95—131no—
279C2×#95—132no—
280C2×#95—131no—
281C2×#95C2×D1312yes—
282C2×#95C2×D1311yescharacteristic
283C2×#95C2×D1312yes—
284C22×C13C2×C4×D411yescharacteristic
285C22×C13C2×C4×D411yescharacteristic
286C22×C13C2×C4×Q812yes—
287C22×C13C4×#4111yescharacteristic
288C22×C13C4×#4112yes—
289C22×C13C2×#12111yescharacteristic
290C22×C13C2×C22⋊Q812yes—
291C22×C13C2×#12311yescharacteristic
292C22×C13#52511yescharacteristic
293C22×C13#52512yes—
294C22×C13#52511yescharacteristic
295C22×C13C2×#12512yes—
296C22×C13#52912yes—
297C22×C13#52911yescharacteristic
298C22×C13#52912yes—
299C22×C13#52912yes—
300C22×C13#52912yes—
301C22×C13C2×C4⋊Q811yescharacteristic
302C22×C13#53211yescharacteristic
303C22×C13#53211yescharacteristic
304C22×C13#53312yes—
305C22×C13#53312yes—
306C22×C13#53312yes—
307C4×C13—24no—
308C4×C13—24no—
309C4×C13—44no—
310C4×C13—44no—
311C4×C13—42no—
312Dic13—28no—
313Dic13—42no—
314Dic13—42no—
315Dic13—42no—
316Dic13—44no—
317Dic13#39818yescomplemented
318C23×C4—131no—
319C23×C4—132no—
320C23×C4—132no—
321C23×C4—131no—
322C23×C4—131no—
323C23×C4—131no—
324C23×C4C22×D1311yescharacteristic
325C23×C4C22×D1312yes—
326C23×C4C22×D1312yes—
327C23×C4C22×D1311yescharacteristic
328C23×C4C22×D1311yescharacteristic
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—138no—
334C2×C4⋊C4—134no—
335C2×C4⋊C4—264no—
336C2×C4⋊C4—264no—
337C2×C4⋊C4—262no—
338C2×C4⋊C4—262no—
339C2×C4⋊C4—264no—
340C2×C4⋊C4—262no—
341C2×C4⋊C4—264no—
342C2×C4⋊C4—262no—
343C2×C4⋊C4—264no—
344C2×C4⋊C4—262no—
345C2×C4⋊C4C4×D1314yes—
346C2×C42—134no—
347C2×C42—134no—
348C2×C42—138no—
349C2×C42—262no—
350C2×C42—264no—
351C2×C42—264no—
352C2×C42—262no—
353C2×C42—264no—
354C2×C42—264no—
355C2×C42—262no—
356C2×C42—264no—
357C2×C42—264no—
358C2×C42—264no—
359#95—24no—
360#95—24no—
361#95—22no—
362#95—134no—
363#95—138no—
364#95—264no—
365#95—264no—
366#95—264no—
367#95—264no—
368#95—262no—
369#95—264no—
370#95—262no—
371C2×C13C4×#12111yescharacteristic
372C2×C13C4×#12311yescharacteristic
373C2×C13C4×C22⋊Q812yes—
374C2×C13C4×#12512yes—
375C2×C13C4×C4⋊Q811yescharacteristic
376C2×C13C2×#39811yescharacteristic
377C2×C13#239211yescharacteristic
378C2×C13#239511yescharacteristic
379C2×C13#239612yes—
380C2×C13#239911yescharacteristic
381C2×C13#240212yes—
382C24C23×D1311yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—132no—
406C22×C4—132no—
407C22×C4—134no—
408C22×C4—132no—
409C22×C4—134no—
410C22×C4—134no—
411C22×C4—134no—
412C22×C4—134no—
413C22×C4—134no—
414C22×C4—132no—
415C22×C4—132no—
416C22×C4—132no—
417C22×C4—262no—
418C22×C4—262no—
419C22×C4—262no—
420C22×C4—262no—
421C22×C4—261no—
422C22×C4—262no—
423C22×C4—262no—
424C22×C4—261no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4—262no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—261no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—261no—
439C22×C4C2×C4×D1312yes—
440C22×C4C2×C4×D1312yes—
441C22×C4C2×C4×D1312yes—
442C22×C4D4×D1312yes—
443C22×C4D4×D1312yes—
444C22×C4#612914yes—
445C22×C4#612912yes—
446C22×C4Q8×D1314yes—
447C22×C4#613112yes—
448C4⋊C4—28no—
449C4⋊C4—28no—
450C4⋊C4—2616no—
451C4⋊C4—268no—
452C4⋊C4—268no—
453C4⋊C4—2616no—
454C42—268no—
455C42—268no—
456C42—2616no—
457C42—528no—
458C42—524no—
459C13C4×#39811yescharacteristic, complemented, Sylow
460C23C22×C4×D1311yescharacteristic
461C23C2×D4×D1311yescharacteristic
462C23C2×D4×D1311yescharacteristic
463C23C2×#612912yes—
464C23C2×#612911yescharacteristic
465C23C2×Q8×D1312yes—
466C23C2×#613111yescharacteristic
467C23#41×D1311yescharacteristic
468C23#41×D1311yescharacteristic
469C23#41×D1312yes—
470C23#41×D1312yes—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—134no—
501C2×C4—134no—
502C2×C4—138no—
503C2×C4—134no—
504C2×C4—138no—
505C2×C4—138no—
506C2×C4—264no—
507C2×C4—264no—
508C2×C4—264no—
509C2×C4—264no—
510C2×C4—264no—
511C2×C4—264no—
512C2×C4—264no—
513C2×C4—264no—
514C2×C4—264no—
515C2×C4—262no—
516C2×C4—264no—
517C2×C4—262no—
518C2×C4—262no—
519C2×C4—262no—
520C2×C4—262no—
521C2×C4—264no—
522C2×C4—521no—
523C2×C4—522no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4#8813514yes—
535C2×C4#8814714yes—
536C22C2×#8813511yescharacteristic
537C22C2×#8814711yescharacteristic
538C22#1171922711yescharacteristic
539C22C4×#612912yes—
540C22C4×Q8×D1312yes—
541C22#1171929111yescharacteristic
542C22#1171930111yescharacteristic
543C22#1171930512yes—
544C22D13×#12111yescharacteristic
545C22#1171931112yes—
546C22#1171932712yes—
547C22#1171932712yes—
548C22#1171932911yescharacteristic
549C22D13×C22⋊Q812yes—
550C22#1171933211yescharacteristic
551C22#1171935412yes—
552C22D13×#12311yescharacteristic
553C22#1171937311yescharacteristic
554C22D13×#12512yes—
555C22#1171939612yes—
556C22#1171941112yes—
557C22D13×C4⋊Q811yescharacteristic
558C22#1171943312yes—
559C4—24no—
560C4—24no—
561C4—44no—
562C4—44no—
563C4—42no—
564C4—138no—
565C4—268no—
566C4—522no—
567C4—522no—
568C4—522no—
569C4—524no—
570C2#1311734211yescharacteristic
571C2#1311736111yescharacteristic
572C2#1311736612yes—
573C2#1311739312yes—
574C2#1311740511yescharacteristic
575C2D13×#39811yescharacteristic
576C2#1311807511yescharacteristic
577C2#1311810211yescharacteristic
578C2#1311811112yes—
579C2#1311812611yescharacteristic
580C2#1311814012yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1441D13
hypocenterC13C4×#398
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
35. #11718644C4semidirect
317. Dic13#398semidirect
459. C13C4×#398semidirect

Maximal subgroups

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

subgroupindex
C2×#117186442
C2×C4⋊C4×Dic132
C2×#117183102
#131131052
#131130992
#131130942
#131130902
#95×Dic132
C13×#14412
C4×#39813