Finite Group Databasebeta

← #16796894

Subgroups — #16796894

Order 3328.

1626 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719146C212yesmaximal
2C2×#11719062C212yesmaximal, complemented
3#13130566C212yesmaximal, complemented
4#13130565C212yesmaximal, complemented
5#13130563C211yesmaximal, characteristic, complemented
6#13130562C211yesmaximal, characteristic, complemented
7C4×#88111C211yesmaximal, characteristic, complemented
8C4×C22⋊#1057C211yesmaximal, characteristic, complemented
9#13130499C211yesmaximal, characteristic, complemented
10C2×#11718290C211yesmaximal, characteristic, complemented
11C2×C4×#6129C211yesmaximal, characteristic
12C22×#6129C2211yescharacteristic
13C22×#6122C2212yes—
14C23×#1057C2212yes—
15C2×C4×D4×C13C411yescharacteristic
16C2×D4×Dic13C411yescharacteristic
17C2×C4×C22⋊D13C411yescharacteristic
18C2×C4×C22⋊D13C411yescharacteristic
19C22×C4×Dic13C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C4×#6129—28no—
22C2×#88146C2211yescharacteristic
23C2×#88141C411yescharacteristic
24C2×#88135C411yescharacteristic
25C2×#88135C411yescharacteristic
26C2×#88131C2211yescharacteristic
27C2×#88131C2211yescharacteristic
28C2×C42×D13C2211yescharacteristic
29C2×C4×Dic26C411yescharacteristic
30C2×C22⋊#1057C2212yes—
31C2×C22⋊#1057C2212yes—
32#11719146C4116yescomplemented
33C2×#88111C2212yes—
34C2×#88111C2212yes—
35C2×#88110C2212yes—
36C2×#88110C2212yes—
37C2×C4×#1057C2212yes—
38C2×C4×#1057C2212yes—
39#11719062—28no—
40#11718290C2211yescharacteristic
41#11718290C2211yescharacteristic
42#11718290C2212yes—
43#11718290C2211yescharacteristic
44#11718290C2211yescharacteristic
45#11718290C2212yes—
46C22×D4×C13C2×C411yescharacteristic
47C23×C4×C13C2×C411yescharacteristic
48C23×C4×C13C2×C411yescharacteristic
49C22×C22⋊D13C2×C411yescharacteristic
50C22×C22⋊D13C2×C411yescharacteristic
51C23×Dic13C2×C411yescharacteristic
52C23×Dic13C2×C411yescharacteristic
53C23×Dic13C2311yescharacteristic
54C23×Dic13C2311yescharacteristic
55C2×#6129—24no—
56C2×#6129—22no—
57C2×#6129—22no—
58C2×#6129C2×C418yes—
59C22×C4×D13C2×C411yescharacteristic
60C22×C4×D13C2×C411yescharacteristic
61C22×C4×D13C2311yescharacteristic
62C22×Dic26C2×C411yescharacteristic
63C2×#6122—24no—
64C2×#6122—24no—
65C2×#6122C2×C418yescomplemented
66C22×#1057—24no—
67C22×#1057—24no—
68C22×#1057C2×C418yescomplemented
69C22×#1057C2312yes—
70C22×#1057C2312yes—
71C22×#1057C2312yes—
72C22×#1057C2312yes—
73C4×D4×C13—24no—
74C2×C13×C4⋊C4C2×C411yescharacteristic
75C2×C13×C22⋊C4C2×C411yescharacteristic
76C2×C13×C22⋊C4C2×C411yescharacteristic
77C2×C42×C13C2×C411yescharacteristic
78C2×C22⋊Dic13C2×C411yescharacteristic
79C2×C22⋊Dic13C2×C411yescharacteristic
80D4×Dic13—24no—
81C4×C22⋊D13—24no—
82C4×C22⋊D13—24no—
83C2×#6103C2×C411yescharacteristic
84C2×#6103C2×C411yescharacteristic
85C2×C4⋊Dic13C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×#6101C2×C411yescharacteristic
90C2×C4×Dic13—24no—
91C2×C4×Dic13—24no—
92C2×C4×Dic13C2×C411yescharacteristic
93C2×C4×Dic13C2×C411yescharacteristic
94C2×C4×Dic13C2×C411yescharacteristic
95C2×C4×Dic13C2×C411yescharacteristic
96C2×C4×Dic13C2×C411yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101#88146—24no—
102#88141—24no—
103#88135—24no—
104#88135—24no—
105#88131—24no—
106#88131D418yes—
107C42×D13—24no—
108C4×Dic26—24no—
109C22⋊#1057C2×C418yescomplemented
110C22⋊#1057C2×C418yescomplemented
111#88111C2×C418yescomplemented
112#88111C2×C418yescomplemented
113#88110—24no—
114#88110—24no—
115C4×#1057—24no—
116C4×#1057—24no—
117#20378—131nomaximal, Sylow
118C24×C13C22×C411yescharacteristic
119C24×C13C22×C411yescharacteristic
120C23×D13C22×C411yescharacteristic
121C2×D4×C13—22no—
122C2×D4×C13—22no—
123C2×D4×C13C4214yes—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C22×C411yescharacteristic
132C22×C4×C13C22×C411yescharacteristic
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C22×C411yescharacteristic
135C2×C22⋊D13—22no—
136C2×C22⋊D13—22no—
137C2×C22⋊D13—22no—
138C2×C22⋊D13—22no—
139C2×C22⋊D13C4214yes—
140C2×C22⋊D13C4214yes—
141C22×Dic13—22no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—41no—
149C22×Dic13—41no—
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C414yes—
153C22×Dic13C22×C411yescharacteristic
154C22×Dic13C22×C411yescharacteristic
155C22×Dic13C22×C411yescharacteristic
156C22×Dic13C22×C411yescharacteristic
157C22×Dic13C22×C414yes—
158C22×Dic13C2×D414yes—
159C22×Dic13#4112yes—
160C22×Dic13#4112yes—
161C22×Dic13C2411yescharacteristic
162#6129—216no—
163#6129—216no—
164C2×C4×D13—22no—
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×C4×D13—22no—
168C2×C4×D13—22no—
169C2×C4×D13—22no—
170C2×C4×D13—22no—
171C2×C4×D13—41no—
172C2×C4×D13—41no—
173C2×C4×D13C22×C414yes—
174C2×Dic26—22no—
175C2×Dic26—22no—
176C2×Dic26C4214yes—
177#6122—216no—
178C2×#1057—216no—
179C2×#1057—22no—
180C2×#1057—22no—
181C2×#1057—22no—
182C2×#1057—22no—
183C2×#1057—22no—
184C2×#1057—22no—
185C2×#1057—22no—
186C2×#1057—22no—
187C2×#1057C22×C414yes—
188C2×#1057C22×C414yes—
189C2×#1057C22×C414yes—
190C2×#1057C22×C414yes—
191C13×C4⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4C22⋊C414yes—
194C42×C13—22no—
195C22⋊Dic13—22no—
196C22⋊Dic13C22⋊C414yes—
197#6103—22no—
198#6103—22no—
199C4⋊Dic13—22no—
200#6101—22no—
201#6101—22no—
202#6101C22⋊C414yes—
203#6101C22⋊C414yes—
204C4×Dic13—22no—
205C4×Dic13—22no—
206C4×Dic13—22no—
207C4×Dic13—22no—
208C4×Dic13—22no—
209C4×Dic13—22no—
210C4×Dic13—22no—
211C4×Dic13C2×D414yes—
212C4×Dic13C2×D414yes—
213C2×C4×#41—131no—
214C2×#408—132no—
215C2×#405—132no—
216#1750—132no—
217#1750—132no—
218#1749—131no—
219#1749—131no—
220C4×C22⋊C8—131no—
221C4×C22⋊C8—131no—
222#1728—131no—
223C2×#336—131no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13C2×C4212yes—
235C23×C13C2×C4212yes—
236C23×C13C2×C22⋊C412yes—
237C23×C13#11712yes—
238C23×C13C23×C411yescharacteristic
239C22×D13—21no—
240C22×D13—21no—
241C22×D13—21no—
242C22×D13—21no—
243C22×D13—21no—
244C22×D13—21no—
245C22×D13C2×C4212yes—
246D4×C13—28no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—44no—
259C2×C4×C13—44no—
260C2×C4×C13C2×C4212yes—
261C2×C4×C13C2×C22⋊C412yes—
262C2×C4×C13C2×C22⋊C412yes—
263C2×C4×C13#13112yes—
264C22⋊D13—28no—
265C22⋊D13—28no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—24no—
275C2×Dic13—24no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—44no—
280C2×Dic13—44no—
281C2×Dic13C2×C4212yes—
282C2×Dic13C2×C4212yes—
283C2×Dic13C2×C22⋊C412yes—
284C2×Dic13C2×C22⋊C412yes—
285C2×Dic13C2×C22⋊C412yes—
286C2×Dic13#11712yes—
287C2×Dic13C4×D418yes—
288C2×Dic13C4×D418yes—
289C2×Dic13#13112yes—
290C2×Dic13C23×C412yes—
291C2×Dic13C22×D412yes—
292C2×Dic13C2×#4111yescharacteristic
293C2×Dic13C2×#4111yescharacteristic
294C4×D13—24no—
295C4×D13—24no—
296C4×D13—44no—
297C4×D13—44no—
298Dic26—28no—
299#1057—24no—
300#1057—24no—
301#1057—24no—
302#1057—24no—
303C22×#41—131no—
304C22×M16—132no—
305C23×C8—132no—
306C4×#41—268no—
307C2×C4×Q8—131no—
308C2×C4×Q8—131no—
309C2×C4×D4—131no—
310C2×C4×D4—131no—
311C2×C4×D4—131no—
312C2×C4×D4—131no—
313C2×C4×D4—131no—
314C2×C4×D4#26111yescharacteristic
315C2×#117—131no—
316C2×#117—131no—
317C2×#117—131no—
318C22×C42—131no—
319C22×C42—131no—
320C22×C42—131no—
321#408—1316no—
322C2×C22⋊C8—132no—
323C2×C22⋊C8—132no—
324C2×C22⋊C8—132no—
325C2×C22⋊C8—132no—
326#405—268no—
327C2×#97—132no—
328C2×#97—132no—
329C2×C4×C8—132no—
330C2×C4×C8—132no—
331#336—131no—
332#336—131no—
333#336—132no—
334#336—131no—
335#336—131no—
336#336—132no—
337C22×C13—22no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—41no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13C4×C22⋊C414yes—
351C22×C13C22×C4211yescharacteristic
352C22×C13C22×C22⋊C411yescharacteristic
353C22×C13C2×#11711yescharacteristic
354C22×C13C2×#13111yescharacteristic
355C22×C13C2×#13111yescharacteristic
356C22×C13#56811yescharacteristic
357C22×C13#56811yescharacteristic
358C2×D13—22no—
359C2×D13—22no—
360C2×D13—22no—
361C2×D13—41no—
362C2×D13—41no—
363C2×D13—41no—
364C2×D13—41no—
365C4×C13—22no—
366C4×C13—22no—
367C4×C13—22no—
368C4×C13—22no—
369C4×C13—41no—
370Dic13—22no—
371Dic13—22no—
372Dic13—22no—
373Dic13—22no—
374Dic13—41no—
375Dic13C4×C22⋊C414yes—
376Dic13C2×C4×D412yes—
377Dic13C2×C4×D412yes—
378C2×#41—138no—
379C2×#41—264no—
380C2×#41—262no—
381C2×#41—262no—
382C22×Q8—131no—
383C22×D4—131no—
384C22×D4—131no—
385C22×D4C2×#26111yescharacteristic
386C23×C4—131no—
387C23×C4—131no—
388C23×C4—131no—
389C23×C4—131no—
390C23×C4—131no—
391C23×C4—131no—
392C23×C4—131no—
393C23×C4C2×#26111yescharacteristic
394C23×C4C2×#26111yescharacteristic
395C2×M16—138no—
396C2×M16—264no—
397C2×M16—264no—
398C22×C8—132no—
399C22×C8—132no—
400C22×C8—138no—
401C22×C8—132no—
402C22×C8—132no—
403C22×C8—264no—
404C22×C8—264no—
405C4×Q8—264no—
406C4×Q8—264no—
407C4×D4—24no—
408C4×D4—264no—
409C4×D4—264no—
410C4×D4—264no—
411C4×D4—264no—
412C4×D4—264no—
413#117—138no—
414#117—264no—
415#117—264no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4C2×#26111yescharacteristic
422C2×C22⋊C4—131no—
423C2×C22⋊C4—131no—
424C2×C22⋊C4—131no—
425C2×C22⋊C4—131no—
426C2×C22⋊C4C2×#26111yescharacteristic
427C2×C22⋊C4C2×#26111yescharacteristic
428C2×C42—131no—
429C2×C42—131no—
430C2×C42—131no—
431C2×C42—131no—
432C2×C42—131no—
433C2×C42—131no—
434C2×C42—131no—
435C2×C42—131no—
436C2×C42—131no—
437C2×C42—264no—
438C2×C42—264no—
439C2×C42—264no—
440C2×C42C2×#26111yescharacteristic
441C22⋊C8—138no—
442C22⋊C8—138no—
443C22⋊C8—138no—
444C22⋊C8—138no—
445#97—264no—
446#97—264no—
447C4×C8—264no—
448C4×C8—264no—
449C2×C13—24no—
450C2×C13—42no—
451C2×C13C2×C4×C22⋊C411yescharacteristic
452C2×C13C4×#13111yescharacteristic
453C2×C13#287511yescharacteristic
454C2×C13#288011yescharacteristic
455C2×C13#288011yescharacteristic
456C2×C13#292511yescharacteristic
457C2×C13#292511yescharacteristic
458D13—42no—
459C24—131no—
460C24C22×#26111yescharacteristic
461C24C22×#26111yescharacteristic
462#41—2616no—
463#41—2616no—
464C2×Q8—134no—
465C2×Q8—262no—
466C2×Q8—262no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—134no—
470C2×D4—134no—
471C2×D4—262no—
472C2×D4—262no—
473C2×D4—262no—
474C2×D4—262no—
475C2×D4C4×#26114yes—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—134no—
483C22×C4—132no—
484C22×C4—132no—
485C22×C4—134no—
486C22×C4—131no—
487C22×C4—131no—
488C22×C4—134no—
489C22×C4—131no—
490C22×C4—131no—
491C22×C4—131no—
492C22×C4—131no—
493C22×C4—134no—
494C22×C4—131no—
495C22×C4—262no—
496C22×C4—261no—
497C22×C4—261no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—261no—
502C22×C4—261no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4—262no—
508C22×C4—262no—
509C22×C4—521no—
510C22×C4—521no—
511C22×C4—521no—
512C22×C4—521no—
513C22×C4C22×#26111yescharacteristic
514C22×C4C22×#26111yescharacteristic
515C22×C4C22×#26111yescharacteristic
516C22×C4C22×#26111yescharacteristic
517C22×C4C22×#26111yescharacteristic
518M16—2616no—
519C2×C8—134no—
520C2×C8—134no—
521C2×C8—134no—
522C2×C8—134no—
523C2×C8—262no—
524C2×C8—262no—
525C2×C8—262no—
526C2×C8—262no—
527C2×C8—262no—
528C2×C8—262no—
529C2×C8—2616no—
530C2×C8—262no—
531C2×C8—262no—
532C4⋊C4—22no—
533C4⋊C4—134no—
534C4⋊C4—134no—
535C4⋊C4—262no—
536C4⋊C4—262no—
537C4⋊C4—262no—
538C22⋊C4—22no—
539C22⋊C4—134no—
540C22⋊C4—262no—
541C22⋊C4—262no—
542C22⋊C4—262no—
543C22⋊C4C22⋊#26114yes—
544C42—22no—
545C42—134no—
546C42—134no—
547C42—262no—
548C42—262no—
549C42—262no—
550C42—262no—
551C42—262no—
552C42—262no—
553C42—262no—
554C13#2037811yescharacteristic, complemented, Sylow
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—132no—
566C23—261no—
567C23—261no—
568C23—261no—
569C23—261no—
570C23—261no—
571C23—261no—
572C23C2×C4×#26112yes—
573C23C2×C4×#26112yes—
574C23#8823712yes—
575C23C2×C22⋊#26112yes—
576C23C23×#26111yescharacteristic
577Q8—268no—
578D4—28no—
579D4—268no—
580D4—268no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—132no—
595C2×C4—132no—
596C2×C4—131no—
597C2×C4—131no—
598C2×C4—132no—
599C2×C4—132no—
600C2×C4—132no—
601C2×C4—138no—
602C2×C4—138no—
603C2×C4—132no—
604C2×C4—132no—
605C2×C4—132no—
606C2×C4—132no—
607C2×C4—264no—
608C2×C4—264no—
609C2×C4—264no—
610C2×C4—264no—
611C2×C4—261no—
612C2×C4—261no—
613C2×C4—261no—
614C2×C4—261no—
615C2×C4—261no—
616C2×C4—261no—
617C2×C4—261no—
618C2×C4—261no—
619C2×C4—261no—
620C2×C4—261no—
621C2×C4—261no—
622C2×C4—524no—
623C2×C4—524no—
624C2×C4—524no—
625C2×C4—524no—
626C2×C4C2×C4×#26112yes—
627C2×C4#8823812yes—
628C2×C4C2×C22⋊#26112yes—
629C2×C4C2×C22⋊#26112yes—
630C8—264no—
631C8—264no—
632C8—264no—
633C8—264no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—262no—
648C22—262no—
649C22—262no—
650C22—521no—
651C22—521no—
652C22—521no—
653C22—521no—
654C22C4×C22⋊#26114yes—
655C22C22×C4×#26111yescharacteristic
656C22C2×#8823711yescharacteristic
657C22C2×#8823811yescharacteristic
658C22#1171962111yescharacteristic
659C22D13⋊#13111yescharacteristic
660C22#1171962911yescharacteristic
661C22C22×C22⋊#26111yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—41no—
667C4—132no—
668C4—132no—
669C4—134no—
670C4—262no—
671C4—262no—
672C4—262no—
673C4—262no—
674C4—521no—
675C2—24no—
676C2—42no—
677C2—522no—
678C2C2×C4×C22⋊#26111yescharacteristic
679C2C4×#8823811yescharacteristic
680C2#1313140711yescharacteristic
681C2#1313142411yescharacteristic
682C2#1313142611yescharacteristic
683C2#1313153111yescharacteristic
684C2#1313153411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC2×C4×D4×C13C4
socleC23×C13C23×C4
prime radicalC22×#6129C22
cosocleC22×Dic13C24
hypercenterC2×C4×D4#261
hypocenterC13#20378
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#11719062C2semidirect
3. #13130566C2semidirect
4. #13130565C2semidirect
5. #13130563C2semidirect
6. #13130562C2semidirect
7. C4×#88111C2semidirect
8. C4×C22⋊#1057C2semidirect
9. #13130499C2semidirect
10. C2×#11718290C2semidirect
32. #11719146C4semidirect
65. C2×#6122C2×C4semidirect
68. C22×#1057C2×C4semidirect
109. C22⋊#1057C2×C4semidirect
110. C22⋊#1057C2×C4semidirect
111. #88111C2×C4semidirect
112. #88111C2×C4semidirect
554. C13#20378semidirect

Maximal subgroups

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

subgroupindex
C2×#117191462
C2×#117190622
#131305662
#131305652
#131305632
#131305622
C4×#881112
C4×C22⋊#10572
#131304992
C2×#117182902
C2×C4×#61292
#2037813