Finite Group Databasebeta

← #25018425

Subgroups — #25018425

Order 11008.

1966 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582834C211yesmaximal, characteristic
2C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
3C2×#14582750C212yesmaximal, complemented
4C2×#14582746C211yesmaximal, characteristic
5C2×#14582746C212yesmaximal
6#19132861C212yesmaximal, complemented
7#19132859C211yesmaximal, characteristic, complemented
8#19132841C211yesmaximal, characteristic
9#19132839C212yesmaximal
10#95×Dic43C211yesmaximal, characteristic, complemented
11C43×#1445C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×Dic43⋊C4C2212yes—
15C22×Dic43⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2211yescharacteristic
17C22×(C2×D43)⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×C4×Dic43C2211yescharacteristic
21C22×C4×Dic43C2212yes—
22C22×C4×Dic43C2212yes—
23C22×C4×Dic43C2211yescharacteristic
24#14582834C418yescomplemented
25C4⋊C4×Dic43—24no—
26#14582750—28no—
27#14582746—28no—
28#14582746—24no—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C2×#95×C43C2211yescharacteristic
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2212yes—
40C24×D43C2311yescharacteristic
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2312yes—
44C23×Dic43C2312yes—
45C23×Dic43C2311yescharacteristic
46C22×C4×D43—24no—
47C22×C4×D43—22no—
48C22×C4×D43—24no—
49C22×C4×D43—22no—
50C22×C4×D43Q814yes—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43—24no—
53C2×Dic43⋊C4—24no—
54C2×Dic43⋊C4—24no—
55C2×Dic43⋊C4—24no—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4C2×C418yescomplemented
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—24no—
61C2×(C2×D43)⋊C4—24no—
62C2×(C2×D43)⋊C4—22no—
63C2×(C2×D43)⋊C4—22no—
64C2×(C2×D43)⋊C4—22no—
65C2×(C2×D43)⋊C4—22no—
66C2×(C2×D43)⋊C4—24no—
67C2×(C2×D43)⋊C4—24no—
68C2×(C2×D43)⋊C4—24no—
69C2×(C2×D43)⋊C4C2×C414yes—
70C2×(C2×D43)⋊C4C2×C418yes—
71C2×C4×Dic43—24no—
72C2×C4×Dic43—24no—
73C2×C4×Dic43—24no—
74C2×C4×Dic43—22no—
75C2×C4×Dic43—24no—
76C2×C4×Dic43—24no—
77C2×C4×Dic43—24no—
78C2×C4×Dic43—24no—
79C2×C4×Dic43D418yes—
80C2×C4×Dic43D414yes—
81C43⋊#95—24no—
82C43⋊#95—22no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C43⋊#95—24no—
86C43⋊#95C2×C414yescomplemented
87C23×C4×C43C2312yes—
88C23×C4×C43C2312yes—
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43C2×C414yescomplemented
95#95×C43—24no—
96#95×C43—22no—
97#95×C43—24no—
98#95×C43—22no—
99C24×C43C2411yescharacteristic
100C23×D43—22no—
101C23×D43—21no—
102C23×D43—22no—
103C23×D43—21no—
104C23×D43—22no—
105C23×D43—21no—
106C23×D43—22no—
107C23×D43—21no—
108C23×D43C22×C412yes—
109C23×D43C2×Q812yes—
110C23×D43#4112yes—
111C22×C4×C43—22no—
112C22×C4×C43—21no—
113C22×C4×C43—22no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—21no—
133C22×C4×C43C22×C414yes—
134C22×C4×C43C22×C412yes—
135C22×C4×C43C2×D414yes—
136C22×C4×C43C2×D412yes—
137C22×C4×C43C2×Q812yes—
138C22×C4×C43#4112yes—
139C22×C4×C43#4112yes—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—21no—
152C22×Dic43—22no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43C22×C412yes—
159C22×Dic43C22×C414yes—
160C22×Dic43C2×D412yes—
161C22×Dic43C2×D414yes—
162C22×Dic43C2×D414yes—
163C22×Dic43C2×D412yes—
164C22×Dic43C2×Q812yes—
165C22×Dic43#4114yes—
166C22×Dic43#4114yes—
167C22×Dic43#4114yes—
168C22×Dic43#4112yes—
169C2×C4×D43—216no—
170C2×C4×D43—28no—
171C2×C4×D43—48no—
172C2×C4×D43—44no—
173C2×C4×D43—44no—
174C4⋊C4×C43—28no—
175(C2×D43)⋊C4—28no—
176(C2×D43)⋊C4—216no—
177(C2×D43)⋊C4—28no—
178(C2×D43)⋊C4—216no—
179C4⋊Dic43—28no—
180Dic43⋊C4—216no—
181Dic43⋊C4—216no—
182C4×Dic43—216no—
183C4×Dic43—28no—
184C4×Dic43—44no—
185C4×Dic43—48no—
186C23×C43C23×C411yescharacteristic
187C23×C43C22×D412yes—
188C23×C43C22×D411yescharacteristic
189C23×C43C22×Q811yescharacteristic
190C23×C43C2×#4112yes—
191C23×C43C2×#4111yescharacteristic
192C23×C43C2×#4112yes—
193C23×C43C2×#4111yescharacteristic
194C23×C43C2×#4112yes—
195C23×C43C2×#4111yescharacteristic
196C23×C43C2×#4111yescharacteristic
197C22×D43—24no—
198C22×D43—22no—
199C22×D43—24no—
200C22×D43—22no—
201C22×D43—24no—
202C22×D43—22no—
203C22×D43—24no—
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—24no—
207C22×D43—22no—
208C22×D43—24no—
209C22×D43—42no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43—42no—
216C22×D43—41no—
217C22×D43—42no—
218C22×D43—41no—
219C22×D43C4×Q814yes—
220C2×C4×C43—24no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—24no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—22no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—22no—
233C2×C4×C43—24no—
234C2×C4×C43—42no—
235C2×C4×C43—41no—
236C2×C4×C43—42no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43C4×D414yes—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—24no—
259C2×Dic43—24no—
260C2×Dic43—22no—
261C2×Dic43—24no—
262C2×Dic43—22no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—41no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—41no—
272C2×Dic43C4×D418yes—
273C2×Dic43C22⋊Q814yes—
274C2×Dic43C22⋊Q818yes—
275C2×Dic43#12318yes—
276C2×Dic43#12314yes—
277C2×Dic43#12714yes—
278C4×D43—416no—
279C4×#399—431nomaximal, Sylow
280C22×C43C2×C4×D412yes—
281C22×C43C2×C4×D411yescharacteristic
282C22×C43C2×C4×Q811yescharacteristic
283C22×C43C4×#4112yes—
284C22×C43C4×#4111yescharacteristic
285C22×C43C2×C22⋊Q811yescharacteristic
286C22×C43C2×C22⋊Q812yes—
287C22×C43C2×#12312yes—
288C22×C43C2×#12311yescharacteristic
289C22×C43#52512yes—
290C22×C43#52511yescharacteristic
291C22×C43#52511yescharacteristic
292C22×C43#52512yes—
293C22×C43#52912yes—
294C22×C43#52911yescharacteristic
295C22×C43#52912yes—
296C22×C43#52912yes—
297C22×C43#52912yes—
298C22×C43C2×#12711yescharacteristic
299C22×C43#53212yes—
300C22×C43#53211yescharacteristic
301C22×C43#53311yescharacteristic
302C22×C43#53312yes—
303C2×D43—28no—
304C2×D43—24no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—44no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—44no—
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—44no—
314C4×C43—24no—
315C4×C43—44no—
316C4×C43—42no—
317C4×C43—44no—
318C4×C43—42no—
319Dic43—28no—
320Dic43—42no—
321Dic43—42no—
322Dic43—44no—
323Dic43#39918yescomplemented
324C2×#399—431no—
325C2×C4×C4⋊C4—432no—
326C2×C4×C4⋊C4—431no—
327C2×C4×C22⋊C4—432no—
328C2×C4×C22⋊C4—431no—
329#1445—432no—
330#1445D4311yescharacteristic, complemented
331#1444—431no—
332#1439—432no—
333#1439—431no—
334C4×#95—431no—
335C2×C43C4×#12311yescharacteristic
336C2×C43C4×#12312yes—
337C2×C43C4×C22⋊Q812yes—
338C2×C43C4×C22⋊Q811yescharacteristic
339C2×C43C4×#12711yescharacteristic
340C2×C43C2×#39911yescharacteristic
341C2×C43#239512yes—
342C2×C43#239511yescharacteristic
343C2×C43#239611yescharacteristic
344C2×C43#239612yes—
345C2×C43#239711yescharacteristic
346D43—44no—
347C24×C4—431no—
348C22×C4⋊C4—432no—
349C22×C4⋊C4—432no—
350C22×C4⋊C4—431no—
351C22×C4⋊C4C2×D4311yescharacteristic
352C22×C22⋊C4—432no—
353C22×C22⋊C4—431no—
354C22×C22⋊C4—432no—
355C22×C22⋊C4—431no—
356C22×C42—432no—
357C22×C42—431no—
358C22×C42—432no—
359C22×C42—431no—
360#399—438no—
361C4×C4⋊C4—868no—
362C4×C4⋊C4—864no—
363C4×C22⋊C4—868no—
364C4×C22⋊C4—864no—
365C2×#95—431no—
366C2×#95—432no—
367C2×#95—432no—
368C2×#95—432no—
369C2×#95—432no—
370C2×#95—431no—
371C2×#95C2×D4311yescharacteristic
372C2×#95C2×D4312yes—
373C2×#95C2×D4311yescharacteristic
374C2×#95C2×D4312yes—
375C43C4×#39911yescharacteristic, complemented, Sylow
376C25—431no—
377C23×C4—431no—
378C23×C4—432no—
379C23×C4—431no—
380C23×C4—432no—
381C23×C4—431no—
382C23×C4—434no—
383C23×C4—864no—
384C23×C4—862no—
385C23×C4—864no—
386C23×C4—862no—
387C23×C4C22×D4312yes—
388C23×C4C22×D4312yes—
389C23×C4C22×D4311yescharacteristic
390C23×C4C22×D4311yescharacteristic
391C23×C4C22×D4311yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—438no—
395C2×C4⋊C4—864no—
396C2×C4⋊C4—864no—
397C2×C4⋊C4—864no—
398C2×C4⋊C4—864no—
399C2×C4⋊C4—864no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—864no—
402C2×C4⋊C4C4×D4314yescomplemented
403C2×C22⋊C4—438no—
404C2×C22⋊C4—434no—
405C2×C22⋊C4—864no—
406C2×C22⋊C4—864no—
407C2×C22⋊C4—864no—
408C2×C22⋊C4—862no—
409C2×C22⋊C4—864no—
410C2×C22⋊C4—862no—
411C2×C22⋊C4—864no—
412C2×C22⋊C4—862no—
413C2×C22⋊C4—862no—
414C2×C22⋊C4—862no—
415C2×C42—438no—
416C2×C42—434no—
417C2×C42—864no—
418C2×C42—864no—
419C2×C42—864no—
420C2×C42—864no—
421C2×C42—862no—
422C2×C42—864no—
423C2×C42—864no—
424C2×C42—864no—
425#95—24no—
426#95—22no—
427#95—24no—
428#95—22no—
429#95—434no—
430#95—864no—
431#95—864no—
432#95—862no—
433#95—864no—
434#95—864no—
435C24—432no—
436C24—432no—
437C24—432no—
438C24—862no—
439C24—861no—
440C24—862no—
441C24—862no—
442C24—862no—
443C24—861no—
444C24—861no—
445C24—861no—
446C24C23×D4311yescharacteristic
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—434no—
470C22×C4—432no—
471C22×C4—432no—
472C22×C4—434no—
473C22×C4—432no—
474C22×C4—434no—
475C22×C4—434no—
476C22×C4—434no—
477C22×C4—432no—
478C22×C4—432no—
479C22×C4—434no—
480C22×C4—868no—
481C22×C4—8616no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—861no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—861no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—862no—
500C22×C4—1728no—
501C22×C4—1724no—
502C22×C4—1724no—
503C22×C4C2×C4×D4314yes—
504C22×C4C2×C4×D4312yes—
505C22×C4D4×D4314yes—
506C22×C4D4×D4312yes—
507C22×C4#1062190012yes—
508C22×C4Q8×D4312yes—
509C22×C4#1062190212yes—
510C4⋊C4—28no—
511C4⋊C4—8616no—
512C4⋊C4—8616no—
513C4⋊C4—868no—
514C22⋊C4—8616no—
515C22⋊C4—8616no—
516C22⋊C4—868no—
517C22⋊C4—868no—
518C42—868no—
519C42—8616no—
520C42—1724no—
521C42—1728no—
522C23—434no—
523C23—864no—
524C23—862no—
525C23—864no—
526C23—862no—
527C23—864no—
528C23—862no—
529C23—864no—
530C23—862no—
531C23—862no—
532C23—864no—
533C23—862no—
534C23—864no—
535C23—1722no—
536C23—1721no—
537C23—1721no—
538C23—1722no—
539C23—1722no—
540C23—1722no—
541C23—1722no—
542C23—1721no—
543C23—1722no—
544C23—1721no—
545C23C22×C4×D4311yescharacteristic
546C23C2×D4×D4312yes—
547C23C2×D4×D4311yescharacteristic
548C23C2×Q8×D4311yescharacteristic
549C23#41×D4312yes—
550C23#41×D4311yescharacteristic
551C23#41×D4312yes—
552C23#41×D4312yes—
553C23#41×D4311yescharacteristic
554C23C2×#1062190011yescharacteristic
555C23C2×#1062190211yescharacteristic
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—434no—
585C2×C4—438no—
586C2×C4—438no—
587C2×C4—434no—
588C2×C4—434no—
589C2×C4—438no—
590C2×C4—864no—
591C2×C4—864no—
592C2×C4—864no—
593C2×C4—864no—
594C2×C4—864no—
595C2×C4—864no—
596C2×C4—864no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—864no—
600C2×C4—864no—
601C2×C4—862no—
602C2×C4—864no—
603C2×C4—862no—
604C2×C4—17216no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1721no—
612C2×C4—1722no—
613C2×C4—1721no—
614C2×C4(C22⋊D43)⋊C414yes—
615C22—868no—
616C22—864no—
617C22—1722no—
618C22—1724no—
619C22—1722no—
620C22—1722no—
621C22—1724no—
622C22—1722no—
623C22—1722no—
624C22—1724no—
625C22—1722no—
626C22C4×D4×D4312yes—
627C22C2×(C22⋊D43)⋊C411yescharacteristic
628C22C4×Q8×D4311yescharacteristic
629C22#1458336712yes—
630C22C4×#1062190211yescharacteristic
631C22C22⋊Q8×D4311yescharacteristic
632C22C22⋊Q8×D4312yes—
633C22#123×D4312yes—
634C22#123×D4311yescharacteristic
635C22#1458340712yes—
636C22#1458340711yescharacteristic
637C22#1458341211yescharacteristic
638C22#1458341212yes—
639C22#1458342612yes—
640C22#1458342811yescharacteristic
641C22#1458343212yes—
642C22#1458343212yes—
643C22#1458343412yes—
644C22#127×D4311yescharacteristic
645C22#1458344412yes—
646C22#1458344811yescharacteristic
647C22#1458345411yescharacteristic
648C22#1458345512yes—
649C4—24no—
650C4—42no—
651C4—44no—
652C4—42no—
653C4—44no—
654C4—438no—
655C4—868no—
656C4—1722no—
657C4—1724no—
658C4—1722no—
659C2—1724no—
660C2#1913711211yescharacteristic
661C2#1913711612yes—
662C2#1913712912yes—
663C2#1913713311yescharacteristic
664C2#1913715911yescharacteristic
665C2#399×D4311yescharacteristic
666C2#1913785312yes—
667C2#1913786111yescharacteristic
668C2#1913786811yescharacteristic
669C2#1913787212yes—
670C2#1913787511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1445C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1445D43
hypocenterC43C4×#399
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic43C2semidirect
3. C2×#14582750C2semidirect
6. #19132861C2semidirect
7. #19132859C2semidirect
10. #95×Dic43C2semidirect
11. C43×#1445C2semidirect
24. #14582834C4semidirect
58. C2×Dic43⋊C4C2×C4semidirect
86. C43⋊#95C2×C4semidirect
94. C2×C4⋊C4×C43C2×C4semidirect
323. Dic43#399semidirect
330. #1445D43semidirect
375. C43C4×#399semidirect
402. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828342
C2×C4⋊C4×Dic432
C2×#145827502
C2×#145827462
#191328612
#191328592
#191328412
#191328392
#95×Dic432
C43×#14452
C4×#39943