Finite Group Databasebeta

← #25018299

Subgroups — #25018299

Order 11008.

1814 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
2C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
3C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
5C2×#14582745C211yesmaximal, characteristic, complemented
6#19132856C212yesmaximal, complemented
7#19132853C212yesmaximal, complemented
8#19132843C212yesmaximal
9#19132839C212yesmaximal
10C4×C43⋊#95C211yesmaximal, characteristic, complemented
11C4×#95×C43C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×Dic43⋊C4C2212yes—
14C22×(C2×D43)⋊C4C2212yes—
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2211yescharacteristic
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×C4×Dic43C2211yescharacteristic
19C22×C4×Dic43C2211yescharacteristic
20C22×C4×Dic43C2211yescharacteristic
21C4×Dic43⋊C4—24no—
22C4×(C2×D43)⋊C4—24no—
23C4×(C2×D43)⋊C4—24no—
24C4×(C2×D43)⋊C4C418yescomplemented
25#14582745—24no—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2211yescharacteristic
35C22×C42×C43C2211yescharacteristic
36C22×C42×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2212yes—
40C24×D43C2311yescharacteristic
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2312yes—
44C23×Dic43C2312yes—
45C23×Dic43C2311yescharacteristic
46C22×C4×D43—22no—
47C22×C4×D43—22no—
48C22×C4×D43—22no—
49C22×C4×D43—22no—
50C22×C4×D43—22no—
51C22×C4×D43—22no—
52C22×C4×D43C2×C414yes—
53C2×Dic43⋊C4—24no—
54C2×Dic43⋊C4—24no—
55C2×Dic43⋊C4—24no—
56C2×(C2×D43)⋊C4—24no—
57C2×(C2×D43)⋊C4—24no—
58C2×(C2×D43)⋊C4—24no—
59C2×(C2×D43)⋊C4—24no—
60C2×(C2×D43)⋊C4—24no—
61C2×(C2×D43)⋊C4—24no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4C2×C414yes—
65C2×(C2×D43)⋊C4C2×C414yes—
66C2×C4×Dic43—22no—
67C2×C4×Dic43—22no—
68C2×C4×Dic43—22no—
69C2×C4×Dic43—22no—
70C2×C4×Dic43—22no—
71C2×C4×Dic43—22no—
72C2×C4×Dic43C2×C414yes—
73C2×C4×Dic43D414yes—
74C2×C4×Dic43D414yes—
75C43⋊#95—24no—
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C43⋊#95—24no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95C2×C414yes—
83C43⋊#95C2×C414yes—
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C23×C4×C43C2312yes—
87C23×C4×C43C2312yes—
88C23×C4×C43C2311yescharacteristic
89C2×C42×C43—22no—
90C2×C42×C43—22no—
91C2×C42×C43—22no—
92C2×C42×C43—22no—
93C2×C42×C43—22no—
94C2×C42×C43—22no—
95C2×C42×C43—22no—
96C2×C42×C43—22no—
97C2×C42×C43C2×C414yes—
98#95×C43—24no—
99#95×C43—24no—
100C24×C43C2411yescharacteristic
101C23×D43—21no—
102C23×D43—21no—
103C23×D43—22no—
104C23×D43—22no—
105C23×D43—22no—
106C23×D43—21no—
107C23×D43—21no—
108C23×D43—21no—
109C23×D43—21no—
110C23×D43C22×C412yes—
111C23×D43#4114yes—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
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—21no—
122C22×C4×C43—21no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43C22×C412yes—
133C22×C4×C43C22×C412yes—
134C22×C4×C43C22×C412yes—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D412yes—
137C22×C4×C43#4114yes—
138C22×C4×C43#4114yes—
139C22×C4×C43#4112yes—
140C22×C4×C43#4112yes—
141C22×C4×C43#4112yes—
142C22×C4×C43#4112yes—
143C22×Dic43—21no—
144C22×Dic43—22no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—21no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43C22×C412yes—
169C22×Dic43C22×C412yes—
170C22×Dic43C22×C412yes—
171C22×Dic43C2×D414yes—
172C22×Dic43C2×D414yes—
173C22×Dic43#4114yes—
174C2×C4×D43—28no—
175C2×C4×D43—28no—
176C2×C4×D43—28no—
177C2×C4×D43—44no—
178C2×C4×D43—44no—
179C2×C4×D43—44no—
180C2×C4×D43—44no—
181C42×C43—28no—
182C42×C43—44no—
183C42×C43—44no—
184(C2×D43)⋊C4—216no—
185(C2×D43)⋊C4—216no—
186(C2×D43)⋊C4—28no—
187(C2×D43)⋊C4—28no—
188Dic43⋊C4—216no—
189C4×Dic43—28no—
190C4×Dic43—28no—
191C4×Dic43—28no—
192C23×C43C23×C411yescharacteristic
193C23×C43C22×D411yescharacteristic
194C23×C43C22×D411yescharacteristic
195C23×C43C2×#4112yes—
196C23×C43C2×#4112yes—
197C23×C43C2×#4111yescharacteristic
198C23×C43C2×#4111yescharacteristic
199C23×C43C2×#4111yescharacteristic
200C23×C43C2×#4112yes—
201C23×C43C2×#4112yes—
202C23×C43C2×#4111yescharacteristic
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—22no—
207C22×D43—22no—
208C22×D43—22no—
209C22×D43—24no—
210C22×D43—24no—
211C22×D43—24no—
212C22×D43—24no—
213C22×D43—24no—
214C22×D43—24no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—42no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—42no—
221C22×D43—42no—
222C22×D43—42no—
223C22×D43—42no—
224C22×D43—42no—
225C22×D43#11714yes—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
237C2×C4×C43—24no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43#11714yes—
251C2×C4×C43C4×D414yes—
252C2×C4×C43C4×D414yes—
253C2×C4×C43#12114yes—
254C2×C4×C43#12314yes—
255C2×C4×C43#12414yes—
256C2×C4×C43#12614yes—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—24no—
268C2×Dic43—24no—
269C2×Dic43—24no—
270C2×Dic43—24no—
271C2×Dic43—24no—
272C2×Dic43—24no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43—42no—
287C2×Dic43#11714yes—
288C4×D43—416no—
289#13842—431nomaximal, Sylow
290C22×C43C2×#11711yescharacteristic
291C22×C43C2×#11711yescharacteristic
292C22×C43C2×#11711yescharacteristic
293C22×C43C2×C4×D411yescharacteristic
294C22×C43C2×C4×D411yescharacteristic
295C22×C43C4×#4111yescharacteristic
296C22×C43C4×#4111yescharacteristic
297C22×C43C2×#12111yescharacteristic
298C22×C43C2×#12311yescharacteristic
299C22×C43#52512yes—
300C22×C43#52512yes—
301C22×C43#52512yes—
302C22×C43C2×#12411yescharacteristic
303C22×C43C2×#12611yescharacteristic
304C22×C43#52912yes—
305C22×C43#52912yes—
306C22×C43#52912yes—
307C22×C43#52912yes—
308C22×C43#52912yes—
309C22×C43#52912yes—
310C22×C43#52912yes—
311C22×C43#52912yes—
312C22×C43#53212yes—
313C2×D43—24no—
314C2×D43—24no—
315C2×D43—24no—
316C2×D43—44no—
317C2×D43—44no—
318C2×D43—44no—
319C2×D43—44no—
320C2×D43—42no—
321C2×D43—42no—
322C2×D43—42no—
323C2×D43—42no—
324C4×C43—44no—
325C4×C43—44no—
326C4×C43—42no—
327C4×C43—42no—
328C4×C43#38818yes—
329Dic43—24no—
330Dic43—44no—
331Dic43—44no—
332Dic43—42no—
333Dic43—42no—
334C2×C4×C4⋊C4—431no—
335C2×C4×C22⋊C4—431no—
336C2×C4×C22⋊C4—431no—
337C2×C4×C22⋊C4—431no—
338C2×#376—431no—
339#1443—432no—
340#1442—432no—
341#1440—432no—
342#1439—432no—
343C4×#95—431no—
344C4×#95D4311yescharacteristic, complemented
345C2×C43#228311yescharacteristic
346C2×C43C2×#38811yescharacteristic
347C2×C43#229011yescharacteristic
348C2×C43#229011yescharacteristic
349C2×C43#229011yescharacteristic
350C2×C43#229311yescharacteristic
351C2×C43#229811yescharacteristic
352C2×C43#239212yes—
353C2×C43#239512yes—
354C2×C43#239812yes—
355C2×C43#240112yes—
356D43—44no—
357C24×C4—431no—
358C22×C4⋊C4—432no—
359C22×C22⋊C4—431no—
360C22×C22⋊C4—431no—
361C22×C22⋊C4—432no—
362C22×C22⋊C4—432no—
363C22×C42—431no—
364C22×C42—431no—
365C22×C42—431no—
366C22×C42C2×D4311yescharacteristic
367C22×C42C2×D4311yescharacteristic
368C22×C42C2×D4311yescharacteristic
369C4×C4⋊C4—864no—
370C4×C22⋊C4—438no—
371C4×C22⋊C4—864no—
372C4×C22⋊C4—864no—
373#376—864no—
374C2×#95—431no—
375C2×#95—431no—
376C2×#95—432no—
377C2×#95—432no—
378C2×#95—432no—
379C2×#95—432no—
380C2×#95—432no—
381C2×#95—432no—
382C2×#95—432no—
383C2×#95C2×D4312yes—
384C2×#95C2×D4312yes—
385C43#1384211yescharacteristic, complemented, Sylow
386C25—431no—
387C23×C4—431no—
388C23×C4—432no—
389C23×C4—431no—
390C23×C4—432no—
391C23×C4—431no—
392C23×C4—434no—
393C23×C4—862no—
394C23×C4—862no—
395C23×C4—862no—
396C23×C4—862no—
397C23×C4—862no—
398C23×C4—862no—
399C23×C4C22×D4311yescharacteristic
400C23×C4C22×D4311yescharacteristic
401C23×C4C22×D4312yes—
402C23×C4C22×D4312yes—
403C23×C4C22×D4311yescharacteristic
404C2×C4⋊C4—864no—
405C2×C4⋊C4—864no—
406C2×C4⋊C4—864no—
407C2×C22⋊C4—434no—
408C2×C22⋊C4—434no—
409C2×C22⋊C4—864no—
410C2×C22⋊C4—864no—
411C2×C22⋊C4—864no—
412C2×C22⋊C4—864no—
413C2×C22⋊C4—864no—
414C2×C22⋊C4—864no—
415C2×C22⋊C4—864no—
416C2×C22⋊C4—864no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—434no—
426C2×C42—434no—
427C2×C42—434no—
428C2×C42—862no—
429C2×C42—862no—
430C2×C42—862no—
431C2×C42—862no—
432C2×C42—862no—
433C2×C42—862no—
434C2×C42C4×D4314yes—
435#95—24no—
436#95—24no—
437#95—434no—
438#95—434no—
439#95—864no—
440#95—864no—
441#95—864no—
442#95—864no—
443#95—864no—
444#95—864no—
445#95—864no—
446C24—432no—
447C24—434no—
448C24—861no—
449C24—861no—
450C24—862no—
451C24—861no—
452C24—862no—
453C24—862no—
454C24—861no—
455C24—861no—
456C24—861no—
457C24C23×D4311yescharacteristic
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—432no—
479C22×C4—434no—
480C22×C4—432no—
481C22×C4—432no—
482C22×C4—434no—
483C22×C4—434no—
484C22×C4—861no—
485C22×C4—862no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—862no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—861no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—862no—
508C22×C4—861no—
509C22×C4—868no—
510C22×C4—868no—
511C22×C4—868no—
512C22×C4—1724no—
513C22×C4—1724no—
514C22×C4—1724no—
515C22×C4—1724no—
516C22×C4C2×C4×D4312yes—
517C22×C4C2×C4×D4312yes—
518C22×C4C2×C4×D4312yes—
519C22×C4#1062189814yes—
520C22×C4#1062189814yes—
521C22×C4#1062189812yes—
522C22×C4#1062189812yes—
523C22×C4D4×D4312yes—
524C22×C4D4×D4312yes—
525C22×C4#1062190012yes—
526C22×C4#1062190212yes—
527C4⋊C4—8616no—
528C22⋊C4—868no—
529C22⋊C4—868no—
530C22⋊C4—8616no—
531C22⋊C4—8616no—
532C42—28no—
533C42—44no—
534C42—44no—
535C42—868no—
536C42—868no—
537C42—868no—
538C23—434no—
539C23—862no—
540C23—862no—
541C23—862no—
542C23—862no—
543C23—862no—
544C23—862no—
545C23—864no—
546C23—864no—
547C23—864no—
548C23—864no—
549C23—864no—
550C23—864no—
551C23—1721no—
552C23—1721no—
553C23—1722no—
554C23—1721no—
555C23—1721no—
556C23—1722no—
557C23—1722no—
558C23—1722no—
559C23—1722no—
560C23—1722no—
561C23C22×C4×D4311yescharacteristic
562C23C2×D4×D4311yescharacteristic
563C23C2×D4×D4311yescharacteristic
564C23#41×D4312yes—
565C23#41×D4312yes—
566C23C2×#1062190011yescharacteristic
567C23C2×#1062189811yescharacteristic
568C23C2×#1062189811yescharacteristic
569C23C2×#1062189812yes—
570C23C2×#1062189812yes—
571C23C2×#1062190211yescharacteristic
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—434no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—864no—
600C2×C4—864no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—864no—
608C2×C4—864no—
609C2×C4—864no—
610C2×C4—864no—
611C2×C4—864no—
612C2×C4—864no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4—1722no—
625C2×C4—1722no—
626C2×C4—1722no—
627C2×C4—17216no—
628C2×C4#1306328214yes—
629C2×C4(C22⋊D43)⋊C414yes—
630C2×C4#1306328714yes—
631C2×C4#1306329814yes—
632C2×C4#1306331014yes—
633C2×C4#1306331114yes—
634C2×C4#1306332014yes—
635C22—864no—
636C22—864no—
637C22—864no—
638C22—1722no—
639C22—1722no—
640C22—1722no—
641C22—1724no—
642C22—1724no—
643C22—1722no—
644C22—1724no—
645C22—1724no—
646C22#117×D4311yescharacteristic
647C22#117×D4311yescharacteristic
648C22C2×#1306328211yescharacteristic
649C22C2×(C22⋊D43)⋊C411yescharacteristic
650C22C2×#1306328711yescharacteristic
651C22C4×#1062189811yescharacteristic
652C22C4×#1062189811yescharacteristic
653C22C2×#1306329811yescharacteristic
654C22C2×#1306331011yescharacteristic
655C22#1458340812yes—
656C22#1458340812yes—
657C22#1458340812yes—
658C22C2×#1306331111yescharacteristic
659C22C2×#1306332011yescharacteristic
660C22#1458342712yes—
661C22#1458342712yes—
662C22#1458342912yes—
663C22#1458343112yes—
664C22#1458343312yes—
665C22#1458343312yes—
666C22#1458343612yes—
667C22#1458343612yes—
668C22#1458344612yes—
669C4—42no—
670C4—42no—
671C4—44no—
672C4—44no—
673C4—864no—
674C4—1722no—
675C4—1722no—
676C4—1724no—
677C4—1724no—
678C4#1458278818yes—
679C2—1724no—
680C2#1913698711yescharacteristic
681C2C2×#1458278811yescharacteristic
682C2#1913703611yescharacteristic
683C2#1913703611yescharacteristic
684C2#1913704111yescharacteristic
685C2#1913705811yescharacteristic
686C2#1913709211yescharacteristic
687C2#1913783912yes—
688C2#1913785812yes—
689C2#1913788212yes—
690C2#1913789612yes—
subgroupG/H
centerC23×C4C22×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC4×#95×C43C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC4×#95D43
hypocenterC43#13842
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic43⋊C4C2semidirect
5. C2×#14582745C2semidirect
6. #19132856C2semidirect
7. #19132853C2semidirect
10. C4×C43⋊#95C2semidirect
11. C4×#95×C43C2semidirect
24. C4×(C2×D43)⋊C4C4semidirect
344. C4×#95D43semidirect
385. C43#13842semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic43⋊C42
C2×C4×(C2×D43)⋊C42
C2×#145827452
#191328562
#191328532
#191328432
#191328392
C4×C43⋊#952
C4×#95×C432
#1384243