Finite Group Databasebeta

← #25018309

Subgroups — #25018309

Order 11008.

2118 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
1C22×#13063283C211yesmaximal, characteristic
2C2×C4⋊C4×Dic43C212yesmaximal, complemented
3C2×#14582746C211yesmaximal, characteristic
4C2×#14582746C211yesmaximal, characteristic
5#19132860C211yesmaximal, characteristic, complemented
6#19132854C211yesmaximal, characteristic, complemented
7#19132851C211yesmaximal, characteristic, complemented
8#19132841C212yesmaximal
9#19132837C212yesmaximal
10#95×Dic43C212yesmaximal, complemented
11C43×#1444C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C2×#13063283—24no—
14C2×#13063283—28no—
15C22×C4⋊Dic43C2212yes—
16C22×C4⋊Dic43C2211yescharacteristic
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×(C2×D43)⋊C4C2211yescharacteristic
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2212yes—
21C22×C4×Dic43C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23C22×C4×Dic43C2212yes—
24C22×C4×Dic43C2212yes—
25C4⋊C4×Dic43—28no—
26#14582746—24no—
27#14582746C418yescomplemented
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2211yescharacteristic
35C22×C4⋊C4×C43C2212yes—
36C22×C4⋊C4×C43C2211yescharacteristic
37C2×#95×C43C2212yes—
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C24×D43C2311yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2312yes—
43C23×Dic43C2311yescharacteristic
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46C22×C4×D43—24no—
47C22×C4×D43—24no—
48C22×C4×D43C2×C414yes—
49C22×C4×D43D414yes—
50C22×C4×D43Q814yes—
51#13063283—232no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—24no—
54C2×C4⋊Dic43—24no—
55C2×C4⋊Dic43—24no—
56C2×C4⋊Dic43—24no—
57C2×(C2×D43)⋊C4—24no—
58C2×(C2×D43)⋊C4—22no—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—24no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—22no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4—22no—
67C2×(C2×D43)⋊C4—22no—
68C2×(C2×D43)⋊C4C2×C418yes—
69C2×C4×Dic43—24no—
70C2×C4×Dic43—24no—
71C2×C4×Dic43—24no—
72C2×C4×Dic43—24no—
73C2×C4×Dic43—22no—
74C2×C4×Dic43—22no—
75C2×C4×Dic43—24no—
76C2×C4×Dic43—24no—
77C2×C4×Dic43C2×C418yes—
78C2×C4×Dic43D418yes—
79C43⋊#95—22no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C43⋊#95C2×C414yes—
86C23×C4×C43C2312yes—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2312yes—
91C2×C4⋊C4×C43—24no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—24no—
94C2×C4⋊C4×C43—24no—
95C2×C4⋊C4×C43—24no—
96#95×C43—22no—
97#95×C43—24no—
98#95×C43C2×C414yes—
99C24×C43C2411yescharacteristic
100C23×D43—22no—
101C23×D43—22no—
102C23×D43—22no—
103C23×D43—21no—
104C23×D43—21no—
105C23×D43—21no—
106C23×D43—21no—
107C23×D43—22no—
108C23×D43C22×C412yes—
109C23×D43C2×D412yes—
110C23×D43C2×Q812yes—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—21no—
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—22no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C22×C412yes—
132C22×C4×C43C22×C414yes—
133C22×C4×C43C2×D414yes—
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×Q812yes—
136C22×C4×C43#4112yes—
137C22×C4×C43#4114yes—
138C22×C4×C43#4112yes—
139C22×C4×C43#4114yes—
140C22×Dic43—22no—
141C22×Dic43—21no—
142C22×Dic43—21no—
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—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—21no—
155C22×Dic43—22no—
156C22×Dic43—21no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43C22×C414yes—
161C22×Dic43C22×C412yes—
162C22×Dic43C2×D414yes—
163C22×Dic43C2×D412yes—
164C22×Dic43C2×D414yes—
165C22×Dic43C2×Q812yes—
166C22×Dic43#4112yes—
167C22×Dic43#4112yes—
168C22×Dic43#4114yes—
169C2×C4×D43—216no—
170C2×C4×D43—28no—
171C2×C4×D43—216no—
172C2×C4×D43—28no—
173C2×C4×D43C4⋊C4116yescomplemented
174C4⋊C4×C43—216no—
175C4⋊C4×C43—28no—
176(C2×D43)⋊C4—28no—
177(C2×D43)⋊C4—28no—
178(C2×D43)⋊C4—216no—
179(C2×D43)⋊C4—216no—
180C4⋊Dic43—216no—
181C4⋊Dic43—28no—
182C4×Dic43—216no—
183C4×Dic43—216no—
184C4×Dic43—44no—
185C4×Dic43—44no—
186C23×C43C23×C411yescharacteristic
187C23×C43C22×D411yescharacteristic
188C23×C43C22×D412yes—
189C23×C43C22×Q811yescharacteristic
190C23×C43C2×#4112yes—
191C23×C43C2×#4111yescharacteristic
192C23×C43C2×#4111yescharacteristic
193C23×C43C2×#4112yes—
194C23×C43C2×#4111yescharacteristic
195C23×C43C2×#4112yes—
196C23×C43C2×#4111yescharacteristic
197C22×D43—24no—
198C22×D43—24no—
199C22×D43—22no—
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—24no—
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—22no—
207C22×D43—22no—
208C22×D43—24no—
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—42no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43C2×C4⋊C414yes—
220C2×C4×C43—24no—
221C2×C4×C43—24no—
222C2×C4×C43—24no—
223C2×C4×C43—22no—
224C2×C4×C43—24no—
225C2×C4×C43—22no—
226C2×C4×C43—24no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—41no—
245C2×C4×C43—42no—
246C2×C4×C43—41no—
247C2×C4×C43C2×C4⋊C414yes—
248C2×C4×C43#11718yescomplemented
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—24no—
258C2×Dic43—24no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—41no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—41no—
272C2×Dic43—42no—
273C2×Dic43C2×C4⋊C414yes—
274C2×Dic43C4×D418yes—
275C2×Dic43#12014yes—
276C2×Dic43C22⋊Q818yes—
277C2×Dic43#12314yes—
278C4×D43—232no—
279#13844—431nomaximal, Sylow
280C22×C43C22×C4⋊C411yescharacteristic
281C22×C43C2×#11712yes—
282C22×C43C2×C4×D412yes—
283C22×C43C4×#4111yescharacteristic
284C22×C43C4×#4111yescharacteristic
285C22×C43C2×#12011yescharacteristic
286C22×C43C2×C22⋊Q812yes—
287C22×C43C2×#12311yescharacteristic
288C22×C43#52512yes—
289C22×C43#52511yescharacteristic
290C22×C43#52511yescharacteristic
291C22×C43#52512yes—
292C22×C43#52912yes—
293C22×C43#52912yes—
294C22×C43#52912yes—
295C22×C43#52912yes—
296C22×C43#53212yes—
297C22×C43#53211yescharacteristic
298C22×C43#53211yescharacteristic
299C22×C43#53212yes—
300C22×C43#53312yes—
301C22×C43#53311yescharacteristic
302C22×C43#53311yescharacteristic
303C2×D43—24no—
304C2×D43—24no—
305C2×D43—24no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—44no—
311C2×D43—44no—
312C2×D43—44no—
313C2×D43—44no—
314C4×C43—24no—
315C4×C43—28no—
316C4×C43—44no—
317C4×C43—42no—
318C4×C43—42no—
319Dic43—44no—
320Dic43—42no—
321Dic43—42no—
322Dic43—44no—
323Dic43#38518yes—
324C22×#117—431no—
325C2×C4×C4⋊C4—432no—
326C2×C4×C22⋊C4—431no—
327C2×C4×C22⋊C4—431no—
328#1444—431no—
329#1444D4311yescharacteristic, complemented
330#1442—431no—
331#1442—431no—
332#1439—432no—
333#1439—432no—
334C4×#95—432no—
335C2×C43#228511yescharacteristic
336C2×C43C2×#38511yescharacteristic
337C2×C43#229012yes—
338C2×C43#229312yes—
339C2×C43#229611yescharacteristic
340C2×C43#238811yescharacteristic
341C2×C43#238811yescharacteristic
342C2×C43#239511yescharacteristic
343C2×C43#239511yescharacteristic
344C2×C43#239612yes—
345C2×C43#239612yes—
346D43—44no—
347C24×C4—431no—
348C2×#117—868no—
349C2×#117—864no—
350C22×C4⋊C4—431no—
351C22×C4⋊C4—432no—
352C22×C4⋊C4C2×D4311yescharacteristic
353C22×C4⋊C4C2×D4312yes—
354C22×C22⋊C4—432no—
355C22×C22⋊C4—432no—
356C22×C22⋊C4—431no—
357C22×C22⋊C4—431no—
358C22×C42—432no—
359C22×C42—432no—
360C22×C42—431no—
361C22×C42—431no—
362C4×C4⋊C4—868no—
363C4×C22⋊C4—438no—
364C4×C22⋊C4—864no—
365C2×#95—431no—
366C2×#95—432no—
367C2×#95—432no—
368C2×#95—432no—
369C2×#95—432no—
370C2×#95—432no—
371C2×#95—431no—
372C2×#95C2×D4312yes—
373C2×#95C2×D4311yescharacteristic
374C2×#95C2×D4311yescharacteristic
375C43#1384411yescharacteristic, complemented, Sylow
376C25—431no—
377C23×C4—431no—
378C23×C4—434no—
379C23×C4—434no—
380C23×C4—434no—
381C23×C4—432no—
382C23×C4—431no—
383C23×C4—432no—
384C23×C4—431no—
385C23×C4—864no—
386C23×C4—864no—
387C23×C4C22×D4312yes—
388C23×C4C22×D4311yescharacteristic
389C23×C4C22×D4311yescharacteristic
390C23×C4C22×D4311yescharacteristic
391C23×C4C22×D4312yes—
392#117—8632no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—864no—
399C2×C4⋊C4—864no—
400C2×C4⋊C4—864no—
401C2×C4⋊C4—862no—
402C2×C4⋊C4—864no—
403C2×C22⋊C4—438no—
404C2×C22⋊C4—864no—
405C2×C22⋊C4—862no—
406C2×C22⋊C4—862no—
407C2×C22⋊C4—864no—
408C2×C22⋊C4—862no—
409C2×C22⋊C4—862no—
410C2×C22⋊C4—864no—
411C2×C22⋊C4—862no—
412C2×C22⋊C4—864no—
413C2×C22⋊C4—862no—
414C2×C22⋊C4—864no—
415C2×C42—438no—
416C2×C42—438no—
417C2×C42—864no—
418C2×C42—864no—
419C2×C42—864no—
420C2×C42—864no—
421C2×C42—862no—
422C2×C42—862no—
423C2×C42—864no—
424C2×C42—864no—
425#95—22no—
426#95—24no—
427#95—434no—
428#95—864no—
429#95—864no—
430#95—862no—
431#95—864no—
432#95—864no—
433#95—864no—
434#95C4×D4314yes—
435C24—432no—
436C24—432no—
437C24—432no—
438C24—862no—
439C24—861no—
440C24—861no—
441C24—862no—
442C24—862no—
443C24—861no—
444C24—862no—
445C24—861no—
446C24C23×D4311yescharacteristic
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—432no—
468C22×C4—434no—
469C22×C4—432no—
470C22×C4—432no—
471C22×C4—434no—
472C22×C4—4316no—
473C22×C4—434no—
474C22×C4—434no—
475C22×C4—432no—
476C22×C4—432no—
477C22×C4—868no—
478C22×C4—8616no—
479C22×C4—8616no—
480C22×C4—868no—
481C22×C4—862no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—861no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—861no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4C2×C4×D4312yes—
502C22×C4C2×C4×D4314yes—
503C22×C4D4×D4314yes—
504C22×C4D4×D4312yes—
505C22×C4#1062190012yes—
506C22×C4#1062190014yes—
507C22×C4Q8×D4312yes—
508C22×C4#1062190212yes—
509C22×C4#1062190214yes—
510C4⋊C4—28no—
511C4⋊C4—216no—
512C4⋊C4—868no—
513C4⋊C4—8616no—
514C22⋊C4—8616no—
515C22⋊C4—868no—
516C22⋊C4—868no—
517C22⋊C4—8616no—
518C42—8616no—
519C42—8616no—
520C42—1724no—
521C42—1724no—
522C23—434no—
523C23—864no—
524C23—864no—
525C23—862no—
526C23—862no—
527C23—862no—
528C23—864no—
529C23—862no—
530C23—862no—
531C23—862no—
532C23—862no—
533C23—862no—
534C23—862no—
535C23—864no—
536C23—862no—
537C23—1722no—
538C23—1722no—
539C23—1722no—
540C23—1722no—
541C23—1722no—
542C23—1722no—
543C23—1722no—
544C23—1722no—
545C23C22×C4×D4311yescharacteristic
546C23C2×D4×D4311yescharacteristic
547C23C2×D4×D4312yes—
548C23C2×Q8×D4311yescharacteristic
549C23#41×D4312yes—
550C23#41×D4311yescharacteristic
551C23#41×D4311yescharacteristic
552C23C2×#1062190012yes—
553C23C2×#1062190011yescharacteristic
554C23C2×#1062190212yes—
555C23C2×#1062190211yescharacteristic
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—434no—
584C2×C4—438no—
585C2×C4—434no—
586C2×C4—438no—
587C2×C4—434no—
588C2×C4—8632no—
589C2×C4—864no—
590C2×C4—864no—
591C2×C4—864no—
592C2×C4—864no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—864no—
596C2×C4—864no—
597C2×C4—864no—
598C2×C4—864no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1721no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4—1721no—
613C2×C4C4⋊C4×D4314yes—
614C2×C4#1306328318yescomplemented
615C22—864no—
616C22—864no—
617C22—864no—
618C22—1724no—
619C22—1722no—
620C22—1722no—
621C22—1724no—
622C22—1722no—
623C22—1722no—
624C22—1724no—
625C22—1724no—
626C22C2×C4⋊C4×D4311yescharacteristic
627C22C2×#1306328312yes—
628C22C4×D4×D4312yes—
629C22C4×#1062190011yescharacteristic
630C22C4×#1062190211yescharacteristic
631C22#120×D4311yescharacteristic
632C22C22⋊Q8×D4312yes—
633C22#123×D4311yescharacteristic
634C22#1458340512yes—
635C22#1458340911yescharacteristic
636C22#1458341212yes—
637C22#1458341211yescharacteristic
638C22#1458342612yes—
639C22#1458343412yes—
640C22#1458343512yes—
641C22#1458343512yes—
642C22#1458344412yes—
643C22#1458344711yescharacteristic
644C22#1458345012yes—
645C22#1458345011yescharacteristic
646C22#1458345411yescharacteristic
647C22#1458345412yes—
648C22#1458345511yescharacteristic
649C4—28no—
650C4—24no—
651C4—44no—
652C4—42no—
653C4—42no—
654C4—438no—
655C4—1724no—
656C4—1722no—
657C4—1724no—
658C4—1722no—
659C2—1724no—
660C2#1913700011yescharacteristic
661C2#385×D4311yescharacteristic
662C2#1913703112yes—
663C2#1913705312yes—
664C2#1913707611yescharacteristic
665C2#1913780711yescharacteristic
666C2#1913781311yescharacteristic
667C2#1913785911yescharacteristic
668C2#1913786011yescharacteristic
669C2#1913786612yes—
670C2#1913787212yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1444C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1444D43
hypocenterC43#13844
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic43C2semidirect
5. #19132860C2semidirect
6. #19132854C2semidirect
7. #19132851C2semidirect
10. #95×Dic43C2semidirect
11. C43×#1444C2semidirect
27. #14582746C4semidirect
173. C2×C4×D43C4⋊C4semidirect
248. C2×C4×C43#117semidirect
329. #1444D43semidirect
375. C43#13844semidirect
614. C2×C4#13063283semidirect

Maximal subgroups

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

subgroupindex
C22×#130632832
C2×C4⋊C4×Dic432
C2×#145827462
#191328602
#191328542
#191328512
#191328412
#191328372
#95×Dic432
C43×#14442
#1384443