Finite Group Databasebeta

← #25018177

Subgroups — #25018177

Order 11008.

1906 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582790C212yesmaximal
2C2×#14582750C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
4C2×#14582746C211yesmaximal, characteristic
5#19132831C212yesmaximal
6#19132830C212yesmaximal, complemented
7#19132822C211yesmaximal, characteristic, complemented
8#19132819C211yesmaximal, characteristic, complemented
9(C2×D43)⋊#95C211yesmaximal, characteristic
10C4×C43⋊#95C212yesmaximal, complemented
11C4×#95×C43C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×Dic43⋊C4C2212yes—
14C22×(C2×D43)⋊C4C2212yes—
15C22×(C2×D43)⋊C4C2211yescharacteristic
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×C4×Dic43C2212yes—
19C22×C4×Dic43C2212yes—
20C22×C4×Dic43C2211yescharacteristic
21#14582790C4116yescomplemented
22#14582750—24no—
23C4×(C2×D43)⋊C4C418yescomplemented
24#14582746—24no—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C22×C42×C43C2211yescharacteristic
35C22×C42×C43C2212yes—
36C2×#95×C43C2211yescharacteristic
37C2×#95×C43C2212yes—
38C2×#95×C43C2211yescharacteristic
39C24×D43C2311yescharacteristic
40C23×Dic43C2312yes—
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C23×Dic43C2311yescharacteristic
45C22×C4×D43—22no—
46C22×C4×D43—22no—
47C22×C4×D43—24no—
48C22×C4×D43—42no—
49C22×C4×D43C2×C414yes—
50C2×Dic43⋊C4—24no—
51C2×Dic43⋊C4—24no—
52C2×Dic43⋊C4C2×C418yescomplemented
53C2×(C2×D43)⋊C4—24no—
54C2×(C2×D43)⋊C4—24no—
55C2×(C2×D43)⋊C4—22no—
56C2×(C2×D43)⋊C4—22no—
57C2×(C2×D43)⋊C4—42no—
58C2×(C2×D43)⋊C4—42no—
59C2×(C2×D43)⋊C4C2×C418yes—
60C2×(C2×D43)⋊C4C2×C414yes—
61C2×(C2×D43)⋊C4C2×C418yes—
62C2×(C2×D43)⋊C4C2×C418yes—
63C2×(C2×D43)⋊C4C2×C414yes—
64C2×C4×Dic43—22no—
65C2×C4×Dic43—22no—
66C2×C4×Dic43—24no—
67C2×C4×Dic43—24no—
68C2×C4×Dic43—24no—
69C2×C4×Dic43—24no—
70C2×C4×Dic43—42no—
71C2×C4×Dic43—42no—
72C2×C4×Dic43C2×C414yes—
73C43⋊#95—22no—
74C43⋊#95—22no—
75C43⋊#95—24no—
76C43⋊#95—24no—
77C43⋊#95—42no—
78C43⋊#95C2×C414yes—
79C43⋊#95C2×C414yes—
80C43⋊#95C2×C418yescomplemented
81C43⋊#95C2×C418yescomplemented
82C23×C4×C43C2312yes—
83C23×C4×C43C2311yescharacteristic
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2312yes—
86C23×C4×C43C2311yescharacteristic
87C2×C42×C43—42no—
88C2×C42×C43—42no—
89C2×C42×C43—42no—
90C2×C42×C43C2×C414yes—
91C2×C42×C43C2×C418yescomplemented
92#95×C43—22no—
93#95×C43—24no—
94#95×C43D414yes—
95C24×C43C2411yescharacteristic
96C23×D43—21no—
97C23×D43—21no—
98C23×D43—21no—
99C23×D43—22no—
100C23×D43—22no—
101C23×D43—21no—
102C23×D43—21no—
103C23×D43—22no—
104C23×D43—21no—
105C23×D43C22×C414yes—
106C23×D43C22×C412yes—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
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—21no—
126C22×C4×C43C22×C412yes—
127C22×C4×C43C22×C414yes—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C22×C414yes—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C22×C414yes—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×D414yes—
134C22×C4×C43#4112yes—
135C22×C4×C43#4114yes—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—22no—
144C22×Dic43—21no—
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—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—21no—
157C22×Dic43—22no—
158C22×Dic43C22×C414yes—
159C22×Dic43C22×C414yes—
160C22×Dic43C22×C412yes—
161C22×Dic43C22×C414yes—
162C22×Dic43C22×C412yes—
163C22×Dic43C22×C412yes—
164C22×Dic43#4112yes—
165C22×Dic43#4114yes—
166C22×Dic43#4112yes—
167C2×C4×D43—28no—
168C2×C4×D43—28no—
169C2×C4×D43—44no—
170C2×C4×D43—48no—
171C2×C4×D43—48no—
172C42×C43—44no—
173C42×C43—48no—
174(C2×D43)⋊C4—216no—
175(C2×D43)⋊C4—28no—
176(C2×D43)⋊C4—48no—
177(C2×D43)⋊C4C42116yescomplemented
178Dic43⋊C4—216no—
179C4×Dic43—28no—
180C4×Dic43—48no—
181C4×Dic43—48no—
182C23×C43C23×C411yescharacteristic
183C23×C43C23×C412yes—
184C23×C43C22×D411yescharacteristic
185C23×C43C2×#4112yes—
186C23×C43C2×#4111yescharacteristic
187C23×C43C2×#4111yescharacteristic
188C23×C43C2×#4111yescharacteristic
189C23×C43C2×#4112yes—
190C23×C43H(5,𝔽2)12yes—
191C23×C43H(5,𝔽2)11yescharacteristic
192C23×C432−1+411yescharacteristic
193C22×D43—22no—
194C22×D43—22no—
195C22×D43—24no—
196C22×D43—22no—
197C22×D43—24no—
198C22×D43—24no—
199C22×D43—22no—
200C22×D43—24no—
201C22×D43—24no—
202C22×D43—22no—
203C22×D43—22no—
204C22×D43—24no—
205C22×D43—42no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—42no—
209C22×D43—41no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—41no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43C2×C4214yes—
216C2×C4×C43—22no—
217C2×C4×C43—24no—
218C2×C4×C43—22no—
219C2×C4×C43—24no—
220C2×C4×C43—22no—
221C2×C4×C43—24no—
222C2×C4×C43—22no—
223C2×C4×C43—24no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—22no—
231C2×C4×C43—24no—
232C2×C4×C43—22no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—22no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43C2×C4214yes—
243C2×C4×C43C4×D414yes—
244C2×C4×C43C4×D418yes—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—24no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—24no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—24no—
255C2×Dic43—22no—
256C2×Dic43—24no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—24no—
263C2×Dic43—24no—
264C2×Dic43—24no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43C2×C4214yes—
274C2×Dic43#11714yes—
275C2×Dic43#11714yes—
276C4×D43—416no—
277#13822—431nomaximal, Sylow
278C22×C43C22×C4211yescharacteristic
279C22×C43C2×#11711yescharacteristic
280C22×C43C2×#11711yescharacteristic
281C22×C43C2×C4×D411yescharacteristic
282C22×C43C2×C4×D412yes—
283C22×C43C4×#4112yes—
284C22×C43C4×#4112yes—
285C22×C43C4×#4111yescharacteristic
286C22×C43C4×#4112yes—
287C22×C43#51811yescharacteristic
288C22×C43#51812yes—
289C22×C43#52011yescharacteristic
290C22×C43#52012yes—
291C22×C43#54612yes—
292C22×C43#54611yescharacteristic
293C22×C43#54811yescharacteristic
294C22×C43#55112yes—
295C22×C43#55211yescharacteristic
296C22×C43#55312yes—
297C22×C43#55312yes—
298C22×C43#55311yescharacteristic
299C22×C43#55612yes—
300C22×C43#55912yes—
301C2×D43—24no—
302C2×D43—24no—
303C2×D43—24no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—44no—
309C2×D43—44no—
310C2×D43—44no—
311C2×D43—44no—
312C4×C43—24no—
313C4×C43—28no—
314C4×C43—24no—
315C4×C43—42no—
316C4×C43—44no—
317Dic43—24no—
318Dic43—24no—
319Dic43—24no—
320Dic43—44no—
321Dic43—44no—
322C2×#388—432no—
323C2×C4×C4⋊C4—431no—
324C2×C4×C22⋊C4—431no—
325C2×C4×C22⋊C4—431no—
326#1437—432no—
327#1436—432no—
328#1434—431no—
329#1434—431no—
330C22⋊#95—431no—
331C4×#95—432no—
332C4×#95D4311yescharacteristic, complemented
333C2×C43C4×#11711yescharacteristic
334C2×C43C42×D411yescharacteristic
335C2×C43#227511yescharacteristic
336C2×C43#234211yescharacteristic
337C2×C43#234711yescharacteristic
338C2×C43#235211yescharacteristic
339C2×C43#235711yescharacteristic
340C2×C43#236412yes—
341C2×C43#236712yes—
342C2×C43#237312yes—
343C2×C43#237412yes—
344D43—44no—
345C24×C4—431no—
346C22×C4⋊C4—432no—
347C22×C22⋊C4—431no—
348C22×C22⋊C4—431no—
349C22×C22⋊C4—432no—
350C22×C22⋊C4—432no—
351C22×C42—431no—
352C22×C42—432no—
353C22×C42—432no—
354C22×C42C2×D4311yescharacteristic
355C22×C42C2×D4312yes—
356#388—4316no—
357C4×C4⋊C4—864no—
358C4×C22⋊C4—438no—
359C4×C22⋊C4—864no—
360C2×#95—431no—
361C2×#95—432no—
362C2×#95—432no—
363C2×#95—431no—
364C2×#95—432no—
365C2×#95—432no—
366C2×#95—431no—
367C2×#95—431no—
368C2×#95—432no—
369C2×#95C2×D4311yescharacteristic
370C2×#95C2×D4312yes—
371C2×#95C2×D4311yescharacteristic
372C43#1382211yescharacteristic, complemented, Sylow
373C25—431no—
374C23×C4—431no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4—432no—
378C23×C4—432no—
379C23×C4—434no—
380C23×C4—864no—
381C23×C4—862no—
382C23×C4—862no—
383C23×C4—1722no—
384C23×C4C22×D4312yes—
385C23×C4C22×D4311yescharacteristic
386C23×C4C22×D4311yescharacteristic
387C23×C4C22×D4312yes—
388C23×C4C22×D4311yescharacteristic
389C2×C4⋊C4—438no—
390C2×C4⋊C4—864no—
391C2×C4⋊C4—864no—
392C2×C22⋊C4—434no—
393C2×C22⋊C4—438no—
394C2×C22⋊C4—434no—
395C2×C22⋊C4—438no—
396C2×C22⋊C4—438no—
397C2×C22⋊C4—862no—
398C2×C22⋊C4—862no—
399C2×C22⋊C4—864no—
400C2×C22⋊C4—864no—
401C2×C22⋊C4—1722no—
402C2×C22⋊C4—1722no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—434no—
407C2×C42—862no—
408C2×C42—862no—
409C2×C42—864no—
410C2×C42—864no—
411C2×C42—864no—
412C2×C42—864no—
413C2×C42—1722no—
414C2×C42—1722no—
415C2×C42C4×D4314yes—
416C2×C42C4×D4318yescomplemented
417#95—22no—
418#95—24no—
419#95—434no—
420#95—434no—
421#95—438no—
422#95—438no—
423#95—864no—
424#95—864no—
425#95—862no—
426#95—862no—
427#95—1722no—
428#95D17214yes—
429C24—434no—
430C24—432no—
431C24—861no—
432C24—861no—
433C24—861no—
434C24—862no—
435C24—862no—
436C24—861no—
437C24—861no—
438C24—862no—
439C24—861no—
440C24C23×D4311yescharacteristic
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—432no—
461C22×C4—432no—
462C22×C4—432no—
463C22×C4—434no—
464C22×C4—432no—
465C22×C4—434no—
466C22×C4—432no—
467C22×C4—434no—
468C22×C4—434no—
469C22×C4—868no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—862no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—862no—
479C22×C4—861no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
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—868no—
493C22×C4—1724no—
494C22×C4—1728no—
495C22×C4—1728no—
496C22×C4C2×C4×D4312yes—
497C22×C4C2×C4×D4314yes—
498C22×C4C2×C4×D4312yes—
499C22×C4C2×C4×D4314yes—
500C22×C4C2×C4×D4312yes—
501C22×C4C2×C4×D4314yes—
502C22×C4C2×D17212yes—
503C22×C4C2×D17214yes—
504C22×C4#1062189812yes—
505C22×C4#1062189814yes—
506C4⋊C4—8616no—
507C22⋊C4—4316no—
508C22⋊C4—868no—
509C22⋊C4—8616no—
510C22⋊C4—1728no—
511C42—44no—
512C42—48no—
513C42—868no—
514C42—1728no—
515C42—1728no—
516C23—434no—
517C23—862no—
518C23—862no—
519C23—864no—
520C23—862no—
521C23—864no—
522C23—864no—
523C23—862no—
524C23—864no—
525C23—864no—
526C23—862no—
527C23—864no—
528C23—862no—
529C23—1721no—
530C23—1722no—
531C23—1721no—
532C23—1722no—
533C23—1722no—
534C23—1721no—
535C23—1722no—
536C23—1722no—
537C23—1722no—
538C23—1721no—
539C23C22×C4×D4311yescharacteristic
540C23C22×C4×D4312yes—
541C23C22×D17211yescharacteristic
542C23#41×D4311yescharacteristic
543C23#41×D4312yes—
544C23#41×D4311yescharacteristic
545C23C2×#1062189811yescharacteristic
546C23C2×#1062189812yes—
547C23#1306337012yes—
548C23#1306337011yescharacteristic
549C23#1306337311yescharacteristic
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—434no—
577C2×C4—434no—
578C2×C4—434no—
579C2×C4—862no—
580C2×C4—864no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—864no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—864no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—864no—
593C2×C4—864no—
594C2×C4—864no—
595C2×C4—864no—
596C2×C4—864no—
597C2×C4—864no—
598C2×C4—864no—
599C2×C4—17216no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4C42×D4314yes—
609C2×C4C4×D17214yes—
610C2×C4C4×D17218yes—
611C22—864no—
612C22—864no—
613C22—864no—
614C22—1722no—
615C22—1724no—
616C22—1724no—
617C22—1722no—
618C22—1724no—
619C22—1724no—
620C22—1722no—
621C22—1722no—
622C22C2×C42×D4311yescharacteristic
623C22#117×D4311yescharacteristic
624C22#117×D4311yescharacteristic
625C22C2×C4×D17212yes—
626C22C2×C4×D17211yescharacteristic
627C22#1458336712yes—
628C22#1458336712yes—
629C22C4×#1062189811yescharacteristic
630C22C4×#1062189812yes—
631C22#1458337211yescharacteristic
632C22#1458337212yes—
633C22#1458338012yes—
634C22#1458338011yescharacteristic
635C22#1458354411yescharacteristic
636C22#1458354412yes—
637C22#1458356111yescharacteristic
638C22#1458357812yes—
639C22#1458359011yescharacteristic
640C22#1458359812yes—
641C22#1458359812yes—
642C22#1458359911yescharacteristic
643C22#1458362112yes—
644C22#1458363212yes—
645C4—28no—
646C4—24no—
647C4—24no—
648C4—42no—
649C4—44no—
650C4—864no—
651C4—864no—
652C4—864no—
653C4—1724no—
654C4—1724no—
655C2—1724no—
656C2#1913693411yescharacteristic
657C2C42×D17211yescharacteristic
658C2#1913695311yescharacteristic
659C2#1913744711yescharacteristic
660C2#1913748911yescharacteristic
661C2#1913752711yescharacteristic
662C2#1913756911yescharacteristic
663C2#1913764512yes—
664C2#1913766612yes—
665C2#1913771112yes—
666C2#1913772612yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC4×#95×C43C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC4×#95D43
hypocenterC43#13822
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×#14582750C2semidirect
6. #19132830C2semidirect
7. #19132822C2semidirect
8. #19132819C2semidirect
10. C4×C43⋊#95C2semidirect
11. C4×#95×C43C2semidirect
21. #14582790C4semidirect
23. C4×(C2×D43)⋊C4C4semidirect
52. C2×Dic43⋊C4C2×C4semidirect
80. C43⋊#95C2×C4semidirect
81. C43⋊#95C2×C4semidirect
91. C2×C42×C43C2×C4semidirect
177. (C2×D43)⋊C4C42semidirect
332. C4×#95D43semidirect
372. C43#13822semidirect
416. C2×C42C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827902
C2×#145827502
C2×C4×(C2×D43)⋊C42
C2×#145827462
#191328312
#191328302
#191328222
#191328192
(C2×D43)⋊#952
C4×C43⋊#952
C4×#95×C432
#1382243