Finite Group Databasebeta

← #25002018

Subgroups — #25002018

Order 11008.

1866 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C211yesmaximal, characteristic
2C22×#13063239C212yesmaximal
3C2×#14582665C212yesmaximal, complemented
4#19132818C211yesmaximal, characteristic, complemented
5C43×C22⋊#95C211yesmaximal, characteristic, complemented
6C23×C22⋊D43C2211yescharacteristic
7C23×C4×D43C411yescharacteristic, complemented
8C2×C4×C22⋊D43—24no—
9C2×C4×C22⋊D43—24no—
10C2×C4×C22⋊D43—22no—
11C2×C4×C22⋊D43—22no—
12C22×Dic43⋊C4C411yescharacteristic, complemented
13C22×C22⋊Dic43C2212yes—
14C22×C22⋊Dic43C2211yescharacteristic
15C22×(C2×D43)⋊C4C411yescharacteristic, complemented
16C22×C4×Dic43C411yescharacteristic, complemented
17C2×#13063239—24no—
18C2×#13063239—24no—
19C2×#13063239C418yescomplemented
20C2×C43⋊#95—22no—
21#14582665—24no—
22C24×C4×C43C2211yescharacteristic
23C22×C22⋊C4×C43C2212yes—
24C2×#95×C43—22no—
25C24×D43C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C22×C22⋊D43—22no—
28C22×C22⋊D43—21no—
29C22×C22⋊D43—22no—
30C22×C22⋊D43—21no—
31C22×C22⋊D43—21no—
32C22×C22⋊D43C2×C414yes—
33C22×C22⋊D43D414yes—
34C22×C22⋊D43D412yes—
35C22×C22⋊D43Q812yes—
36C23×Dic43—22no—
37C23×Dic43C2×C411yescharacteristic
38C23×Dic43C2×C411yescharacteristic
39C23×Dic43C2×C411yescharacteristic
40C22×C4×D43—22no—
41C22×C4×D43—22no—
42C22×C4×D43—22no—
43C22×C4×D43—44no—
44C4×C22⋊D43—216no—
45C4×C22⋊D43—216no—
46C2×Dic43⋊C4—22no—
47C2×Dic43⋊C4—22no—
48C2×Dic43⋊C4—22no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—22no—
51C2×C22⋊Dic43—21no—
52C2×C22⋊Dic43—22no—
53C2×C22⋊Dic43—22no—
54C2×C22⋊Dic43—22no—
55C2×C22⋊Dic43—22no—
56C2×C22⋊Dic43—22no—
57C2×C22⋊Dic43C2×C414yescomplemented
58C2×C22⋊Dic43D414yes—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—22no—
62C2×C4×Dic43—22no—
63C2×C4×Dic43—22no—
64C2×C4×Dic43—22no—
65#13063239—216no—
66C43⋊#95—44no—
67C25×C43C2311yescharacteristic
68C23×C4×C43—22no—
69C23×C4×C43—22no—
70C23×C4×C43—22no—
71C23×C4×C43—44no—
72C23×C4×C43C2×C411yescharacteristic
73C23×C4×C43C2×C411yescharacteristic
74C23×C4×C43D412yes—
75C23×C4×C43D412yes—
76C2×C22⋊C4×C43—22no—
77C2×C22⋊C4×C43—22no—
78C2×C22⋊C4×C43—22no—
79C2×C22⋊C4×C43—22no—
80C2×C22⋊C4×C43—22no—
81C2×C22⋊C4×C43C2×C414yescomplemented
82#95×C43—44no—
83C24×C43—42no—
84C24×C43—42no—
85C24×C43C22×C411yescharacteristic
86C24×C43C22×C412yes—
87C24×C43C2×D411yescharacteristic
88C24×C43C2×D411yescharacteristic
89C24×C43C2×D412yes—
90C24×C43C2×D411yescharacteristic
91C24×C43C2×D412yes—
92C24×C43C2×Q811yescharacteristic
93C24×C43#4112yes—
94C24×C43#4111yescharacteristic
95C24×C43#4111yescharacteristic
96C23×D43—21no—
97C23×D43—21no—
98C23×D43—21no—
99C23×D43—21no—
100C23×D43—42no—
101C23×D43—42no—
102C23×D43C4212yes—
103C23×D43C22⋊C412yes—
104C23×D43C4⋊C412yes—
105C22×C4×C43—24no—
106C22×C4×C43—24no—
107C22×C4×C43—24no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—24no—
113C22×C4×C43—24no—
114C22×C4×C43—24no—
115C22×C4×C43—42no—
116C22×C4×C43—42no—
117C22×C4×C43—42no—
118C22×C4×C43—44no—
119C22×C4×C43—44no—
120C22×C4×C43—48no—
121C22×C4×C43—48no—
122C22×C4×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43C22⋊C412yes—
125C22×C4×C43C22⋊C412yes—
126C2×C22⋊D43—24no—
127C2×C22⋊D43—24no—
128C2×C22⋊D43—24no—
129C2×C22⋊D43—24no—
130C2×C22⋊D43—24no—
131C2×C22⋊D43—24no—
132C2×C22⋊D43—22no—
133C2×C22⋊D43—24no—
134C2×C22⋊D43—22no—
135C2×C22⋊D43—22no—
136C2×C22⋊D43—24no—
137C2×C22⋊D43—22no—
138C2×C22⋊D43—24no—
139C2×C22⋊D43—24no—
140C2×C22⋊D43C22⋊C418yes—
141C2×C22⋊D43C4⋊C418yes—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—24no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—44no—
154C22×Dic43—44no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43C4212yes—
158C22×Dic43C22⋊C412yes—
159C22×Dic43C22⋊C412yes—
160C22×Dic43C22⋊C412yes—
161C22×Dic43C4⋊C412yes—
162C2×C4×D43—28no—
163C2×C4×D43—48no—
164C2×C4×D43—44no—
165C2×C4×D43—48no—
166C2×C4×D43—44no—
167C22⋊C4×C43—24no—
168C22⋊C4×C43—24no—
169C22⋊C4×C43—42no—
170C22⋊C4×C43—42no—
171C22⋊Dic43—24no—
172C22⋊Dic43—24no—
173C22⋊Dic43—24no—
174C22⋊Dic43—24no—
175C22⋊Dic43—42no—
176C22⋊Dic43—42no—
177(C2×D43)⋊C4—28no—
178Dic43⋊C4—28no—
179C4×Dic43—28no—
180C23×C43—22no—
181C23×C43—22no—
182C23×C43—22no—
183C23×C43—22no—
184C23×C43—22no—
185C23×C43—22no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—44no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—44no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43C2×C4211yescharacteristic
197C23×C43C2×C22⋊C411yescharacteristic
198C23×C43C2×C22⋊C411yescharacteristic
199C23×C43C2×C22⋊C412yes—
200C23×C43C2×C22⋊C411yescharacteristic
201C23×C43C2×C4⋊C411yescharacteristic
202C23×C43C2×C4⋊C412yes—
203C23×C43#11711yescharacteristic
204C23×C43#11711yescharacteristic
205C23×C43C4×D412yes—
206C23×C43C4×D412yes—
207C23×C43C4×D412yes—
208C23×C43C4×D412yes—
209C23×C43#12012yes—
210C23×C43#12012yes—
211C23×C43#12111yescharacteristic
212C23×C43#12112yes—
213C23×C43#12111yescharacteristic
214C23×C43C22⋊Q811yescharacteristic
215C23×C43C22⋊Q812yes—
216C23×C43C22⋊Q811yescharacteristic
217C23×C43#12312yes—
218C23×C43#12312yes—
219C22×D43—22no—
220C22×D43—22no—
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—42no—
226C22×D43—44no—
227C22×D43—44no—
228C22×D43—42no—
229C22×D43—42no—
230C22×D43—42no—
231C22×D43—42no—
232C22×D43—44no—
233C22×D43—42no—
234C22×D43—44no—
235C22×D43#9514yescomplemented
236C2×C4×C43—24no—
237C2×C4×C43—24no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—48no—
244C2×C4×C43—48no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—48no—
248C2×C4×C43—44no—
249C2×C4×C43—84no—
250C2×C4×C43—82no—
251C2×C4×C43—82no—
252C2×C4×C43#9914yescomplemented
253C22⋊D43—28no—
254C22⋊D43—28no—
255C22⋊D43—28no—
256C22⋊D43—28no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—48no—
272C2×Dic43—44no—
273C2×Dic43—84no—
274C2×Dic43—82no—
275C2×Dic43—82no—
276C2×Dic43#9514yescomplemented
277C4×D43—416no—
278#10761—431nomaximal, Sylow
279C22×C43—22no—
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—24no—
288C22×C43—24no—
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43C2×#9511yescharacteristic
306C22×C43C4×C22⋊C411yescharacteristic
307C22×C43C4×C22⋊C411yescharacteristic
308C22×C43#37911yescharacteristic
309C22×C43#38011yescharacteristic
310C22×C43#38011yescharacteristic
311C22×C43#38111yescharacteristic
312C22×C43#38512yes—
313C22×C43#38512yes—
314C22×C43#38612yes—
315C22×C43#38612yes—
316C22×C43C2×#9912yes—
317C22×C43#41012yes—
318C2×D43—24no—
319C2×D43—44no—
320C2×D43—44no—
321C2×D43—44no—
322C2×D43—44no—
323C2×D43—44no—
324C2×D43—42no—
325C2×D43—42no—
326C2×D43—44no—
327C4×C43—24no—
328C4×C43—42no—
329C4×C43—84no—
330Dic43—24no—
331Dic43—42no—
332Dic43—42no—
333Dic43—84no—
334C22×C4×D4—431no—
335C22×#99—432no—
336C2×#342—432no—
337C22⋊#95—431no—
338C22⋊#95D4311yescharacteristic, complemented
339C2×C43—22no—
340C2×C43—22no—
341C2×C43—21no—
342C2×C43—21no—
343C2×C43—21no—
344C2×C43—21no—
345C2×C43—22no—
346C2×C43—22no—
347C2×C43C22⋊#9511yescharacteristic
348C2×C43C4×#9912yes—
349C2×C43#178111yescharacteristic
350C2×C43#178211yescharacteristic
351C2×C43#179912yes—
352D43—44no—
353C23×D4—431no—
354C24×C4—431no—
355C24×C4C2×D4311yescharacteristic
356C2×C4×D4—864no—
357C2×C4×D4—864no—
358C2×C4×D4—862no—
359C2×C4×D4—862no—
360C22×C4⋊C4—431no—
361C22×C22⋊C4—431no—
362C22×C22⋊C4—432no—
363C22×C22⋊C4—431no—
364C22×C22⋊C4C2×D4312yes—
365C22×C42—431no—
366C2×#99—438no—
367C2×#99—864no—
368C2×#99—864no—
369C2×#95—22no—
370C2×#95—862no—
371#342—864no—
372C43#1076111yescharacteristic, complemented, Sylow
373C25—431no—
374C25C22×D4311yescharacteristic
375C22×D4—434no—
376C22×D4—434no—
377C22×D4—432no—
378C22×D4—432no—
379C22×D4—861no—
380C22×D4—862no—
381C22×D4—862no—
382C22×D4—861no—
383C22×D4—861no—
384C22×D4—861no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—44no—
389C23×C4—431no—
390C23×C4—431no—
391C23×C4—431no—
392C23×C4—862no—
393C23×C4—862no—
394C23×C4—862no—
395C23×C4—862no—
396C23×C4—1724no—
397C23×C4C4×D4311yescharacteristic
398C23×C4C4×D4311yescharacteristic
399C23×C4D17212yes—
400C23×C4C22⋊D4312yes—
401C4×D4—8616no—
402C4×D4—8616no—
403C2×C4⋊C4—862no—
404C2×C4⋊C4—862no—
405C2×C4⋊C4—862no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—434no—
412C2×C22⋊C4—434no—
413C2×C22⋊C4—862no—
414C2×C22⋊C4—862no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—862no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—862no—
419C2×C22⋊C4—862no—
420C2×C22⋊C4—862no—
421C2×C22⋊C4—862no—
422C2×C22⋊C4—862no—
423C2×C22⋊C4—862no—
424C2×C22⋊C4C4×D4314yescomplemented
425C2×C42—862no—
426C2×C42—862no—
427C2×C42—862no—
428#99—8616no—
429#95—44no—
430#95—1724no—
431C24—42no—
432C24—42no—
433C24—432no—
434C24—432no—
435C24—432no—
436C24—861no—
437C24—861no—
438C24—861no—
439C24—861no—
440C24—1722no—
441C24—1722no—
442C24C2×C4×D4311yescharacteristic
443C24C2×C4×D4312yes—
444C24C2×D17211yescharacteristic
445C24#1062189812yes—
446C24D4×D4312yes—
447C24D4×D4311yescharacteristic
448C24D4×D4312yes—
449C24#1062190011yescharacteristic
450C24Q8×D4311yescharacteristic
451C24#1062190211yescharacteristic
452C24C2×C22⋊D4311yescharacteristic
453C2×D4—438no—
454C2×D4—438no—
455C2×D4—864no—
456C2×D4—864no—
457C2×D4—864no—
458C2×D4—864no—
459C2×D4—864no—
460C2×D4—864no—
461C2×D4—862no—
462C2×D4—864no—
463C2×D4—862no—
464C2×D4—862no—
465C2×D4—864no—
466C2×D4—862no—
467C2×D4—864no—
468C2×D4—864no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—48no—
483C22×C4—48no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—432no—
489C22×C4—432no—
490C22×C4—432no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—868no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—864no—
503C22×C4—1728no—
504C22×C4—1728no—
505C22×C4—1724no—
506C22×C4—1724no—
507C22×C4—1724no—
508C22×C4—1722no—
509C22×C4—1722no—
510C22×C4—1724no—
511C22×C4—1722no—
512C22×C4—1722no—
513C22×C4(C2×D43)⋊C412yes—
514C22×C4(C2×D43)⋊C412yes—
515C4⋊C4—868no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—868no—
521C22⋊C4—864no—
522C22⋊C4—864no—
523C22⋊C4—864no—
524C22⋊C4—864no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C42—868no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—42no—
535C23—42no—
536C23—44no—
537C23—44no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—434no—
545C23—862no—
546C23—862no—
547C23—862no—
548C23—862no—
549C23—862no—
550C23—862no—
551C23—1722no—
552C23—1722no—
553C23—1724no—
554C23—1724no—
555C23—1722no—
556C23—1722no—
557C23—1724no—
558C23—1724no—
559C23—1722no—
560C23—1722no—
561C23C42×D4311yescharacteristic
562C23C22⋊C4×D4311yescharacteristic
563C23C22⋊C4×D4311yescharacteristic
564C23C22⋊C4×D4312yes—
565C23C2×(C2×D43)⋊C411yescharacteristic
566C23C4⋊C4×D4311yescharacteristic
567C23C4⋊C4×D4312yes—
568C23#1306328211yescharacteristic
569C23#1306328311yescharacteristic
570C23(C22⋊D43)⋊C412yes—
571C23C4×C22⋊D4312yes—
572C23#1306328712yes—
573C23C4×D17212yes—
574C23#1306329312yes—
575C23#1306329512yes—
576C23#1306329611yescharacteristic
577C23#1306329812yes—
578C23#1306330011yescharacteristic
579C23#1306330111yescharacteristic
580C23#1306330312yes—
581C23#1306330511yescharacteristic
582C23#1306330712yes—
583C23#1306331012yes—
584D4—868no—
585D4—868no—
586D4—868no—
587D4—868no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—48no—
596C2×C4—48no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—48no—
600C2×C4—44no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4—84no—
604C2×C4—434no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—3442no—
614C2×C4—3442no—
615C2×C4—3444no—
616C2×C4—17216no—
617C2×C4—1728no—
618C2×C4—1724no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4—1722no—
625C2×C4#1306323914yescomplemented
626C22—21no—
627C22—21no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—21no—
633C22—21no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—24no—
641C22—24no—
642C22—22no—
643C22—22no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—864no—
653C22—1724no—
654C22—1724no—
655C22—1724no—
656C22—1724no—
657C22—1722no—
658C22—1722no—
659C22—1724no—
660C22—1724no—
661C22#95×D4311yescharacteristic
662C22#1458274611yescharacteristic
663C22C4×(C2×D43)⋊C411yescharacteristic
664C22#1458275411yescharacteristic
665C22#1458275611yescharacteristic
666C22#1458275811yescharacteristic
667C22#1458276111yescharacteristic
668C22#1458277012yes—
669C22#1458277312yes—
670C22#1458277512yes—
671C22#1458277712yes—
672C22C2×#1306323912yes—
673C22#1458287212yes—
674C4—24no—
675C4—42no—
676C4—84no—
677C4—864no—
678C4—3444no—
679C4—1722no—
680C4—1722no—
681C2—22no—
682C2—22no—
683C2—21no—
684C2—21no—
685C2—21no—
686C2—21no—
687C2—22no—
688C2—22no—
689C2—1724no—
690C2(C2×D43)⋊#9511yescharacteristic
691C2C4×#1306323912yes—
692C2#1913450911yescharacteristic
693C2#1913451211yescharacteristic
694C2#1913458012yes—
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC23×C43C2×C42
FrattiniC25C22×D43
FittingC43×C22⋊#95C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenterC22⋊#95D43
hypocenterC43#10761
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#14582665C2semidirect
4. #19132818C2semidirect
5. C43×C22⋊#95C2semidirect
7. C23×C4×D43C4semidirect
12. C22×Dic43⋊C4C4semidirect
15. C22×(C2×D43)⋊C4C4semidirect
16. C22×C4×Dic43C4semidirect
19. C2×#13063239C4semidirect
57. C2×C22⋊Dic43C2×C4semidirect
81. C2×C22⋊C4×C43C2×C4semidirect
235. C22×D43#95semidirect
252. C2×C4×C43#99semidirect
276. C2×Dic43#95semidirect
338. C22⋊#95D43semidirect
372. C43#10761semidirect
424. C2×C22⋊C4C4×D43semidirect
625. C2×C4#13063239semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C22×#130632392
C2×#145826652
#191328182
C43×C22⋊#952
#1076143