Finite Group Databasebeta

← #25021898

Subgroups — #25021898

Order 11008.

2062 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic86C211yesmaximal, characteristic, complemented
2C2×#14582811C211yesmaximal, characteristic
3C2×#14582772C212yesmaximal
4#19132865C211yesmaximal, characteristic, complemented
5#19132859C211yesmaximal, characteristic, complemented
6#19132840C211yesmaximal, characteristic
7#19132832C212yesmaximal
8#19132828C212yesmaximal, complemented
9#19132826C212yesmaximal, complemented
10#19132822C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C43C211yesmaximal, characteristic
12C23×Dic86C2211yescharacteristic
13C2×C4×Dic86—28no—
14C2×C4×Dic86—24no—
15C22×C4⋊Dic43C2211yescharacteristic
16C22×Dic43⋊C4C2212yes—
17C22×Dic43⋊C4C2212yes—
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2212yes—
20C22×C4×Dic43C2212yes—
21#14582811C418yescomplemented
22#14582772—28no—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2212yes—
32C24×C4×C43C2211yescharacteristic
33C22×C22⋊C4×C43C2211yescharacteristic
34C22×C22⋊C4×C43C2211yescharacteristic
35C22×C42×C43C2211yescharacteristic
36C22×C42×C43C2211yescharacteristic
37C4×C22⋊C4×C43—24no—
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C22×Dic86—22no—
41C22×Dic86—22no—
42C22×Dic86—24no—
43C22×Dic86—24no—
44C22×Dic86C2×C414yescomplemented
45C23×Dic43C2312yes—
46C23×Dic43C2312yes—
47C23×Dic43C2312yes—
48C23×Dic43C2312yes—
49C4×Dic86—232no—
50C2×C4⋊Dic43—22no—
51C2×C4⋊Dic43—24no—
52C2×Dic43⋊C4—24no—
53C2×Dic43⋊C4—24no—
54C2×Dic43⋊C4—24no—
55C2×Dic43⋊C4—24no—
56C2×Dic43⋊C4—42no—
57C2×Dic43⋊C4D418yes—
58C2×C22⋊Dic43—24no—
59C2×C22⋊Dic43—24no—
60C2×C22⋊Dic43—24no—
61C2×C22⋊Dic43—24no—
62C2×C22⋊Dic43—42no—
63C2×C22⋊Dic43C2×C418yes—
64C2×C4×Dic43—24no—
65C2×C4×Dic43—24no—
66C2×C4×Dic43—24no—
67C43⋊#95—24no—
68C43⋊#95—24no—
69C43⋊#95—22no—
70C43⋊#95—24no—
71C43⋊#95—24no—
72C43⋊#95—42no—
73C43⋊#95—42no—
74C43⋊#95C2×C414yescomplemented
75C43⋊#95C2×C418yescomplemented
76C25×C43C2311yescharacteristic
77C23×C4×C43—22no—
78C23×C4×C43—22no—
79C23×C4×C43—22no—
80C23×C4×C43—24no—
81C23×C4×C43—42no—
82C23×C4×C43C2311yescharacteristic
83C23×C4×C43C2311yescharacteristic
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C23×C4×C43C2311yescharacteristic
87C23×C4×C43C2311yescharacteristic
88C2×C22⋊C4×C43—22no—
89C2×C22⋊C4×C43—22no—
90C2×C22⋊C4×C43—22no—
91C2×C22⋊C4×C43—22no—
92C2×C22⋊C4×C43C2×C414yes—
93C2×C22⋊C4×C43Q814yescomplemented
94C2×C42×C43—24no—
95C2×C42×C43—22no—
96C2×C42×C43—42no—
97C2×C42×C43D414yes—
98#95×C43—22no—
99#95×C43—22no—
100C24×C43—21no—
101C24×C43—22no—
102C24×C43—21no—
103C24×C43—21no—
104C24×C43—21no—
105C24×C43—22no—
106C24×C43—22no—
107C24×C43—22no—
108C24×C43C22×C412yes—
109C24×C43C2×Q812yes—
110C24×C43#4112yes—
111C24×C43C2411yescharacteristic
112C22×C4×C43—28no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
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×C43—48no—
133C22×C4×C43—48no—
134C22×C4×C43—44no—
135C22×C4×C43—44no—
136C22×C4×C43C22×C412yes—
137C22×C4×C43C22×C412yes—
138C22×C4×C43C2×D414yes—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2×D412yes—
142C22×C4×C43C2×Q812yes—
143C22×C4×C43C2×Q812yes—
144C22×C4×C43#4112yes—
145C22×C4×C43#4112yes—
146C22×C4×C43#4112yes—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
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—22no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43C22×C414yes—
171C22×Dic43C22×C414yes—
172C22×Dic43C2×D414yes—
173C22×Dic43C2×D414yes—
174C22×Dic43#4114yes—
175C2×Dic86—28no—
176C2×Dic86—216no—
177C2×Dic86—28no—
178C2×Dic86—28no—
179C2×Dic86—216no—
180C22⋊C4×C43—28no—
181C22⋊C4×C43—28no—
182C42×C43—28no—
183C42×C43—44no—
184C22⋊Dic43—216no—
185C22⋊Dic43—48no—
186C4⋊Dic43—28no—
187Dic43⋊C4—216no—
188Dic43⋊C4—48no—
189C4×Dic43—216no—
190C23×C43—24no—
191C23×C43—22no—
192C23×C43—22no—
193C23×C43—24no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43—22no—
197C23×C43—22no—
198C23×C43—24no—
199C23×C43—24no—
200C23×C43—24no—
201C23×C43—24no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—42no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—42no—
212C23×C43C4×Q814yescomplemented
213C23×C43C23×C411yescharacteristic
214C23×C43C22×D412yes—
215C23×C43C22×D411yescharacteristic
216C23×C43C22×Q811yescharacteristic
217C23×C43C2×#4112yes—
218C23×C43C2×#4111yescharacteristic
219C23×C43C2×#4111yescharacteristic
220C23×C43C2×#4111yescharacteristic
221C23×C43C2×#4111yescharacteristic
222C23×C43H(5,𝔽2)12yes—
223C23×C432−1+412yes—
224C2×C4×C43—24no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—24no—
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—22no—
237C2×C4×C43—24no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—24no—
241C2×C4×C43—24no—
242C2×C4×C43—416no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43C4×D414yes—
253C2×C4×C43#12014yes—
254C2×C4×C43C22⋊Q814yes—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—24no—
258C2×Dic43—24no—
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—24no—
263C2×Dic43—24no—
264C2×Dic43—24no—
265C2×Dic43—24no—
266C2×Dic43—24no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43C4×D418yes—
283Dic86—232no—
284#14172—431nomaximal, Sylow
285C22×C43—28no—
286C22×C43—24no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—44no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—44no—
294C22×C43—44no—
295C22×C43—42no—
296C22×C43C2×C4×D412yes—
297C22×C43C2×C4×D411yescharacteristic
298C22×C43C2×C4×Q811yescharacteristic
299C22×C43C4×#4111yescharacteristic
300C22×C43#52012yes—
301C22×C43C2×#12011yescharacteristic
302C22×C43C2×C22⋊Q811yescharacteristic
303C22×C43#52511yescharacteristic
304C22×C43#52512yes—
305C22×C43#52511yescharacteristic
306C22×C43#52911yescharacteristic
307C22×C43#53311yescharacteristic
308C22×C43#53511yescharacteristic
309C22×C43#53611yescharacteristic
310C22×C43#54212yes—
311C22×C43#54612yes—
312C22×C43#54612yes—
313C22×C43#54812yes—
314C22×C43D4×Q812yes—
315C22×C43#55212yes—
316C22×C43#55412yes—
317C22×C43#55612yes—
318C22×C43#55912yes—
319C4×C43—24no—
320C4×C43—24no—
321C4×C43—24no—
322C4×C43—42no—
323C4×C43—42no—
324C4×C43—42no—
325Dic43—28no—
326Dic43—44no—
327Dic43—44no—
328Dic43—82no—
329C22×C4×Q8—431no—
330C2×#393—431no—
331C2×#385—432no—
332C2×C4×C22⋊C4D4311yescharacteristic
333#1446—431no—
334#1444—431no—
335#1439—431no—
336#1437—432no—
337#1436—432no—
338#1436—432no—
339#1434—431no—
340C2×C43—44no—
341C2×C43C4×#12011yescharacteristic
342C2×C43C4×C22⋊Q811yescharacteristic
343C2×C43#232611yescharacteristic
344C2×C43#236012yes—
345C2×C43#236712yes—
346C2×C43#240411yescharacteristic
347C2×C43#240911yescharacteristic
348C2×C43#245812yes—
349C2×C43#246512yes—
350C2×C43#258011yescharacteristic
351C2×C43#259911yescharacteristic
352C23×Q8—431no—
353C24×C4C2×D4311yescharacteristic
354C2×C4×Q8—868no—
355C2×C4×Q8—864no—
356C22×C4⋊C4—432no—
357C22×C4⋊C4—431no—
358C22×C4⋊C4—432no—
359C22×C22⋊C4—432no—
360C22×C22⋊C4—432no—
361C22×C22⋊C4C2×D4311yescharacteristic
362C22×C22⋊C4C2×D4311yescharacteristic
363C22×C42—432no—
364C22×C42C2×D4311yescharacteristic
365C22×C42C2×D4311yescharacteristic
366#393—438no—
367#385—868no—
368C4×C22⋊C4—24no—
369C2×#95—431no—
370C2×#95—432no—
371C2×#95—432no—
372C2×#95—432no—
373C2×#95—431no—
374C2×#95—432no—
375C2×#95—432no—
376C2×#95—432no—
377C2×#95—432no—
378C2×#95C2×D4311yescharacteristic
379C2×#95C2×D4311yescharacteristic
380C43#1417211yescharacteristic, complemented, Sylow
381C25C22×D4311yescharacteristic
382C22×Q8—434no—
383C22×Q8—864no—
384C22×Q8—864no—
385C22×Q8—862no—
386C22×Q8—862no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—24no—
391C23×C4—42no—
392C23×C4—432no—
393C23×C4—432no—
394C23×C4—432no—
395C23×C4—432no—
396C23×C4C22×D4311yescharacteristic
397C23×C4C22×D4311yescharacteristic
398C23×C4C22×D4311yescharacteristic
399C23×C4C22×D4311yescharacteristic
400C23×C4C22×D4311yescharacteristic
401C23×C4C22×D4311yescharacteristic
402C4×Q8—8632no—
403C2×C4⋊C4—438no—
404C2×C4⋊C4—864no—
405C2×C4⋊C4—864no—
406C2×C4⋊C4—864no—
407C2×C4⋊C4—862no—
408C2×C4⋊C4—864no—
409C2×C4⋊C4—864no—
410C2×C4⋊C4—1722no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—438no—
416C2×C22⋊C4—864no—
417C2×C22⋊C4—864no—
418C2×C22⋊C4—864no—
419C2×C22⋊C4—864no—
420C2×C22⋊C4—1722no—
421C2×C22⋊C4Dic8614yescomplemented
422C2×C22⋊C4C4×D4314yes—
423C2×C42—24no—
424C2×C42—22no—
425C2×C42—42no—
426C2×C42—864no—
427C2×C42—864no—
428C2×C42—864no—
429C2×C42C22⋊D4314yes—
430#95—22no—
431#95—22no—
432#95—438no—
433#95—434no—
434#95—864no—
435#95—864no—
436#95—864no—
437#95—862no—
438#95—864no—
439#95—1722no—
440#95—1722no—
441C24—22no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—22no—
448C24—22no—
449C24C2×Dic8612yes—
450C24C2×C4×D4312yes—
451C24#1062189812yes—
452C24C23×D4311yescharacteristic
453C2×Q8—8616no—
454C2×Q8—868no—
455C2×Q8—868no—
456C2×Q8—8616no—
457C2×Q8—868no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—28no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—48no—
479C22×C4—48no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—434no—
483C22×C4—434no—
484C22×C4—434no—
485C22×C4—434no—
486C22×C4—434no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—862no—
509C22×C4—862no—
510C22×C4C2×Dic8612yes—
511C22×C4C2×Dic8612yes—
512C22×C4C2×C4×D4312yes—
513C22×C4C2×C4×D4312yes—
514C22×C4#1062189812yes—
515C22×C4#1062189812yes—
516C22×C4#1062189812yes—
517C22×C4D4×D4314yes—
518C22×C4C2×C22⋊D4312yes—
519C22×C4C2×C22⋊D4312yes—
520C22×C4C2×C22⋊D4312yes—
521C4⋊C4—868no—
522C4⋊C4—8616no—
523C4⋊C4—1728no—
524C22⋊C4—28no—
525C22⋊C4—28no—
526C22⋊C4—8616no—
527C22⋊C4—1728no—
528C42—28no—
529C42—44no—
530C42—8616no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—22no—
536C23—22no—
537C23—24no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—24no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—41no—
547C23—41no—
548C23—42no—
549C23—41no—
550C23—41no—
551C23—42no—
552C23—42no—
553C23C4×Dic8614yescomplemented
554C23C22×C4×D4311yescharacteristic
555C23C2×D4×D4312yes—
556C23C22×C22⋊D4311yescharacteristic
557C23C22×Dic8611yescharacteristic
558C23#41×D4312yes—
559C23C2×#1062189811yescharacteristic
560C23C2×#1062189811yescharacteristic
561C23C2×#1062189811yescharacteristic
562C23C2×#1062189811yescharacteristic
563C23#1306337012yes—
564C23#1306337212yes—
565Q8—8632no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—416no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—438no—
595C2×C4—864no—
596C2×C4—864no—
597C2×C4—864no—
598C2×C4—864no—
599C2×C4—864no—
600C2×C4—864no—
601C2×C4—864no—
602C2×C4—864no—
603C2×C4—864no—
604C2×C4—864no—
605C2×C4—864no—
606C2×C4—864no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4—1722no—
614C2×C4—1722no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4C4×C22⋊D4314yes—
623C2×C4#1306329314yes—
624C2×C4#1306330414yes—
625C22—28no—
626C22—24no—
627C22—42no—
628C22—44no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—44no—
634C22—42no—
635C22—44no—
636C22C4×D4×D4312yes—
637C22C2×C4×C22⋊D4311yescharacteristic
638C22C2×C4×Dic8611yescharacteristic
639C22C4×#1062189811yescharacteristic
640C22#1458337812yes—
641C22C2×#1306329311yescharacteristic
642C22C2×#1306330411yescharacteristic
643C22#1458340611yescharacteristic
644C22#1458340812yes—
645C22#1458341011yescharacteristic
646C22#1458343311yescharacteristic
647C22#1458345611yescharacteristic
648C22#1458346611yescharacteristic
649C22#1458347011yescharacteristic
650C22#1458351412yes—
651C22#1458353912yes—
652C22#1458353912yes—
653C22#1458355812yes—
654C22D4×Dic8612yes—
655C22#1458358212yes—
656C22#1458360812yes—
657C22#1458361712yes—
658C22#1458363212yes—
659C4—24no—
660C4—24no—
661C4—24no—
662C4—42no—
663C4—42no—
664C4—42no—
665C4—868no—
666C4—3442no—
667C4—1724no—
668C4—1724no—
669C2—44no—
670C2C4×#1306329311yescharacteristic
671C2C4×#1306330411yescharacteristic
672C2#1913730711yescharacteristic
673C2#1913760112yes—
674C2#1913766712yes—
675C2#1913791411yescharacteristic
676C2#1913796011yescharacteristic
677C2#1913851712yes—
678C2#1913861612yes—
679C2#1913994911yescharacteristic
680C2#1914017211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C4×C22⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×C4×C22⋊C4D43
hypocenterC43#14172
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic86C2semidirect
4. #19132865C2semidirect
5. #19132859C2semidirect
8. #19132828C2semidirect
9. #19132826C2semidirect
10. #19132822C2semidirect
21. #14582811C4semidirect
44. C22×Dic86C2×C4semidirect
74. C43⋊#95C2×C4semidirect
75. C43⋊#95C2×C4semidirect
93. C2×C22⋊C4×C43Q8semidirect
212. C23×C43C4×Q8semidirect
380. C43#14172semidirect
421. C2×C22⋊C4Dic86semidirect
553. C23C4×Dic86semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic862
C2×#145828112
C2×#145827722
#191328652
#191328592
#191328402
#191328322
#191328282
#191328262
#191328222
C2×C4×C22⋊C4×C432
#1417243