Finite Group Databasebeta

← #25033240

Subgroups — #25033240

Order 11008.

1814 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
1C2×#14582835C211yesmaximal, characteristic
2C2×#14582794C212yesmaximal, complemented
3C2×#14582768C211yesmaximal, characteristic, complemented
4C2×#14582757C212yesmaximal
5C2×C22⋊C4×Dic43C211yesmaximal, characteristic
6#19132863C211yesmaximal, characteristic, complemented
7#19132862C211yesmaximal, characteristic, complemented
8#19132858C212yesmaximal, complemented
9#19132838C212yesmaximal
10Dic43⋊#95C211yesmaximal, characteristic, complemented
11C2×C43×#399C211yesmaximal, characteristic
12C24×Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×Dic43⋊C4C2212yes—
15C22×Dic43⋊C4C2212yes—
16C22×Dic43⋊C4C2212yes—
17C22×Dic43⋊C4C2212yes—
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C4×Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22#14582835—24no—
23#14582794—28no—
24#14582768—24no—
25#14582757—28no—
26C22⋊C4×Dic43—24no—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2212yes—
37C22×C22⋊C4×C43C2212yes—
38C22×C22⋊C4×C43C2211yescharacteristic
39C43×#399—24no—
40C2×#95×C43C2211yescharacteristic
41C23×Dic43—22no—
42C23×Dic43—24no—
43C23×Dic43—24no—
44C23×Dic43—22no—
45C23×Dic43Q814yes—
46C23×Dic43C2312yes—
47C23×Dic43C2312yes—
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2311yescharacteristic
50C23×Dic43C2311yescharacteristic
51C23×Dic43C2311yescharacteristic
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×Dic43⋊C4—24no—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×Dic43⋊C4—24no—
61C2×Dic43⋊C4—24no—
62C2×Dic43⋊C4—24no—
63C2×Dic43⋊C4—42no—
64C2×Dic43⋊C4—42no—
65C2×Dic43⋊C4—42no—
66C2×Dic43⋊C4D418yes—
67C2×C22⋊Dic43—22no—
68C2×C22⋊Dic43—22no—
69C2×C22⋊Dic43—24no—
70C2×C22⋊Dic43—24no—
71C2×C22⋊Dic43—42no—
72C2×C22⋊Dic43Q814yes—
73C2×C4×Dic43—24no—
74C2×C4×Dic43—24no—
75C2×C4×Dic43—22no—
76C2×C4×Dic43D414yes—
77C43⋊#95—24no—
78C43⋊#95—22no—
79C43⋊#95—22no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—22no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C25×C43C2311yescharacteristic
86C23×C4×C43C2312yes—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2312yes—
89C23×C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43—24no—
91C2×C4⋊C4×C43—24no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43—42no—
96C2×C22⋊C4×C43—22no—
97C2×C22⋊C4×C43—22no—
98C2×C22⋊C4×C43—24no—
99C2×C22⋊C4×C43—24no—
100C2×C22⋊C4×C43—42no—
101C2×C22⋊C4×C43D414yes—
102#95×C43—22no—
103C24×C43—21no—
104C24×C43—22no—
105C24×C43—21no—
106C24×C43—21no—
107C24×C43—21no—
108C24×C43—22no—
109C24×C43—22no—
110C24×C43—22no—
111C24×C43C2×D412yes—
112C24×C43C2×Q812yes—
113C24×C43C2×Q812yes—
114C24×C43C2411yescharacteristic
115C22×C4×C43—22no—
116C22×C4×C43—21no—
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—21no—
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×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43C2×D414yes—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D412yes—
137C22×C4×C43C2×D412yes—
138C22×C4×C43#4112yes—
139C22×Dic43—28no—
140C22×Dic43—216no—
141C22×Dic43—22no—
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—22no—
152C22×Dic43—21no—
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—44no—
165C22×Dic43—48no—
166C22×Dic43—44no—
167C22×Dic43C2×D414yes—
168C22×Dic43C2×D412yes—
169C22×Dic43C2×D412yes—
170C22×Dic43C2×D414yes—
171C22×Dic43C2×Q812yes—
172C22×Dic43C2×Q812yes—
173C22×Dic43C2×Q812yes—
174C22×Dic43C2×Q812yes—
175C22×Dic43#4112yes—
176C22×Dic43#4114yes—
177C22×Dic43#4112yes—
178C4⋊C4×C43—48no—
179C4⋊C4×C43—44no—
180C22⋊C4×C43—28no—
181C22⋊C4×C43—48no—
182C22⋊Dic43—28no—
183C22⋊Dic43—48no—
184C4⋊Dic43—44no—
185Dic43⋊C4—216no—
186Dic43⋊C4—48no—
187Dic43⋊C4—48no—
188Dic43⋊C4—48no—
189C4×Dic43—28no—
190C4×Dic43—44no—
191C23×C43—22no—
192C23×C43—22no—
193C23×C43—22no—
194C23×C43—24no—
195C23×C43—22no—
196C23×C43—22no—
197C23×C43—22no—
198C23×C43—24no—
199C23×C43—24no—
200C23×C43—24no—
201C23×C43—24no—
202C23×C43—24no—
203C23×C43—42no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43C4⋊Q814yes—
214C23×C43C22×D411yescharacteristic
215C23×C43C22×D412yes—
216C23×C43C22×D411yescharacteristic
217C23×C43C22×Q811yescharacteristic
218C23×C43C22×Q811yescharacteristic
219C23×C43C2×#4111yescharacteristic
220C23×C43C2×#4112yes—
221C23×C43C2×#4111yescharacteristic
222C23×C43C2×#4111yescharacteristic
223C23×C43H(5,𝔽2)12yes—
224C23×C432−1+412yes—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—22no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—41no—
235C2×C4×C43—42no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
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#12114yes—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—24no—
258C2×Dic43—24no—
259C2×Dic43—24no—
260C2×Dic43—42no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—42no—
265C2×Dic43—41no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—416no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43C22⋊Q814yes—
279C2×Dic43C22⋊Q814yes—
280C2×Dic43C22⋊Q818yes—
281C2×Dic43#12314yes—
282C2×Dic43#12318yes—
283C2×Dic43#12714yes—
284#15135—431nomaximal, Sylow
285C22×C43—24no—
286C22×C43—28no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—44no—
290C22×C43—44no—
291C22×C43—44no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43C2×#12111yescharacteristic
297C22×C43C2×C22⋊Q811yescharacteristic
298C22×C43C2×C22⋊Q811yescharacteristic
299C22×C43C2×C22⋊Q812yes—
300C22×C43C2×#12312yes—
301C22×C43C2×#12311yescharacteristic
302C22×C43C2×#12711yescharacteristic
303C22×C43C2×C4⋊Q811yescharacteristic
304C22×C43#53211yescharacteristic
305C22×C43#53311yescharacteristic
306C22×C43#53311yescharacteristic
307C22×C43#53511yescharacteristic
308C22×C43#53611yescharacteristic
309C22×C43#54212yes—
310C22×C43#54412yes—
311C22×C43D4212yes—
312C22×C43#54712yes—
313C22×C43#54712yes—
314C22×C43D4×Q812yes—
315C22×C43#55012yes—
316C22×C43#55212yes—
317C22×C43#55312yes—
318C22×C43#55412yes—
319C4×C43—24no—
320C4×C43—44no—
321C4×C43—42no—
322C4×C43—82no—
323Dic43—24no—
324Dic43—42no—
325Dic43—44no—
326Dic43—42no—
327Dic43—82no—
328Dic43#39918yescomplemented
329C2×#399—431no—
330C2×#399D4311yescharacteristic
331C2×#389—432no—
332C2×#384—431no—
333C2×#380—432no—
334C2×C4×C22⋊C4—431no—
335#1445—431no—
336#1445—431no—
337#1444—432no—
338#1439—432no—
339C4⋊#95—431no—
340C2×C43—44no—
341C2×C43C2×#39911yescharacteristic
342C2×C43#242212yes—
343C2×C43#242312yes—
344C2×C43#244012yes—
345C2×C43#244112yes—
346C2×C43#248611yescharacteristic
347C2×C43#248711yescharacteristic
348C2×C43#254111yescharacteristic
349C2×C43#254211yescharacteristic
350C2×C43#262811yescharacteristic
351C2×C43#285711yescharacteristic
352C24×C4—431no—
353C22×C4⋊C4—432no—
354C22×C4⋊C4—432no—
355C22×C4⋊C4—431no—
356C22×C4⋊C4—432no—
357C22×C4⋊C4—432no—
358C22×C4⋊C4C2×D4311yescharacteristic
359C22×C4⋊C4C2×D4312yes—
360C22×C22⋊C4—431no—
361C22×C22⋊C4—432no—
362C22×C22⋊C4C2×D4312yes—
363C22×C22⋊C4C2×D4311yescharacteristic
364C22×C42—431no—
365C22×C42—431no—
366#399—24no—
367#399—864no—
368#389—868no—
369#384—864no—
370#380—868no—
371C4×C22⋊C4—864no—
372C2×#95—431no—
373C2×#95—432no—
374C2×#95—432no—
375C2×#95—432no—
376C2×#95—431no—
377C2×#95—432no—
378C2×#95—432no—
379C2×#95—431no—
380C2×#95C2×D4311yescharacteristic
381C43#1513511yescharacteristic, complemented, Sylow
382C25C22×D4311yescharacteristic
383C23×C4—431no—
384C23×C4—431no—
385C23×C4—434no—
386C23×C4—432no—
387C23×C4—431no—
388C23×C4—431no—
389C23×C4—432no—
390C23×C4—862no—
391C23×C4—864no—
392C23×C4—864no—
393C23×C4—862no—
394C23×C4C22×D4312yes—
395C23×C4C22×D4312yes—
396C23×C4C22×D4311yescharacteristic
397C23×C4C22×D4311yescharacteristic
398C2×C4⋊C4—22no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—438no—
405C2×C4⋊C4—864no—
406C2×C4⋊C4—864no—
407C2×C4⋊C4—864no—
408C2×C4⋊C4—864no—
409C2×C4⋊C4—864no—
410C2×C4⋊C4—864no—
411C2×C4⋊C4—864no—
412C2×C4⋊C4—862no—
413C2×C4⋊C4—862no—
414C2×C4⋊C4—864no—
415C2×C4⋊C4—862no—
416C2×C4⋊C4—1722no—
417C2×C4⋊C4—1722no—
418C2×C4⋊C4—1722no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—434no—
425C2×C22⋊C4—862no—
426C2×C22⋊C4—862no—
427C2×C22⋊C4—864no—
428C2×C22⋊C4—864no—
429C2×C22⋊C4—1722no—
430C2×C22⋊C4C22⋊D4314yes—
431C2×C42—434no—
432C2×C42—864no—
433C2×C42—862no—
434C2×C42—864no—
435#95—22no—
436#95—864no—
437#95—862no—
438#95—864no—
439#95—864no—
440#95—862no—
441#95—864no—
442#95—864no—
443#95—862no—
444C24—22no—
445C24—21no—
446C24—21no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—22no—
451C24—22no—
452C24Q8×D4312yes—
453C24Q8×D4312yes—
454C24C2×C22⋊D4312yes—
455C24C23×D4311yescharacteristic
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—432no—
476C22×C4—434no—
477C22×C4—432no—
478C22×C4—434no—
479C22×C4—432no—
480C22×C4—432no—
481C22×C4—432no—
482C22×C4—432no—
483C22×C4—434no—
484C22×C4—432no—
485C22×C4—432no—
486C22×C4—868no—
487C22×C4—8616no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—861no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—861no—
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×C4—862no—
511C22×C4—1724no—
512C22×C4—1728no—
513C22×C4—1724no—
514C22×C4D4×D4314yes—
515C22×C4D4×D4312yes—
516C22×C4#1062190012yes—
517C22×C4C2×C22⋊D4312yes—
518C22×C4C2×C22⋊D4312yes—
519C4⋊C4—48no—
520C4⋊C4—44no—
521C4⋊C4—8616no—
522C4⋊C4—1728no—
523C4⋊C4—1728no—
524C4⋊C4—1728no—
525C4⋊C4—1724no—
526C22⋊C4—28no—
527C22⋊C4—48no—
528C22⋊C4—868no—
529C22⋊C4—1728no—
530C42—868no—
531C42—1724no—
532C23—24no—
533C23—24no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—24no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—42no—
553C23—42no—
554C23#1306332314yes—
555C23C2×D4×D4312yes—
556C23C2×D4×D4311yescharacteristic
557C23C22×C22⋊D4311yescharacteristic
558C23C2×Q8×D4311yescharacteristic
559C23C2×Q8×D4311yescharacteristic
560C23#41×D4312yes—
561C23#41×D4311yescharacteristic
562C23#41×D4311yescharacteristic
563C23C2×#1062190011yescharacteristic
564C23#1306337012yes—
565C23#1306337212yes—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—434no—
590C2×C4—438no—
591C2×C4—434no—
592C2×C4—438no—
593C2×C4—434no—
594C2×C4—434no—
595C2×C4—864no—
596C2×C4—864no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—864no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—864no—
603C2×C4—864no—
604C2×C4—864no—
605C2×C4—864no—
606C2×C4—17216no—
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—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1722no—
620C2×C4—1721no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4#1306329714yes—
625C22—24no—
626C22—28no—
627C22—42no—
628C22—44no—
629C22—44no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—44no—
636C22C2×#1306329711yescharacteristic
637C22C22⋊Q8×D4311yescharacteristic
638C22C22⋊Q8×D4311yescharacteristic
639C22C22⋊Q8×D4312yes—
640C22#123×D4312yes—
641C22#123×D4311yescharacteristic
642C22#127×D4311yescharacteristic
643C22C2×#1306332311yescharacteristic
644C22#1458344511yescharacteristic
645C22#1458345111yescharacteristic
646C22#1458345111yescharacteristic
647C22#1458346211yescharacteristic
648C22#1458347111yescharacteristic
649C22#1458351712yes—
650C22#1458352812yes—
651C22D4×C22⋊D4312yes—
652C22#1458354712yes—
653C22#1458354812yes—
654C22#1458356212yes—
655C22#1458356912yes—
656C22#1458358612yes—
657C22#1458359412yes—
658C22#1458360312yes—
659C4—24no—
660C4—44no—
661C4—42no—
662C4—82no—
663C4—438no—
664C4—864no—
665C4—3442no—
666C4—1722no—
667C4—1724no—
668C4—1722no—
669C2—44no—
670C2#399×D4311yescharacteristic
671C2#1913810612yes—
672C2#1913811312yes—
673C2#1913829412yes—
674C2#1913830112yes—
675C2#1913890011yescharacteristic
676C2#1913890511yescharacteristic
677C2#1913953911yescharacteristic
678C2#1913954311yescharacteristic
679C2#1914042111yescharacteristic
680C2#1914294311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
FittingC2×C43×#399C2
prime radicalC25×C43C23
hypercenterC2×#399D43
hypocenterC43#15135
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
2. C2×#14582794C2semidirect
3. C2×#14582768C2semidirect
6. #19132863C2semidirect
7. #19132862C2semidirect
8. #19132858C2semidirect
10. Dic43⋊#95C2semidirect
328. Dic43#399semidirect
381. C43#15135semidirect

Maximal subgroups

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

subgroupindex
C2×#145828352
C2×#145827942
C2×#145827682
C2×#145827572
C2×C22⋊C4×Dic432
#191328632
#191328622
#191328582
#191328382
Dic43⋊#952
C2×C43×#3992
#1513543