Finite Group Databasebeta

← #25018588

Subgroups — #25018588

Order 11008.

2222 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D43C211yesmaximal, characteristic
2C2×#14582765C211yesmaximal, characteristic, complemented
3C2×#14582764C211yesmaximal, characteristic, complemented
4C2×#14582756C211yesmaximal, characteristic
5C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
6#19132850C214yesmaximal, complemented
7#19132824C211yesmaximal, characteristic, complemented
8(C2×D43)⋊#95C214yesmaximal
9C43×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×C4×D43C2212yes—
11C23×C4×D43C2211yescharacteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×Dic43⋊C4C2212yes—
15C2×C4⋊C4×D43—24no—
16C2×C4⋊C4×D43—24no—
17C2×C4⋊C4×D43—24no—
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20C22×C4×Dic43C2211yescharacteristic
21#14582765—24no—
22#14582764—24no—
23#14582756—24no—
24C4×(C2×D43)⋊C4C418yescomplemented
25C2×C43⋊#95C2214yes—
26C2×C43⋊#95C2214yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2214yes—
29C2×C43⋊#95C2212yes—
30C22×C4⋊C4×C43C2211yescharacteristic
31C22×C4⋊C4×C43C2211yescharacteristic
32C22×C42×C43C2211yescharacteristic
33C2×#95×C43C2214yes—
34C24×D43C2311yescharacteristic
35C23×Dic43C2312yes—
36C23×Dic43C2312yes—
37C23×Dic43C2312yes—
38C23×Dic43C2311yescharacteristic
39C22×C4×D43—22no—
40C22×C4×D43—22no—
41C22×C4×D43—22no—
42C22×C4×D43—22no—
43C22×C4×D43—24no—
44C22×C4×D43—24no—
45C22×C4×D43—24no—
46C22×C4×D43—28no—
47C22×C4×D43—44no—
48C22×C4×D43C2×C414yes—
49C22×C4×D43D414yes—
50C22×C4×D43Q814yes—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43D414yes—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C4⋊C4×D43—232no—
61C2×(C2×D43)⋊C4—24no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—28no—
65C2×(C2×D43)⋊C4C2×C418yes—
66C2×C4×Dic43—22no—
67C2×C4×Dic43—22no—
68C2×C4×Dic43C2×C414yescomplemented
69C43⋊#95—28no—
70C43⋊#95—24no—
71C43⋊#95—28no—
72C43⋊#95—44no—
73C43⋊#95C2×C418yescomplemented
74C23×C4×C43C2312yes—
75C23×C4×C43C2312yes—
76C23×C4×C43C2312yes—
77C23×C4×C43C2311yescharacteristic
78C2×C4⋊C4×C43—22no—
79C2×C4⋊C4×C43—22no—
80C2×C4⋊C4×C43—22no—
81C2×C4⋊C4×C43—22no—
82C2×C4⋊C4×C43—22no—
83C2×C4⋊C4×C43D414yes—
84C2×C42×C43—22no—
85C2×C42×C43—22no—
86C2×C42×C43C2×C414yescomplemented
87#95×C43—44no—
88C24×C43C2411yescharacteristic
89C23×D43—21no—
90C23×D43—21no—
91C23×D43—21no—
92C23×D43—21no—
93C23×D43—22no—
94C23×D43—22no—
95C23×D43C22×C412yes—
96C23×D43C2×D412yes—
97C23×D43C2×Q812yes—
98C23×D43#4114yes—
99C23×D43#4114yes—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—24no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—24no—
111C22×C4×C43—22no—
112C22×C4×C43—24no—
113C22×C4×C43—24no—
114C22×C4×C43—22no—
115C22×C4×C43C22×C414yes—
116C22×C4×C43C22×C412yes—
117C22×C4×C43C2×D414yes—
118C22×C4×C43C2×D412yes—
119C22×C4×C43C2×D412yes—
120C22×C4×C43C2×D412yes—
121C22×C4×C43C2×Q812yes—
122C22×C4×C43#4112yes—
123C22×C4×C43#4112yes—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—24no—
138C22×Dic43—24no—
139C22×Dic43—22no—
140C22×Dic43—24no—
141C22×Dic43—22no—
142C22×Dic43—24no—
143C22×Dic43C22×C414yes—
144C22×Dic43C22×C412yes—
145C22×Dic43C2×D414yes—
146C22×Dic43C2×D412yes—
147C22×Dic43C2×Q812yes—
148C2×C4×D43—28no—
149C2×C4×D43—28no—
150C2×C4×D43—28no—
151C2×C4×D43—28no—
152C2×C4×D43—28no—
153C2×C4×D43—28no—
154C2×C4×D43—216no—
155C2×C4×D43—416no—
156C2×C4×D43—416no—
157C2×C4×D43—48no—
158C2×C4×D43—48no—
159C2×C4×D43C4⋊C4116yes—
160C4⋊C4×C43—28no—
161C4⋊C4×C43—44no—
162C42×C43—28no—
163(C2×D43)⋊C4—216no—
164(C2×D43)⋊C4—48no—
165C4⋊Dic43—28no—
166C4⋊Dic43—44no—
167Dic43⋊C4—216no—
168C4×Dic43—28no—
169C23×C43C23×C411yescharacteristic
170C23×C43C22×D411yescharacteristic
171C23×C43C22×D411yescharacteristic
172C23×C43C22×D411yescharacteristic
173C23×C43C22×Q811yescharacteristic
174C23×C43C2×#4112yes—
175C23×C43C2×#4112yes—
176C23×C43C2×#4111yescharacteristic
177C23×C43C2×#4111yescharacteristic
178C23×C43H(5,𝔽2)12yes—
179C23×C432−1+412yes—
180C22×D43—22no—
181C22×D43—22no—
182C22×D43—24no—
183C22×D43—22no—
184C22×D43—22no—
185C22×D43—22no—
186C22×D43—22no—
187C22×D43—22no—
188C22×D43—22no—
189C22×D43—24no—
190C22×D43—24no—
191C22×D43—24no—
192C22×D43—24no—
193C22×D43—24no—
194C22×D43—24no—
195C22×D43—24no—
196C22×D43—24no—
197C22×D43—24no—
198C22×D43C2×C4⋊C414yes—
199C22×D43#11718yes—
200C22×D43#12414yes—
201C22×D43#12414yes—
202C22×D43#12518yes—
203C2×C4×C43—24no—
204C2×C4×C43—24no—
205C2×C4×C43—24no—
206C2×C4×C43—24no—
207C2×C4×C43—28no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—44no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—44no—
219C2×C4×C43—44no—
220C2×C4×C43C2×C4⋊C414yes—
221C2×C4×C43C4×D414yes—
222C2×C4×C43C4×D414yes—
223C2×C4×C43#12014yes—
224C2×C4×C43C22⋊Q814yes—
225C2×C4×C43C22⋊Q814yes—
226C2×C4×C43#12314yes—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—24no—
234C2×Dic43—24no—
235C2×Dic43—24no—
236C2×Dic43—24no—
237C2×Dic43—28no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—44no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—44no—
249C2×Dic43—44no—
250C2×Dic43C2×C4⋊C414yes—
251C4×D43—232no—
252C4×D43—432no—
253#13881—431nomaximal, Sylow
254C22×C43C22×C4⋊C411yescharacteristic
255C22×C43C2×#11712yes—
256C22×C43C2×C4×D411yescharacteristic
257C22×C43C2×C4×D411yescharacteristic
258C22×C43#52012yes—
259C22×C43C2×#12011yescharacteristic
260C22×C43C2×C22⋊Q811yescharacteristic
261C22×C43C2×C22⋊Q811yescharacteristic
262C22×C43C2×#12311yescharacteristic
263C22×C43C2×#12411yescharacteristic
264C22×C43C2×#12411yescharacteristic
265C22×C43C2×#12512yes—
266C22×C43#53511yescharacteristic
267C22×C43#53611yescharacteristic
268C22×C43#54412yes—
269C22×C43#54612yes—
270C22×C43#54612yes—
271C22×C43#54812yes—
272C22×C43#54812yes—
273C22×C43#55212yes—
274C22×C43#55212yes—
275C22×C43#55312yes—
276C22×C43#55312yes—
277C2×D43—24no—
278C2×D43—28no—
279C2×D43—28no—
280C2×D43—24no—
281C2×D43—24no—
282C2×D43—28no—
283C2×D43—28no—
284C2×D43—24no—
285C2×D43—24no—
286C2×D43—24no—
287C2×D43#38218yescomplemented
288C4×C43—44no—
289C4×C43—44no—
290C4×C43—82no—
291C4×C43#38518yes—
292Dic43—24no—
293Dic43—44no—
294Dic43—44no—
295Dic43—82no—
296C23×C4⋊C4—431no—
297C2×#382—431no—
298C2×#382—431no—
299C2×#380—431no—
300C2×C4×C22⋊C4—431no—
301#1442—434no—
302C4⋊#95—431no—
303C4⋊#95D4311yescharacteristic, complemented
304C22⋊#95—434no—
305C2×C43C2×#38211yescharacteristic
306C2×C43C2×#38511yescharacteristic
307C2×C43#231711yescharacteristic
308C2×C43#235212yes—
309C2×C43#235212yes—
310C2×C43#243511yescharacteristic
311C2×C43#243611yescharacteristic
312C2×C43#244212yes—
313C2×C43#244212yes—
314C2×C43#250311yescharacteristic
315C2×C43#250411yescharacteristic
316D43—28no—
317C24×C4—431no—
318C24×C4—432no—
319C22×C4⋊C4—431no—
320C22×C4⋊C4—432no—
321C22×C4⋊C4—431no—
322C22×C4⋊C4—864no—
323C22×C4⋊C4—864no—
324C22×C4⋊C4—864no—
325C22×C4⋊C4C2×D4311yescharacteristic
326C22×C4⋊C4C2×D4311yescharacteristic
327C22×C22⋊C4—432no—
328C22×C22⋊C4—432no—
329C22×C42—431no—
330C22×C42C2×D4311yescharacteristic
331#382—864no—
332#382—864no—
333#380—864no—
334C4×C22⋊C4—438no—
335C2×#95—432no—
336C2×#95—434no—
337C2×#95—434no—
338C2×#95—432no—
339C2×#95—434no—
340C2×#95C2×D4314yes—
341C43#1388111yescharacteristic, complemented, Sylow
342C25—431no—
343C23×C4—431no—
344C23×C4—434no—
345C23×C4—434no—
346C23×C4—434no—
347C23×C4—432no—
348C23×C4—432no—
349C23×C4—432no—
350C23×C4—864no—
351C23×C4—864no—
352C23×C4—868no—
353C23×C4—862no—
354C23×C4—862no—
355C23×C4—862no—
356C23×C4—862no—
357C23×C4—864no—
358C23×C4—1724no—
359C23×C4C22×D4312yes—
360C23×C4C22×D4312yes—
361C23×C4C22×D4312yes—
362C23×C4C22×D4311yescharacteristic
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—434no—
369C2×C4⋊C4—8632no—
370C2×C4⋊C4—864no—
371C2×C4⋊C4—864no—
372C2×C4⋊C4—864no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4—862no—
375C2×C4⋊C4—862no—
376C2×C4⋊C4—862no—
377C2×C4⋊C4—862no—
378C2×C4⋊C4D17214yes—
379C2×C22⋊C4—438no—
380C2×C22⋊C4—864no—
381C2×C22⋊C4—864no—
382C2×C22⋊C4—868no—
383C2×C22⋊C4—864no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—434no—
387C2×C42—862no—
388C2×C42—862no—
389C2×C42C4×D4314yescomplemented
390#95—44no—
391#95—438no—
392#95—864no—
393#95—868no—
394#95—868no—
395#95—1724no—
396C24—432no—
397C24—432no—
398C24—432no—
399C24—434no—
400C24—434no—
401C24—861no—
402C24—861no—
403C24—861no—
404C24—861no—
405C24—862no—
406C24—862no—
407C24C23×D4311yescharacteristic
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—432no—
424C22×C4—432no—
425C22×C4—432no—
426C22×C4—4316no—
427C22×C4—434no—
428C22×C4—434no—
429C22×C4—8616no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—868no—
435C22×C4—868no—
436C22×C4—868no—
437C22×C4—868no—
438C22×C4—868no—
439C22×C4—868no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—864no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—864no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—864no—
454C22×C4—864no—
455C22×C4—17216no—
456C22×C4—17216no—
457C22×C4—1728no—
458C22×C4—1728no—
459C22×C4C2×C4×D4314yes—
460C22×C4C2×C4×D4312yes—
461C22×C4C2×D17214yes—
462C22×C4C2×D17212yes—
463C22×C4#1062189812yes—
464C22×C4D4×D4312yes—
465C22×C4D4×D4312yes—
466C22×C4#1062190012yes—
467C22×C4Q8×D4312yes—
468C4⋊C4—28no—
469C4⋊C4—44no—
470C4⋊C4—8616no—
471C4⋊C4—868no—
472C4⋊C4—1724no—
473C22⋊C4—8616no—
474C22⋊C4—1728no—
475C42—28no—
476C42—868no—
477C23—434no—
478C23—438no—
479C23—434no—
480C23—434no—
481C23—438no—
482C23—864no—
483C23—864no—
484C23—864no—
485C23—864no—
486C23—864no—
487C23—864no—
488C23—862no—
489C23—862no—
490C23—864no—
491C23—862no—
492C23—862no—
493C23—862no—
494C23—862no—
495C23—862no—
496C23—862no—
497C23—864no—
498C23—864no—
499C23—864no—
500C23C22×C4×D4311yescharacteristic
501C23C2×D4×D4311yescharacteristic
502C23C2×D4×D4311yescharacteristic
503C23C22×D17211yescharacteristic
504C23C2×Q8×D4311yescharacteristic
505C23#41×D4312yes—
506C23#41×D4312yes—
507C23C2×#1062190011yescharacteristic
508C23C2×#1062189811yescharacteristic
509C23#1306337012yes—
510C23#1306337312yes—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—28no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—434no—
529C2×C4—862no—
530C2×C4—862no—
531C2×C4—862no—
532C2×C4—862no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—8632no—
536C2×C4—864no—
537C2×C4—864no—
538C2×C4—864no—
539C2×C4—864no—
540C2×C4—868no—
541C2×C4—17232no—
542C2×C4—1724no—
543C2×C4—1724no—
544C2×C4—1722no—
545C2×C4—1722no—
546C2×C4—1722no—
547C2×C4—1722no—
548C2×C4—1722no—
549C2×C4—1722no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4—1724no—
553C2×C4—1722no—
554C2×C4C4⋊C4×D4314yes—
555C2×C4(C22⋊D43)⋊C414yes—
556C2×C4C4×D17214yes—
557C2×C4#1306329514yes—
558C2×C4#1306330314yes—
559C2×C4#1306330514yes—
560C2×C4#1306330714yes—
561C22—438no—
562C22—864no—
563C22—868no—
564C22—864no—
565C22—868no—
566C22—864no—
567C22—864no—
568C22—864no—
569C22—868no—
570C22—864no—
571C22—868no—
572C22C2×C4⋊C4×D4311yescharacteristic
573C22#117×D4312yes—
574C22C2×(C22⋊D43)⋊C411yescharacteristic
575C22C2×C4×D17211yescharacteristic
576C22#1458338012yes—
577C22C2×#1306329511yescharacteristic
578C22C2×#1306330311yescharacteristic
579C22C2×#1306330511yescharacteristic
580C22C2×#1306330711yescharacteristic
581C22#124×D4311yescharacteristic
582C22#124×D4311yescharacteristic
583C22#125×D4312yes—
584C22#1458346211yescharacteristic
585C22#1458347411yescharacteristic
586C22#1458352612yes—
587C22#1458354412yes—
588C22#1458354612yes—
589C22#1458355912yes—
590C22#1458356112yes—
591C22#1458358312yes—
592C22#1458359012yes—
593C22#1458359612yes—
594C22#1458359912yes—
595C4—44no—
596C4—44no—
597C4—82no—
598C4—864no—
599C4—3442no—
600C4—1724no—
601C4—1724no—
602C4#1458277318yes—
603C2—868no—
604C2#382×D4311yescharacteristic
605C2C2×#1458277311yescharacteristic
606C2#1913721611yescharacteristic
607C2#1913751712yes—
608C2#1913752712yes—
609C2#1913824511yescharacteristic
610C2#1913825211yescharacteristic
611C2#1913831712yes—
612C2#1913832112yes—
613C2#1913907911yescharacteristic
614C2#1913908611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C4⋊#95C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC4⋊#95D43
hypocenterC43#13881
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#14582765C2semidirect
3. C2×#14582764C2semidirect
6. #19132850C2semidirect
7. #19132824C2semidirect
9. C43×C4⋊#95C2semidirect
24. C4×(C2×D43)⋊C4C4semidirect
68. C2×C4×Dic43C2×C4semidirect
73. C43⋊#95C2×C4semidirect
86. C2×C42×C43C2×C4semidirect
287. C2×D43#382semidirect
303. C4⋊#95D43semidirect
341. C43#13881semidirect
389. C2×C42C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D432
C2×#145827652
C2×#145827642
C2×#145827562
C2×C4×(C2×D43)⋊C42
#191328502
#191328242
(C2×D43)⋊#952
C43×C4⋊#952
#1388143