Finite Group Databasebeta

← #25019205

Subgroups — #25019205

Order 11008.

1486 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Dic43C211yesmaximal, characteristic
2#19132855C212yesmaximal, complemented
3#19132842C212yesmaximal
4#19132832C212yesmaximal
5#19132821C212yesmaximal, complemented
6#19132821C211yesmaximal, characteristic, complemented
7#19132821C211yesmaximal, characteristic, complemented
8#19132820C211yesmaximal, characteristic, complemented
9#19132818C211yesmaximal, characteristic
10#95×Dic43C211yesmaximal, characteristic, complemented
11C43×C22⋊#95C211yesmaximal, characteristic
12C22×C22⋊Dic43C2212yes—
13C22×C22⋊Dic43C2211yescharacteristic
14C22×C22⋊Dic43C2211yescharacteristic
15C22×C4×Dic43C2212yes—
16C22×C4×Dic43C2211yescharacteristic
17C22×C4×Dic43C2211yescharacteristic
18C4×C22⋊Dic43C418yescomplemented
19C2×C43⋊#95C2211yescharacteristic
20C2×C43⋊#95C2212yes—
21C2×C43⋊#95C2211yescharacteristic
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2211yescharacteristic
31C24×C4×C43C2211yescharacteristic
32C22×C22⋊C4×C43C2212yes—
33C2×#95×C43C2211yescharacteristic
34C2×#95×C43C2211yescharacteristic
35C2×#95×C43C2212yes—
36C23×Dic43C2312yes—
37C23×Dic43C2311yescharacteristic
38C23×Dic43C2311yescharacteristic
39C23×Dic43C2311yescharacteristic
40C23×Dic43C2312yes—
41C23×Dic43C2311yescharacteristic
42C2×C22⋊Dic43—22no—
43C2×C22⋊Dic43—22no—
44C2×C22⋊Dic43—22no—
45C2×C22⋊Dic43—22no—
46C2×C22⋊Dic43—24no—
47C2×C22⋊Dic43—24no—
48C2×C22⋊Dic43—42no—
49C2×C22⋊Dic43C2×C414yes—
50C2×C22⋊Dic43C2×C414yes—
51C2×C4×Dic43—24no—
52C2×C4×Dic43—24no—
53C2×C4×Dic43—42no—
54C2×C4×Dic43—42no—
55C2×C4×Dic43—42no—
56C2×C4×Dic43C2×C414yes—
57C2×C4×Dic43C2×C414yes—
58C43⋊#95—24no—
59C43⋊#95—24no—
60C43⋊#95—22no—
61C43⋊#95—22no—
62C43⋊#95—24no—
63C43⋊#95—24no—
64C43⋊#95—42no—
65C43⋊#95—42no—
66C43⋊#95—42no—
67C43⋊#95—42no—
68C43⋊#95C2×C414yes—
69C43⋊#95C2×C414yes—
70C25×C43C2311yescharacteristic
71C23×C4×C43—22no—
72C23×C4×C43—22no—
73C23×C4×C43—42no—
74C23×C4×C43—42no—
75C23×C4×C43C2×C414yes—
76C23×C4×C43C2312yes—
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2312yes—
79C23×C4×C43C2311yescharacteristic
80C2×C22⋊C4×C43—24no—
81C2×C22⋊C4×C43—24no—
82C2×C22⋊C4×C43—42no—
83#95×C43—22no—
84#95×C43—22no—
85#95×C43—42no—
86C24×C43—22no—
87C24×C43—21no—
88C24×C43—21no—
89C24×C43—21no—
90C24×C43—21no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—22no—
94C24×C43C22×C412yes—
95C24×C43#4112yes—
96C24×C43#4112yes—
97C24×C43C2411yescharacteristic
98C22×C4×C43—28no—
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
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—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—44no—
119C22×C4×C43—44no—
120C22×C4×C43—48no—
121C22×C4×C43—48no—
122C22×C4×C43C22×C412yes—
123C22×C4×C43C22×C412yes—
124C22×C4×C43#4114yes—
125C22×C4×C43#4112yes—
126C22×C4×C43#4112yes—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43C22×C412yes—
155C22×Dic43C22×C412yes—
156C22×Dic43C22×C412yes—
157C22×Dic43C22×C412yes—
158C22×Dic43#4114yes—
159C22×Dic43#4112yes—
160C22×Dic43#4112yes—
161C22⋊C4×C43—48no—
162C22⋊Dic43—28no—
163C22⋊Dic43—28no—
164C22⋊Dic43—48no—
165C4×Dic43—44no—
166C4×Dic43—44no—
167C4×Dic43—48no—
168C23×C43—22no—
169C23×C43—22no—
170C23×C43—22no—
171C23×C43—22no—
172C23×C43—22no—
173C23×C43—22no—
174C23×C43—22no—
175C23×C43—22no—
176C23×C43—22no—
177C23×C43—22no—
178C23×C43—24no—
179C23×C43—24no—
180C23×C43—24no—
181C23×C43—24no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43#11714yes—
191C23×C43C23×C411yescharacteristic
192C23×C43C2×#4111yescharacteristic
193C23×C43C2×#4111yescharacteristic
194C23×C43C2×#4112yes—
195C23×C43C2×#4111yescharacteristic
196C23×C43C2×#4111yescharacteristic
197C23×C43C2×#4111yescharacteristic
198C23×C43C2×#4112yes—
199C23×C43C2×#4111yescharacteristic
200C23×C43H(5,𝔽2)12yes—
201C23×C43H(5,𝔽2)12yes—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—24no—
205C2×C4×C43—24no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—24no—
210C2×C4×C43—24no—
211C2×C4×C43—24no—
212C2×C4×C43—416no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43#11714yes—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—24no—
230C2×Dic43—24no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—24no—
241C2×Dic43—24no—
242C2×Dic43—24no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43#11714yes—
261#13947—431nomaximal, Sylow
262C22×C43—24no—
263C22×C43—24no—
264C22×C43—24no—
265C22×C43—42no—
266C22×C43—44no—
267C22×C43—44no—
268C22×C43—44no—
269C22×C43—44no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43C2×#11711yescharacteristic
274C22×C43C2×#11711yescharacteristic
275C22×C43C2×#11711yescharacteristic
276C22×C43C4×#4111yescharacteristic
277C22×C43C4×#4111yescharacteristic
278C22×C43#51811yescharacteristic
279C22×C43#51811yescharacteristic
280C22×C43#52912yes—
281C22×C43#52911yescharacteristic
282C22×C43#52911yescharacteristic
283C22×C43#52912yes—
284C22×C43#52911yescharacteristic
285C22×C43#52911yescharacteristic
286C22×C43#53812yes—
287C22×C43#53812yes—
288C22×C43#55112yes—
289C22×C43#55112yes—
290C22×C43#55112yes—
291C22×C43#55312yes—
292C22×C43#55312yes—
293C22×C43#55312yes—
294C22×C43#55312yes—
295C22×C43#55912yes—
296C4×C43—24no—
297C4×C43—42no—
298C4×C43—44no—
299C4×C43—82no—
300Dic43—24no—
301Dic43—44no—
302Dic43—42no—
303Dic43—42no—
304Dic43—42no—
305Dic43—82no—
306C2×C4×C22⋊C4—431no—
307#1443—432no—
308#1440—432no—
309#1437—432no—
310#1434—431no—
311#1434—432no—
312#1434—431no—
313#1434—431no—
314C22⋊#95—431no—
315C22⋊#95D4311yescharacteristic
316C4×#95—431no—
317C2×C43—44no—
318C2×C43#228311yescharacteristic
319C2×C43#229811yescharacteristic
320C2×C43#231211yescharacteristic
321C2×C43#235311yescharacteristic
322C2×C43#235311yescharacteristic
323C2×C43#235311yescharacteristic
324C2×C43#235711yescharacteristic
325C2×C43#257612yes—
326C2×C43#257812yes—
327C2×C43#259512yes—
328C2×C43#259712yes—
329C24×C4C2×D4311yescharacteristic
330C22×C22⋊C4—431no—
331C22×C22⋊C4—431no—
332C22×C22⋊C4—432no—
333C22×C22⋊C4C2×D4312yes—
334C22×C42—431no—
335C22×C42—431no—
336C22×C42—432no—
337C4×C22⋊C4—438no—
338C2×#95—431no—
339C2×#95—431no—
340C2×#95—431no—
341C2×#95—432no—
342C2×#95—431no—
343C2×#95—432no—
344C2×#95—432no—
345C2×#95—432no—
346C2×#95—432no—
347C2×#95—432no—
348C2×#95—432no—
349C2×#95—432no—
350C2×#95C2×D4311yescharacteristic
351C2×#95C2×D4311yescharacteristic
352C2×#95C2×D4312yes—
353C43#1394711yescharacteristic, complemented, Sylow
354C25C22×D4311yescharacteristic
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—42no—
358C23×C4—42no—
359C23×C4—431no—
360C23×C4—431no—
361C23×C4—431no—
362C23×C4—431no—
363C23×C4—432no—
364C23×C4—432no—
365C23×C4C4×D4314yes—
366C23×C4C22×D4312yes—
367C23×C4C22×D4311yescharacteristic
368C23×C4C22×D4312yes—
369C23×C4C22×D4311yescharacteristic
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—434no—
374C2×C22⋊C4—434no—
375C2×C22⋊C4—862no—
376C2×C22⋊C4—862no—
377C2×C22⋊C4—862no—
378C2×C22⋊C4—862no—
379C2×C22⋊C4—864no—
380C2×C22⋊C4—864no—
381C2×C22⋊C4—1722no—
382C2×C42—434no—
383C2×C42—434no—
384C2×C42—864no—
385C2×C42—864no—
386C2×C42—1722no—
387C2×C42—1722no—
388C2×C42—1722no—
389#95—22no—
390#95—22no—
391#95—42no—
392#95—434no—
393#95—434no—
394#95—864no—
395#95—864no—
396#95—864no—
397#95—864no—
398#95—862no—
399#95—862no—
400#95—1722no—
401#95—1722no—
402#95—1722no—
403#95—1722no—
404C24—22no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24C2×C4×D4312yes—
413C24#1062190012yes—
414C24#1062190212yes—
415C24C23×D4311yescharacteristic
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—28no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—48no—
439C22×C4—48no—
440C22×C4—432no—
441C22×C4—432no—
442C22×C4—432no—
443C22×C4—432no—
444C22×C4—432no—
445C22×C4—432no—
446C22×C4—434no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—862no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4C2×C4×D4312yes—
475C22×C4C2×C4×D4312yes—
476C22×C4#1062189814yes—
477C22×C4#1062190012yes—
478C22×C4#1062190012yes—
479C22⋊C4—48no—
480C22⋊C4—868no—
481C22⋊C4—868no—
482C22⋊C4—1728no—
483C42—1724no—
484C42—1724no—
485C42—1728no—
486C23—24no—
487C23—24no—
488C23—24no—
489C23—24no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23#1306328314yes—
509C23C22×C4×D4311yescharacteristic
510C23#41×D4312yes—
511C23#41×D4311yescharacteristic
512C23#41×D4311yescharacteristic
513C23C2×#1062190011yescharacteristic
514C23C2×#1062190011yescharacteristic
515C23C2×#1062190011yescharacteristic
516C23C2×#1062189812yes—
517C23C2×#1062190211yescharacteristic
518C23#1306337012yes—
519C23#1306337012yes—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—416no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—434no—
545C2×C4—864no—
546C2×C4—864no—
547C2×C4—862no—
548C2×C4—862no—
549C2×C4—864no—
550C2×C4—864no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—864no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4#1306328114yes—
579C22—24no—
580C22—24no—
581C22—24no—
582C22—44no—
583C22—42no—
584C22—44no—
585C22—44no—
586C22—42no—
587C22—44no—
588C22—42no—
589C22—42no—
590C22#117×D4311yescharacteristic
591C22C2×#1306328111yescharacteristic
592C22C2×#1306328311yescharacteristic
593C22#1458336711yescharacteristic
594C22C4×#1062189811yescharacteristic
595C22#1458337211yescharacteristic
596C22#1458337211yescharacteristic
597C22#1458342912yes—
598C22#1458343011yescharacteristic
599C22#1458343011yescharacteristic
600C22#1458343112yes—
601C22#1458343511yescharacteristic
602C22#1458343511yescharacteristic
603C22#1458348412yes—
604C22#1458348412yes—
605C22#1458357512yes—
606C22#1458357612yes—
607C22#1458357712yes—
608C22#1458359212yes—
609C22#1458359412yes—
610C22#1458359712yes—
611C22#1458359812yes—
612C22#1458363212yes—
613C4—24no—
614C4—44no—
615C4—42no—
616C4—82no—
617C4—864no—
618C4—3442no—
619C4—1722no—
620C4—1722no—
621C4—1724no—
622C4—1722no—
623C2—44no—
624C2#1913699011yescharacteristic
625C2#1913709111yescharacteristic
626C2#1913719111yescharacteristic
627C2#1913753111yescharacteristic
628C2#1913753211yescharacteristic
629C2#1913753711yescharacteristic
630C2#1913756911yescharacteristic
631C2#1913989812yes—
632C2#1913992612yes—
633C2#1914011512yes—
634C2#1914014312yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC22⋊#95D43
hypocenterC43#13947
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. #19132855C2semidirect
5. #19132821C2semidirect
6. #19132821C2semidirect
7. #19132821C2semidirect
8. #19132820C2semidirect
10. #95×Dic43C2semidirect
18. C4×C22⋊Dic43C4semidirect
353. C43#13947semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic432
#191328552
#191328422
#191328322
#191328212
#191328202
#191328182
#95×Dic432
C43×C22⋊#952
#1394743