Finite Group Databasebeta

← #25022894

Subgroups — #25022894

Order 11008.

1470 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582792C211yesmaximal, characteristic
2C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
3#19132863C211yesmaximal, characteristic, complemented
4#19132852C211yesmaximal, characteristic, complemented
5#19132840C211yesmaximal, characteristic
6#19132832C212yesmaximal
7#19132832C212yesmaximal
8#19132829C212yesmaximal, complemented
9#19132820C212yesmaximal, complemented
10#95×Dic43C211yesmaximal, characteristic, complemented
11C2×C43×#397C211yesmaximal, characteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×C22⋊Dic43C2211yescharacteristic
15C22×C22⋊Dic43C2211yescharacteristic
16C22×C22⋊Dic43C2212yes—
17C22×C4×Dic43C2212yes—
18C22×C4×Dic43C2211yescharacteristic
19C22×C4×Dic43C2212yes—
20#14582792—24no—
21C4⋊C4×Dic43—24no—
22C2×C43⋊#95C2211yescharacteristic
23C2×C43⋊#95C2211yescharacteristic
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C22×C4⋊C4×C43C2211yescharacteristic
33C22×C22⋊C4×C43C2211yescharacteristic
34C22×C22⋊C4×C43C2212yes—
35C43×#397C418yescomplemented
36C2×#95×C43C2211yescharacteristic
37C2×#95×C43C2212yes—
38C23×Dic43C2311yescharacteristic
39C23×Dic43C2311yescharacteristic
40C23×Dic43C2312yes—
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C2×C4⋊Dic43—22no—
45C2×C4⋊Dic43—24no—
46C2×C4⋊Dic43—22no—
47C2×C4⋊Dic43—24no—
48C2×C22⋊Dic43—22no—
49C2×C22⋊Dic43—22no—
50C2×C22⋊Dic43—24no—
51C2×C22⋊Dic43—24no—
52C2×C22⋊Dic43—24no—
53C2×C22⋊Dic43—24no—
54C2×C22⋊Dic43—42no—
55C2×C4×Dic43—24no—
56C2×C4×Dic43—24no—
57C2×C4×Dic43—24no—
58C2×C4×Dic43—24no—
59C2×C4×Dic43—42no—
60C2×C4×Dic43—42no—
61C2×C4×Dic43—42no—
62C2×C4×Dic43D414yes—
63C43⋊#95—22no—
64C43⋊#95—22no—
65C43⋊#95—22no—
66C43⋊#95—24no—
67C43⋊#95—24no—
68C43⋊#95—24no—
69C43⋊#95—24no—
70C43⋊#95—42no—
71C43⋊#95—42no—
72C43⋊#95—42no—
73C25×C43C2311yescharacteristic
74C23×C4×C43C2312yes—
75C23×C4×C43C2312yes—
76C23×C4×C43C2311yescharacteristic
77C23×C4×C43C2311yescharacteristic
78C2×C4⋊C4×C43—22no—
79C2×C4⋊C4×C43—22no—
80C2×C4⋊C4×C43C2×C414yes—
81C2×C22⋊C4×C43—22no—
82C2×C22⋊C4×C43—22no—
83C2×C22⋊C4×C43—42no—
84C2×C22⋊C4×C43—42no—
85C2×C22⋊C4×C43C2×C414yes—
86C2×C22⋊C4×C43C2×C418yes—
87#95×C43C2×C418yes—
88#95×C43C2×C414yes—
89C24×C43—21no—
90C24×C43—21no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—22no—
94C24×C43—22no—
95C24×C43—21no—
96C24×C43—21no—
97C24×C43—21no—
98C24×C43—21no—
99C24×C43C22×C412yes—
100C24×C43C2411yescharacteristic
101C22×C4×C43—21no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—21no—
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—22no—
119C22×C4×C43C22×C412yes—
120C22×C4×C43C22×C414yes—
121C22×C4×C43C22×C414yes—
122C22×C4×C43C22×C412yes—
123C22×C4×C43C2×D412yes—
124C22×C4×C43#4112yes—
125C22×Dic43—22no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43C2×D412yes—
154C22×Dic43C2×D412yes—
155C22×Dic43#4114yes—
156C22×Dic43#4114yes—
157C22×Dic43#4114yes—
158C22×Dic43#4114yes—
159C4⋊C4×C43—28no—
160C22⋊C4×C43—28no—
161C22⋊C4×C43—48no—
162C22⋊Dic43—48no—
163C22⋊Dic43—44no—
164C22⋊Dic43—44no—
165C4⋊Dic43—28no—
166C4⋊Dic43—44no—
167C4×Dic43—28no—
168C4×Dic43—48no—
169C4×Dic43—48no—
170C23×C43—22no—
171C23×C43—24no—
172C23×C43—24no—
173C23×C43—22no—
174C23×C43—22no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43—41no—
178C23×C43—42no—
179C23×C43—42no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43C23×C411yescharacteristic
194C23×C43C22×D411yescharacteristic
195C23×C43C2×#4112yes—
196C23×C43C2×#4112yes—
197C23×C43C2×#4112yes—
198C23×C43C2×#4112yes—
199C23×C43C2×#4111yescharacteristic
200C23×C43H(5,𝔽2)11yescharacteristic
201C23×C43H(5,𝔽2)11yescharacteristic
202C23×C43H(5,𝔽2)11yescharacteristic
203C23×C432−1+411yescharacteristic
204C2×C4×C43—24no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—24no—
208C2×C4×C43—22no—
209C2×C4×C43—24no—
210C2×C4×C43—24no—
211C2×C4×C43—24no—
212C2×C4×C43—24no—
213C2×C4×C43—24no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—41no—
217C2×C4×C43—42no—
218C2×C4×C43—41no—
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—42no—
227C2×C4×C43C4×D414yes—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—24no—
233C2×Dic43—24no—
234C2×Dic43—24no—
235C2×Dic43—24no—
236C2×Dic43—24no—
237C2×Dic43—24no—
238C2×Dic43—24no—
239C2×Dic43—24no—
240C2×Dic43—24no—
241C2×Dic43—24no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43#12314yes—
261C2×Dic43#12414yes—
262#14249—431nomaximal, Sylow
263C22×C43—42no—
264C22×C43—44no—
265C22×C43—44no—
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—82no—
273C22×C43—82no—
274C22×C43C2×C4×D411yescharacteristic
275C22×C43C4×#4112yes—
276C22×C43C4×#4112yes—
277C22×C43#51811yescharacteristic
278C22×C43#52011yescharacteristic
279C22×C43C2×#12311yescharacteristic
280C22×C43#52511yescharacteristic
281C22×C43C2×#12411yescharacteristic
282C22×C43#52912yes—
283C22×C43#52912yes—
284C22×C43#53211yescharacteristic
285C22×C43#53511yescharacteristic
286C22×C43#53711yescharacteristic
287C22×C43#54011yescharacteristic
288C22×C43#54211yescharacteristic
289C22×C43#55112yes—
290C22×C43#55112yes—
291C22×C43#55212yes—
292C22×C43#55312yes—
293C22×C43#55312yes—
294C22×C43#55312yes—
295C22×C43#55612yes—
296C22×C43#55912yes—
297C4×C43—24no—
298C4×C43—44no—
299C4×C43—44no—
300C4×C43—42no—
301Dic43—24no—
302Dic43—24no—
303Dic43—44no—
304Dic43—44no—
305Dic43—81no—
306Dic43—81no—
307C2×#397D4311yescharacteristic
308C2×#388—431no—
309C2×C4×C4⋊C4—431no—
310#1445—431no—
311#1442—431no—
312#1439—431no—
313#1437—432no—
314#1437—432no—
315#1436—432no—
316#1434—432no—
317C4×#95—431no—
318C2×C43—82no—
319C2×C43C4×#12311yescharacteristic
320C2×C43C4×#12411yescharacteristic
321C2×C43#232411yescharacteristic
322C2×C43#237312yes—
323C2×C43#237412yes—
324C2×C43#249811yescharacteristic
325C2×C43#250411yescharacteristic
326C2×C43#251612yes—
327C2×C43#252512yes—
328C2×C43#259211yescharacteristic
329C2×C43#260311yescharacteristic
330C22×C4⋊C4—431no—
331C22×C4⋊C4—431no—
332C22×C4⋊C4C2×D4311yescharacteristic
333C22×C22⋊C4—431no—
334C22×C22⋊C4—431no—
335C22×C22⋊C4—432no—
336C22×C22⋊C4C2×D4311yescharacteristic
337C22×C22⋊C4C2×D4312yes—
338C22×C42—431no—
339C22×C42—432no—
340C22×C42—432no—
341#397Dic4318yescomplemented
342#388—864no—
343C4×C4⋊C4—864no—
344C2×#95—432no—
345C2×#95—431no—
346C2×#95—431no—
347C2×#95—432no—
348C2×#95—432no—
349C2×#95—432no—
350C2×#95—431no—
351C2×#95—432no—
352C2×#95—432no—
353C2×#95—432no—
354C2×#95C2×D4311yescharacteristic
355C2×#95C2×D4312yes—
356C43#1424911yescharacteristic, complemented, Sylow
357C25C22×D4311yescharacteristic
358C23×C4—431no—
359C23×C4—431no—
360C23×C4—432no—
361C23×C4—432no—
362C23×C4—431no—
363C23×C4—431no—
364C23×C4C22×D4311yescharacteristic
365C23×C4C22×D4312yes—
366C23×C4C22×D4312yes—
367C23×C4C22×D4311yescharacteristic
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—864no—
371C2×C4⋊C4—862no—
372C2×C4⋊C4—864no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4C2×Dic4314yes—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—864no—
380C2×C22⋊C4—864no—
381C2×C22⋊C4—864no—
382C2×C22⋊C4—864no—
383C2×C22⋊C4—862no—
384C2×C22⋊C4—862no—
385C2×C22⋊C4—1722no—
386C2×C22⋊C4C2×Dic4314yes—
387C2×C22⋊C4C2×Dic4318yes—
388C2×C42—434no—
389C2×C42—864no—
390C2×C42—864no—
391C2×C42—864no—
392C2×C42—864no—
393C2×C42—1722no—
394C2×C42—1722no—
395C2×C42—1722no—
396#95—864no—
397#95—864no—
398#95—864no—
399#95—864no—
400#95—862no—
401#95—862no—
402#95—862no—
403#95—1722no—
404#95—1722no—
405#95—1722no—
406#95C2×Dic4318yes—
407#95C2×Dic4314yes—
408C24—21no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24C22×Dic4312yes—
419C24C23×D4311yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—432no—
439C22×C4—432no—
440C22×C4—434no—
441C22×C4—434no—
442C22×C4—434no—
443C22×C4—434no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4—862no—
461C22×C4—862no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4D4×D4312yes—
473C22×C4#1062190012yes—
474C22×C4C22×Dic4312yes—
475C22×C4C22×Dic4314yes—
476C22×C4C22×Dic4314yes—
477C22×C4C22×Dic4312yes—
478C4⋊C4—28no—
479C4⋊C4—868no—
480C4⋊C4—1724no—
481C22⋊C4—28no—
482C22⋊C4—48no—
483C22⋊C4—1724no—
484C22⋊C4—1724no—
485C22⋊C4—1728no—
486C42—868no—
487C42—1728no—
488C42—1728no—
489C23—22no—
490C23—24no—
491C23—24no—
492C23—22no—
493C23—22no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—42no—
506C23—42no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23C23×Dic4311yescharacteristic
513C23C2×D4×D4311yescharacteristic
514C23#41×D4312yes—
515C23#41×D4312yes—
516C23#41×D4312yes—
517C23#41×D4312yes—
518C23C2×#1062190011yescharacteristic
519C23#1306337011yescharacteristic
520C23#1306337011yescharacteristic
521C23#1306337111yescharacteristic
522C23#1306337211yescharacteristic
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—434no—
547C2×C4—434no—
548C2×C4—864no—
549C2×C4—864no—
550C2×C4—864no—
551C2×C4—864no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—864no—
557C2×C4—864no—
558C2×C4—864no—
559C2×C4—864no—
560C2×C4—864no—
561C2×C4—864no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4D4×Dic4314yes—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—44no—
585C22—44no—
586C22—81no—
587C22—82no—
588C22—81no—
589C22—82no—
590C22—81no—
591C22—81no—
592C22C2×D4×Dic4311yescharacteristic
593C22#41×Dic4312yes—
594C22#41×Dic4312yes—
595C22#1458337411yescharacteristic
596C22#1458338211yescharacteristic
597C22#123×D4311yescharacteristic
598C22#1458340711yescharacteristic
599C22#124×D4311yescharacteristic
600C22#1458342612yes—
601C22#1458342812yes—
602C22#1458344811yescharacteristic
603C22#1458346511yescharacteristic
604C22#1458347811yescharacteristic
605C22#1458350211yescharacteristic
606C22#1458351611yescharacteristic
607C22#1458357412yes—
608C22#1458357712yes—
609C22#1458358512yes—
610C22#1458359412yes—
611C22#1458359412yes—
612C22#1458360012yes—
613C22#1458361612yes—
614C22#1458363312yes—
615C4—24no—
616C4—44no—
617C4—42no—
618C4—44no—
619C4—864no—
620C4—864no—
621C4—3441no—
622C4—3441no—
623C4—1724no—
624C4—1724no—
625C2—82no—
626C2#123×Dic4311yescharacteristic
627C2#124×Dic4311yescharacteristic
628C2#1913729011yescharacteristic
629C2#1913771912yes—
630C2#1913773112yes—
631C2#1913904211yescharacteristic
632C2#1913908211yescharacteristic
633C2#1913922412yes—
634C2#1913934712yes—
635C2#1914007911yescharacteristic
636C2#1914022511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#397C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#397D43
hypocenterC43#14249
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic43C2semidirect
3. #19132863C2semidirect
4. #19132852C2semidirect
8. #19132829C2semidirect
9. #19132820C2semidirect
10. #95×Dic43C2semidirect
35. C43×#397C4semidirect
341. #397Dic43semidirect
356. C43#14249semidirect

Maximal subgroups

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

subgroupindex
C2×#145827922
C2×C4⋊C4×Dic432
#191328632
#191328522
#191328402
#191328322
#191328292
#191328202
#95×Dic432
C2×C43×#3972
#1424943