Finite Group Databasebeta

← #25133142

Subgroups — #25133142

Order 11008.

1068 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583629C211yesmaximal, characteristic, complemented
2C2×#14583177C211yesmaximal, characteristic
3C2×#14582996C211yesmaximal, characteristic
4#19139951C211yesmaximal, characteristic
5#19135922C211yesmaximal, characteristic, complemented
6#19135920C211yesmaximal, characteristic, complemented
7#19135729C211yesmaximal, characteristic
8#19135566C211yesmaximal, characteristic, complemented
9#19135533C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic
11#19134947C211yesmaximal, characteristic
12#19134852C211yesmaximal, characteristic, complemented
13#19134850C211yesmaximal, characteristic, complemented
14#19134609C211yesmaximal, characteristic, complemented
15C43×#2023C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17#14583629—24no—
18#14583629—24no—
19C2×#13063324—21no—
20C2×#13063324C2211yescharacteristic
21C2×#13063324C2211yescharacteristic
22C2×#13063323—21no—
23C2×#13063323—21no—
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×#13063290—21no—
27C2×#13063290C2211yescharacteristic
28C2×#13063290C2211yescharacteristic
29C2×D4×Dic43C2211yescharacteristic
30#14583177—24no—
31#14582996—24no—
32C2×#13063259C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063235C2211yescharacteristic
41#14582835—21no—
42#14582811—21no—
43#14582802C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582774—21no—
47#14582771—21no—
48#14582764C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86—21no—
65C22×Dic86D411yescharacteristic
66C22×Dic86C2311yescharacteristic
67C23×Dic43—21no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883Q814yescomplemented
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063324—28no—
74#13063324—22no—
75#13063324—22no—
76#13063324—22no—
77#13063324D414yes—
78#13063323—28no—
79#13063323—28no—
80C4×Dic86—22no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84#13063290—28no—
85#13063290—22no—
86#13063290—22no—
87#13063290—22no—
88#13063290D414yes—
89D4×Dic43—22no—
90D4×Dic43—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43D411yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4D411yescharacteristic
103C2×Dic43⋊C4D411yescharacteristic
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111C2×C4×Dic43C2311yescharacteristic
112#13063259—22no—
113#13063258—22no—
114#13063258—22no—
115Dic43⋊C8—22no—
116#13063250—22no—
117#13063250—22no—
118#13063248—22no—
119#13063246—22no—
120#13063235—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×Q8×C43—21no—
126C22×D4×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C4⋊Q8×C43—22no—
130C4⋊Q8×C43—22no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138#102×C43—22no—
139#102×C43—22no—
140C24×C43—21no—
141C2×Q8×C43—24no—
142C2×Q8×C43—81no—
143C2×Q8×C43—81no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C2×Q812yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—42no—
161C22×Dic43—81no—
162C22×Dic43—81no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C2×Dic86—22no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—22no—
172C2×Dic86—22no—
173C2×Dic86—24no—
174C2×Dic86—24no—
175C2×Dic86—81no—
176C2×Dic86—81no—
177C2×Dic86—81no—
178C2×Dic86—81no—
179C2×Dic86C2×D412yes—
180C2×Dic86C2×Q812yes—
181C2×Dic86#4112yes—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C4⋊C4×C43—24no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43C2×D412yes—
194C4⋊C4×C43C2×D412yes—
195C22⋊C4×C43—42no—
196C22⋊C4×C43—81no—
197C42×C43—21no—
198C42×C43—21no—
199C22⋊Dic43—42no—
200C22⋊Dic43—42no—
201C22⋊Dic43—81no—
202#10621883—28no—
203C4⋊Dic43—21no—
204C4⋊Dic43—22no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—81no—
210C4⋊Dic43C2×D412yes—
211Dic43⋊C4—24no—
212Dic43⋊C4—24no—
213Dic43⋊C4—24no—
214Dic43⋊C4—24no—
215Dic43⋊C4—24no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218Dic43⋊C4—81no—
219C4×Dic43—24no—
220C4×Dic43—24no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—24no—
224C4×Dic43C2×D412yes—
225C4×Dic43C2×D412yes—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8C2×Q812yes—
232C23×C43—22no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43C22×D411yescharacteristic
240Q8×C43—84no—
241D4×C43—22no—
242D4×C43—22no—
243D4×C43—41no—
244D4×C43—41no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43#13712yes—
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×Q811yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C432−1+411yescharacteristic
265C2×C4×C432−1+411yescharacteristic
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—22no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—84no—
288C2×Dic43#12012yes—
289C2×Dic43#12012yes—
290C2×Dic43#13712yes—
291Dic86—28no—
292Dic86—22no—
293Dic86—22no—
294Dic86—22no—
295Dic86—84no—
296Dic86—84no—
297Dic86C22⋊Q814yes—
298C8×C43—41no—
299C8×C43—41no—
300C43⋊C8—22no—
301C43⋊C8—41no—
302#24341—431nomaximal, Sylow
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43C2×#12011yescharacteristic
311C22×C43#54811yescharacteristic
312C22×C43D4×Q811yescharacteristic
313C22×C43C2×#13711yescharacteristic
314C22×C43C2×#13711yescharacteristic
315C22×C43#57611yescharacteristic
316C22×C43#57611yescharacteristic
317C4×C43—22no—
318C4×C43—42no—
319C4×C43—42no—
320C4×C43—41no—
321C4×C43—81no—
322C4×C43C2×C22⋊Q811yescharacteristic
323C4×C43#53611yescharacteristic
324C4×C43#54811yescharacteristic
325C4×C43D4×Q811yescharacteristic
326Dic43—24no—
327Dic43—22no—
328Dic43—22no—
329Dic43—22no—
330Dic43—41no—
331Dic43—42no—
332Dic43—81no—
333Dic43—81no—
334C2×Q82—431no—
335C2×#474—431no—
336C2×#440—431no—
337#2580—431no—
338#2057—431no—
339#2057—431no—
340#2023—431no—
341#2023D4311yescharacteristic
342#1993—431no—
343#1985—431no—
344#1880—431no—
345#1880—431no—
346#1863—431no—
347#1863—431no—
348#1805—431no—
349C2×C43—82no—
350C2×C43#240911yescharacteristic
351C2×C43#300411yescharacteristic
352C2×C43#300811yescharacteristic
353C2×C43#337511yescharacteristic
354C2×C43#337511yescharacteristic
355C2×C43#338511yescharacteristic
356C2×C43#338511yescharacteristic
357C22×SD16—431no—
358Q82—864no—
359Q82—864no—
360C2×C4⋊Q8—431no—
361C2×C4⋊Q8—431no—
362C2×C4⋊Q8—861no—
363C2×C4⋊Q8—861no—
364C2×C4⋊Q8—861no—
365C2×C4⋊Q8C2×D4311yescharacteristic
366C2×C4×Q8—431no—
367C2×C4×Q8—431no—
368C2×C4×Q8—431no—
369C2×C4×Q8—431no—
370C2×C4×Q8—861no—
371C2×C4×D4—431no—
372#474—864no—
373#440—864no—
374C2×#107—431no—
375C2×#107—431no—
376C2×#107—431no—
377C2×C4⋊C8—431no—
378C2×#103—431no—
379C2×#103—431no—
380C2×#103—431no—
381C2×#102—431no—
382C2×#102C2×D4311yescharacteristic
383C2×#102C2×D4311yescharacteristic
384C2×#97—431no—
385#399—861no—
386#393—861no—
387#390—431no—
388#390C2×D4311yescharacteristic
389#389—431no—
390#389—431no—
391#385—861no—
392#385—861no—
393#382—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340C2×D4311yescharacteristic
399#340C2×D4311yescharacteristic
400#336—431no—
401#336—431no—
402#336—431no—
403#336C2×D4311yescharacteristic
404C43#2434111yescharacteristic, complemented, Sylow
405C22×Q8—21no—
406C22×Q8—431no—
407C22×Q8—431no—
408C22×Q8—861no—
409C22×Q8—861no—
410C22×D4C22×D4311yescharacteristic
411C23×C4—861no—
412C2×SD16—434no—
413C2×SD16—862no—
414C2×SD16—862no—
415C22×C8—431no—
416C22×C8—431no—
417C22×C8C22×D4311yescharacteristic
418C22×C8C22×D4311yescharacteristic
419C4⋊Q8—22no—
420C4⋊Q8—22no—
421C4⋊Q8—434no—
422C4⋊Q8—862no—
423C4⋊Q8—862no—
424C4⋊Q8—868no—
425C4⋊Q8—868no—
426C4⋊Q8—868no—
427C4⋊Q8—862no—
428C4×Q8—434no—
429C4×Q8—862no—
430C4×Q8—862no—
431C4×Q8—862no—
432C4×Q8—862no—
433C4×Q8—862no—
434C4×Q8—862no—
435C4×Q8—868no—
436C4×Q8—862no—
437C4×D4—862no—
438C4×D4—862no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4C22×D4311yescharacteristic
454C2×C4⋊C4C22×D4311yescharacteristic
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—861no—
459C2×C22⋊C4—861no—
460C2×C22⋊C4—861no—
461C2×C42—431no—
462C2×C42—431no—
463C2×C42—861no—
464C2×C42—861no—
465C2×C42—861no—
466C2×C42C22×D4311yescharacteristic
467#107—862no—
468#107—862no—
469#107—862no—
470C4⋊C8—862no—
471#103—862no—
472#103—862no—
473#103—862no—
474#102—22no—
475#102—22no—
476#102—862no—
477#97—862no—
478#95—861no—
479#95—861no—
480#95—861no—
481#95—861no—
482C24—21no—
483C2×Q8—24no—
484C2×Q8—81no—
485C2×Q8—81no—
486C2×Q8—432no—
487C2×Q8—432no—
488C2×Q8—432no—
489C2×Q8—862no—
490C2×Q8—862no—
491C2×Q8—864no—
492C2×Q8—864no—
493C2×Q8—862no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—3441no—
498C2×Q8—3441no—
499C2×Q8—3441no—
500C2×Q8—3441no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4Q8×D4312yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—3441no—
519C22×C4—3441no—
520C22×C4—1722no—
521C22×C4D4×D4311yescharacteristic
522C22×C4D4×D4311yescharacteristic
523C22×C4C23×D4311yescharacteristic
524SD16—868no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—432no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C4⋊C4—24no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—432no—
543C4⋊C4—862no—
544C4⋊C4—862no—
545C4⋊C4—862no—
546C4⋊C4—864no—
547C4⋊C4—864no—
548C4⋊C4—864no—
549C4⋊C4—864no—
550C4⋊C4—864no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—3441no—
557C4⋊C4—3441no—
558C4⋊C4D4×D4312yes—
559C4⋊C4D4×D4312yes—
560C22⋊C4—42no—
561C22⋊C4—81no—
562C22⋊C4—3441no—
563C22⋊C4—1722no—
564C22⋊C4—1722no—
565C42—21no—
566C42—21no—
567C42—432no—
568C42—432no—
569C42—864no—
570C42—864no—
571C42—864no—
572C42—861no—
573C42—861no—
574C23—22no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23C2×D4×D4311yescharacteristic
582Q8—84no—
583Q8—434no—
584Q8—868no—
585Q8—862no—
586Q8—862no—
587Q8—862no—
588Q8—3444no—
589Q8—3444no—
590D4—22no—
591D4—22no—
592D4—41no—
593D4—41no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—432no—
609C2×C4—432no—
610C2×C4—432no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—861no—
614C2×C4—862no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—862no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—3444no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4#1306335412yes—
634C2×C4C2×D4×D4311yescharacteristic
635C2×C4C2×D4×D4311yescharacteristic
636C2×C4C2×Q8×D4311yescharacteristic
637C2×C4#41×D4311yescharacteristic
638C2×C4#1306337211yescharacteristic
639C2×C4#1306337211yescharacteristic
640C8—41no—
641C8—41no—
642C8—862no—
643C8—1721no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22#120×D4311yescharacteristic
652C22#1458355711yescharacteristic
653C22#1458356211yescharacteristic
654C22#137×D4311yescharacteristic
655C22C2×#1306335411yescharacteristic
656C22#1458370011yescharacteristic
657C22#1458370311yescharacteristic
658C4—22no—
659C4—41no—
660C4—42no—
661C4—42no—
662C4—81no—
663C4—862no—
664C4—862no—
665C4—864no—
666C4—862no—
667C4—3441no—
668C4—3441no—
669C4—1721no—
670C4—1722no—
671C4C22⋊Q8×D4311yescharacteristic
672C4#1458346911yescharacteristic
673C4#1458355711yescharacteristic
674C4#1458356211yescharacteristic
675C2—82no—
676C2#1913795311yescharacteristic
677C2#1914382611yescharacteristic
678C2#1914385811yescharacteristic
679C2#1914740611yescharacteristic
680C2#1914741411yescharacteristic
681C2#1914750011yescharacteristic
682C2#1914750911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2023C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2023D43
hypocenterC43#24341
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. C2×#14583629C2semidirect
5. #19135922C2semidirect
6. #19135920C2semidirect
8. #19135566C2semidirect
9. #19135533C2semidirect
12. #19134852C2semidirect
13. #19134850C2semidirect
14. #19134609C2semidirect
70. C2×#10621883Q8semidirect
404. C43#24341semidirect

Maximal subgroups

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

subgroupindex
C2×#145836292
C2×#145831772
C2×#145829962
#191399512
#191359222
#191359202
#191357292
#191355662
#191355332
#191349532
#191349472
#191348522
#191348502
#191346092
C43×#20232
#2434143