Finite Group Databasebeta

← #25196583

Subgroups — #25196583

Order 11008.

912 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142945C211yesmaximal, characteristic, complemented
2#121×Dic43C211yesmaximal, characteristic
3#19136156C211yesmaximal, characteristic, complemented
4#19136121C211yesmaximal, characteristic, complemented
5#19135922C211yesmaximal, characteristic, complemented
6#19135729C211yesmaximal, characteristic, complemented
7#19135169C211yesmaximal, characteristic, complemented
8#19135165C211yesmaximal, characteristic, complemented
9#19135024C211yesmaximal, characteristic
10#19134844C211yesmaximal, characteristic, complemented
11#19134840C211yesmaximal, characteristic, complemented
12#19134624C211yesmaximal, characteristic, complemented
13#19134622C211yesmaximal, characteristic, complemented
14C2×#14582653C211yesmaximal, characteristic, complemented
15C43×#1893C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063302—21no—
19C2×D4×Dic43—21no—
20C2×D4×Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063259C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28#14582803—21no—
29#14582802C2211yescharacteristic
30#14582798C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582796—21no—
33#14582795C2211yescharacteristic
34#14582792—21no—
35#14582779—21no—
36#14582768C2211yescharacteristic
37#14582759C2211yescharacteristic
38#14582759C2211yescharacteristic
39#14582757—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C22⋊C4×Dic43—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C23×C8×C43C2211yescharacteristic
53C2×#121×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C23×Dic43—21no—
61C23×Dic43D411yescharacteristic
62C23×Dic43D411yescharacteristic
63C22×C43⋊C8—22no—
64C22×C43⋊C8—22no—
65C22×C43⋊C8—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063324—41no—
69#13063324—41no—
70#13063302—44no—
71D4×Dic43—41no—
72D4×Dic43—41no—
73D4×Dic43—44no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—41no—
91C2×C4×Dic43—41no—
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063259—22no—
97#13063259—41no—
98#13063258—22no—
99#13063258—41no—
100#13063246—22no—
101#13063246—41no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×D4×C43—21no—
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43C2311yescharacteristic
111C22×C8×C43—22no—
112C22×C8×C43—22no—
113C22×C8×C43—41no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116#121×C43—22no—
117#121×C43Q814yescomplemented
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123#102×C43—22no—
124#102×C43—41no—
125#95×C43—21no—
126C24×C43—21no—
127C24×C43C2×D411yescharacteristic
128C2×D4×C43—21no—
129C2×D4×C43—24no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—42no—
135C2×D4×C43—42no—
136C2×D4×C43C2×Q812yes—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×Q812yes—
146C22×C4×C43#4112yes—
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—41no—
155C22×Dic43—41no—
156C22×Dic43—41no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43D814yes—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C2×Dic86—42no—
166C2×Dic86—42no—
167C2×Dic86—42no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—44no—
174C2×C8×C43#4112yes—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43C2×Q812yes—
181C22⋊C4×C43—24no—
182C22⋊C4×C43—42no—
183C22⋊Dic43—42no—
184C22⋊Dic43—42no—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187C22⋊Dic43—42no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—42no—
197C4⋊Dic43—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—41no—
207C4×Dic43—41no—
208C4×Dic43—42no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—44no—
215C2×C43⋊C8#4112yes—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—22no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43C22⋊Q812yes—
228C23×C43C2×D812yes—
229C23×C43#13712yes—
230C23×C43C22×D411yescharacteristic
231D4×C43—22no—
232D4×C43—22no—
233D4×C43—48no—
234D4×C43—41no—
235D4×C43—41no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43C22⋊Q812yes—
252C2×C4×C43C22×Q811yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—44no—
268C2×Dic43—44no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—84no—
282C2×Dic43C2×D812yes—
283C2×Dic43C2×D812yes—
284C2×Dic43#13512yes—
285Dic86—84no—
286C8×C43—22no—
287C8×C43—41no—
288C43⋊C8—22no—
289C43⋊C8—41no—
290#29157—431nomaximal, Sylow
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43#47414yes—
305C22×C43C2×C22⋊Q811yescharacteristic
306C22×C43#53211yescharacteristic
307C22×C43#53411yescharacteristic
308C22×C43C22×D811yescharacteristic
309C22×C43C2×#13511yescharacteristic
310C22×C43C2×#13711yescharacteristic
311C22×C43#57511yescharacteristic
312C4×C43—22no—
313C4×C43—42no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43#55111yescharacteristic
317C4×C43#55111yescharacteristic
318C4×C43#55411yescharacteristic
319C4×C43#55411yescharacteristic
320Dic43—22no—
321Dic43—22no—
322Dic43—22no—
323Dic43—41no—
324Dic43—81no—
325Dic43—81no—
326Dic43—81no—
327Dic43—81no—
328#2857—431no—
329C4×#121—431no—
330#2099—431no—
331#2093—431no—
332#2057—431no—
333#2023—431no—
334#1918—431no—
335#1918—431no—
336#1893—431no—
337#1893D4311yescharacteristic
338#1862—431no—
339#1862—431no—
340#1808—431no—
341#1808—431no—
342C2×#336—431no—
343C2×C43—24no—
344C2×C43—82no—
345C2×C43#256411yescharacteristic
346C2×C43C2×#47411yescharacteristic
347C2×C43#307611yescharacteristic
348C2×C43#316911yescharacteristic
349C2×C43#318111yescharacteristic
350C2×C43#318611yescharacteristic
351C2×C43#319011yescharacteristic
352C23×C8—431no—
353C23×C8C2×D4311yescharacteristic
354C2×C4⋊Q8—431no—
355C2×C22⋊Q8—861no—
356C2×#121C2×D4311yescharacteristic
357C2×C4×D4—431no—
358C2×C4×D4—861no—
359C22×C42—431no—
360C2×#107—431no—
361C2×#107—431no—
362C2×#107—431no—
363C2×#107—431no—
364C2×#102—431no—
365C2×#102—431no—
366C2×#102C2×D4311yescharacteristic
367C2×#102C2×D4311yescharacteristic
368#391—861no—
369#390—431no—
370#389—431no—
371#389—431no—
372#389—431no—
373#389—861no—
374#388—861no—
375#386—861no—
376#384—431no—
377#380—431no—
378#380—431no—
379#380—861no—
380#380C2×D4311yescharacteristic
381C4×C4⋊C4—431no—
382C4×C22⋊C4—861no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340C2×D4311yescharacteristic
390#340C2×D4311yescharacteristic
391#336—431no—
392#336—431no—
393#336—431no—
394#336—431no—
395C43#2915711yescharacteristic, complemented, Sylow
396C22×Q8—861no—
397C22×D4—21no—
398C22×D4C22×D4311yescharacteristic
399C23×C4—431no—
400C23×C4—431no—
401C23×C4—861no—
402C23×C4C22×D4311yescharacteristic
403C22×C8—22no—
404C22×C8—22no—
405C22×C8—41no—
406C22×C8—431no—
407C22×C8—431no—
408C22×C8—862no—
409C22×C8—862no—
410C22×C8—1721no—
411C22×C8C22×D4311yescharacteristic
412C22×C8C22×D4311yescharacteristic
413C4⋊Q8—1721no—
414C4⋊Q8—1721no—
415C22⋊Q8—1724no—
416#121—22no—
417#121Dic8614yescomplemented
418C4×D4—1721no—
419C4×D4—1721no—
420C4×D4—1724no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—861no—
446C2×C42—1721no—
447C2×C42—1721no—
448#107—862no—
449#107—862no—
450#107—1721no—
451#107—1721no—
452#102—22no—
453#102—41no—
454#102—862no—
455#102—1721no—
456#95—21no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463C24—21no—
464C24D4×D4311yescharacteristic
465C2×Q8—1722no—
466C2×Q8—1722no—
467C2×Q8—1722no—
468C2×D4—24no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4C2×Dic8612yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—434no—
488C22×C4—431no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—1722no—
496C22×C4—1721no—
497C22×C4—1721no—
498C22×C4—1721no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4C2×Dic8612yes—
502C22×C4D4×D4311yescharacteristic
503C22×C4#1062190012yes—
504C22×C4C23×D4311yescharacteristic
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—44no—
511C2×C8—432no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—1724no—
518C2×C8#1062190012yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4C2×Dic8612yes—
539C22⋊C4—24no—
540C22⋊C4—42no—
541C22⋊C4—1722no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C42—861no—
547C42—861no—
548C42—861no—
549C42—861no—
550C42—1721no—
551C42—1721no—
552C42—1722no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—22no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23#1306330212yes—
565C23D8×D4312yes—
566C23#1306335412yes—
567C23C2×D4×D4311yescharacteristic
568Q8—3444no—
569D4—22no—
570D4—22no—
571D4—48no—
572D4—41no—
573D4—41no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—3444no—
602C2×C4—1724no—
603C2×C4—1724no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4#1306330212yes—
617C2×C4C22×Dic8611yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4C2×#1062190011yescharacteristic
620C2×C4C2×#1062190011yescharacteristic
621C2×C4#1306337011yescharacteristic
622C2×C4#1306337111yescharacteristic
623C8—22no—
624C8—41no—
625C8—862no—
626C8—1721no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22#1458317714yes—
641C22C2×#1306330211yescharacteristic
642C22#1458344411yescharacteristic
643C22#1458345711yescharacteristic
644C22C2×D8×D4311yescharacteristic
645C22#135×D4311yescharacteristic
646C22C2×#1306335411yescharacteristic
647C22#1458369611yescharacteristic
648C4—22no—
649C4—42no—
650C4—81no—
651C4—81no—
652C4—862no—
653C4—862no—
654C4—862no—
655C4—3441no—
656C4—3441no—
657C4—3441no—
658C4—3441no—
659C4—1721no—
660C4#1458357211yescharacteristic
661C4#1458358011yescharacteristic
662C4#1458360611yescharacteristic
663C4#1458360811yescharacteristic
664C2—24no—
665C2—82no—
666C2#1913977911yescharacteristic
667C2C2×#1458317711yescharacteristic
668C2#1914437911yescharacteristic
669C2#1914516911yescharacteristic
670C2#1914529711yescharacteristic
671C2#1914534211yescharacteristic
672C2#1914537111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1893C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#1893D43
hypocenterC43#29157
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
1. #19142945C2semidirect
3. #19136156C2semidirect
4. #19136121C2semidirect
5. #19135922C2semidirect
6. #19135729C2semidirect
7. #19135169C2semidirect
8. #19135165C2semidirect
10. #19134844C2semidirect
11. #19134840C2semidirect
12. #19134624C2semidirect
13. #19134622C2semidirect
14. C2×#14582653C2semidirect
117. #121×C43Q8semidirect
395. C43#29157semidirect
417. #121Dic86semidirect

Maximal subgroups

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

subgroupindex
#191429452
#121×Dic432
#191361562
#191361212
#191359222
#191357292
#191351692
#191351652
#191350242
#191348442
#191348402
#191346242
#191346222
C2×#145826532
C43×#18932
#2915743