Finite Group Databasebeta

← #25155461

Subgroups — #25155461

Order 11008.

818 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583307C211yesmaximal, characteristic, complemented
2C2×#14582942C211yesmaximal, characteristic
3#19138302C211yesmaximal, characteristic
4#19138298C211yesmaximal, characteristic
5#19136075C211yesmaximal, characteristic, complemented
6#19136069C211yesmaximal, characteristic, complemented
7#19135932C211yesmaximal, characteristic, complemented
8#19135926C211yesmaximal, characteristic, complemented
9#19135332C211yesmaximal, characteristic, complemented
10#19135327C211yesmaximal, characteristic, complemented
11#19134790C211yesmaximal, characteristic
12#19134750C211yesmaximal, characteristic, complemented
13#19134626C211yesmaximal, characteristic
14#19134381C211yesmaximal, characteristic
15C43×#1854C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063316C2211yescharacteristic
19C2×#13063302—21no—
20C22×C4⋊Dic43C2211yescharacteristic
21#14583307—24no—
22#14582942—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582835—21no—
34#14582833—21no—
35#14582822—21no—
36#14582820—21no—
37#14582798C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582797—21no—
40#14582795C2211yescharacteristic
41#14582795C2211yescharacteristic
42#14582783—21no—
43#14582771—21no—
44#14582768C2211yescharacteristic
45#14582768C2211yescharacteristic
46#14582759C2211yescharacteristic
47C4×C22⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C23×Dic43—21no—
63C2×#10621877—22no—
64C2×#10621877—22no—
65C2×#10621877Q814yescomplemented
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063324—22no—
69#13063324—41no—
70#13063316—22no—
71#13063316—41no—
72#13063302—44no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—41no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43D411yescharacteristic
93C2×C22⋊Dic43D411yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063258—22no—
97#13063258—22no—
98#13063258D414yes—
99#13063257—22no—
100#13063257—41no—
101#13063256—22no—
102#13063256—22no—
103#13063256—22no—
104#13063235—22no—
105C8×Dic43—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95D411yescharacteristic
112C43⋊#95D411yescharacteristic
113C23×C4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116#117×C43—22no—
117#117×C43—41no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43—21no—
125#107×C43—22no—
126#106×C43—41no—
127C22⋊C8×C43Q814yescomplemented
128#95×C43—21no—
129C24×C43C2×D411yescharacteristic
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×Q812yes—
140C22×C4×C43C2×Q812yes—
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—42no—
147C22×Dic43—42no—
148C22×Dic43—81no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×Dic86—42no—
154C2×Dic86—42no—
155C2×Dic86—81no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C2×Q812yes—
161C2×C8×C43C2×Q812yes—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C2×D412yes—
170C22⋊C4×C43—42no—
171C22⋊C4×C43—42no—
172C42×C43—42no—
173C22⋊Dic43—22no—
174C22⋊Dic43—22no—
175C22⋊Dic43—81no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—42no—
184C4⋊Dic43—42no—
185C4⋊Dic43—42no—
186C4⋊Dic43—42no—
187C4⋊Dic43C2×D412yes—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—81no—
194Dic43⋊C4—81no—
195Dic43⋊C4—81no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200#10621877—28no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C2×D412yes—
204C2×C43⋊C8C2×Q812yes—
205C2×C43⋊C8C2×Q812yes—
206C2×C43⋊C8#4112yes—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43C4⋊Q812yes—
214C23×C43C22×D411yescharacteristic
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C4⋊Q812yes—
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×Q811yescharacteristic
236C2×C4×C43C22×Q811yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—22no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—84no—
263C2×Dic43AGL(1,ℤ/8)12yes—
264C2×Dic43#13712yes—
265Dic86—84no—
266C8×C43—22no—
267C8×C43—22no—
268C43⋊C8—22no—
269C43⋊C8C22⋊Q814yescomplemented
270#26078—431nomaximal, Sylow
271C22×C43—22no—
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43C2×C4⋊Q811yescharacteristic
279C22×C43D4211yescharacteristic
280C22×C43#54711yescharacteristic
281C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C43C2×#13711yescharacteristic
283C22×C43#57711yescharacteristic
284C22×C43#57711yescharacteristic
285C4×C43—22no—
286C4×C43—42no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43C2×C22⋊Q811yescharacteristic
291C4×C43#54411yescharacteristic
292C4×C43D4×Q811yescharacteristic
293C4×C43#55411yescharacteristic
294Dic43—22no—
295Dic43—22no—
296Dic43—41no—
297Dic43—42no—
298Dic43—41no—
299Dic43—81no—
300Dic43—81no—
301Dic43—81no—
302C2×#501—431no—
303C2×#428—431no—
304#2441—431no—
305#2440—431no—
306#2084—431no—
307#2083—431no—
308#2059—431no—
309#2058—431no—
310#1943—431no—
311#1942—431no—
312#1854D4311yescharacteristic
313#1853—431no—
314#1844—431no—
315#1809—431no—
316#1753—431no—
317C2×C43—42no—
318C2×C43#244011yescharacteristic
319C2×C43#316311yescharacteristic
320C2×C43#316511yescharacteristic
321C2×C43#327211yescharacteristic
322C2×C43#327811yescharacteristic
323C2×C43#334411yescharacteristic
324C2×C43#334511yescharacteristic
325C22×M16—431no—
326C2×C4⋊Q8—431no—
327C2×#125—431no—
328C2×C22⋊Q8—861no—
329C2×#117C2×D4311yescharacteristic
330C22×C4⋊C4—431no—
331#501—864no—
332#428—864no—
333C2×#107—431no—
334C2×#107—431no—
335C2×#107—431no—
336C2×#107C2×D4311yescharacteristic
337C2×#106—431no—
338C2×#106—431no—
339C2×#106—431no—
340C2×#106—431no—
341C2×#106—431no—
342C2×#106C2×D4311yescharacteristic
343C2×C22⋊C8C2×D4311yescharacteristic
344C2×#97—431no—
345C2×C4×C8—431no—
346#399—861no—
347#398—861no—
348#396—861no—
349#395—861no—
350#389—431no—
351#389—431no—
352#389—431no—
353#389—431no—
354#389—861no—
355#387—861no—
356#385—861no—
357#384—431no—
358#384—431no—
359#380—431no—
360#380C2×D4311yescharacteristic
361C4×C22⋊C4—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340C2×D4311yescharacteristic
367#340C2×D4311yescharacteristic
368#336—431no—
369#336—431no—
370C43#2607811yescharacteristic, complemented, Sylow
371C22×Q8—861no—
372C23×C4—861no—
373C23×C4C22×D4311yescharacteristic
374C2×M16—434no—
375C2×M16—862no—
376C2×M16—862no—
377C22×C8—431no—
378C22×C8—431no—
379C22×C8C22×D4311yescharacteristic
380C22×C8C22×D4311yescharacteristic
381C4⋊Q8—862no—
382C4⋊Q8—1721no—
383#125—862no—
384#125—1721no—
385C22⋊Q8—1724no—
386#117—22no—
387#117—41no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—862no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—1721no—
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—431no—
413C2×C22⋊C4—431no—
414C2×C22⋊C4—861no—
415C2×C42—21no—
416C2×C42—431no—
417C2×C42—431no—
418#107—22no—
419#107—434no—
420#107—862no—
421#107—862no—
422#106—41no—
423#106—862no—
424#106—862no—
425#106—862no—
426#106—862no—
427#106—1721no—
428C22⋊C8Dic8614yescomplemented
429#97—862no—
430C4×C8—862no—
431#95—21no—
432#95—431no—
433#95—431no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439C24D4×D4311yescharacteristic
440C2×Q8—3441no—
441C2×Q8—1722no—
442C2×Q8—1722no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—3441no—
460C22×C4—1722no—
461C22×C4—1722no—
462C22×C4C2×Dic8612yes—
463C22×C4D4×D4311yescharacteristic
464C22×C4Q8×D4312yes—
465C22×C4C23×D4311yescharacteristic
466M16—868no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—432no—
472C2×C8—432no—
473C2×C8—432no—
474C2×C8—432no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8C2×Dic8612yes—
478C2×C8C2×Dic8612yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—432no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—3441no—
495C4⋊C4—3441no—
496C4⋊C4—3441no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4—1722no—
502C4⋊C4—1722no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C4⋊C4D4×D4312yes—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—862no—
510C22⋊C4—862no—
511C22⋊C4—3441no—
512C42—42no—
513C42—861no—
514C42—861no—
515C42—861no—
516C42—861no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23#1306332412yes—
524C23C2×D4×D4311yescharacteristic
525Q8—3444no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—432no—
545C2×C4—432no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—862no—
557C2×C4—3444no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4#1306332412yes—
570C2×C4C2×D4×D4311yescharacteristic
571C2×C4C2×Q8×D4311yescharacteristic
572C2×C4C22×Dic8611yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4#1306337011yescharacteristic
575C2×C4#1306337211yescharacteristic
576C8—22no—
577C8—22no—
578C8—434no—
579C8—862no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C2×#1306332411yescharacteristic
588C22#1458353111yescharacteristic
589C22#1458354711yescharacteristic
590C22AGL(1,ℤ/8)×D4311yescharacteristic
591C22#137×D4311yescharacteristic
592C22#1458370611yescharacteristic
593C22#1458370611yescharacteristic
594C4—22no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4—862no—
600C4—862no—
601C4—3441no—
602C4—3441no—
603C4—3441no—
604C4—1721no—
605C4—1721no—
606C4—1722no—
607C4C22⋊Q8×D4311yescharacteristic
608C4#1458352811yescharacteristic
609C4D4×Dic8611yescharacteristic
610C4#1458360811yescharacteristic
611C2—42no—
612C2#1913829611yescharacteristic
613C2#1914512711yescharacteristic
614C2#1914513911yescharacteristic
615C2#1914618811yescharacteristic
616C2#1914625411yescharacteristic
617C2#1914704311yescharacteristic
618C2#1914706811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1854D43
hypocenterC43#26078
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
1. C2×#14583307C2semidirect
5. #19136075C2semidirect
6. #19136069C2semidirect
7. #19135932C2semidirect
8. #19135926C2semidirect
9. #19135332C2semidirect
10. #19135327C2semidirect
12. #19134750C2semidirect
65. C2×#10621877Q8semidirect
127. C22⋊C8×C43Q8semidirect
269. C43⋊C8C22⋊Q8semidirect
370. C43#26078semidirect
428. C22⋊C8Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145833072
C2×#145829422
#191383022
#191382982
#191360752
#191360692
#191359322
#191359262
#191353322
#191353272
#191347902
#191347502
#191346262
#191343812
C43×#18542
#2607843