Finite Group Databasebeta

← #25116075

Subgroups — #25116075

Order 11008.

740 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143397C211yesmaximal, characteristic
2#19143260C211yesmaximal, characteristic, complemented
3#19143160C211yesmaximal, characteristic, complemented
4#19135306C211yesmaximal, characteristic, complemented
5#19135299C211yesmaximal, characteristic, complemented
6#19135195C211yesmaximal, characteristic, complemented
7#19135195C211yesmaximal, characteristic, complemented
8#19134921C211yesmaximal, characteristic
9#19134921C211yesmaximal, characteristic
10#19134736C211yesmaximal, characteristic, complemented
11#19134616C211yesmaximal, characteristic, complemented
12#19134616C211yesmaximal, characteristic, complemented
13#19134439C211yesmaximal, characteristic, complemented
14#19134432C211yesmaximal, characteristic, complemented
15C43×#1771C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19C4×#10621898C2211yescharacteristic
20C4×#10621898C2211yescharacteristic
21#14583012C411yescharacteristic, complemented
22#14583012C411yescharacteristic, complemented
23#14583007C411yescharacteristic, complemented
24#14583007C411yescharacteristic, complemented
25#14583001C411yescharacteristic, complemented
26#14583001C411yescharacteristic, complemented
27#14583001C411yescharacteristic, complemented
28#14583001C411yescharacteristic, complemented
29#14582959—21no—
30#14582959—21no—
31#14582955—21no—
32#14582951—21no—
33#14582937C2211yescharacteristic
34#14582925C2211yescharacteristic
35#14582925C2211yescharacteristic
36#14582924—21no—
37#14582924—21no—
38#14582923C2211yescharacteristic
39#14582923C2211yescharacteristic
40#14582921—21no—
41C4⋊C8×D43—21no—
42C2×#13063253C2211yescharacteristic
43C2×#13063253C2211yescharacteristic
44C2×#13063253C2211yescharacteristic
45C2×#13063253C2211yescharacteristic
46#14582896C2211yescharacteristic
47#14582896C2211yescharacteristic
48#14582865C2211yescharacteristic
49#14582865C2211yescharacteristic
50#14582854C2211yescharacteristic
51#14582854C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582664C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582664C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582659C2211yescharacteristic
59#14582659C2211yescharacteristic
60C2×C4⋊C8×C43C2211yescharacteristic
61C2×#97×C43C2211yescharacteristic
62C2×#97×C43C2211yescharacteristic
63C2×C4×C8×C43C2211yescharacteristic
64C4×C4⋊C4×C43C2211yescharacteristic
65C43×#336C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C2×#10621898C2311yescharacteristic
69#13063347—22no—
70#13063347—22no—
71C2×Dic172C2×C411yescharacteristic
72C2×#10621873C2×C411yescharacteristic
73C2×#10621873C2×C411yescharacteristic
74C2×D344C2×C411yescharacteristic
75#13063331—22no—
76#13063331—22no—
77#13063331—41no—
78#13063331—41no—
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621872—21no—
84C2×#10621872—21no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87C4×Dic86C2×C411yescharacteristic
88C4×Dic86C2×C411yescharacteristic
89C4×Dic86C2×C411yescharacteristic
90C4×Dic86C2×C411yescharacteristic
91C4×D172C2×C411yescharacteristic
92C4×D172C2×C411yescharacteristic
93C4×D172C2×C411yescharacteristic
94C4×D172C2×C411yescharacteristic
95C4×C22⋊D43—21no—
96C4×C22⋊D43—21no—
97C4×C22⋊D43—21no—
98C4×C22⋊D43—21no—
99#13063284C2311yescharacteristic
100#13063284C2311yescharacteristic
101#13063282—21no—
102#13063282—21no—
103C42×D43—21no—
104C42×D43—21no—
105#13063259C2×C411yescharacteristic
106#13063259C2×C411yescharacteristic
107#13063257C2×C411yescharacteristic
108#13063257C2×C411yescharacteristic
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)—21no—
111C4⋊(C43⋊C8)—21no—
112C4⋊(C43⋊C8)—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117#13063253—22no—
118#13063253—22no—
119#13063253—41no—
120#13063253—41no—
121#13063250C2×C411yescharacteristic
122#13063250C2×C411yescharacteristic
123#13063250C2×C411yescharacteristic
124#13063250C2×C411yescharacteristic
125#13063247C2×C411yescharacteristic
126#13063247C2×C411yescharacteristic
127#13063247C2×C411yescharacteristic
128#13063247C2×C411yescharacteristic
129(C2×D43)⋊C8—21no—
130(C2×D43)⋊C8—21no—
131(C2×D43)⋊C8—21no—
132(C2×D43)⋊C8—21no—
133#13063235—21no—
134#13063235—21no—
135C8×Dic43—21no—
136C8×Dic43—21no—
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C2×C4⋊C4×C43—21no—
142C2×C42×C43C2311yescharacteristic
143C2×C42×C43C2311yescharacteristic
144C2×C42×C43C2311yescharacteristic
145C4⋊C8×C43D411yescharacteristic
146C4⋊C8×C43D411yescharacteristic
147C4⋊C8×C43D411yescharacteristic
148C4⋊C8×C43D411yescharacteristic
149#97×C43—41no—
150#97×C43C2×C411yescharacteristic
151#97×C43C2×C411yescharacteristic
152#97×C43C2×C411yescharacteristic
153#97×C43C2×C411yescharacteristic
154C4×C8×C43—41no—
155#95×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43#4111yescharacteristic
159C22×C4×C43#4111yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—21no—
162C2×C22⋊D43—21no—
163#10621898—21no—
164#10621898—21no—
165#10621898—21no—
166#10621898—21no—
167#10621898—21no—
168#10621898—21no—
169#10621898#4112yes—
170#10621898#4112yes—
171C2×D172C22×C411yescharacteristic
172C2×D172C22×C411yescharacteristic
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×Dic86C22×C411yescharacteristic
180C2×Dic86C22×C411yescharacteristic
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43C22×C411yescharacteristic
190C2×C8×C43C22×C411yescharacteristic
191C2×C8×C43C22×C411yescharacteristic
192C2×C8×C43C22×C411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C2×C8×C43C2×D411yescharacteristic
196C2×C8×C43C2×D411yescharacteristic
197C4⋊C4×C43—42no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43C22×C411yescharacteristic
203C42×C43C22×C411yescharacteristic
204C42×C43C2×D411yescharacteristic
205C42×C43C2×D411yescharacteristic
206C22⋊Dic43—21no—
207C22⋊Dic43—21no—
208(C2×D43)⋊C4—21no—
209(C2×D43)⋊C4—21no—
210(C2×D43)⋊C4—21no—
211(C2×D43)⋊C4—21no—
212C4⋊Dic43C22×C411yescharacteristic
213C4⋊Dic43C22×C411yescharacteristic
214C4⋊Dic43C22×C411yescharacteristic
215C4⋊Dic43C22×C411yescharacteristic
216Dic43⋊C4—21no—
217Dic43⋊C4—21no—
218Dic43⋊C4—21no—
219Dic43⋊C4—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226#10621877—21no—
227#10621877—21no—
228#10621877—21no—
229#10621877—21no—
230#10621877—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238Dic172—22no—
239D344—22no—
240#10621873—22no—
241#10621873—22no—
242#10621872—42no—
243#10621872—42no—
244C8×D43—42no—
245C8×D43—42no—
246C23×C43C2×#4111yescharacteristic
247C22×D43—21no—
248C22×D43—21no—
249C2×C4×C43—22no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43C4×D411yescharacteristic
258C2×C4×C43C4×D411yescharacteristic
259C2×C4×C43C4×D411yescharacteristic
260C2×C4×C43C4×D411yescharacteristic
261C2×C4×C43C23×C411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×C4×C432−1+411yescharacteristic
267C22⋊D43—22no—
268C22⋊D43—22no—
269C22⋊D43—41no—
270C22⋊D43—41no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277D172—21no—
278D172—21no—
279D172—21no—
280D172#11712yes—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—42no—
284C4×D43—42no—
285C4×D43—41no—
286C4×D43—41no—
287C4×D43—81no—
288C4×D43—81no—
289Dic86—21no—
290Dic86—21no—
291Dic86—21no—
292Dic86#11712yes—
293C8×C43—21no—
294C8×C43—21no—
295C8×C43—21no—
296C8×C43—21no—
297C8×C43—21no—
298C8×C43—21no—
299C8×C43—21no—
300C8×C43—21no—
301C43⋊C8—41no—
302C43⋊C8—41no—
303C43⋊C8—41no—
304C43⋊C8—41no—
305#22784—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43C2×C4×D411yescharacteristic
309C22×C43#55211yescharacteristic
310C22×C43#55311yescharacteristic
311C2×D43—22no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43—41no—
315C2×D43—41no—
316C2×D43—41no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43—42no—
322C4×C43—81no—
323C4×C43C2×#11711yescharacteristic
324C4×C43#52011yescharacteristic
325C4×C43#54611yescharacteristic
326C4×C43#54811yescharacteristic
327Dic43—22no—
328Dic43—41no—
329Dic43—41no—
330Dic43—41no—
331Dic43—41no—
332Dic43—41no—
333#2943—431no—
334#2925—431no—
335#2906—431no—
336#1938—431no—
337#1937—431no—
338#1922—431no—
339#1922—431no—
340#1876—431no—
341#1876—431no—
342#1838—431no—
343#1806—431no—
344#1806—431no—
345#1771D4311yescharacteristic, complemented
346#1765—431no—
347#1764—431no—
348C2×C43—21no—
349C2×C43—21no—
350C2×C43#235211yescharacteristic
351C2×C43#295511yescharacteristic
352C2×C43#295611yescharacteristic
353D43—42no—
354D43—81no—
355C2×#135—431no—
356C2×#131—431no—
357C2×#131—431no—
358C4×#41—431no—
359C4×#41—431no—
360#442—431no—
361#442—431no—
362#441—431no—
363#441—431no—
364#440—431no—
365#440—431no—
366#440—431no—
367#440—431no—
368#433—861no—
369#433—861no—
370#432—861no—
371#431—861no—
372#427—431no—
373#424—431no—
374#424—431no—
375#424—861no—
376#424—861no—
377#423—431no—
378#423—431no—
379#423—861no—
380C2×C4⋊C8—861no—
381C2×C4⋊C8C2×D4311yescharacteristic
382C2×#104—431no—
383C2×#104—431no—
384C2×#104—431no—
385C2×#104—431no—
386#416—431no—
387#416—431no—
388#408—431no—
389#408—431no—
390#405—431no—
391#405—431no—
392C2×#97C2×D4311yescharacteristic
393C2×#97C2×D4311yescharacteristic
394C2×C4×C8C2×D4311yescharacteristic
395C4×C4⋊C4C2×D4311yescharacteristic
396#341—431no—
397#341—431no—
398#341—431no—
399#341—431no—
400#339—431no—
401#339—431no—
402#339—431no—
403#339—431no—
404#336C2×D4311yescharacteristic
405#336C2×D4311yescharacteristic
406C43#2278411yescharacteristic, complemented, Sylow
407C2×#41—431no—
408C2×#41—431no—
409#135—862no—
410#135—862no—
411C2×Q16—431no—
412C2×SD16—431no—
413C2×SD16—431no—
414C2×D8—431no—
415#131—862no—
416#131—862no—
417#131—1721no—
418#131—1721no—
419C2×M16—431no—
420C2×M16—431no—
421C2×M16—431no—
422C2×M16—431no—
423C2×M16—861no—
424C2×M16—861no—
425C22×C8—861no—
426C22×C8—861no—
427C22×C8C22×D4311yescharacteristic
428C22×C8C22×D4311yescharacteristic
429C22×C8C22×D4311yescharacteristic
430C22×C8C22×D4311yescharacteristic
431C4×Q8—431no—
432C4×Q8—431no—
433C4×Q8—431no—
434C4×Q8—431no—
435C4×D4—431no—
436C4×D4—431no—
437C4×D4—431no—
438C4×D4—431no—
439C4×D4—861no—
440C4×D4—861no—
441C4×D4—861no—
442C4×D4—861no—
443#117—431no—
444#117—431no—
445#117—861no—
446#117—861no—
447C2×C4⋊C4—21no—
448C2×C42—861no—
449C2×C42—861no—
450C2×C42C22×D4311yescharacteristic
451C2×C42C22×D4311yescharacteristic
452C2×C42C22×D4311yescharacteristic
453#107—431no—
454#107—431no—
455#106—431no—
456#106—431no—
457C4⋊C8—861no—
458C4⋊C8—861no—
459C4⋊C8—861no—
460C4⋊C8—861no—
461C4⋊C8—861no—
462C4⋊C8—861no—
463C4⋊C8—861no—
464C4⋊C8—861no—
465C4⋊C8D17211yescharacteristic
466C4⋊C8D17211yescharacteristic
467C4⋊C8D17211yescharacteristic
468C4⋊C8D17211yescharacteristic
469#104—862no—
470#104—862no—
471#104—1721no—
472#104—1721no—
473#103—431no—
474#103—431no—
475#103—431no—
476#103—431no—
477#102—431no—
478#102—431no—
479#102—431no—
480#102—431no—
481C22⋊C8—861no—
482C22⋊C8—861no—
483C22⋊C8—861no—
484C22⋊C8—861no—
485#97—41no—
486#97—861no—
487#97—861no—
488#97C4×D4311yescharacteristic
489#97C4×D4311yescharacteristic
490#97C4×D4311yescharacteristic
491#97C4×D4311yescharacteristic
492C4×C8—41no—
493C4×C8—861no—
494C4×C8—861no—
495#95—21no—
496#41—432no—
497#41—432no—
498#41—861no—
499#41—861no—
500#41—861no—
501#41—861no—
502#41—861no—
503#41—861no—
504C2×Q8—431no—
505C2×Q8—431no—
506C2×D4—431no—
507C2×D4—431no—
508C2×D4—861no—
509C2×D4—861no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4#1062189811yescharacteristic
519C22×C4#1062189811yescharacteristic
520C22×C4C23×D4311yescharacteristic
521Q16—862no—
522SD16—862no—
523SD16—862no—
524D8—862no—
525M16—861no—
526M16—861no—
527M16—861no—
528M16—861no—
529M16—861no—
530M16—861no—
531M16—861no—
532M16—861no—
533M16—1722no—
534M16—1722no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—1722no—
548C2×C8—1722no—
549C2×C8C2×C4×D4311yescharacteristic
550C2×C8C2×C4×D4311yescharacteristic
551C2×C8C2×C4×D4311yescharacteristic
552C2×C8C2×C4×D4311yescharacteristic
553C2×C8C2×D17211yescharacteristic
554C2×C8C2×D17211yescharacteristic
555C2×C8C2×D17211yescharacteristic
556C2×C8C2×D17211yescharacteristic
557C4⋊C4—42no—
558C4⋊C4—431no—
559C4⋊C4—431no—
560C4⋊C4—431no—
561C4⋊C4—431no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C4⋊C4—861no—
565C4⋊C4—861no—
566C22⋊C4—861no—
567C22⋊C4—861no—
568C22⋊C4—861no—
569C22⋊C4—861no—
570C22⋊C4—861no—
571C22⋊C4—861no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—861no—
577C42—861no—
578C42—861no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42C2×C4×D4311yescharacteristic
583C42C2×C4×D4311yescharacteristic
584C42C2×D17211yescharacteristic
585C42C2×D17211yescharacteristic
586C23—861no—
587C23—861no—
588C23C2×#1062189811yescharacteristic
589Q8—432no—
590Q8—861no—
591Q8—861no—
592Q8—861no—
593D4—432no—
594D4—862no—
595D4—862no—
596D4—861no—
597D4—861no—
598D4—861no—
599D4—1721no—
600D4—1721no—
601C2×C4—22no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—861no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—3441no—
618C2×C4—3441no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4C4×D17211yescharacteristic
624C2×C4C4×D17211yescharacteristic
625C2×C4C4×D17211yescharacteristic
626C2×C4C4×D17211yescharacteristic
627C2×C4C22×C4×D4311yescharacteristic
628C2×C4C22×D17211yescharacteristic
629C2×C4#41×D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4#1306337011yescharacteristic
632C2×C4#1306337311yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—21no—
638C8—21no—
639C8—21no—
640C8—21no—
641C8—1721no—
642C8—1721no—
643C8—1721no—
644C8—1721no—
645C22—21no—
646C22—21no—
647C22—862no—
648C22—1721no—
649C22—1721no—
650C22—1721no—
651C22—1721no—
652C22—1721no—
653C22C2×C4×D17211yescharacteristic
654C22#1458359011yescharacteristic
655C22#1458359911yescharacteristic
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—42no—
661C4—81no—
662C4—862no—
663C4—1721no—
664C4—1721no—
665C4—1721no—
666C4—1721no—
667C4—1721no—
668C4#117×D4311yescharacteristic
669C4#1458338011yescharacteristic
670C4#1458354411yescharacteristic
671C4#1458356111yescharacteristic
672C2—21no—
673C2—21no—
674C2—3441no—
675C2—1722no—
676C2#1913752711yescharacteristic
677C2#1914349911yescharacteristic
678C2#1914350611yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1771C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063347C22
cosocleC22×C4×C43C24
hypercenter#1771D43
hypocenterC43#22784
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #19143260C2semidirect
3. #19143160C2semidirect
4. #19135306C2semidirect
5. #19135299C2semidirect
6. #19135195C2semidirect
7. #19135195C2semidirect
10. #19134736C2semidirect
11. #19134616C2semidirect
12. #19134616C2semidirect
13. #19134439C2semidirect
14. #19134432C2semidirect
15. C43×#1771C2semidirect
21. #14583012C4semidirect
22. #14583012C4semidirect
23. #14583007C4semidirect
24. #14583007C4semidirect
25. #14583001C4semidirect
26. #14583001C4semidirect
27. #14583001C4semidirect
28. #14583001C4semidirect
345. #1771D43semidirect
406. C43#22784semidirect

Maximal subgroups

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

subgroupindex
#191433972
#191432602
#191431602
#191353062
#191352992
#191351952
#191349212
#191347362
#191346162
#191344392
#191344322
C43×#17712
#2278443