Finite Group Databasebeta

← #25116063

Subgroups — #25116063

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#19143393C211yesmaximal, characteristic
2#19143261C211yesmaximal, characteristic, complemented
3#19143164C211yesmaximal, characteristic, complemented
4#19135303C211yesmaximal, characteristic, complemented
5#19135296C211yesmaximal, characteristic, complemented
6#19135192C211yesmaximal, characteristic, complemented
7#19135192C211yesmaximal, characteristic, complemented
8#19134919C211yesmaximal, characteristic
9#19134919C211yesmaximal, characteristic
10#19134735C211yesmaximal, characteristic, complemented
11#19134616C211yesmaximal, characteristic, complemented
12#19134470C211yesmaximal, characteristic, complemented
13#19134436C211yesmaximal, characteristic, complemented
14#19134429C211yesmaximal, characteristic, complemented
15C43×#1806C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063333C2211yescharacteristic
18C2×#13063333C2211yescharacteristic
19C4×#10621898C2211yescharacteristic
20#14583009C411yescharacteristic, complemented
21#14583009C411yescharacteristic, complemented
22#14583004C411yescharacteristic, complemented
23#14583004C411yescharacteristic, complemented
24#14582999C411yescharacteristic, complemented
25#14582999C411yescharacteristic, complemented
26#14582997C411yescharacteristic, complemented
27#14582997C411yescharacteristic, complemented
28#14582960—21no—
29#14582960—21no—
30#14582956—21no—
31#14582952—21no—
32#14582935C2211yescharacteristic
33#14582927C2211yescharacteristic
34#14582927C2211yescharacteristic
35#14582924—21no—
36#14582924—21no—
37#14582923C2211yescharacteristic
38#14582921—21no—
39C2×C4⋊(C43⋊C8)C2211yescharacteristic
40C4⋊C8×D43—21no—
41C2×#13063253C2211yescharacteristic
42C2×#13063253C2211yescharacteristic
43#14582895C2211yescharacteristic
44#14582893C2211yescharacteristic
45#14582866C2211yescharacteristic
46#14582866C2211yescharacteristic
47#14582855C2211yescharacteristic
48#14582855C2211yescharacteristic
49C2×#13063236C2211yescharacteristic
50C2×#13063236C2211yescharacteristic
51C2×C4×C43⋊C8C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582654C2211yescharacteristic
59#14582654C2211yescharacteristic
60C4×#41×C43C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C4×C4⋊C4×C43C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063345—22no—
69#13063345—22no—
70C2×#10621885C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C2×#10621884C2×C411yescharacteristic
73C2×#10621882C2×C411yescharacteristic
74#13063333—22no—
75#13063333—22no—
76#13063333—41no—
77#13063333—41no—
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80C2×#10621872—21no—
81C2×#10621872—21no—
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C2×C8×D43—21no—
87C2×C8×D43—21no—
88C4×Dic86C2×C411yescharacteristic
89C4×Dic86C2×C411yescharacteristic
90C4×D172C2×C411yescharacteristic
91C4×D172C2×C411yescharacteristic
92C4×C22⋊D43—21no—
93C4×C22⋊D43—21no—
94#13063284C2311yescharacteristic
95#13063282—21no—
96C42×D43—21no—
97#13063258C2×C411yescharacteristic
98#13063258C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100#13063256C2×C411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)D411yescharacteristic
104C4⋊(C43⋊C8)D411yescharacteristic
105C4⋊(C43⋊C8)D411yescharacteristic
106C4⋊(C43⋊C8)D411yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063253—22no—
112#13063253—22no—
113#13063249C2×C411yescharacteristic
114#13063249C2×C411yescharacteristic
115#13063248C2×C411yescharacteristic
116#13063248C2×C411yescharacteristic
117#13063246C2×C411yescharacteristic
118#13063246C2×C411yescharacteristic
119#13063245C2×C411yescharacteristic
120#13063245C2×C411yescharacteristic
121C22⋊(C43⋊C8)—21no—
122C22⋊(C43⋊C8)—21no—
123C22⋊(C43⋊C8)—21no—
124C22⋊(C43⋊C8)—21no—
125#13063236—21no—
126#13063236—21no—
127#13063236—41no—
128#13063236C2×C411yescharacteristic
129#13063236C2×C411yescharacteristic
130#13063236C2×C411yescharacteristic
131#13063236C2×C411yescharacteristic
132C4×C43⋊C8—21no—
133C4×C43⋊C8—21no—
134C4×C43⋊C8—41no—
135C2×#41×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C4×Q8×C43C2×C411yescharacteristic
139C4×Q8×C43C2×C411yescharacteristic
140C4×D4×C43—21no—
141C4×D4×C43—21no—
142C4×D4×C43C2×C411yescharacteristic
143C4×D4×C43C2×C411yescharacteristic
144#117×C43—21no—
145#117×C43C2311yescharacteristic
146C2×C4⋊C4×C43—21no—
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149C2×C42×C43C2311yescharacteristic
150C2×C42×C43C2311yescharacteristic
151C4⋊C8×C43—21no—
152C4⋊C8×C43—21no—
153#104×C43—41no—
154#104×C43—41no—
155#95×C43—21no—
156#41×C43—21no—
157#41×C43—21no—
158#41×C43—21no—
159#41×C43—21no—
160C2×Q8×C43C22×C411yescharacteristic
161C2×D4×C43—21no—
162C2×D4×C43C22×C411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43#4111yescharacteristic
169C22×C4×C43#4111yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C2×C22⋊D43—21no—
172#10621898—21no—
173#10621898—21no—
174#10621898#4112yes—
175#10621898#4112yes—
176C2×D172C22×C411yescharacteristic
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×Dic86C22×C411yescharacteristic
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—42no—
190C4⋊C4×C43C22×C411yescharacteristic
191C4⋊C4×C43C22×C411yescharacteristic
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
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—
207#10621885—22no—
208#10621884—22no—
209#10621883—22no—
210#10621882—22no—
211(C2×D43)⋊C4—21no—
212(C2×D43)⋊C4—21no—
213C4⋊Dic43C22×C411yescharacteristic
214C4⋊Dic43C22×C411yescharacteristic
215Dic43⋊C4—21no—
216Dic43⋊C4—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877—21no—
223#10621877—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8C22×C411yescharacteristic
235C2×C43⋊C8C22×C411yescharacteristic
236C2×C43⋊C8C22×C411yescharacteristic
237C2×C43⋊C8C22×C411yescharacteristic
238C2×C43⋊C8C2×D411yescharacteristic
239C2×C43⋊C8C2×D411yescharacteristic
240C2×C43⋊C8C2×D411yescharacteristic
241C2×C43⋊C8C2×D411yescharacteristic
242#10621872—42no—
243#10621872—42no—
244C8×D43—42no—
245C8×D43—42no—
246C23×C43—21no—
247C23×C43C2×#4111yescharacteristic
248C22×D43—21no—
249Q8×C43—21no—
250Q8×C43—21no—
251D4×C43—21no—
252D4×C43—21no—
253D4×C43—41no—
254D4×C43—41no—
255C2×C4×C43—22no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—42no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—81no—
270C2×C4×C43C4×D411yescharacteristic
271C2×C4×C43C4×D411yescharacteristic
272C2×C4×C43C4×D411yescharacteristic
273C2×C4×C43C4×D411yescharacteristic
274C2×C4×C43C23×C411yescharacteristic
275C2×C4×C43C22×D411yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43C2×#4111yescharacteristic
278C2×C4×C43H(5,𝔽2)11yescharacteristic
279C2×C4×C432−1+411yescharacteristic
280C22⋊D43—22no—
281C22⋊D43—22no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285D172—21no—
286D172#11712yes—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—42no—
290C4×D43—81no—
291Dic86—21no—
292Dic86#11712yes—
293C8×C43—41no—
294C8×C43—41no—
295C43⋊C8—21no—
296C43⋊C8—21no—
297C43⋊C8—21no—
298C43⋊C8—21no—
299C43⋊C8—21no—
300C43⋊C8—21no—
301C43⋊C8—21no—
302C43⋊C8—21no—
303C43⋊C8—41no—
304C43⋊C8—41no—
305#22784—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43C2×C4×D411yescharacteristic
312C22×C43#55211yescharacteristic
313C22×C43#55311yescharacteristic
314C2×D43—22no—
315C2×D43—41no—
316C2×D43—41no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43—42no—
322C4×C43—41no—
323C4×C43—41no—
324C4×C43—41no—
325C4×C43—81no—
326C4×C43C2×#11711yescharacteristic
327C4×C43#52011yescharacteristic
328C4×C43#54611yescharacteristic
329C4×C43#54811yescharacteristic
330Dic43—22no—
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#1806D4311yescharacteristic, complemented
345#1771—431no—
346#1765—431no—
347#1764—431no—
348C2×C43—21no—
349C2×C43—21no—
350C2×C43—81no—
351C2×C43#235211yescharacteristic
352C2×C43#295511yescharacteristic
353C2×C43#295611yescharacteristic
354D43—42no—
355C2×#135—431no—
356C2×#131—431no—
357C2×#131—431no—
358C4×#41—431no—
359C4×#41C2×D4311yescharacteristic
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—861no—
379#423C2×D4311yescharacteristic
380C2×C4⋊C8—431no—
381C2×C4⋊C8—861no—
382C2×#104—431no—
383C2×#104—431no—
384C2×#104C2×D4311yescharacteristic
385C2×#104C2×D4311yescharacteristic
386#416—431no—
387#416—431no—
388#408—431no—
389#408—431no—
390#405—431no—
391#405—431no—
392C2×#97—431no—
393C2×#97—431no—
394C2×C4×C8—431no—
395C4×C4⋊C4C2×D4311yescharacteristic
396#341—431no—
397#341—431no—
398#341—431no—
399#341—431no—
400#339—431no—
401#339—431no—
402#339C2×D4311yescharacteristic
403#339C2×D4311yescharacteristic
404#336—431no—
405#336—431no—
406C43#2278411yescharacteristic, complemented, Sylow
407C2×#41—431no—
408C2×#41C22×D4311yescharacteristic
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—861no—
422C2×M16—861no—
423C2×M16C22×D4311yescharacteristic
424C2×M16C22×D4311yescharacteristic
425C22×C8—431no—
426C22×C8—431no—
427C22×C8—431no—
428C22×C8—431no—
429C22×C8—861no—
430C22×C8—861no—
431C4×Q8—431no—
432C4×Q8—431no—
433C4×Q8C4×D4311yescharacteristic
434C4×Q8C4×D4311yescharacteristic
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—431no—
438C4×D4—431no—
439C4×D4—861no—
440C4×D4—861no—
441C4×D4C4×D4311yescharacteristic
442C4×D4C4×D4311yescharacteristic
443#117—21no—
444#117—431no—
445#117—861no—
446#117C22×D4311yescharacteristic
447C2×C4⋊C4—21no—
448C2×C42—21no—
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—21no—
458C4⋊C8—21no—
459C4⋊C8—431no—
460C4⋊C8—431no—
461C4⋊C8—431no—
462C4⋊C8—431no—
463C4⋊C8—861no—
464C4⋊C8—861no—
465C4⋊C8—861no—
466C4⋊C8—861no—
467C4⋊C8—861no—
468C4⋊C8—861no—
469#104—41no—
470#104—41no—
471#104—862no—
472#104—862no—
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—431no—
486#97—431no—
487#97—431no—
488#97—431no—
489#97—861no—
490#97—861no—
491#97—1721no—
492C4×C8—861no—
493C4×C8—861no—
494C4×C8—1721no—
495#95—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41—432no—
501#41—432no—
502#41—861no—
503#41—861no—
504C2×Q8—431no—
505C2×Q8C2×C4×D4311yescharacteristic
506C2×D4—21no—
507C2×D4—431no—
508C2×D4—861no—
509C2×D4C2×C4×D4311yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4#1062190011yescharacteristic
519C22×C4#1062190011yescharacteristic
520C22×C4C23×D4311yescharacteristic
521Q16—862no—
522SD16—862no—
523SD16—862no—
524D8—862no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—861no—
530M16—861no—
531M16—861no—
532M16—861no—
533M16—1722no—
534M16—1722no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—431no—
538C2×C8—431no—
539C2×C8—431no—
540C2×C8—431no—
541C2×C8—431no—
542C2×C8—431no—
543C2×C8—431no—
544C2×C8—431no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—861no—
554C2×C8—861no—
555C2×C8—1722no—
556C2×C8—1722no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—42no—
560C4⋊C4—431no—
561C4⋊C4—431no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C4⋊C4C2×C4×D4311yescharacteristic
565C4⋊C4C2×C4×D4311yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—861no—
570C22⋊C4—861no—
571C22⋊C4—861no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42C2×C4×D4311yescharacteristic
583C42C2×C4×D4311yescharacteristic
584C42D4×D4311yescharacteristic
585C42D4×D4311yescharacteristic
586C23—21no—
587C23—861no—
588C23C2×#1062190011yescharacteristic
589Q8—21no—
590Q8—21no—
591Q8—432no—
592Q8—861no—
593D4—21no—
594D4—21no—
595D4—41no—
596D4—41no—
597D4—432no—
598D4—862no—
599D4—862no—
600D4—861no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—81no—
616C2×C4—861no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—3441no—
622C2×C4—1722no—
623C2×C4(C22⋊D43)⋊C411yescharacteristic
624C2×C4(C22⋊D43)⋊C411yescharacteristic
625C2×C4(C22⋊D43)⋊C411yescharacteristic
626C2×C4(C22⋊D43)⋊C411yescharacteristic
627C2×C4C22×C4×D4311yescharacteristic
628C2×C4C2×D4×D4311yescharacteristic
629C2×C4#41×D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4#1306337011yescharacteristic
632C2×C4#1306337311yescharacteristic
633C8—41no—
634C8—41no—
635C8—861no—
636C8—861no—
637C8—861no—
638C8—861no—
639C8—861no—
640C8—861no—
641C8—861no—
642C8—861no—
643C8—1721no—
644C8—1721no—
645C22—21no—
646C22—21no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—862no—
651C22—1721no—
652C22—1721no—
653C22C2×(C22⋊D43)⋊C411yescharacteristic
654C22#1458358311yescharacteristic
655C22#1458359611yescharacteristic
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—42no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—81no—
665C4—862no—
666C4—1721no—
667C4—1721no—
668C4#117×D4311yescharacteristic
669C4#1458338011yescharacteristic
670C4#1458354611yescharacteristic
671C4#1458355911yescharacteristic
672C2—21no—
673C2—21no—
674C2—81no—
675C2—1722no—
676C2#1913751711yescharacteristic
677C2#1914349411yescharacteristic
678C2#1914350111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063345C22
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#22784
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #19143261C2semidirect
3. #19143164C2semidirect
4. #19135303C2semidirect
5. #19135296C2semidirect
6. #19135192C2semidirect
7. #19135192C2semidirect
10. #19134735C2semidirect
11. #19134616C2semidirect
12. #19134470C2semidirect
13. #19134436C2semidirect
14. #19134429C2semidirect
15. C43×#1806C2semidirect
20. #14583009C4semidirect
21. #14583009C4semidirect
22. #14583004C4semidirect
23. #14583004C4semidirect
24. #14582999C4semidirect
25. #14582999C4semidirect
26. #14582997C4semidirect
27. #14582997C4semidirect
344. #1806D43semidirect
406. C43#22784semidirect

Maximal subgroups

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

subgroupindex
#191433932
#191432612
#191431642
#191353032
#191352962
#191351922
#191349192
#191347352
#191346162
#191344702
#191344362
#191344292
C43×#18062
#2278443