Finite Group Databasebeta

← #25118690

Subgroups — #25118690

Order 11008.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144385C211yesmaximal, characteristic
2#19143538C211yesmaximal, characteristic, complemented
3#19143160C211yesmaximal, characteristic
4#19135576C211yesmaximal, characteristic, complemented
5#19135371C211yesmaximal, characteristic, complemented
6#19135348C211yesmaximal, characteristic, complemented
7#19135343C211yesmaximal, characteristic, complemented
8#19135195C211yesmaximal, characteristic, complemented
9#19135195C211yesmaximal, characteristic, complemented
10#19134873C211yesmaximal, characteristic
11#19134873C211yesmaximal, characteristic
12#19134439C211yesmaximal, characteristic
13#19134432C211yesmaximal, characteristic
14#19134406C211yesmaximal, characteristic
15C43×#1768C211yesmaximal, characteristic, complemented
16C2×#13063331C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18#14583456C2211yescharacteristic
19C4×#10621898C2211yescharacteristic
20#14583207C411yescharacteristic, complemented
21#14583207C411yescharacteristic, complemented
22#14583200C411yescharacteristic, complemented
23#14583200C411yescharacteristic, complemented
24#14583195C411yescharacteristic, complemented
25#14583190C411yescharacteristic, complemented
26#14583185C411yescharacteristic, complemented
27#14583180C411yescharacteristic, complemented
28#14583028—21no—
29#14583028—21no—
30#14583026—21no—
31#14583023—21no—
32C2×#13063261C2211yescharacteristic
33C2×#13063261C2211yescharacteristic
34#14582937C2211yescharacteristic
35#14582937C2211yescharacteristic
36#14582925C2211yescharacteristic
37#14582925C2211yescharacteristic
38#14582925C2211yescharacteristic
39#14582925C2211yescharacteristic
40#14582924—21no—
41#14582924—21no—
42#14582923C2211yescharacteristic
43#14582921—21no—
44C4⋊C8×D43—21no—
45C2×#13063253C2211yescharacteristic
46C2×#13063253C2211yescharacteristic
47#14582896C2211yescharacteristic
48#14582896C2211yescharacteristic
49#14582854C2211yescharacteristic
50#14582854C2211yescharacteristic
51C4×#10621877C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582664C2211yescharacteristic
54#14582659C2211yescharacteristic
55#14582659C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582659C2211yescharacteristic
59#14582659C2211yescharacteristic
60C2×C4⋊C8×C43C2211yescharacteristic
61C2×C4⋊C8×C43C2211yescharacteristic
62C2×#97×C43C2211yescharacteristic
63C2×C4×C8×C43C2211yescharacteristic
64C43×#376C2211yescharacteristic
65C43×#336C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063331—22no—
69#13063331—22no—
70#13063331—41no—
71#13063331—41no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621872—21no—
77C2×#10621872—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80#13063325C2×C411yescharacteristic
81#13063325C2×C411yescharacteristic
82#13063317C2×C411yescharacteristic
83#13063317C2×C411yescharacteristic
84#13063304—21no—
85#13063304—21no—
86C4×Dic86—21no—
87C4×Dic86—21no—
88C4×Dic86C2×C411yescharacteristic
89C4×Dic86C2×C411yescharacteristic
90C4×D172C2×C411yescharacteristic
91C4×D172C2×C411yescharacteristic
92C4×C22⋊D43—21no—
93C4×C22⋊D43—21no—
94#13063284C2311yescharacteristic
95#13063284C2311yescharacteristic
96#13063284C2311yescharacteristic
97#13063282—21no—
98C42×D43—21no—
99#13063261—41no—
100#13063261—41no—
101#13063259C2×C411yescharacteristic
102#13063259C2×C411yescharacteristic
103#13063259C2×C411yescharacteristic
104#13063259C2×C411yescharacteristic
105#13063257C2×C411yescharacteristic
106#13063257C2×C411yescharacteristic
107#13063257C2×C411yescharacteristic
108#13063257C2×C411yescharacteristic
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118Dic43⋊C8—21no—
119#13063253—22no—
120#13063253Q814yescomplemented
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#13063236—21no—
130#13063235—21no—
131#13063235—21no—
132C4×C43⋊C8—21no—
133C8×Dic43—21no—
134C8×Dic43—21no—
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C2×C42×C43C2311yescharacteristic
141C2×C42×C43C2311yescharacteristic
142C4⋊C8×C43C2×C411yescharacteristic
143C4⋊C8×C43C2×C411yescharacteristic
144C4⋊C8×C43C2×C411yescharacteristic
145C4⋊C8×C43C2×C411yescharacteristic
146C4⋊C8×C43D411yescharacteristic
147C4⋊C8×C43D411yescharacteristic
148C4⋊C8×C43D411yescharacteristic
149C4⋊C8×C43D411yescharacteristic
150#97×C43—41no—
151C4×C8×C43—41no—
152#95×C43—21no—
153#95×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43#4111yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—21no—
160#10621898—21no—
161#10621898—21no—
162#10621898C2×Q812yes—
163#10621898#4112yes—
164C2×D172C22×C411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86C22×C411yescharacteristic
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C22×C411yescharacteristic
180C2×C8×C43C22×C411yescharacteristic
181C2×C8×C43C22×C411yescharacteristic
182C2×C8×C43C22×C411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43C22×C411yescharacteristic
191C42×C43C22×C411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2×Q812yes—
195C22⋊Dic43—21no—
196C22⋊Dic43—21no—
197C22⋊Dic43—21no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43C22×C411yescharacteristic
203C4⋊Dic43C22×C411yescharacteristic
204C4⋊Dic43C22×C411yescharacteristic
205C4⋊Dic43C22×C411yescharacteristic
206C4⋊Dic43C22×C411yescharacteristic
207C4⋊Dic43C22×C411yescharacteristic
208Dic43⋊C4—21no—
209Dic43⋊C4—21no—
210Dic43⋊C4—21no—
211Dic43⋊C4—21no—
212Dic43⋊C4—21no—
213Dic43⋊C4—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877—21no—
223#10621877—21no—
224#10621877—21no—
225#10621877—21no—
226#10621877C2×Q812yes—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231#10621872—42no—
232#10621872—42no—
233C8×D43—42no—
234C8×D43—42no—
235C23×C43C2×#4111yescharacteristic
236C22×D43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43C4×D411yescharacteristic
246C2×C4×C43C4×D411yescharacteristic
247C2×C4×C43C4×D411yescharacteristic
248C2×C4×C43C4×D411yescharacteristic
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×Q811yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C22⋊D43—22no—
256C22⋊D43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264D172—21no—
265D172C4×Q812yes—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—42no—
269C4×D43—81no—
270Dic86—21no—
271Dic86—42no—
272Dic86—81no—
273Dic86C4×Q812yes—
274C8×C43—21no—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—21no—
279C8×C43—21no—
280C8×C43—21no—
281C8×C43—21no—
282C43⋊C8—22no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286#22984—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43C2×C4×D411yescharacteristic
290C22×C43#55211yescharacteristic
291C22×C43#55411yescharacteristic
292C2×D43—22no—
293C2×D43—41no—
294C2×D43—41no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—42no—
300C4×C43—81no—
301C4×C43C2×C4×Q811yescharacteristic
302C4×C43#52011yescharacteristic
303C4×C43#54611yescharacteristic
304C4×C43D4×Q811yescharacteristic
305Dic43—22no—
306Dic43—41no—
307Dic43—41no—
308Dic43—41no—
309Dic43—41no—
310Dic43—41no—
311Dic43—41no—
312#3076—431no—
313#2962—431no—
314#2906—431no—
315#1995—431no—
316#1950—431no—
317#1946—431no—
318#1945—431no—
319#1922—431no—
320#1922—431no—
321#1866—431no—
322#1866—431no—
323#1768D4311yescharacteristic, complemented
324#1765—431no—
325#1764—431no—
326#1759—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43#236011yescharacteristic
330C2×C43#295511yescharacteristic
331C2×C43#295711yescharacteristic
332D43—42no—
333C2×#131—431no—
334C2×#131—431no—
335#533—431no—
336C4×#41—431no—
337#479—431no—
338#479—431no—
339#478—431no—
340#478—431no—
341#477—431no—
342#476—431no—
343#475—431no—
344#474—431no—
345#446—861no—
346#446—861no—
347#446—861no—
348C8×Q8—861no—
349C2×#108—431no—
350C2×#108—431no—
351#427—431no—
352#427—431no—
353#424—431no—
354#424—431no—
355#424—431no—
356#424—431no—
357#424—861no—
358#424—861no—
359#423—431no—
360#423—861no—
361C2×C4⋊C8—861no—
362C2×C4⋊C8C2×D4311yescharacteristic
363C2×C4⋊C8C2×D4311yescharacteristic
364C2×#104—431no—
365C2×#104—431no—
366#416—431no—
367#416—431no—
368#405—431no—
369#405—431no—
370C4×M16—431no—
371C2×#97C2×D4311yescharacteristic
372C2×C4×C8C2×D4311yescharacteristic
373#376C2×D4311yescharacteristic
374#341—431no—
375#341—431no—
376#339—431no—
377#339—431no—
378#339—431no—
379#339—431no—
380#339—431no—
381#339—431no—
382#336C2×D4311yescharacteristic
383#336C2×D4311yescharacteristic
384C43#2298411yescharacteristic, complemented, Sylow
385C2×#41—431no—
386#131—862no—
387#131—862no—
388#131—1721no—
389#131—1721no—
390C2×M16—431no—
391C2×M16—431no—
392C2×M16—431no—
393C2×M16—431no—
394C2×M16—861no—
395C2×M16—861no—
396C22×C8—861no—
397C22×C8—861no—
398C22×C8C22×D4311yescharacteristic
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402C4⋊Q8—431no—
403C4⋊Q8—431no—
404#125—431no—
405#125—431no—
406C22⋊Q8—861no—
407C22⋊Q8—861no—
408C4×Q8—431no—
409C4×Q8—431no—
410C4×Q8—861no—
411C4×Q8—861no—
412C4×D4—431no—
413C4×D4—431no—
414C4×D4—861no—
415C4×D4—861no—
416#117—431no—
417#117—431no—
418#117—431no—
419#117—861no—
420C2×C42—861no—
421C2×C42C22×D4311yescharacteristic
422C2×C42C22×D4311yescharacteristic
423C2×C42C22×D4311yescharacteristic
424#108—1721no—
425#108—1721no—
426#107—431no—
427#107—431no—
428#107—431no—
429#107—431no—
430#106—431no—
431#106—431no—
432#106—431no—
433#106—431no—
434C4⋊C8—861no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437C4⋊C8—861no—
438C4⋊C8—861no—
439C4⋊C8—861no—
440C4⋊C8—861no—
441C4⋊C8—861no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8C4×D4311yescharacteristic
445C4⋊C8C4×D4311yescharacteristic
446C4⋊C8C4×D4311yescharacteristic
447C4⋊C8C4×D4311yescharacteristic
448C4⋊C8D17211yescharacteristic
449C4⋊C8D17211yescharacteristic
450C4⋊C8D17211yescharacteristic
451C4⋊C8D17211yescharacteristic
452#104—434no—
453#104—862no—
454#103—431no—
455#103—431no—
456#103—431no—
457#103—431no—
458#102—431no—
459#102—431no—
460#102—431no—
461#102—431no—
462#97—41no—
463#97—861no—
464#97—861no—
465#97—861no—
466C4×C8—41no—
467C4×C8—861no—
468C4×C8—861no—
469C4×C8—861no—
470#95—21no—
471#95—21no—
472#41—432no—
473#41—432no—
474#41—861no—
475#41—861no—
476C2×Q8—431no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×D4—431no—
480C2×D4—861no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4#1062189811yescharacteristic
487C22×C4#1062189811yescharacteristic
488C22×C4C23×D4311yescharacteristic
489M16—432no—
490M16—861no—
491M16—861no—
492M16—861no—
493M16—861no—
494M16—861no—
495M16—861no—
496M16—861no—
497M16—1722no—
498M16—1722no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—1722no—
512C2×C8—1722no—
513C2×C8C2×C4×D4311yescharacteristic
514C2×C8C2×C4×D4311yescharacteristic
515C2×C8C2×C4×D4311yescharacteristic
516C2×C8C2×C4×D4311yescharacteristic
517C2×C8C2×D17211yescharacteristic
518C2×C8C2×D17211yescharacteristic
519C2×C8C2×D17211yescharacteristic
520C2×C8C2×D17211yescharacteristic
521C4⋊C4—431no—
522C4⋊C4—431no—
523C4⋊C4—431no—
524C4⋊C4—431no—
525C4⋊C4—431no—
526C4⋊C4—431no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C22⋊C4—861no—
536C22⋊C4—861no—
537C22⋊C4—861no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—861no—
544C42—861no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42C2×C4×D4311yescharacteristic
549C42C2×C4×D4311yescharacteristic
550C42C2×D17211yescharacteristic
551C42C2×D17211yescharacteristic
552C42Q8×D4312yes—
553C23—861no—
554C23C2×#1062189811yescharacteristic
555Q8—432no—
556Q8—861no—
557Q8—3441no—
558Q8—1722no—
559D4—432no—
560D4—862no—
561D4—862no—
562D4—861no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—861no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—3441no—
581C2×C4—1722no—
582C2×C4C4×D17211yescharacteristic
583C2×C4C4×D17211yescharacteristic
584C2×C4C4×D17211yescharacteristic
585C2×C4C4×D17211yescharacteristic
586C2×C4C22×C4×D4311yescharacteristic
587C2×C4C22×D17211yescharacteristic
588C2×C4C2×Q8×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4#1306337011yescharacteristic
591C2×C4#1306337211yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—21no—
599C8—21no—
600C8—862no—
601C8—1721no—
602C8—1721no—
603C8—1721no—
604C22—21no—
605C22—21no—
606C22—862no—
607C22—1721no—
608C22—1721no—
609C22C2×C4×D17211yescharacteristic
610C22#1458358811yescharacteristic
611C22#1458360411yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—81no—
618C4—862no—
619C4—1721no—
620C4—1721no—
621C4—1721no—
622C4—1721no—
623C4—1721no—
624C4—1721no—
625C4C4×Q8×D4311yescharacteristic
626C4#1458337811yescharacteristic
627C4#1458354411yescharacteristic
628C4Q8×D17211yescharacteristic
629C2—21no—
630C2—21no—
631C2—1722no—
632C2#1913760211yescharacteristic
633C2#1914349911yescharacteristic
634C2#1914351311yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1768C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621898C23
cosocleC22×C4×C43C24
hypercenter#1768D43
hypocenterC43#22984
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #1768

Complements

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

NH ≅ G/Ntype
2. #19143538C2semidirect
4. #19135576C2semidirect
5. #19135371C2semidirect
6. #19135348C2semidirect
7. #19135343C2semidirect
8. #19135195C2semidirect
9. #19135195C2semidirect
15. C43×#1768C2semidirect
20. #14583207C4semidirect
21. #14583207C4semidirect
22. #14583200C4semidirect
23. #14583200C4semidirect
24. #14583195C4semidirect
25. #14583190C4semidirect
26. #14583185C4semidirect
27. #14583180C4semidirect
120. #13063253Q8semidirect
323. #1768D43semidirect
384. C43#22984semidirect

Maximal subgroups

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

subgroupindex
#191443852
#191435382
#191431602
#191355762
#191353712
#191353482
#191353432
#191351952
#191348732
#191344392
#191344322
#191344062
C43×#17682
#2298443