Finite Group Databasebeta

← #25159534

Subgroups — #25159534

Order 11008.

804 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583208C211yesmaximal, characteristic, complemented
2C2×#14582940C211yesmaximal, characteristic
3#19138317C211yesmaximal, characteristic
4#19137627C211yesmaximal, characteristic
5#19136143C211yesmaximal, characteristic, complemented
6#19136092C211yesmaximal, characteristic, complemented
7#19135931C211yesmaximal, characteristic, complemented
8#19135365C211yesmaximal, characteristic, complemented
9#19135170C211yesmaximal, characteristic, complemented
10#19135025C211yesmaximal, characteristic
11#19134899C211yesmaximal, characteristic
12#19134865C211yesmaximal, characteristic, complemented
13#19134797C211yesmaximal, characteristic
14#19134776C211yesmaximal, characteristic
15C43×#2068C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22#14583208—24no—
23#14582940—24no—
24C2×#13063259C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33#14582839—21no—
34#14582829—21no—
35#14582798C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582791—21no—
38#14582788—21no—
39#14582786—21no—
40#14582773—21no—
41#14582765C2211yescharacteristic
42#14582756—21no—
43#14582756C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582750—21no—
46C4×(C2×D43)⋊C4C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×C4×D43—21no—
62C22×C4×D43C2311yescharacteristic
63C2×#10621872—22no—
64C2×#10621872—22no—
65C2×#10621872—22no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063316—22no—
69#13063316—41no—
70#13063301—22no—
71#13063301Q814yes—
72Q8×Dic43—22no—
73Q8×Dic43—41no—
74#13063283—22no—
75#13063283—41no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
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—
87C4⋊C4×D43—22no—
88C4⋊C4×D43—41no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4D411yescharacteristic
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98#13063259—22no—
99#13063258—22no—
100#13063257—22no—
101#13063256—41no—
102#13063256D414yes—
103Dic43⋊C8—22no—
104#13063249—22no—
105#13063249—41no—
106(C2×D43)⋊C8—22no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C22×Q8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#107×C43—22no—
124C4⋊C8×C43—22no—
125#103×C43—22no—
126#103×C43—22no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130C23×D43C2×D411yescharacteristic
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43C2×Q812yes—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43—81no—
158C2×C4×D43C2×Q812yes—
159C2×C4×D43#4112yes—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43#4112yes—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43C2×D412yes—
173C42×C43—21no—
174C42×C43—21no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—41no—
177(C2×D43)⋊C4—41no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—42no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—42no—
187C4⋊Dic43—42no—
188C4⋊Dic43—81no—
189C4⋊Dic43C2×D412yes—
190C4⋊Dic43C2×Q812yes—
191Dic43⋊C4—24no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—42no—
198C4×Dic43—42no—
199C4×Dic43—42no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C2×D412yes—
206#10621872—28no—
207C23×C43C22×D411yescharacteristic
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43C22⋊Q812yes—
215Q8×C43—22no—
216Q8×C43—22no—
217Q8×C43—41no—
218Q8×C43—41no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
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×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×Q811yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
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—41no—
263C2×Dic43C22⋊Q812yes—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—84no—
269C8×C43—22no—
270C8×C43—41no—
271C43⋊C8—22no—
272C43⋊C8—41no—
273#26367—431nomaximal, Sylow
274C22×C43C2×C22⋊Q811yescharacteristic
275C22×C43D4211yescharacteristic
276C22×C43#54711yescharacteristic
277C22×C43#57511yescharacteristic
278C22×C43#57511yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57811yescharacteristic
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—22no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—42no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43#52511yescharacteristic
295C4×C43#53911yescharacteristic
296C4×C43D4×Q811yescharacteristic
297C4×C43#55411yescharacteristic
298Dic43—22no—
299Dic43—42no—
300Dic43—41no—
301Dic43—42no—
302Dic43—41no—
303Dic43—81no—
304Dic43—81no—
305C2×#479—431no—
306C2×#428—431no—
307#2442—431no—
308#2362—431no—
309#2097—431no—
310#2087—431no—
311#2068D4311yescharacteristic, complemented
312#2059—431no—
313#1949—431no—
314#1919—431no—
315#1894—431no—
316#1872—431no—
317#1865—431no—
318#1854—431no—
319#1851—431no—
320C2×C43#244911yescharacteristic
321C2×C43#308011yescharacteristic
322C2×C43#308211yescharacteristic
323C2×C43#326911yescharacteristic
324C2×C43#327511yescharacteristic
325C2×C43#334911yescharacteristic
326C2×C43#335111yescharacteristic
327D43—42no—
328C22×M16—431no—
329C2×#125—431no—
330C2×C22⋊Q8—431no—
331C2×C4×Q8—431no—
332C2×#117—431no—
333C22×C4⋊C4—431no—
334#479—864no—
335#428—864no—
336C2×#107—431no—
337C2×#107—431no—
338C2×#107C2×D4311yescharacteristic
339C2×#106—431no—
340C2×#106—431no—
341C2×#106—431no—
342C2×C4⋊C8—431no—
343C2×C4⋊C8C2×D4311yescharacteristic
344C2×#103—431no—
345C2×#103—431no—
346C2×#103C2×D4311yescharacteristic
347C2×#103C2×D4311yescharacteristic
348C2×C22⋊C8—431no—
349#400—861no—
350#398—861no—
351#391C2×D4311yescharacteristic
352#389—431no—
353#389—431no—
354#389C2×D4311yescharacteristic
355#388—861no—
356#388—861no—
357#387—861no—
358#385—861no—
359#382—431no—
360#380—431no—
361#380—861no—
362C4×C4⋊C4—431no—
363C4×C4⋊C4—861no—
364C4×C22⋊C4—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340C2×D4311yescharacteristic
371#336—431no—
372#336—431no—
373C43#2636711yescharacteristic, complemented, Sylow
374C22×Q8C22×D4311yescharacteristic
375C23×C4—431no—
376C23×C4—861no—
377C2×M16—862no—
378C2×M16—862no—
379C2×M16—862no—
380C22×C8—431no—
381C22×C8—431no—
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384#125—862no—
385#125—1721no—
386C22⋊Q8—434no—
387C22⋊Q8—862no—
388C4×Q8—862no—
389C4×Q8—1721no—
390#117—862no—
391#117—1721no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—862no—
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×C22⋊C4—431no—
410C2×C22⋊C4—431no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—431no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42—861no—
418C2×C42C22×D4311yescharacteristic
419#107—22no—
420#107—862no—
421#107—862no—
422#106—434no—
423#106—862no—
424#106—1721no—
425C4⋊C8—22no—
426C4⋊C8—862no—
427#103—22no—
428#103—22no—
429#103—862no—
430#103—1721no—
431C22⋊C8—862no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—431no—
436#95—431no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443C24—431no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8Q8×D4312yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—431no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—3441no—
468C22×C4—1722no—
469C22×C4—1722no—
470C22×C4D4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4C23×D4311yescharacteristic
473M16—868no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—432no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8#1062190012yes—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—81no—
492C4⋊C4—432no—
493C4⋊C4—432no—
494C4⋊C4—864no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—3441no—
502C4⋊C4—1722no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C4⋊C4—1722no—
507C4⋊C4D4×D4312yes—
508C22⋊C4—864no—
509C22⋊C4—1721no—
510C22⋊C4—1721no—
511C22⋊C4—1722no—
512C22⋊C4—1722no—
513C42—21no—
514C42—21no—
515C42—861no—
516C42—861no—
517C42—1722no—
518C42—1722no—
519C42—1722no—
520C23—432no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23—861no—
525C23—861no—
526C23—861no—
527C23C2×D4×D4311yescharacteristic
528Q8—22no—
529Q8—22no—
530Q8—41no—
531Q8—41no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—432no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—862no—
565C2×C4—3444no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4C2×D4×D4311yescharacteristic
577C2×C4C2×Q8×D4311yescharacteristic
578C2×C4#41×D4311yescharacteristic
579C2×C4C2×#1062190011yescharacteristic
580C2×C4#1306337111yescharacteristic
581C2×C4#1306337211yescharacteristic
582C8—22no—
583C8—41no—
584C8—862no—
585C8—1721no—
586C22—862no—
587C22—862no—
588C22—862no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22C22⋊Q8×D4311yescharacteristic
594C22#1458353311yescharacteristic
595C22#1458354911yescharacteristic
596C22#1458369611yescharacteristic
597C22#1458369811yescharacteristic
598C22#1458370911yescharacteristic
599C22#1458371211yescharacteristic
600C4—42no—
601C4—41no—
602C4—41no—
603C4—42no—
604C4—81no—
605C4—81no—
606C4—862no—
607C4—3441no—
608C4—3441no—
609C4—1721no—
610C4—1722no—
611C4—1722no—
612C4—1721no—
613C4#1458340911yescharacteristic
614C4#1458349011yescharacteristic
615C4#1458356211yescharacteristic
616C4#1458360711yescharacteristic
617C2—1722no—
618C2#1913840511yescharacteristic
619C2#1914441411yescharacteristic
620C2#1914443211yescharacteristic
621C2#1914614511yescharacteristic
622C2#1914623211yescharacteristic
623C2#1914713111yescharacteristic
624C2#1914716111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2068C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2068D43
hypocenterC43#26367
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2068

Complements

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

NH ≅ G/Ntype
1. C2×#14583208C2semidirect
5. #19136143C2semidirect
6. #19136092C2semidirect
7. #19135931C2semidirect
8. #19135365C2semidirect
9. #19135170C2semidirect
12. #19134865C2semidirect
15. C43×#2068C2semidirect
311. #2068D43semidirect
373. C43#26367semidirect

Maximal subgroups

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

subgroupindex
C2×#145832082
C2×#145829402
#191383172
#191376272
#191361432
#191360922
#191359312
#191353652
#191351702
#191350252
#191348992
#191348652
#191347972
#191347762
C43×#20682
#2636743