Finite Group Databasebeta

← #25126591

Subgroups — #25126591

Order 11008.

880 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063300C211yesmaximal, characteristic
2#19136999C211yesmaximal, characteristic, complemented
3#19136156C211yesmaximal, characteristic, complemented
4#19136120C211yesmaximal, characteristic, complemented
5#19136069C211yesmaximal, characteristic, complemented
6#19136022C211yesmaximal, characteristic, complemented
7#19136019C211yesmaximal, characteristic, complemented
8#19136002C211yesmaximal, characteristic, complemented
9#19135780C211yesmaximal, characteristic
10#19135779C211yesmaximal, characteristic
11C4×#13063258C211yesmaximal, characteristic, complemented
12C4×#13063245C211yesmaximal, characteristic, complemented
13C4×#13063247C211yesmaximal, characteristic, complemented
14C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C4×#107×C43C211yesmaximal, characteristic, complemented
16C2×#13063300C2211yescharacteristic
17C2×C4×D172—21no—
18C2×C4×D172C2211yescharacteristic
19C2×#13063282—21no—
20C2×C42×D43C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582800C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582791—21no—
33#14582777—21no—
34#14582768C2211yescharacteristic
35#14582768C2211yescharacteristic
36#14582763—21no—
37#14582758—21no—
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41C4×Dic43⋊C4—21no—
42C4×C4⋊Dic43C2211yescharacteristic
43C4×(C2×D43)⋊C4—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×C4×C8×C43C2211yescharacteristic
55C4×C4⋊C4×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×D172—21no—
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063300—22no—
68#13063300—22no—
69C4×D172—22no—
70C4×D172—22no—
71C4×D172—44no—
72#13063282—44no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92C42×D43—22no—
93C42×D43—22no—
94#13063258—22no—
95#13063258—22no—
96#13063247—22no—
97#13063247—22no—
98#13063245—22no—
99#13063245—22no—
100(C2×D43)⋊C8—22no—
101(C2×D43)⋊C8—22no—
102C4×C43⋊C8—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#107×C43—22no—
118#107×C43—22no—
119C4×C8×C43—22no—
120#95×C43—21no—
121#95×C43—21no—
122C23×D43—21no—
123C23×D43C2×D411yescharacteristic
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C2×D172—24no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—42no—
144C2×D172—42no—
145C2×D172#4112yes—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—22no—
156C2×C4×D43—41no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43D814yes—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43#4112yes—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43#4112yes—
175C42×C43—42no—
176C42×C43—42no—
177C42×C43#4112yes—
178C42×C43#4112yes—
179(C2×D43)⋊C4—24no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197C4×Dic43—22no—
198C4×Dic43—22no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—42no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8#4112yes—
208C23×C43C22×D411yescharacteristic
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43—22no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43C2×D812yes—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
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×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43#12312yes—
238C2×C4×C43#12312yes—
239C2×C4×C43C2×D812yes—
240C2×C4×C43#13712yes—
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
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×Dic43C2×D812yes—
264C2×Dic43#13512yes—
265D172—22no—
266D172—22no—
267D172—48no—
268D172—41no—
269D172—41no—
270C4×D43—28no—
271C4×D43—44no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—84no—
277C8×C43—22no—
278C8×C43—41no—
279C43⋊C8—22no—
280C43⋊C8—41no—
281#23754—431nomaximal, Sylow
282C22×C43C2×#12311yescharacteristic
283C22×C43#52511yescharacteristic
284C22×C43#53211yescharacteristic
285C22×C43C22×D811yescharacteristic
286C22×C43C2×#13511yescharacteristic
287C22×C43C2×#13711yescharacteristic
288C22×C43#57511yescharacteristic
289C2×D43—22no—
290C2×D43—22no—
291C2×D43—22no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C4×C43—22no—
304C4×C43—42no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43#48014yes—
309C4×C43#52911yescharacteristic
310C4×C43#52911yescharacteristic
311C4×C43#52911yescharacteristic
312C4×C43#52911yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—41no—
316Dic43—81no—
317Dic43—81no—
318Dic43—81no—
319C4×#121—431no—
320#2285—431no—
321#2099—431no—
322#2093—431no—
323#2083—431no—
324#2075—431no—
325#2075—431no—
326#2071—431no—
327#2033—431no—
328#2033—431no—
329C4×#107—431no—
330C4×#107D4311yescharacteristic, complemented
331C4×#102—431no—
332C4×#102—431no—
333C4×C22⋊C8—431no—
334C2×C43#239511yescharacteristic
335C2×C43C2×#48011yescharacteristic
336C2×C43#309111yescharacteristic
337C2×C43#310011yescharacteristic
338C2×C43#310711yescharacteristic
339C2×C43#316911yescharacteristic
340C2×C43#317211yescharacteristic
341D43—42no—
342D43—82no—
343C2×#121—431no—
344C2×C4×D4—431no—
345C2×C4×D4—861no—
346C2×#117—861no—
347C22×C42—431no—
348C2×#107—431no—
349C2×#107—431no—
350C2×#107C2×D4311yescharacteristic
351C2×#107C2×D4311yescharacteristic
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×C22⋊C8—431no—
357C2×C22⋊C8—431no—
358C2×C4×C8—431no—
359C2×C4×C8C2×D4311yescharacteristic
360#390—431no—
361#389—431no—
362#388—861no—
363#386—861no—
364#384—431no—
365#384—431no—
366#382—861no—
367#380—431no—
368#380—431no—
369#380—431no—
370#380—861no—
371C4×C4⋊C4—431no—
372C4×C4⋊C4—861no—
373C4×C4⋊C4C2×D4311yescharacteristic
374C4×C4⋊C4C2×D4311yescharacteristic
375C4×C22⋊C4—861no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340C2×D4311yescharacteristic
383#340C2×D4311yescharacteristic
384#336—431no—
385#336—431no—
386C43#2375411yescharacteristic, complemented, Sylow
387C22×D4—431no—
388C22×D4—861no—
389C23×C4—431no—
390C23×C4—431no—
391C23×C4—431no—
392C23×C4—861no—
393C22×C8—431no—
394C22×C8—431no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397#121—862no—
398#121—862no—
399C4×D4—862no—
400C4×D4—862no—
401C4×D4—1724no—
402#117—1724no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C4⋊C4C22×D4311yescharacteristic
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—862no—
428C2×C42—862no—
429C2×C42—861no—
430C2×C42C22×D4311yescharacteristic
431#107—22no—
432#107—22no—
433#107—862no—
434#107—862no—
435#102—862no—
436#102—862no—
437#102—862no—
438#102—862no—
439C22⋊C8—862no—
440C22⋊C8—862no—
441C4×C8—22no—
442C4×C8—862no—
443#95—21no—
444#95—21no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450C24—431no—
451C24—861no—
452C2×D4—432no—
453C2×D4—864no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—1722no—
460C2×D4—1722no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—434no—
468C22×C4—431no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—1721no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4—1722no—
486C22×C4D4×D4311yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4C23×D4311yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—432no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8#1062189812yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4#1062189812yes—
520C22⋊C4—864no—
521C22⋊C4—1722no—
522C22⋊C4—1722no—
523C22⋊C4—1722no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C42—42no—
528C42—42no—
529C42—862no—
530C42—862no—
531C42—861no—
532C42—861no—
533C42—1722no—
534C42#1062189812yes—
535C42#1062190212yes—
536C23—432no—
537C23—861no—
538C23—861no—
539C23—861no—
540C23—861no—
541C23—861no—
542C23—861no—
543C23—862no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23—1721no—
550C23C2×D4×D4311yescharacteristic
551D4—862no—
552D4—862no—
553D4—1728no—
554D4—1721no—
555D4—1721no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—432no—
571C2×C4—432no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—868no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—3444no—
581C2×C4—1724no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4#1306331012yes—
596C2×C4#1306331012yes—
597C2×C4D8×D4312yes—
598C2×C4#1306335712yes—
599C2×C4#41×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4C2×#1062189811yescharacteristic
602C2×C4C2×#1062189811yescharacteristic
603C2×C4C2×#1062189811yescharacteristic
604C2×C4C2×#1062190211yescharacteristic
605C8—22no—
606C8—41no—
607C8—862no—
608C8—1721no—
609C22—862no—
610C22—862no—
611C22—862no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—3441no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22—1721no—
620C22—1721no—
621C22—1721no—
622C22—1721no—
623C22C2×#1306331011yescharacteristic
624C22#1458340811yescharacteristic
625C22#1458344611yescharacteristic
626C22C2×D8×D4311yescharacteristic
627C22#135×D4311yescharacteristic
628C22C2×#1306335711yescharacteristic
629C22#1458369611yescharacteristic
630C4—22no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—862no—
636C4—862no—
637C4—3441no—
638C4—3441no—
639C4—3441no—
640C4—1721no—
641C4#1458321414yes—
642C4#1458342711yescharacteristic
643C4#1458343311yescharacteristic
644C4#1458343611yescharacteristic
645C4#1458343611yescharacteristic
646C2—3442no—
647C2—1722no—
648C2#1913785811yescharacteristic
649C2C2×#1458321411yescharacteristic
650C2#1914451211yescharacteristic
651C2#1914459311yescharacteristic
652C2#1914466411yescharacteristic
653C2#1914517111yescharacteristic
654C2#1914519911yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#107×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenterC4×#107D43
hypocenterC43#23754
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
2. #19136999C2semidirect
3. #19136156C2semidirect
4. #19136120C2semidirect
5. #19136069C2semidirect
6. #19136022C2semidirect
7. #19136019C2semidirect
8. #19136002C2semidirect
11. C4×#13063258C2semidirect
12. C4×#13063245C2semidirect
13. C4×#13063247C2semidirect
14. C4×(C2×D43)⋊C8C2semidirect
15. C4×#107×C43C2semidirect
330. C4×#107D43semidirect
386. C43#23754semidirect

Maximal subgroups

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

subgroupindex
C4×#130633002
#191369992
#191361562
#191361202
#191360692
#191360222
#191360192
#191360022
#191357802
#191357792
C4×#130632582
C4×#130632452
C4×#130632472
C4×(C2×D43)⋊C82
C4×#107×C432
#2375443