Finite Group Databasebeta

← #25065226

Subgroups — #25065226

Order 11008.

952 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic
3C2×#14582955C211yesmaximal, characteristic
4#19133319C212yesmaximal, complemented
5#19133310C212yesmaximal, complemented
6#19133304C212yesmaximal, complemented
7#19133302C212yesmaximal, complemented
8#19133286C211yesmaximal, characteristic, complemented
9#19133285C211yesmaximal, characteristic, complemented
10#19133283C211yesmaximal, characteristic, complemented
11C43×#1550C211yesmaximal, characteristic, complemented
12#14583456C2211yescharacteristic
13#14583455—21no—
14#14583454C2211yescharacteristic
15#14583454C2211yescharacteristic
16#14583453—21no—
17#14583453C412yes—
18#14583452—21no—
19#14583451—21no—
20#14583451C412yes—
21C4⋊Q8×D43C2211yescharacteristic
22C4⋊Q8×D43C2211yescharacteristic
23#125×D43—21no—
24C22⋊Q8×D43—21no—
25C22⋊Q8×D43C412yes—
26C4×Q8×D43—21no—
27C4×Q8×D43C412yes—
28#117×D43—21no—
29C2×C42×D43C2211yescharacteristic
30#14582955—21no—
31#14582955—21no—
32#14582955—21no—
33#14582955C2212yes—
34#14582955C2212yes—
35#14582955C2212yes—
36#14582951—21no—
37#14582951C2212yes—
38#14582923C2211yescharacteristic
39C2×C4⋊(C43⋊C8)C2211yescharacteristic
40#14582862—21no—
41C2×(C2×D43)⋊C8—21no—
42M16×Dic43—21no—
43C2×#13063235—21no—
44#14582648C2212yescomplemented
45#14582647C2212yescomplemented
46#14582647C2212yescomplemented
47#14582646C2212yescomplemented
48#14582645C2212yescomplemented
49#14582644C2212yescomplemented
50C43×#533C2211yescharacteristic
51C43×#423C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C43×#333C2212yescomplemented
54C43×#332C2212yescomplemented
55C2×Q8×D43—21no—
56C2×Q8×D43C2×C412yes—
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43D411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C2×#10621877—21no—
61C22×C43⋊C8—21no—
62#13063325C2311yescharacteristic
63#13063325C2311yescharacteristic
64#13063324—21no—
65#13063324—21no—
66#13063324—21no—
67#13063324C2×C412yes—
68#13063323—21no—
69#13063323C2×C412yes—
70#13063317—21no—
71#13063316—21no—
72#13063316—21no—
73#13063315—22no—
74#13063315—22no—
75#13063305—21no—
76#13063305C2×C412yes—
77#13063304—21no—
78#13063304C2×C412yes—
79#13063303—22no—
80#13063303—22no—
81#13063302—22no—
82#13063302—22no—
83#13063301—21no—
84#13063301C2×C412yes—
85Q8×Dic43—21no—
86Q8×Dic43C2×C412yes—
87C4×Dic86—21no—
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×Dic86C2×C412yes—
91#13063290—22no—
92#13063290—22no—
93#13063290—21no—
94#13063290C2×C412yes—
95#13063284—21no—
96#13063283—21no—
97#13063283—21no—
98#13063282—22no—
99#13063281—22no—
100C4⋊C4×D43—22no—
101C4⋊C4×D43—22no—
102C4⋊C4×D43—21no—
103C4⋊C4×D43—21no—
104C4⋊C4×D43—21no—
105C4⋊C4×D43C2×C412yes—
106C22⋊C4×D43—22no—
107C2×C4×Dic43C2×C411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C42×D43—22no—
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43C2311yescharacteristic
118C42×D43C2311yescharacteristic
119C4⋊(C43⋊C8)—21no—
120C4⋊(C43⋊C8)—21no—
121C4⋊(C43⋊C8)C2312yes—
122C4⋊(C43⋊C8)C2312yes—
123(C2×D43)⋊C8—22no—
124(C2×D43)⋊C8—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—22no—
127#13063235—22no—
128#13063235—22no—
129#13063235—22no—
130C8×Dic43—22no—
131C2×M16×C43—21no—
132C22×C8×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134C4⋊Q8×C43C2311yescharacteristic
135#125×C43—21no—
136C22⋊Q8×C43—21no—
137C22⋊Q8×C43C2×C412yes—
138C4×Q8×C43—21no—
139C4×Q8×C43C2×C412yes—
140#117×C43—21no—
141C2×C42×C43C2311yescharacteristic
142C4⋊C8×C43—21no—
143C4⋊C8×C43—21no—
144C4⋊C8×C43C2312yes—
145C4⋊C8×C43C2312yes—
146C23×D43C22⋊C411yescharacteristic
147C2×Q8×C43—21no—
148C2×Q8×C43C22×C412yes—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×Dic43C22⋊C411yescharacteristic
153C22×Dic43C22⋊C411yescharacteristic
154C22×Dic43C22⋊C411yescharacteristic
155Q8×D43—42no—
156Q8×D43—42no—
157Q8×D43—44no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—42no—
163C2×C4×D43—41no—
164C2×C4×D43—41no—
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22×C411yescharacteristic
172C2×C4×D43C22×C411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×Dic86—21no—
178C2×Dic86—22no—
179C2×Dic86—22no—
180C2×Dic86C22×C412yes—
181M16×C43—42no—
182C2×C8×C43—22no—
183C2×C8×C43—22no—
184C2×C8×C43—42no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43C22×C412yes—
191C22⋊C4×C43—22no—
192C42×C43—22no—
193C42×C43C22×C411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C42×C43C2×D411yescharacteristic
196C42×C43C2411yescharacteristic
197C22⋊Dic43—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43C22×C412yes—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214C4×Dic43—22no—
215C4×Dic43—22no—
216C4×Dic43—22no—
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22×C411yescharacteristic
224C4×Dic43C22×C411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227C4×Dic43C2×D411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229#10621877—42no—
230C2×C43⋊C8—22no—
231C2×C43⋊C8—22no—
232C2×C43⋊C8—42no—
233C23×C43C2×C22⋊C411yescharacteristic
234C22×D43—22no—
235C22×D43—22no—
236C22×D43—41no—
237C22×D43C2×C22⋊C411yescharacteristic
238C22×D43C2×C22⋊C411yescharacteristic
239Q8×C43—42no—
240Q8×C43—41no—
241Q8×C43—41no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—41no—
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43#13712yes—
251C2×C4×C43#13712yes—
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—21no—
269C4×D43—21no—
270C4×D43—21no—
271C4×D43—21no—
272C4×D43—21no—
273C4×D43—21no—
274C4×D43—21no—
275C4×D43—21no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—44no—
283C4×D43—44no—
284Dic86—44no—
285Dic86—44no—
286Dic86—41no—
287Dic86—41no—
288Dic86—42no—
289C8×C43—42no—
290C8×C43—42no—
291C43⋊C8—42no—
292C43⋊C8—42no—
293#17748—431nomaximal, Sylow
294C22×C43—21no—
295C22×C43—21no—
296C22×C43#41912yes—
297C22×C43C22×C22⋊C411yescharacteristic
298C2×D43—21no—
299C2×D43—21no—
300C2×D43—21no—
301C2×D43—21no—
302C2×D43—21no—
303C2×D43—44no—
304C2×D43#41312yes—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—42no—
309C4×C43—42no—
310C4×C43#41912yes—
311C4×C43C2×#13711yescharacteristic
312C4×C43C2×#13711yescharacteristic
313C4×C43#57511yescharacteristic
314C4×C43#57511yescharacteristic
315Dic43—21no—
316Dic43—21no—
317Dic43—21no—
318Dic43—21no—
319Dic43—21no—
320Dic43—21no—
321Dic43—42no—
322Dic43—42no—
323C2×#533—431no—
324#2920—431no—
325C2×#432—431no—
326#1558—432no—
327#1556—432no—
328#1554—432no—
329#1554—432no—
330#1550—431no—
331#1550—431no—
332#1550—431no—
333#1550D4311yescharacteristic, complemented
334C2×C43—22no—
335C2×C43C2×#41311yescharacteristic
336C2×C43C2×#41911yescharacteristic
337C2×C43#289611yescharacteristic
338D43—22no—
339D43—41no—
340#533—431no—
341#533—431no—
342#533—432no—
343#533—432no—
344#533—431no—
345#533—861no—
346#533—861no—
347#533—861no—
348#533—861no—
349#533C2×D4311yescharacteristic
350C2×C4⋊Q8—431no—
351C2×C4⋊Q8—431no—
352C2×#125—861no—
353C2×C22⋊Q8—432no—
354C2×C22⋊Q8—861no—
355C2×C4×Q8—432no—
356C2×C4×Q8—861no—
357C2×#117—861no—
358C22×C42—431no—
359#432—432no—
360#432—432no—
361#432—432no—
362#432—861no—
363#432—861no—
364#432—861no—
365#431—432no—
366#431—861no—
367#423—431no—
368#423C2×D4311yescharacteristic
369C2×C4⋊C8—431no—
370C2×C4⋊C8C2×D4311yescharacteristic
371#407—861no—
372C2×C22⋊C8—861no—
373C4×M16—861no—
374C2×#97—861no—
375#333—432no—
376#333—432no—
377#333—432no—
378#333C2×D4312yescomplemented
379#332—432no—
380#332—432no—
381#332—432no—
382#332C2×D4312yescomplemented
383C43#1774811yescharacteristic, complemented, Sylow
384C22×Q8—432no—
385C22×Q8—861no—
386C23×C4—431no—
387C23×C4—431no—
388C23×C4—431no—
389C2×M16—21no—
390C2×M16—861no—
391C22×C8—21no—
392C22×C8—861no—
393C4⋊Q8—432no—
394C4⋊Q8—432no—
395C4⋊Q8—431no—
396C4⋊Q8—431no—
397C4⋊Q8—861no—
398C4⋊Q8—861no—
399C4⋊Q8—861no—
400C4⋊Q8—861no—
401C4⋊Q8C22×D4311yescharacteristic
402C4⋊Q8C22×D4311yescharacteristic
403#125—21no—
404#125—862no—
405#125—862no—
406#125—861no—
407#125—861no—
408#125—861no—
409C22⋊Q8—21no—
410C22⋊Q8—432no—
411C22⋊Q8—432no—
412C22⋊Q8—432no—
413C22⋊Q8—862no—
414C22⋊Q8—862no—
415C22⋊Q8—862no—
416C22⋊Q8—862no—
417C22⋊Q8—861no—
418C22⋊Q8—861no—
419C22⋊Q8—861no—
420C22⋊Q8C4×D4312yes—
421C4×Q8—21no—
422C4×Q8—432no—
423C4×Q8—432no—
424C4×Q8—432no—
425C4×Q8—862no—
426C4×Q8—862no—
427C4×Q8—862no—
428C4×Q8—862no—
429C4×Q8—861no—
430C4×Q8—861no—
431C4×Q8—861no—
432C4×Q8C4×D4312yes—
433#117—21no—
434#117—862no—
435#117—862no—
436#117—861no—
437#117—861no—
438#117—861no—
439C2×C4⋊C4—432no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—862no—
443C2×C4⋊C4—862no—
444C2×C4⋊C4—861no—
445C2×C22⋊C4—862no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—862no—
458C2×C42C22×D4311yescharacteristic
459C4⋊C8—21no—
460C4⋊C8—21no—
461C4⋊C8—432no—
462C4⋊C8—432no—
463C4⋊C8—861no—
464C4⋊C8—861no—
465C4⋊C8C22×D4312yes—
466C4⋊C8C22×D4312yes—
467C22⋊C8—862no—
468C22⋊C8—862no—
469C22⋊C8—862no—
470C22⋊C8—862no—
471#97—862no—
472#97—862no—
473#97—862no—
474C4×C8—862no—
475C24—431no—
476C2×Q8—21no—
477C2×Q8—432no—
478C2×Q8—862no—
479C2×Q8—862no—
480C2×Q8—861no—
481C2×Q8—1722no—
482C2×Q8—1722no—
483C2×Q8—1724no—
484C2×Q8C2×C4×D4312yes—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—1721no—
505C22×C4—1721no—
506C22×C4—1722no—
507C22×C4C2×C4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510M16—42no—
511M16—1722no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—42no—
515C2×C8—862no—
516C2×C8—862no—
517C2×C8—1722no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—432no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—862no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4C2×C4×D4312yes—
538C22⋊C4—22no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C42—22no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—431no—
551C42—431no—
552C42—431no—
553C42—431no—
554C42—431no—
555C42—862no—
556C42—862no—
557C42—862no—
558C42C2×C4×D4311yescharacteristic
559C42D4×D4311yescharacteristic
560C42D4×D4311yescharacteristic
561C42C23×D4311yescharacteristic
562C23—431no—
563C23—431no—
564C23—862no—
565C23—862no—
566C23—1721no—
567C23C22⋊C4×D4311yescharacteristic
568Q8—42no—
569Q8—41no—
570Q8—41no—
571Q8—1722no—
572Q8—1724no—
573Q8—1724no—
574Q8—1721no—
575Q8—1721no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—431no—
582C2×C4—431no—
583C2×C4—431no—
584C2×C4—431no—
585C2×C4—431no—
586C2×C4—431no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1724no—
607C2×C4—1724no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4C22⋊C4×D4311yescharacteristic
611C2×C4C22⋊C4×D4311yescharacteristic
612C2×C4C22⋊C4×D4311yescharacteristic
613C2×C4#1306335412yes—
614C2×C4#1306335712yes—
615C2×C4C22×C4×D4311yescharacteristic
616C2×C4C2×D4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C8—42no—
619C8—42no—
620C8—1722no—
621C8—1722no—
622C22—21no—
623C22—21no—
624C22—432no—
625C22—861no—
626C22—861no—
627C22—861no—
628C22—861no—
629C22—861no—
630C22—1724no—
631C22#1458290612yes—
632C22C2×C22⋊C4×D4311yescharacteristic
633C4—21no—
634C4—21no—
635C4—21no—
636C4—42no—
637C4—42no—
638C4—861no—
639C4—861no—
640C4—861no—
641C4—861no—
642C4—861no—
643C4—861no—
644C4—1722no—
645C4—1722no—
646C4#1458290612yes—
647C4C2×#1306335411yescharacteristic
648C4C2×#1306335711yescharacteristic
649C4#1458369511yescharacteristic
650C4#1458369811yescharacteristic
651C2—22no—
652C2—862no—
653C2—1721no—
654C2#413×D4311yescharacteristic
655C2C2×#1458290611yescharacteristic
656C2#1914311111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1550C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1550D43
hypocenterC43#17748
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
4. #19133319C2semidirect
5. #19133310C2semidirect
6. #19133304C2semidirect
7. #19133302C2semidirect
8. #19133286C2semidirect
9. #19133285C2semidirect
10. #19133283C2semidirect
11. C43×#1550C2semidirect
44. #14582648C22semidirect
45. #14582647C22semidirect
46. #14582647C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
53. C43×#333C22semidirect
54. C43×#332C22semidirect
333. #1550D43semidirect
378. #333C2×D43semidirect
382. #332C2×D43semidirect
383. C43#17748semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191432272
C2×#145829552
#191333192
#191333102
#191333042
#191333022
#191332862
#191332852
#191332832
C43×#15502
#1774843