Finite Group Databasebeta

← #25101971

Subgroups — #25101971

Order 11008.

1100 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic
3C4×M16×D43C211yesmaximal, characteristic
4#19135582C212yesmaximal, complemented
5#19135437C212yesmaximal, complemented
6#19135062C212yesmaximal
7#19135060C212yesmaximal
8C4×#13063243C211yesmaximal, characteristic, complemented
9C4×#13063243C211yesmaximal, characteristic, complemented
10C4×#13063244C211yesmaximal, characteristic, complemented
11C4×#101×C43C211yesmaximal, characteristic, complemented
12C2×M16×D43C2212yes—
13#14583453—21no—
14#14583453—21no—
15#14583453—21no—
16#14583453—21no—
17#14583453—21no—
18#14583453—21no—
19#14583453—21no—
20#14583453—21no—
21C2×#13063324C2211yescharacteristic
22C2×#13063323C2211yescharacteristic
23C2×#13063315C412yes—
24C2×#13063305C2211yescharacteristic
25C2×#13063303C412yes—
26C2×#13063301C2211yescharacteristic
27C2×C4×Dic86C412yes—
28C2×C4×Dic86C2211yescharacteristic
29C2×#13063282C412yes—
30C2×C42×D43C2211yescharacteristic
31#14582954—21no—
32#14582954—21no—
33#14582950—21no—
34#14582950—21no—
35#14582922C2212yes—
36C2×#13063244C2212yes—
37C2×#13063243C2212yes—
38C2×#13063243C2212yes—
39#14582862C2212yes—
40C4×#10621877C2211yescharacteristic
41C4×#10621877C2211yescharacteristic
42#14582851—21no—
43M16×Dic43C2212yes—
44C4×#10621872—21no—
45#97×D43—21no—
46C4×C8×D43—21no—
47#14582668C2212yes—
48#14582667C2212yes—
49#14582667C2212yes—
50C2×C4×Q8×C43C2211yescharacteristic
51C2×#101×C43C2212yes—
52C4×M16×C43C2211yescharacteristic
53C4×M16×C43C2211yescharacteristic
54C43×#343C2212yes—
55C22×Dic86C2×C412yes—
56C22×Dic86C2311yescharacteristic
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43C2×C411yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C2×#10621877C2312yes—
61C2×#10621877C2312yes—
62C2×#10621872—22no—
63M16×D43—24no—
64M16×D43—24no—
65C2×C8×D43—22no—
66#13063324—21no—
67#13063324—21no—
68#13063324—21no—
69#13063324—21no—
70#13063323—21no—
71#13063323—21no—
72#13063323—21no—
73#13063323—21no—
74#13063315—22no—
75#13063315—22no—
76#13063315—22no—
77#13063315—22no—
78#13063305—21no—
79#13063305—21no—
80#13063305—21no—
81#13063305—21no—
82#13063303—22no—
83#13063303—22no—
84#13063303—22no—
85#13063303—22no—
86#13063301—21no—
87#13063301—21no—
88#13063301—21no—
89#13063301—21no—
90C4×Dic86—21no—
91C4×Dic86—21no—
92C4×Dic86—21no—
93C4×Dic86—21no—
94C4×Dic86—22no—
95C4×Dic86—22no—
96C4×Dic86—22no—
97C4×Dic86—22no—
98#13063282—22no—
99#13063282—22no—
100#13063282—22no—
101#13063282—22no—
102C2×C4⋊Dic43C2×C412yes—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4C2×C412yes—
105C2×Dic43⋊C4C2×C412yes—
106C2×Dic43⋊C4C2×C412yes—
107C2×Dic43⋊C4C2×C412yes—
108C2×Dic43⋊C4C2×C412yes—
109C2×(C2×D43)⋊C4C2×C412yes—
110C2×(C2×D43)⋊C4C2×C412yes—
111C2×C4×Dic43C2×C412yes—
112C2×C4×Dic43C2×C411yescharacteristic
113C2×C4×Dic43C2×C411yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43D411yescharacteristic
118C42×D43D411yescharacteristic
119C42×D43D411yescharacteristic
120C42×D43D411yescharacteristic
121C42×D43D411yescharacteristic
122C42×D43D411yescharacteristic
123Dic43⋊C8—22no—
124Dic43⋊C8—22no—
125#13063244—24no—
126#13063243—24no—
127#13063243—24no—
128(C2×D43)⋊C8—22no—
129(C2×D43)⋊C8—22no—
130#13063236—21no—
131#13063236—21no—
132#13063235—22no—
133C4×C43⋊C8—21no—
134C4×C43⋊C8—21no—
135C8×Dic43—22no—
136C22×Q8×C43C2311yescharacteristic
137C2×M16×C43C2312yes—
138C2×M16×C43C2312yes—
139C4×Q8×C43—21no—
140C4×Q8×C43—21no—
141C4×Q8×C43—21no—
142C4×Q8×C43—21no—
143C2×C4⋊C4×C43C2×C412yes—
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C42×C43C2×C412yes—
146C2×C42×C43C2311yescharacteristic
147#101×C43—24no—
148#97×C43—21no—
149#97×C43—21no—
150C4×C8×C43—21no—
151C4×C8×C43—21no—
152C23×D43C22×C411yescharacteristic
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—22no—
156C2×Q8×C43—22no—
157C22×C4×C43C22×C412yes—
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C22×C412yes—
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C22×Dic43C22×C412yes—
163C22×Dic43C22×C411yescharacteristic
164C22×Dic43C22×C411yescharacteristic
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C412yes—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—24no—
170C2×C4×D43—42no—
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C22⋊C411yescharacteristic
174C2×C4×D43C22⋊C411yescharacteristic
175C2×C4×D43C22⋊C411yescharacteristic
176C2×C4×D43C22⋊C411yescharacteristic
177C2×C4×D43C22⋊C411yescharacteristic
178C2×C4×D43C22⋊C411yescharacteristic
179C2×C4×D43C2×D411yescharacteristic
180C2×C4×D43C2×D411yescharacteristic
181C2×C4×D43C2×D411yescharacteristic
182C2×C4×D43C2×D411yescharacteristic
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—22no—
186C2×Dic86—22no—
187C2×Dic86—22no—
188C2×Dic86—22no—
189C2×Dic86—44no—
190M16×C43—22no—
191M16×C43—22no—
192M16×C43—22no—
193M16×C43#4114yes—
194C2×C8×C43—22no—
195C2×C8×C43—22no—
196C4⋊C4×C43—22no—
197C4⋊C4×C43—22no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C42×C43—22no—
201C42×C43—22no—
202C42×C43C2×D411yescharacteristic
203C42×C43C2×D411yescharacteristic
204C42×C43C2×D411yescharacteristic
205C42×C43C2×D411yescharacteristic
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—22no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—22no—
213C4⋊Dic43—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219Dic43⋊C4—22no—
220Dic43⋊C4—22no—
221Dic43⋊C4—22no—
222Dic43⋊C4—22no—
223Dic43⋊C4—22no—
224C4×Dic43—22no—
225C4×Dic43—22no—
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22⋊C411yescharacteristic
231C4×Dic43C22⋊C411yescharacteristic
232C4×Dic43C22⋊C411yescharacteristic
233C4×Dic43C22⋊C411yescharacteristic
234C4×Dic43C2×D411yescharacteristic
235C4×Dic43C2×D411yescharacteristic
236C4×Dic43C2×D411yescharacteristic
237C4×Dic43C2×D411yescharacteristic
238#10621877—22no—
239#10621877—22no—
240#10621877—22no—
241#10621877#4114yes—
242C2×C43⋊C8—22no—
243C2×C43⋊C8—22no—
244#10621872—28no—
245C8×D43—28no—
246C23×C43C23×C411yescharacteristic
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—22no—
250C22×D43—41no—
251C22×D43C2×C22⋊C411yescharacteristic
252C22×D43C2×C22⋊C411yescharacteristic
253Q8×C43—42no—
254Q8×C43—42no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—41no—
261C2×C4×C43—42no—
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C2×C22⋊C411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C2×#4112yes—
269C2×C4×C43C2×#4112yes—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—42no—
279C2×Dic43C2×C22⋊C411yescharacteristic
280C2×Dic43C2×C22⋊C411yescharacteristic
281C2×Dic43C2×C22⋊C411yescharacteristic
282C2×Dic43C2×C22⋊C411yescharacteristic
283C2×Dic43C2×C22⋊C411yescharacteristic
284C2×Dic43C2×C22⋊C411yescharacteristic
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—22no—
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—41no—
295C4×D43—41no—
296C4×D43#10114yescomplemented
297Dic86—44no—
298Dic86—42no—
299Dic86—42no—
300Dic86—44no—
301C8×C43—24no—
302C8×C43—42no—
303C43⋊C8—24no—
304C43⋊C8—42no—
305#21425—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43C22×C22⋊C411yescharacteristic
309C22×C43C4×#4111yescharacteristic
310C22×C43C4×#4111yescharacteristic
311C2×D43—21no—
312C2×D43—21no—
313C2×D43—21no—
314C2×D43—21no—
315C2×D43—21no—
316C2×D43—42no—
317C2×D43—42no—
318C2×D43C2×#10112yes—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43—21no—
322C4×C43—42no—
323C4×C43—42no—
324C4×C43C2×#10112yes—
325C4×C43#52512yes—
326C4×C43#53212yes—
327Dic43—21no—
328Dic43—21no—
329Dic43—21no—
330Dic43—21no—
331Dic43—42no—
332Dic43—42no—
333Dic43C2×#10112yes—
334Dic43#41312yes—
335C2×#533—431no—
336#2920—431no—
337C2×C4×M16—431no—
338#1997—432no—
339#1966—432no—
340#1901—432no—
341#1901—432no—
342C4×#101—431no—
343C4×#101—431no—
344C4×#101—431no—
345C4×#101D4311yescharacteristic, complemented
346C2×C43—21no—
347C2×C43—21no—
348C2×C43#229711yescharacteristic
349C2×C43C22×#10111yescharacteristic
350C2×C43C2×#41311yescharacteristic
351D43—22no—
352D43—41no—
353C22×M16—432no—
354#533—861no—
355#533—861no—
356#533—861no—
357#533—861no—
358#533—861no—
359#533—861no—
360#533—861no—
361#533—861no—
362C2×C4⋊Q8—431no—
363C2×C4⋊Q8—431no—
364C2×#125—432no—
365C2×C22⋊Q8—431no—
366C2×C22⋊Q8—431no—
367C2×C22⋊Q8—432no—
368C2×C4×Q8—431no—
369C2×C4×Q8—432no—
370C2×C4×Q8C2×D4311yescharacteristic
371C2×#117—432no—
372C22×C42—431no—
373#432—861no—
374#432—861no—
375#431—861no—
376#431—861no—
377#423—432no—
378C2×#101—432no—
379C2×#101—432no—
380C2×#101—432no—
381C2×#101C2×D4312yes—
382#407—432no—
383C4×M16—432no—
384C4×M16—431no—
385C4×M16—431no—
386C4×M16—861no—
387C4×M16—861no—
388C4×M16C2×D4311yescharacteristic
389C4×M16C2×D4311yescharacteristic
390C2×#97—861no—
391C2×C4×C8—861no—
392#343—432no—
393#343—432no—
394#343—432no—
395#343C2×D4312yes—
396C43#2142511yescharacteristic, complemented, Sylow
397C22×Q8—432no—
398C22×Q8—431no—
399C22×Q8C22×D4311yescharacteristic
400C23×C4—431no—
401C23×C4—431no—
402C23×C4—431no—
403C2×M16—432no—
404C2×M16—432no—
405C2×M16—862no—
406C2×M16—864no—
407C2×M16—864no—
408C2×M16C22×D4312yes—
409C2×M16C22×D4312yes—
410C22×C8—862no—
411C4⋊Q8—861no—
412C4⋊Q8—861no—
413C4⋊Q8—861no—
414C4⋊Q8—861no—
415C4⋊Q8—861no—
416C4⋊Q8—861no—
417C4⋊Q8—861no—
418C4⋊Q8—861no—
419#125—862no—
420#125—862no—
421#125—862no—
422#125—862no—
423C22⋊Q8—862no—
424C22⋊Q8—862no—
425C22⋊Q8—862no—
426C22⋊Q8—862no—
427C22⋊Q8—861no—
428C22⋊Q8—861no—
429C22⋊Q8—861no—
430C22⋊Q8—861no—
431C22⋊Q8—861no—
432C22⋊Q8—861no—
433C22⋊Q8—861no—
434C22⋊Q8—861no—
435C4×Q8—21no—
436C4×Q8—21no—
437C4×Q8—21no—
438C4×Q8—21no—
439C4×Q8—862no—
440C4×Q8—862no—
441C4×Q8—862no—
442C4×Q8—862no—
443C4×Q8—861no—
444C4×Q8—861no—
445C4×Q8—861no—
446C4×Q8—861no—
447#117—862no—
448#117—862no—
449#117—862no—
450#117—862no—
451C2×C4⋊C4—432no—
452C2×C4⋊C4—432no—
453C2×C4⋊C4—432no—
454C2×C4⋊C4—432no—
455C2×C4⋊C4—432no—
456C2×C4⋊C4—432no—
457C2×C4⋊C4—431no—
458C2×C4⋊C4C4×D4312yes—
459C2×C4⋊C4C22×D4311yescharacteristic
460C2×C22⋊C4—432no—
461C2×C22⋊C4—432no—
462C2×C42—431no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—431no—
469C2×C42—431no—
470C2×C42—431no—
471C2×C42—431no—
472C2×C42—431no—
473C2×C42—432no—
474C2×C42C4×D4312yes—
475C2×C42C22×D4311yescharacteristic
476C4⋊C8—862no—
477C4⋊C8—862no—
478#101—24no—
479#101—864no—
480#101—864no—
481#101—864no—
482C22⋊C8—862no—
483C22⋊C8—862no—
484#97—21no—
485#97—21no—
486#97—862no—
487#97—861no—
488#97—861no—
489C4×C8—21no—
490C4×C8—21no—
491C4×C8—862no—
492C4×C8—861no—
493C4×C8—861no—
494C24—431no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—862no—
500C2×Q8—862no—
501C2×Q8—861no—
502C2×Q8—861no—
503C2×Q8—862no—
504C2×Q8—862no—
505C2×Q8—1724no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—432no—
522C22×C4—432no—
523C22×C4—864no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—1722no—
527C22×C4C2×C4×D4312yes—
528C22×C4C2×C4×D4311yescharacteristic
529C22×C4C2×C4×D4312yes—
530C22×C4C2×C4×D4311yescharacteristic
531C22×C4C23×D4311yescharacteristic
532M16—22no—
533M16—22no—
534M16—22no—
535M16—434no—
536M16—868no—
537M16—862no—
538M16—862no—
539M16—862no—
540M16#1062189814yes—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—868no—
544C2×C8—862no—
545C2×C8—862no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—862no—
551C4⋊C4—862no—
552C4⋊C4—862no—
553C4⋊C4—862no—
554C4⋊C4—862no—
555C4⋊C4—862no—
556C4⋊C4—862no—
557C4⋊C4—862no—
558C4⋊C4—862no—
559C4⋊C4—862no—
560C4⋊C4—862no—
561C4⋊C4—862no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C22⋊C4—862no—
565C22⋊C4—862no—
566C22⋊C4—862no—
567C22⋊C4—862no—
568C42—22no—
569C42—22no—
570C42—431no—
571C42—431no—
572C42—431no—
573C42—431no—
574C42—431no—
575C42—431no—
576C42—431no—
577C42—431no—
578C42—431no—
579C42—431no—
580C42—431no—
581C42—431no—
582C42—862no—
583C42—862no—
584C42D4×D4311yescharacteristic
585C42D4×D4311yescharacteristic
586C42D4×D4311yescharacteristic
587C42D4×D4311yescharacteristic
588C23—431no—
589C23—431no—
590C23—862no—
591C23—861no—
592C23—861no—
593C23—1721no—
594C23C22×C4×D4311yescharacteristic
595Q8—42no—
596Q8—42no—
597Q8—1724no—
598Q8—1724no—
599Q8—1722no—
600Q8—1722no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—431no—
609C2×C4—431no—
610C2×C4—434no—
611C2×C4—431no—
612C2×C4—431no—
613C2×C4—431no—
614C2×C4—431no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—862no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1722no—
635C2×C4C22⋊C4×D4311yescharacteristic
636C2×C4C22⋊C4×D4311yescharacteristic
637C2×C4C22⋊C4×D4311yescharacteristic
638C2×C4C22⋊C4×D4311yescharacteristic
639C2×C4C2×D4×D4311yescharacteristic
640C2×C4C2×D4×D4311yescharacteristic
641C2×C4#41×D4312yes—
642C2×C4C2×#1062189812yes—
643C8—24no—
644C8—42no—
645C8—864no—
646C8—1722no—
647C22—21no—
648C22—21no—
649C22—432no—
650C22—861no—
651C22—861no—
652C22—861no—
653C22—861no—
654C22—861no—
655C22—1722no—
656C22—1722no—
657C22C2×C22⋊C4×D4311yescharacteristic
658C22#1458336711yescharacteristic
659C22C4×#1062189811yescharacteristic
660C4—21no—
661C4—21no—
662C4—21no—
663C4—42no—
664C4—42no—
665C4—432no—
666C4—432no—
667C4—861no—
668C4—861no—
669C4—861no—
670C4—861no—
671C4—1722no—
672C4—1722no—
673C4#101×D4312yes—
674C4#1458340812yes—
675C4#1458344612yes—
676C2—21no—
677C2—21no—
678C2—862no—
679C2—1721no—
680C2#1913708111yescharacteristic
681C2C2×#101×D4311yescharacteristic
682C2#413×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#101×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22×C4
cosocleC22×C4×C43C24
hypercenterC4×#101D43
hypocenterC43#21425
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
4. #19135582C2semidirect
5. #19135437C2semidirect
8. C4×#13063243C2semidirect
9. C4×#13063243C2semidirect
10. C4×#13063244C2semidirect
11. C4×#101×C43C2semidirect
296. C4×D43#101semidirect
345. C4×#101D43semidirect
396. C43#21425semidirect

Maximal subgroups

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

subgroupindex
C2×#145834532
#191432262
C4×M16×D432
#191355822
#191354372
#191350622
#191350602
C4×#130632432
C4×#130632442
C4×#101×C432
#2142543