Finite Group Databasebeta

← #25256749

Subgroups — #25256749

Order 11008.

2342 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583367C211yesmaximal, characteristic
2#19137565C214yesmaximal, complemented
3#19137557C214yesmaximal, complemented
4#19137534C214yesmaximal, complemented
5#19137530C214yesmaximal, complemented
6#19137205C211yesmaximal, characteristic, complemented
7#19137204C211yesmaximal, characteristic, complemented
8#19137203C211yesmaximal, characteristic, complemented
9#19137184C212yesmaximal
10#19137000C211yesmaximal, characteristic, complemented
11#19136991C212yesmaximal, complemented
12#19136990C212yesmaximal, complemented
13#382×D43C211yesmaximal, characteristic, complemented
14#19136949C212yesmaximal, complemented
15C43×#2314C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17#14583367C4116yescomplemented
18C2×#13063290C2212yes—
19C2×#13063287C2212yes—
20C2×(C22⋊D43)⋊C4C2212yes—
21C2×(C22⋊D43)⋊C4C2212yes—
22C2×#13063283C2212yes—
23C2×#13063282C2211yescharacteristic
24C2×#13063282C2211yescharacteristic
25C2×C4⋊C4×D43C2212yes—
26C22×C4×Dic43C2211yescharacteristic
27C2×C42×D43C2211yescharacteristic
28C2×C42×D43C2211yescharacteristic
29#14582803C2214yes—
30#14582799C2214yes—
31#14582792C2214yes—
32#14582791C2214yes—
33#14582789C2214yes—
34#14582786C2214yes—
35#14582785C2214yes—
36#14582780C2214yes—
37#14582777C2214yes—
38#14582775C2214yes—
39#14582769C2211yescharacteristic
40#14582766C2214yes—
41#14582766C2214yes—
42#14582765C2211yescharacteristic
43#14582764C2212yes—
44#14582764C2212yes—
45#14582763C2214yes—
46#14582761C2214yes—
47#14582760C2214yes—
48#14582759C2212yes—
49#14582756C2212yes—
50#14582756C2212yes—
51#14582756C2214yes—
52C4⋊C4×Dic43C2214yes—
53C4⋊C4×Dic43C2212yes—
54C4⋊C4×Dic43C2212yes—
55C4×Dic43⋊C4C2214yes—
56C4×C4⋊Dic43C2212yes—
57#14582750C2214yes—
58C22⋊C4×Dic43C2214yes—
59C4×(C2×D43)⋊C4C2214yes—
60C4×(C2×D43)⋊C4C2214yes—
61#14582746C2214yes—
62#14582745C2214yes—
63#14582744C2214yes—
64#95×D43C2214yes—
65C2×#117×C43C2211yescharacteristic
66C43×#388C2214yes—
67C43×#387C2214yes—
68C43×#384C2211yescharacteristic
69C43×#382C2211yescharacteristic
70C43×#380C2212yes—
71C4×C4⋊C4×C43C2212yes—
72C2×#10621898—24no—
73C2×#10621898—24no—
74C2×#10621898C2×C418yes—
75C22×Dic86C2311yescharacteristic
76C22×D172C2311yescharacteristic
77C22×C22⋊D43C2311yescharacteristic
78C22×C22⋊D43C2311yescharacteristic
79C23×Dic43C2312yes—
80C22×C4×D43C2311yescharacteristic
81C22×C4×D43C2314yes—
82C22×C4×D43C2312yes—
83C22×C4×D43C2312yes—
84C22×C4×D43C2311yescharacteristic
85#13063290C2×C4116yescomplemented
86#13063287C2×C4116yes—
87(C22⋊D43)⋊C4C2×C4116yes—
88(C22⋊D43)⋊C4C2×C4116yescomplemented
89#13063283—28no—
90#13063282C2×C418yes—
91#13063282C2×C418yescomplemented
92C2×C4⋊Dic43C2312yes—
93C2×C4⋊Dic43C2312yes—
94C2×C4⋊Dic43C2314yes—
95C2×Dic43⋊C4C2314yes—
96C2×Dic43⋊C4C2312yes—
97C2×Dic43⋊C4C2312yes—
98C4⋊C4×D43—28no—
99C2×C22⋊Dic43C2314yes—
100C2×(C2×D43)⋊C4C2314yes—
101C2×(C2×D43)⋊C4C2314yes—
102C2×(C2×D43)⋊C4C2314yes—
103C2×(C2×D43)⋊C4C2312yes—
104C2×(C2×D43)⋊C4C2312yes—
105C2×C4×Dic43C2×C418yescomplemented
106C2×C4×Dic43C2314yes—
107C2×C4×Dic43C2314yes—
108C2×C4×Dic43C2314yes—
109C2×C4×Dic43C2314yes—
110C2×C4×Dic43C2311yescharacteristic
111C2×C4×Dic43C2312yes—
112C2×C4×Dic43C2312yes—
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2312yes—
115C42×D43C2×C418yes—
116C42×D43C2×C418yescomplemented
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C23×C4×C43C2311yescharacteristic
129#117×C43C2×C418yescomplemented
130C2×C4⋊C4×C43C2312yes—
131C2×C4⋊C4×C43C2312yes—
132C2×C4⋊C4×C43C2314yes—
133C2×C4⋊C4×C43C2312yes—
134C2×C22⋊C4×C43C2314yes—
135C2×C22⋊C4×C43C2312yes—
136C2×C42×C43C2314yes—
137C2×C42×C43C2311yescharacteristic
138C2×C42×C43C2311yescharacteristic
139#95×C43C2314yes—
140#95×C43C2314yes—
141#95×C43C2314yes—
142C24×C43C2411yescharacteristic
143C23×D43C2411yescharacteristic
144C23×D43C2411yescharacteristic
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43C22×C414yes—
148C22×C4×C43C2414yes—
149C22×C4×C43C2414yes—
150C22×C4×C43C2411yescharacteristic
151C22×C4×C43C2412yes—
152C22×C4×C43C2412yes—
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43C22×C414yes—
159C2×C22⋊D43C22×C414yes—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C22×Dic43C22×C418yes—
163C22×Dic43C2414yes—
164C22×Dic43C2414yes—
165C22×Dic43C2412yes—
166C22×Dic43C2411yescharacteristic
167C22×Dic43C2412yes—
168C22×Dic43C2411yescharacteristic
169#10621898—232no—
170C2×D172—22no—
171C2×D172—22no—
172C2×D172C22×C414yes—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—28no—
176C2×C4×D43—42no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43—42no—
180C2×C4×D43—44no—
181C2×C4×D43—44no—
182C2×C4×D43C22×C414yes—
183C2×C4×D43C22×C418yes—
184C2×C4×D43C22×C418yes—
185C2×C4×D43C22×C414yes—
186C2×C4×D43#4114yes—
187C2×C4×D43#4114yes—
188C2×Dic86—22no—
189C2×Dic86—22no—
190C2×Dic86C22×C414yes—
191C4⋊C4×C43—24no—
192C4⋊C4×C43—24no—
193C4⋊C4×C43—44no—
194C4⋊C4×C43C22×C418yes—
195C22⋊C4×C43—44no—
196C22⋊C4×C43C22×C418yes—
197C42×C43—44no—
198C42×C43C22×C414yes—
199C42×C43C22×C414yes—
200C22⋊Dic43—44no—
201(C2×D43)⋊C4—28no—
202(C2×D43)⋊C4—44no—
203(C2×D43)⋊C4—44no—
204(C2×D43)⋊C4C22×C418yes—
205(C2×D43)⋊C4C22×C418yes—
206C4⋊Dic43—24no—
207C4⋊Dic43—24no—
208C4⋊Dic43—44no—
209Dic43⋊C4—28no—
210Dic43⋊C4C22×C418yes—
211Dic43⋊C4C22×C418yes—
212C4×Dic43—28no—
213C4×Dic43—44no—
214C4×Dic43—44no—
215C4×Dic43—44no—
216C4×Dic43C22×C414yes—
217C4×Dic43C22×C418yes—
218C4×Dic43C22×C418yes—
219C4×Dic43C22×C414yes—
220C4×Dic43C22×C418yes—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43C23×C412yes—
226C23×C43C2511yescharacteristic
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—22no—
232C22×D43—22no—
233C22×D43C23×C412yes—
234C22×D43C23×C412yes—
235C22×D43C2×#4112yes—
236C22×D43C2×#4112yes—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—28no—
244C2×C4×C43—24no—
245C2×C4×C43—24no—
246C2×C4×C43—24no—
247C2×C4×C43—24no—
248C2×C4×C43—24no—
249C2×C4×C43—24no—
250C2×C4×C43C23×C412yes—
251C2×C4×C43C23×C414yes—
252C2×C4×C43C23×C414yes—
253C2×C4×C43C23×C412yes—
254C2×C4×C43C2×#4112yes—
255C2×C4×C43C2×#4112yes—
256C22⋊D43—28no—
257C22⋊D43—28no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—24no—
265C2×Dic43—24no—
266C2×Dic43—24no—
267C2×Dic43—24no—
268C2×Dic43—24no—
269C2×Dic43—24no—
270C2×Dic43—48no—
271C2×Dic43C23×C414yes—
272C2×Dic43C23×C414yes—
273C2×Dic43C23×C412yes—
274C2×Dic43C23×C412yes—
275C2×Dic43C2×#4112yes—
276C2×Dic43C2×#4112yes—
277D172—28no—
278C4×D43—28no—
279C4×D43—48no—
280C4×D43—48no—
281C4×D43—88no—
282C4×D43#117116yes—
283Dic86—28no—
284#34189—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—24no—
287C22×C43—42no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43C24×C411yescharacteristic
291C22×C43C22×#4111yescharacteristic
292C22×C43C22×#4111yescharacteristic
293C22×C43#58512yes—
294C22×C43#58512yes—
295C2×D43—24no—
296C2×D43—24no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—24no—
301C2×D43—42no—
302C2×D43—41no—
303C2×D43—41no—
304C2×D43C2×#11714yes—
305C4×C43—22no—
306C4×C43—24no—
307C4×C43—24no—
308C4×C43—44no—
309C4×C43—44no—
310C4×C43C2×#11714yes—
311Dic43—22no—
312Dic43—24no—
313Dic43—24no—
314Dic43—44no—
315Dic43—44no—
316Dic43C2×#11714yes—
317C2×C4×#41—431no—
318#2357—434no—
319#2356—434no—
320#2353—434no—
321#2353—434no—
322#2314—431no—
323#2314—431no—
324#2314—431no—
325#2314D4311yescharacteristic, complemented
326#2311—432no—
327#2285—431no—
328#2283—432no—
329#2283—432no—
330C2×#382—431no—
331#2274—432no—
332C2×C43—42no—
333C2×C43C22×#11711yescharacteristic
334C2×C43#342812yes—
335C2×C43#351012yes—
336C2×C43#351211yescharacteristic
337C2×C43#351211yescharacteristic
338D43—24no—
339D43—42no—
340C22×#41—431no—
341C4×#41—4316no—
342C2×C4×Q8—432no—
343C2×C4×D4—432no—
344C2×C4×D4—432no—
345C2×C4×D4—432no—
346C2×#117—432no—
347C2×#117—431no—
348C2×#117—431no—
349C2×#117C2×D4311yescharacteristic
350C22×C4⋊C4—432no—
351C22×C42—431no—
352C22×C42—431no—
353C22×C42—431no—
354#391—434no—
355#390—434no—
356#388—434no—
357#388—434no—
358#388—434no—
359#388C2×D4314yes—
360#387—434no—
361#387—434no—
362#387—434no—
363#387C2×D4314yes—
364#386—434no—
365#386—434no—
366#384—431no—
367#384C2×D4311yescharacteristic
368#383—434no—
369#383—434no—
370#382—432no—
371#382—432no—
372#382—431no—
373#382—434no—
374#382C2×D4311yescharacteristic
375#381—434no—
376#381—434no—
377#380—432no—
378#380—432no—
379#380—432no—
380#380—434no—
381#380C2×D4312yes—
382C4×C4⋊C4—432no—
383C4×C4⋊C4—432no—
384C4×C4⋊C4—434no—
385C4×C4⋊C4—432no—
386C4×C4⋊C4—434no—
387C4×C4⋊C4—434no—
388C4×C4⋊C4C2×D4312yes—
389C4×C22⋊C4—434no—
390C4×C22⋊C4—434no—
391C4×C22⋊C4—434no—
392C4×C22⋊C4—434no—
393#376—434no—
394#376—434no—
395C2×#95—434no—
396C43#3418911yescharacteristic, complemented, Sylow
397C2×#41—438no—
398C2×#41—864no—
399C2×#41—864no—
400C22×Q8—431no—
401C22×D4—431no—
402C22×D4—431no—
403C22×D4—431no—
404C23×C4—431no—
405C23×C4—432no—
406C23×C4—431no—
407C23×C4—432no—
408C23×C4—432no—
409C23×C4—434no—
410C23×C4C22×D4311yescharacteristic
411C4×Q8—4316no—
412C4×D4—4316no—
413C4×D4—4316no—
414C4×D4—4316no—
415#117—438no—
416#117—438no—
417#117—868no—
418#117C4×D4318yescomplemented
419C2×C4⋊C4—432no—
420C2×C4⋊C4—432no—
421C2×C4⋊C4—434no—
422C2×C4⋊C4—432no—
423C2×C4⋊C4—432no—
424C2×C4⋊C4—434no—
425C2×C4⋊C4—868no—
426C2×C4⋊C4C22×D4312yes—
427C2×C4⋊C4C22×D4312yes—
428C2×C4⋊C4C22×D4314yes—
429C2×C4⋊C4C22×D4312yes—
430C2×C22⋊C4—432no—
431C2×C22⋊C4—432no—
432C2×C22⋊C4—434no—
433C2×C22⋊C4—434no—
434C2×C22⋊C4—434no—
435C2×C22⋊C4—434no—
436C2×C22⋊C4C22×D4314yes—
437C2×C22⋊C4C22×D4312yes—
438C2×C42—438no—
439C2×C42—431no—
440C2×C42—432no—
441C2×C42—432no—
442C2×C42—432no—
443C2×C42—431no—
444C2×C42—438no—
445C2×C42—438no—
446C2×C42—434no—
447C2×C42—434no—
448C2×C42—434no—
449C2×C42—434no—
450C2×C42C22×D4314yes—
451C2×C42C22×D4311yescharacteristic
452C2×C42C22×D4311yescharacteristic
453#95—434no—
454#95—434no—
455#95—434no—
456#95—434no—
457#95—434no—
458#95—434no—
459#95—434no—
460#95—434no—
461#95—434no—
462#95—434no—
463#95—434no—
464#95C22×D4314yes—
465#95C22×D4314yes—
466#95C22×D4314yes—
467C24—431no—
468C24—431no—
469C24C23×D4311yescharacteristic
470#41—8632no—
471C2×Q8—434no—
472C2×Q8—862no—
473C2×Q8—862no—
474C2×D4—434no—
475C2×D4—434no—
476C2×D4—434no—
477C2×D4—862no—
478C2×D4—862no—
479C2×D4—862no—
480C2×D4—862no—
481C2×D4—862no—
482C2×D4—862no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—431no—
486C22×C4—434no—
487C22×C4—434no—
488C22×C4—434no—
489C22×C4—432no—
490C22×C4—431no—
491C22×C4—432no—
492C22×C4—438no—
493C22×C4—434no—
494C22×C4—438no—
495C22×C4—438no—
496C22×C4—434no—
497C22×C4—434no—
498C22×C4—868no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—1724no—
502C22×C4—1724no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4—1722no—
508C22×C4—1722no—
509C22×C4C2×C4×D4314yes—
510C22×C4C23×D4314yes—
511C22×C4C23×D4314yes—
512C22×C4C23×D4311yescharacteristic
513C22×C4C23×D4312yes—
514C22×C4C23×D4312yes—
515C22×C4C23×D4311yescharacteristic
516C4⋊C4—24no—
517C4⋊C4—24no—
518C4⋊C4—44no—
519C4⋊C4—438no—
520C4⋊C4—438no—
521C4⋊C4—868no—
522C4⋊C4—864no—
523C4⋊C4—864no—
524C4⋊C4—1724no—
525C4⋊C4C2×C4×D4318yes—
526C22⋊C4—44no—
527C22⋊C4—438no—
528C22⋊C4—438no—
529C22⋊C4—868no—
530C22⋊C4—1724no—
531C22⋊C4—1724no—
532C22⋊C4—1724no—
533C22⋊C4C2×C4×D4318yes—
534C42—44no—
535C42—434no—
536C42—434no—
537C42—438no—
538C42—438no—
539C42—438no—
540C42—868no—
541C42—1724no—
542C42—1724no—
543C42—1724no—
544C42C2×C4×D4314yes—
545C42C2×C4×D4314yes—
546C23—21no—
547C23—21no—
548C23—22no—
549C23—22no—
550C23—432no—
551C23—432no—
552C23—432no—
553C23—432no—
554C23—862no—
555C23—862no—
556C23—861no—
557C23—861no—
558C23—862no—
559C23—862no—
560C23C22×C4×D4312yes—
561C23C24×D4311yescharacteristic
562Q8—868no—
563D4—868no—
564D4—868no—
565D4—868no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—28no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—432no—
580C2×C4—432no—
581C2×C4—432no—
582C2×C4—4316no—
583C2×C4—434no—
584C2×C4—434no—
585C2×C4—432no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—868no—
593C2×C4—864no—
594C2×C4—864no—
595C2×C4—864no—
596C2×C4—864no—
597C2×C4—864no—
598C2×C4—864no—
599C2×C4—3448no—
600C2×C4—1728no—
601C2×C4—1728no—
602C2×C4—1728no—
603C2×C4C22×C4×D4312yes—
604C2×C4C22×C4×D4314yes—
605C2×C4C22×C4×D4314yes—
606C2×C4C22×C4×D4312yes—
607C2×C4#41×D4312yes—
608C2×C4#41×D4312yes—
609C22—24no—
610C22—22no—
611C22—42no—
612C22—41no—
613C22—41no—
614C22—434no—
615C22—864no—
616C22—864no—
617C22—862no—
618C22—862no—
619C22—864no—
620C22—862no—
621C22—1722no—
622C22—1721no—
623C22—1721no—
624C22C23×C4×D4311yescharacteristic
625C22C2×#41×D4311yescharacteristic
626C22C2×#41×D4311yescharacteristic
627C22#1458373412yes—
628C22#1458373612yes—
629C4—24no—
630C4—24no—
631C4—22no—
632C4—44no—
633C4—44no—
634C4—434no—
635C4—864no—
636C4—864no—
637C4—862no—
638C4—1724no—
639C4—1724no—
640C4#117×D4314yes—
641C2—42no—
642C2—864no—
643C2—1722no—
644C2C2×#117×D4311yescharacteristic
645C2#1914779512yes—
646C2#1914848712yes—
647C2#1914851411yescharacteristic
648C2#1914851811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2314C2
socle, cosocleC23×C43C25
prime radicalC22×#10621898C22
hypercenter#2314D43
hypocenterC43#34189
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #19137565C2semidirect
3. #19137557C2semidirect
4. #19137534C2semidirect
5. #19137530C2semidirect
6. #19137205C2semidirect
7. #19137204C2semidirect
8. #19137203C2semidirect
10. #19137000C2semidirect
11. #19136991C2semidirect
12. #19136990C2semidirect
13. #382×D43C2semidirect
14. #19136949C2semidirect
15. C43×#2314C2semidirect
17. #14583367C4semidirect
85. #13063290C2×C4semidirect
88. (C22⋊D43)⋊C4C2×C4semidirect
91. #13063282C2×C4semidirect
105. C2×C4×Dic43C2×C4semidirect
116. C42×D43C2×C4semidirect
129. #117×C43C2×C4semidirect
325. #2314D43semidirect
396. C43#34189semidirect
418. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833672
#191375652
#191375572
#191375342
#191375302
#191372052
#191372042
#191372032
#191371842
#191370002
#191369912
#191369902
#382×D432
#191369492
C43×#23142
#3418943