Finite Group Databasebeta

← #25103285

Subgroups — #25103285

Order 11008.

954 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
1C2×#14583155C211yesmaximal, characteristic
2C2×C4×#10621885C211yesmaximal, characteristic, complemented
3C2×#14582855C211yesmaximal, characteristic
4#19137277C211yesmaximal, characteristic
5#19135465C211yesmaximal, characteristic, complemented
6#19135335C211yesmaximal, characteristic, complemented
7#19135274C211yesmaximal, characteristic, complemented
8#19135270C211yesmaximal, characteristic, complemented
9#19135019C211yesmaximal, characteristic
10#19135016C211yesmaximal, characteristic
11#19134626C211yesmaximal, characteristic
12C4×#13063256C211yesmaximal, characteristic, complemented
13#19134428C211yesmaximal, characteristic, complemented
14#19134425C211yesmaximal, characteristic, complemented
15C43×#2323C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21#14583155C418yescomplemented
22C4×#10621885—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32#14582855—24no—
33C2×#13063236C2211yescharacteristic
34C2×#13063236C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582794—21no—
40#14582793—21no—
41#14582787—21no—
42#14582780—21no—
43#14582759C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51C2×C22⋊Q8×C43C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C43×#391C2211yescharacteristic
55C43×#389—21no—
56C43×#389C2211yescharacteristic
57C43×#388—21no—
58C43×#388—21no—
59C43×#387—21no—
60C43×#380C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C2×#10621885—22no—
64C2×#10621885—22no—
65C2×#10621885C2×C414yes—
66C2×#10621877—22no—
67C2×#10621877—22no—
68C2×#10621877C2×C414yes—
69C22×C43⋊C8—22no—
70C22×C43⋊C8—22no—
71C22×C43⋊C8—22no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063304—22no—
77#13063304C2×C414yes—
78C4×Dic86—22no—
79C4×Dic86—22no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90#13063258—22no—
91#13063256—22no—
92#13063256C2×C414yes—
93#13063249—22no—
94#13063249—22no—
95#13063249C2×C414yes—
96#13063248—22no—
97#13063248—22no—
98#13063248C2×C414yes—
99#13063236—22no—
100#13063236—22no—
101C4×C43⋊C8—22no—
102C4×C43⋊C8D414yes—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C23×C4×C43C2311yescharacteristic
110C22⋊Q8×C43—22no—
111C22⋊Q8×C43C2×C414yes—
112C4×Q8×C43—22no—
113C4×Q8×C43—22no—
114#117×C43—22no—
115#117×C43—22no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43D411yescharacteristic
120C2×C4⋊C4×C43D411yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137C24×C43C2×D411yescharacteristic
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C22×C412yes—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4112yes—
159C22×C4×C43C2411yescharacteristic
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86C22×C412yes—
170C4⋊C4×C43—24no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43—81no—
180C4⋊C4×C43C22×C412yes—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—22no—
183C22⋊C4×C43—24no—
184C22⋊C4×C43—81no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—42no—
188C42×C43—81no—
189C42×C43C2×D412yes—
190C42×C43#4112yes—
191C22⋊Dic43—24no—
192C22⋊Dic43—81no—
193#10621885—28no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C22×C412yes—
200Dic43⋊C4—24no—
201Dic43⋊C4—42no—
202Dic43⋊C4—81no—
203C4×Dic43—42no—
204C4×Dic43—81no—
205#10621877—28no—
206C2×C43⋊C8—28no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C22×C412yes—
214C2×C43⋊C8C22×C412yes—
215C2×C43⋊C8C2×D412yes—
216C2×C43⋊C8C2×D412yes—
217C2×C43⋊C8#4112yes—
218C2×C43⋊C8#4112yes—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43C4×D412yes—
226C23×C43C22×D411yescharacteristic
227Q8×C43—22no—
228Q8×C43—22no—
229Q8×C43—41no—
230Q8×C43—41no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43C4×D412yes—
260C2×C4×C43#12112yes—
261C2×C4×C43#12112yes—
262C2×C4×C43C23×C411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280Dic86—22no—
281Dic86—22no—
282Dic86—41no—
283Dic86—41no—
284C43⋊C8—22no—
285C43⋊C8—22no—
286C43⋊C8—22no—
287C43⋊C8C4×D414yes—
288#21537—431nomaximal, Sylow
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43C2×C4×D411yescharacteristic
297C22×C43C2×#12111yescharacteristic
298C22×C43#53211yescharacteristic
299C22×C43#57711yescharacteristic
300C22×C43#57711yescharacteristic
301C22×C43#57811yescharacteristic
302C22×C43#57811yescharacteristic
303C4×C43—22no—
304C4×C43—22no—
305C4×C43—22no—
306C4×C43—42no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—42no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43C2×C4×D411yescharacteristic
313C4×C43C4×#4111yescharacteristic
314C4×C43#52511yescharacteristic
315C4×C43#52911yescharacteristic
316Dic43—42no—
317Dic43—42no—
318Dic43—81no—
319Dic43—81no—
320C2×#470—431no—
321C2×C4×Q16—431no—
322C2×#405—431no—
323#2323—431no—
324#2323D4311yescharacteristic
325#1971—431no—
326#1944—431no—
327#1933—431no—
328#1933—431no—
329#1892—431no—
330#1892—431no—
331#1809—431no—
332C4×#106—431no—
333#1763—431no—
334#1763—431no—
335C2×C43—42no—
336C2×C43C4×#12111yescharacteristic
337C2×C43#294711yescharacteristic
338C2×C43#294711yescharacteristic
339C2×C43#305911yescharacteristic
340C2×C43#306011yescharacteristic
341C2×C43#317811yescharacteristic
342C2×C43#317811yescharacteristic
343C22×Q16—431no—
344C22×M16—431no—
345C23×C8—431no—
346C2×C22⋊Q8—431no—
347C2×C22⋊Q8C2×D4311yescharacteristic
348C2×C4×Q8—431no—
349C2×C4×Q8C2×D4311yescharacteristic
350C2×#117C2×D4311yescharacteristic
351#470—438no—
352C4×Q16—864no—
353C2×#107—431no—
354C2×#106—431no—
355C2×#106—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103—431no—
361C2×#103—431no—
362#405—864no—
363C2×#97—431no—
364C2×#97—431no—
365C2×C4×C8—431no—
366C2×C4×C8—431no—
367#391—431no—
368#391C2×D4311yescharacteristic
369#389—21no—
370#389—431no—
371#389—861no—
372#389C2×D4311yescharacteristic
373#388—21no—
374#388—21no—
375#388—861no—
376#388—861no—
377#387—21no—
378#387—861no—
379#380—431no—
380#380C2×D4311yescharacteristic
381C4×C4⋊C4—431no—
382C4×C4⋊C4C2×D4311yescharacteristic
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389C43#2153711yescharacteristic, complemented, Sylow
390C22×Q8—431no—
391C22×Q8C22×D4311yescharacteristic
392C23×C4C22×D4311yescharacteristic
393C2×Q16—434no—
394C2×Q16—862no—
395C2×Q16—862no—
396C2×M16—434no—
397C2×M16—862no—
398C2×M16—862no—
399C22×C8—431no—
400C22×C8—431no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8—862no—
404C22×C8—862no—
405C22×C8—862no—
406C22⋊Q8—22no—
407C22⋊Q8—434no—
408C22⋊Q8—862no—
409C22⋊Q8C4×D4314yes—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×Q8—862no—
413C4×Q8—862no—
414#117—22no—
415#117—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4C22⋊D4311yescharacteristic
426C2×C4⋊C4C22⋊D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4C22⋊D4311yescharacteristic
435C2×C22⋊C4C22⋊D4311yescharacteristic
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42C22×D4311yescharacteristic
441C2×C42C22×D4311yescharacteristic
442#107—862no—
443#106—434no—
444#106—862no—
445#103—434no—
446#103—434no—
447#103—862no—
448#103—862no—
449#103—862no—
450#103—862no—
451#97—862no—
452#97—862no—
453C4×C8—434no—
454C4×C8—862no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465C24C2×C22⋊D4311yescharacteristic
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—432no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8C2×C4×D4312yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4C2×C4×D4312yes—
491C22×C4#1062189812yes—
492C22×C4C2×C22⋊D4311yescharacteristic
493C22×C4C2×C22⋊D4311yescharacteristic
494C22×C4C2×C22⋊D4311yescharacteristic
495C22×C4C2×C22⋊D4311yescharacteristic
496C22×C4C2×C22⋊D4311yescharacteristic
497C22×C4C23×D4311yescharacteristic
498Q16—868no—
499M16—868no—
500C2×C8—432no—
501C2×C8—432no—
502C2×C8—432no—
503C2×C8—432no—
504C2×C8—432no—
505C2×C8—432no—
506C2×C8—868no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C4⋊C4—24no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4—432no—
524C4⋊C4—864no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—3441no—
531C4⋊C4—1722no—
532C4⋊C4C2×C4×D4312yes—
533C22⋊C4—24no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—81no—
537C22⋊C4—864no—
538C22⋊C4—3441no—
539C42—21no—
540C42—21no—
541C42—42no—
542C42—81no—
543C42—3441no—
544C42—1722no—
545C42D4×D4312yes—
546C42#1062190012yes—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23C4×C22⋊D4312yes—
554C23C22×C22⋊D4311yescharacteristic
555Q8—22no—
556Q8—22no—
557Q8—41no—
558Q8—41no—
559Q8—862no—
560Q8—862no—
561Q8—1721no—
562Q8—1721no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4C4×C22⋊D4312yes—
604C2×C4#1306329712yes—
605C2×C4#1306329712yes—
606C2×C4C22×C4×D4311yescharacteristic
607C2×C4C2×D4×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4C2×#1062190011yescharacteristic
611C2×C4C2×#1062189811yescharacteristic
612C8—434no—
613C8—862no—
614C8—862no—
615C8—862no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22C2×C4×C22⋊D4311yescharacteristic
624C22C2×#1306329711yescharacteristic
625C22#1458344511yescharacteristic
626C22#1458370711yescharacteristic
627C22#1458371011yescharacteristic
628C22#1458371411yescharacteristic
629C22#1458371411yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—42no—
634C4—41no—
635C4—41no—
636C4—42no—
637C4—81no—
638C4—81no—
639C4—3441no—
640C4—3441no—
641C4—1722no—
642C4—1722no—
643C4C4×D4×D4311yescharacteristic
644C4C4×#1062190011yescharacteristic
645C4#1458340811yescharacteristic
646C4#1458342911yescharacteristic
647C2—42no—
648C2C4×#1306329711yescharacteristic
649C2#1914343411yescharacteristic
650C2#1914343811yescharacteristic
651C2#1914424711yescharacteristic
652C2#1914425411yescharacteristic
653C2#1914525711yescharacteristic
654C2#1914526511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2323C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#2323D43
hypocenterC43#21537
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621885C2semidirect
5. #19135465C2semidirect
6. #19135335C2semidirect
7. #19135274C2semidirect
8. #19135270C2semidirect
12. C4×#13063256C2semidirect
13. #19134428C2semidirect
14. #19134425C2semidirect
21. #14583155C4semidirect
389. C43#21537semidirect

Maximal subgroups

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

subgroupindex
C2×#145831552
C2×C4×#106218852
C2×#145828552
#191372772
#191354652
#191353352
#191352742
#191352702
#191350192
#191350162
#191346262
C4×#130632562
#191344282
#191344252
C43×#23232
#2153743