Finite Group Databasebeta

← #25249339

Subgroups — #25249339

Order 11008.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147924C211yesmaximal, characteristic
2C2×#14582883C211yesmaximal, characteristic, complemented
3#19136248C212yesmaximal, complemented
4#19136244C212yesmaximal, complemented
5#19136239C214yesmaximal, complemented
6#19136234C214yesmaximal, complemented
7C2×C43×#410C211yesmaximal, characteristic, complemented
8C22×#10621898C411yescharacteristic, complemented
9C22×#10621877—21no—
10#14583477—21no—
11#14583477—21no—
12#14583473—21no—
13#14583470C411yescharacteristic, complemented
14#14583470C2211yescharacteristic
15#14583466—21no—
16#14583463C411yescharacteristic, complemented
17#14583463C2211yescharacteristic
18#14583458C412yescomplemented
19#14583458C2212yes—
20#14583445—21no—
21#14583445—21no—
22#14583410—21no—
23#14583410—21no—
24#14583406C412yescomplemented
25#14583406C2212yes—
26C2×#13063284C411yescharacteristic, complemented
27#14582883—21no—
28#14582883—21no—
29#14582883C2212yes—
30#14582883C2212yes—
31C2×#13063244—21no—
32C2×#13063242C2212yes—
33#14582688C2218yescomplemented
34#14582685C2218yescomplemented
35C22×#41×C43C2211yescharacteristic
36C2×#117×C43—21no—
37C43×#410—21no—
38C43×#410—21no—
39C43×#410C2212yes—
40C43×#410C2212yes—
41C2×#99×C43—21no—
42C2×#99×C43C2212yes—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—41no—
48C2×#10621898—41no—
49C2×#10621898—41no—
50C2×#10621898—41no—
51C22×Dic86C2×C411yescharacteristic, complemented
52C22×D172C2×C411yescharacteristic, complemented
53C22×C22⋊D43C2×C412yes—
54C22×C4×D43C2×C412yescomplemented
55C2×#10621877—22no—
56C2×#10621877—22no—
57C2×#10621877—22no—
58C2×#10621877—41no—
59C2×#10621877—41no—
60C2×#10621877—41no—
61C22×C43⋊C8—41no—
62#13063323—21no—
63#13063323—21no—
64#13063321—21no—
65#13063321—21no—
66#13063314—21no—
67#13063314—21no—
68#13063312—21no—
69#13063312—21no—
70#13063308—22no—
71#13063308—22no—
72#13063306C2×C412yes—
73#13063306C2×C412yescomplemented
74#13063306C2×C412yescomplemented
75#13063306C2312yes—
76#13063304—21no—
77#13063304—21no—
78#13063304—21no—
79#13063304—21no—
80#13063301—22no—
81#13063301—22no—
82#13063299—21no—
83#13063299—21no—
84#13063299—21no—
85#13063299—21no—
86#13063297—22no—
87#13063297—22no—
88#13063297—22no—
89#13063297—22no—
90#13063296—22no—
91#13063296—22no—
92#13063294—22no—
93#13063294—22no—
94#13063293C2×C412yes—
95#13063293C2×C412yescomplemented
96#13063293C2×C412yescomplemented
97#13063293C2312yes—
98C4×C22⋊D43—22no—
99C4×C22⋊D43—22no—
100C4×C22⋊D43—22no—
101C4×C22⋊D43—22no—
102#13063284—21no—
103#13063284—21no—
104#13063284C2×C412yescomplemented
105#13063284C2×C411yescharacteristic, complemented
106#13063284C2×C411yescharacteristic, complemented
107C2×C4⋊Dic43—21no—
108C2×C22⋊Dic43C2×C412yes—
109C2×C4×Dic43—21no—
110#13063244—22no—
111#13063244—22no—
112#13063242—22no—
113#13063242C2314yes—
114C2×#41×C43—41no—
115C2×#41×C43—41no—
116C2×#41×C43—41no—
117C2×#41×C43—41no—
118C2×#41×C43C2×C411yescharacteristic
119C2×#41×C43C2×C411yescharacteristic
120C2×#41×C43D411yescharacteristic
121C2×#41×C43D411yescharacteristic
122C2×#41×C43D411yescharacteristic
123C2×#41×C43D411yescharacteristic
124C2×#41×C43C2311yescharacteristic
125C2×#41×C43C2311yescharacteristic
126C22×Q8×C43D411yescharacteristic
127C22×D4×C43C2×C411yescharacteristic
128C22×D4×C43D411yescharacteristic
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43C2×C411yescharacteristic
131C23×C4×C43D411yescharacteristic
132C23×C4×C43D411yescharacteristic
133#117×C43—22no—
134#117×C43—22no—
135#117×C43—41no—
136#117×C43—41no—
137C2×C4⋊C4×C43—41no—
138C2×C22⋊C4×C43—22no—
139C2×C42×C43—41no—
140#99×C43—22no—
141#99×C43—22no—
142#99×C43—22no—
143#99×C43C2314yes—
144C24×C43C22⋊C411yescharacteristic
145C24×C43C22×C411yescharacteristic
146C24×C43C2×D411yescharacteristic
147C23×D43C22×C412yes—
148#41×C43—41no—
149#41×C43—41no—
150#41×C43—41no—
151#41×C43—41no—
152#41×C43—41no—
153#41×C43—41no—
154#41×C43—41no—
155#41×C43—41no—
156#41×C43—41no—
157#41×C43—41no—
158#41×C43—41no—
159#41×C43—41no—
160#41×C43—41no—
161#41×C43—41no—
162#41×C43—41no—
163#41×C43—41no—
164C2×Q8×C43—41no—
165C2×Q8×C43—41no—
166C2×Q8×C43C22⋊C411yescharacteristic
167C2×Q8×C43C22⋊C411yescharacteristic
168C2×Q8×C43C2×D411yescharacteristic
169C2×Q8×C43C2×D411yescharacteristic
170C2×D4×C43—41no—
171C2×D4×C43—41no—
172C2×D4×C43—41no—
173C2×D4×C43—41no—
174C2×D4×C43—41no—
175C2×D4×C43—41no—
176C2×D4×C43C22⋊C411yescharacteristic
177C2×D4×C43C22⋊C411yescharacteristic
178C2×D4×C43C22⋊C411yescharacteristic
179C2×D4×C43C22⋊C411yescharacteristic
180C2×D4×C43C22×C411yescharacteristic
181C2×D4×C43C22×C411yescharacteristic
182C2×D4×C43C22×C411yescharacteristic
183C2×D4×C43C2×D411yescharacteristic
184C2×D4×C43C2×D411yescharacteristic
185C2×D4×C43C2×D411yescharacteristic
186C2×D4×C43C2×D411yescharacteristic
187C2×D4×C43C2411yescharacteristic
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—42no—
201C22×C4×C43C22⋊C411yescharacteristic
202C22×C4×C43C22⋊C411yescharacteristic
203C22×C4×C43C22⋊C411yescharacteristic
204C22×C4×C43C22⋊C411yescharacteristic
205C22×C4×C43C22⋊C411yescharacteristic
206C22×C4×C43C22⋊C411yescharacteristic
207C22×C4×C43C22⋊C411yescharacteristic
208C22×C4×C43C22⋊C411yescharacteristic
209C22×C4×C43C22⋊C411yescharacteristic
210C22×C4×C43C22×C411yescharacteristic
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C2×C22⋊D43—22no—
218C2×C22⋊D43—22no—
219C2×C22⋊D43—22no—
220C2×C22⋊D43—22no—
221C2×C22⋊D43—22no—
222C2×C22⋊D43—22no—
223C2×C22⋊D43—42no—
224C2×C22⋊D43—42no—
225C22×Dic43—22no—
226C22×Dic43C22×C412yes—
227#10621898—42no—
228#10621898—42no—
229#10621898—42no—
230#10621898—42no—
231#10621898—42no—
232#10621898—42no—
233#10621898—41no—
234#10621898—41no—
235#10621898—41no—
236#10621898—41no—
237C2×D172—21no—
238C2×D172—21no—
239C2×D172—41no—
240C2×D172—41no—
241C2×C4×D43—22no—
242C2×C4×D43—22no—
243C2×C4×D43—42no—
244C2×C4×D43—42no—
245C2×Dic86—21no—
246C2×Dic86—21no—
247C2×Dic86—41no—
248C2×Dic86—41no—
249C4⋊C4×C43—42no—
250C4⋊C4×C43—42no—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—42no—
253C42×C43—42no—
254C42×C43—42no—
255C22⋊Dic43—22no—
256C22⋊Dic43—22no—
257C22⋊Dic43—22no—
258C22⋊Dic43—22no—
259C22⋊Dic43—22no—
260C22⋊Dic43C22×C412yes—
261C22⋊Dic43C22×C412yes—
262(C2×D43)⋊C4—22no—
263(C2×D43)⋊C4—22no—
264(C2×D43)⋊C4—22no—
265(C2×D43)⋊C4—22no—
266C4⋊Dic43—22no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269Dic43⋊C4—22no—
270Dic43⋊C4—22no—
271Dic43⋊C4—22no—
272Dic43⋊C4—22no—
273C4×Dic43—22no—
274C4×Dic43—21no—
275C4×Dic43—21no—
276#10621877—24no—
277#10621877—42no—
278#10621877—42no—
279#10621877—42no—
280C2×C43⋊C8—42no—
281C2×C43⋊C8—42no—
282C2×C43⋊C8—42no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—81no—
290C23×C43—81no—
291C23×C43—81no—
292C23×C43C2×C22⋊C411yescharacteristic
293C23×C43C2×C22⋊C411yescharacteristic
294C23×C43C2×C22⋊C411yescharacteristic
295C23×C43C2×C22⋊C411yescharacteristic
296C23×C43C2×C22⋊C411yescharacteristic
297C23×C43C23×C411yescharacteristic
298C23×C43C22×D411yescharacteristic
299C22×D43—22no—
300C22×D43—42no—
301C22×D43—82no—
302Q8×C43—41no—
303Q8×C43—41no—
304Q8×C43—41no—
305Q8×C43—41no—
306D4×C43—41no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—41no—
314D4×C43—41no—
315D4×C43—41no—
316D4×C43—41no—
317D4×C43—41no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—44no—
349C2×C4×C43—84no—
350C2×C4×C43#9911yescharacteristic
351C2×C4×C43#9911yescharacteristic
352C2×C4×C43#9911yescharacteristic
353C2×C4×C43#9911yescharacteristic
354C2×C4×C43C2×C22⋊C411yescharacteristic
355C2×C4×C43C2×C22⋊C411yescharacteristic
356C2×C4×C43C2×C22⋊C411yescharacteristic
357C2×C4×C43C2×C22⋊C411yescharacteristic
358C2×C4×C43C2×C22⋊C411yescharacteristic
359C2×C4×C43C2×C22⋊C411yescharacteristic
360C2×C4×C43C2×C22⋊C411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C22⋊D43—44no—
363C22⋊D43—42no—
364C22⋊D43—42no—
365C22⋊D43—82no—
366C22⋊D43—82no—
367C22⋊D43—82no—
368C22⋊D43—82no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—42no—
373C2×Dic43—82no—
374D172—42no—
375D172—41no—
376D172—41no—
377C4×D43—44no—
378C4×D43—42no—
379C4×D43—42no—
380Dic86—42no—
381Dic86—41no—
382Dic86—41no—
383C43⋊C8—44no—
384#33347—431nomaximal, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—81no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43C2×#9911yescharacteristic
405C22×C43C2×#9911yescharacteristic
406C22×C43C22×C22⋊C411yescharacteristic
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—84no—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—21no—
414C4×C43—21no—
415C4×C43—21no—
416C4×C43—21no—
417C4×C43—84no—
418C4×C43C2×#9911yescharacteristic
419C4×C43C2×#9911yescharacteristic
420C4×C43C2×#9911yescharacteristic
421C4×C43C2×#9911yescharacteristic
422Dic43—42no—
423Dic43—42no—
424Dic43—42no—
425#3449—431no—
426C2×#413—431no—
427C2×#410D4311yescharacteristic, complemented
428#2123—432no—
429#2122—432no—
430#2121—434no—
431#2120—434no—
432C2×C43—21no—
433C2×C43—21no—
434C2×C43—21no—
435C2×C43—41no—
436C2×C43—41no—
437C2×C43—41no—
438C2×C43—41no—
439C2×C43—41no—
440C2×C43—41no—
441C2×C43C22×#9911yescharacteristic
442D43—82no—
443C22×#41—431no—
444C22×#41C2×D4311yescharacteristic
445C22×M16—861no—
446#537—861no—
447#537—861no—
448#536—431no—
449#536—431no—
450#536—861no—
451#535—431no—
452#535—431no—
453#535—861no—
454#534—432no—
455#534—432no—
456#532—861no—
457#532—861no—
458#525—432no—
459#525—432no—
460#525—861no—
461#525—861no—
462C2×#117—21no—
463C2×#117—431no—
464#413—432no—
465#413—432no—
466#413—861no—
467#413—861no—
468C2×#101—861no—
469C2×#100—432no—
470#410—21no—
471#410—21no—
472#410C2×D4312yes—
473#410C2×D4312yes—
474C2×#99—21no—
475C2×#99C2×D4312yes—
476#352—438no—
477AΣL(1,𝔽16)—438no—
478C43#3334711yescharacteristic, complemented, Sylow
479C2×#41—41no—
480C2×#41—41no—
481C2×#41—41no—
482C2×#41—41no—
483C2×#41—861no—
484C2×#41—861no—
485C2×#41—861no—
486C2×#41—861no—
487C2×#41—1721no—
488C2×#41—1721no—
489C2×#41—1721no—
490C2×#41—1721no—
491C2×#41C4×D4311yescharacteristic
492C2×#41C4×D4311yescharacteristic
493C2×#41D17211yescharacteristic
494C2×#41D17211yescharacteristic
495C2×#41C22⋊D4311yescharacteristic
496C2×#41C22⋊D4311yescharacteristic
497C2×#41C22×D4311yescharacteristic
498C2×#41C22×D4311yescharacteristic
499C22×Q8—431no—
500C22×Q8D17211yescharacteristic
501C22×D4—432no—
502C22×D4—431no—
503C22×D4C4×D4311yescharacteristic
504C22×D4C22⋊D4311yescharacteristic
505C22×D4C22×D4311yescharacteristic
506C23×C4—432no—
507C23×C4C4×D4311yescharacteristic
508C23×C4D17211yescharacteristic
509C23×C4C22⋊D4311yescharacteristic
510C2×M16—862no—
511C2×M16—862no—
512C2×M16—862no—
513C2×M16—1721no—
514C2×M16—1721no—
515C2×M16—1721no—
516C22×C8—1721no—
517C4⋊Q8—861no—
518C4⋊Q8—861no—
519#127—861no—
520#127—861no—
521#124—861no—
522#124—861no—
523#124—861no—
524#124—861no—
525#123—432no—
526#123—432no—
527#123—432no—
528#123—432no—
529#123—862no—
530#123—862no—
531C22⋊Q8—862no—
532C22⋊Q8—862no—
533C22⋊Q8—861no—
534C22⋊Q8—861no—
535C22⋊Q8—861no—
536C22⋊Q8—861no—
537#121—862no—
538#121—862no—
539#121—862no—
540#121—862no—
541#121—862no—
542#121—862no—
543#121—861no—
544#121—861no—
545#121—861no—
546#121—861no—
547#120—432no—
548#120—432no—
549#120—432no—
550#120—432no—
551#120—862no—
552#120—862no—
553C4×D4—862no—
554C4×D4—862no—
555C4×D4—862no—
556C4×D4—862no—
557#117—22no—
558#117—22no—
559#117—41no—
560#117—41no—
561#117—432no—
562#117—431no—
563#117—431no—
564#117—861no—
565#117—861no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—861no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—432no—
570C2×C42—41no—
571C2×C42—861no—
572#101—862no—
573#101—862no—
574#100—434no—
575#100—862no—
576#99—22no—
577#99—22no—
578#99—22no—
579#99C22×D4314yes—
580C24—432no—
581C24(C2×D43)⋊C411yescharacteristic
582C24C2×C4×D4311yescharacteristic
583C24C2×C22⋊D4311yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—1722no—
601#41—1722no—
602#41—1722no—
603#41—1722no—
604#41—1722no—
605#41—1722no—
606#41—1721no—
607#41—1721no—
608#41—1721no—
609#41—1721no—
610C2×Q8—41no—
611C2×Q8—41no—
612C2×Q8—861no—
613C2×Q8—861no—
614C2×Q8—1721no—
615C2×Q8—1721no—
616C2×Q8(C2×D43)⋊C411yescharacteristic
617C2×Q8(C2×D43)⋊C411yescharacteristic
618C2×Q8C2×D17211yescharacteristic
619C2×Q8C2×D17211yescharacteristic
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—862no—
627C2×D4—862no—
628C2×D4—862no—
629C2×D4—862no—
630C2×D4—862no—
631C2×D4—862no—
632C2×D4—861no—
633C2×D4—861no—
634C2×D4—1721no—
635C2×D4—1721no—
636C2×D4—1722no—
637C2×D4—1722no—
638C2×D4(C2×D43)⋊C411yescharacteristic
639C2×D4(C2×D43)⋊C411yescharacteristic
640C2×D4(C2×D43)⋊C411yescharacteristic
641C2×D4(C2×D43)⋊C411yescharacteristic
642C2×D4C2×C4×D4311yescharacteristic
643C2×D4C2×C4×D4311yescharacteristic
644C2×D4C2×C4×D4311yescharacteristic
645C2×D4C2×D17211yescharacteristic
646C2×D4C2×C22⋊D4311yescharacteristic
647C2×D4C2×C22⋊D4311yescharacteristic
648C2×D4C2×C22⋊D4311yescharacteristic
649C2×D4C23×D4311yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—42no—
663C22×C4—432no—
664C22×C4—862no—
665C22×C4—862no—
666C22×C4—862no—
667C22×C4—1722no—
668C22×C4—1722no—
669C22×C4(C2×D43)⋊C411yescharacteristic
670C22×C4(C2×D43)⋊C411yescharacteristic
671C22×C4(C2×D43)⋊C411yescharacteristic
672C22×C4(C2×D43)⋊C411yescharacteristic
673C22×C4(C2×D43)⋊C411yescharacteristic
674C22×C4(C2×D43)⋊C411yescharacteristic
675C22×C4(C2×D43)⋊C411yescharacteristic
676C22×C4(C2×D43)⋊C411yescharacteristic
677C22×C4(C2×D43)⋊C411yescharacteristic
678C22×C4C2×C4×D4311yescharacteristic
679C22×C4C2×C4×D4311yescharacteristic
680C22×C4C2×D17211yescharacteristic
681C22×C4C2×D17211yescharacteristic
682C22×C4C2×D17211yescharacteristic
683C22×C4C2×C22⋊D4311yescharacteristic
684C22×C4C2×C22⋊D4311yescharacteristic
685M16—864no—
686M16—1722no—
687M16—1722no—
688M16—1722no—
689C2×C8—1722no—
690C2×C8—1722no—
691C2×C8—1722no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—862no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—862no—
698C4⋊C4—862no—
699C4⋊C4—862no—
700C4⋊C4—862no—
701C22⋊C4—24no—
702C22⋊C4—42no—
703C22⋊C4—432no—
704C22⋊C4—432no—
705C22⋊C4—862no—
706C22⋊C4—862no—
707C22⋊C4—862no—
708C22⋊C4—862no—
709C22⋊C4—862no—
710C22⋊C4—862no—
711C22⋊C4—862no—
712C22⋊C4—862no—
713C22⋊C4—862no—
714C42—42no—
715C42—42no—
716C42—862no—
717C42—861no—
718C42—861no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—862no—
729C23—3442no—
730C23—1722no—
731C23C2×(C2×D43)⋊C411yescharacteristic
732C23C2×(C2×D43)⋊C411yescharacteristic
733C23C2×(C2×D43)⋊C411yescharacteristic
734C23C2×(C2×D43)⋊C411yescharacteristic
735C23C2×(C2×D43)⋊C411yescharacteristic
736C23C22×C4×D4311yescharacteristic
737C23C22×C22⋊D4311yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—1722no—
743Q8—1721no—
744Q8—1721no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—3442no—
758D4—3442no—
759D4—3442no—
760D4—3442no—
761D4—1722no—
762D4—1724no—
763D4—1722no—
764D4—1722no—
765D4—1721no—
766D4—1721no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—44no—
798C2×C4—84no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—3442no—
803C2×C4—1724no—
804C2×C4—1722no—
805C2×C4—1722no—
806C2×C4—1722no—
807C2×C4#1306323911yescharacteristic
808C2×C4#1306323911yescharacteristic
809C2×C4#1306323911yescharacteristic
810C2×C4#1306323911yescharacteristic
811C2×C4C2×(C2×D43)⋊C411yescharacteristic
812C2×C4C2×(C2×D43)⋊C411yescharacteristic
813C2×C4C2×(C2×D43)⋊C411yescharacteristic
814C2×C4C2×(C2×D43)⋊C411yescharacteristic
815C2×C4C2×(C2×D43)⋊C411yescharacteristic
816C2×C4C2×(C2×D43)⋊C411yescharacteristic
817C2×C4C2×(C2×D43)⋊C411yescharacteristic
818C2×C4C22×D17211yescharacteristic
819C8—1724no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—3444no—
840C22—1722no—
841C22—1722no—
842C22—1722no—
843C22C2×#1306323911yescharacteristic
844C22C2×#1306323911yescharacteristic
845C22C22×(C2×D43)⋊C411yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—84no—
853C4—1722no—
854C4—1722no—
855C4—1722no—
856C4C2×#1306323911yescharacteristic
857C4C2×#1306323911yescharacteristic
858C4C2×#1306323911yescharacteristic
859C4C2×#1306323911yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—3442no—
870C2C22×#1306323911yescharacteristic
subgroupG/H
centerC4C2×#13063239
commutatorC23×C43C23×C4
FrattiniC2×D4C23×D43
FittingC2×C43×#410C2
socleC2×C43C22×#99
prime radical#19147924C2
cosocleC2×D4×C43C24
hypercenterC2×#410D43
hypocenterC43#33347
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#14582883C2semidirect
3. #19136248C2semidirect
4. #19136244C2semidirect
5. #19136239C2semidirect
6. #19136234C2semidirect
7. C2×C43×#410C2semidirect
8. C22×#10621898C4semidirect
13. #14583470C4semidirect
16. #14583463C4semidirect
18. #14583458C4semidirect
24. #14583406C4semidirect
26. C2×#13063284C4semidirect
33. #14582688C22semidirect
34. #14582685C22semidirect
51. C22×Dic86C2×C4semidirect
52. C22×D172C2×C4semidirect
54. C22×C4×D43C2×C4semidirect
73. #13063306C2×C4semidirect
74. #13063306C2×C4semidirect
95. #13063293C2×C4semidirect
96. #13063293C2×C4semidirect
104. #13063284C2×C4semidirect
105. #13063284C2×C4semidirect
106. #13063284C2×C4semidirect
427. C2×#410D43semidirect
478. C43#33347semidirect

Maximal subgroups

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

subgroupindex
#191479242
C2×#145828832
#191362482
#191362442
#191362392
#191362342
C2×C43×#4102
#3334743