Finite Group Databasebeta

← #25112011

Subgroups — #25112011

Order 11008.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583544C211yesmaximal, characteristic
2C2×#14582964C211yesmaximal, characteristic, complemented
3C2×#14582892C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5#19137521C211yesmaximal, characteristic, complemented
6#19135525C211yesmaximal, characteristic, complemented
7#19135404C211yesmaximal, characteristic, complemented
8#19135022C211yesmaximal, characteristic, complemented
9#19135017C211yesmaximal, characteristic, complemented
10#19134916C211yesmaximal, characteristic, complemented
11#19134901C211yesmaximal, characteristic, complemented
12#19134532C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14C4×#13063246C211yesmaximal, characteristic, complemented
15C43×#1804C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic, complemented
20#14583544—24no—
21#14583544C418yescomplemented
22C2×#13063313C2211yescharacteristic
23C2×#13063309—21no—
24C2×#13063305C2211yescharacteristic
25C2×#13063300C2211yescharacteristic
26C2×#13063299—21no—
27C2×#13063295—21no—
28C2×C4×D172C2211yescharacteristic
29C2×#13063283C2211yescharacteristic, complemented
30C2×C4⋊C4×D43C2211yescharacteristic
31C22×(C2×D43)⋊C4—21no—
32#14582964—24no—
33#14582892—24no—
34C2×#13063250C2211yescharacteristic, complemented
35C2×#13063250C2211yescharacteristic, complemented
36C2×#13063248C2211yescharacteristic, complemented
37C2×#13063248C2211yescharacteristic, complemented
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44#102×D43—24no—
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
47C2×C4×C43⋊C8C2211yescharacteristic, complemented
48#14582788—21no—
49#14582782—21no—
50#14582777—21no—
51#14582756C2211yescharacteristic
52#14582756C2211yescharacteristic, complemented
53C4×C4⋊Dic43C2211yescharacteristic, complemented
54#14582746—21no—
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C2×C4×D4×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#382C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—41no—
69C2×#10621900—41no—
70C2×#10621900C2×C414yescomplemented
71C22×Dic86C2311yescharacteristic
72C22×D172—21no—
73C22×D172D411yescharacteristic
74C22×D172C2311yescharacteristic
75C22×C22⋊D43—21no—
76C22×C22⋊D43—21no—
77C2×D4×D43—22no—
78C2×D4×D43—22no—
79C2×D4×D43—22no—
80C2×D4×D43—41no—
81C2×D4×D43—41no—
82C2×D4×D43C2×C414yes—
83C23×Dic43—21no—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C22×C4×D43C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C2×C8×D43—22no—
90C2×C8×D43—22no—
91C2×C8×D43—22no—
92C2×C8×D43—22no—
93C2×C8×D43—41no—
94C2×C8×D43—41no—
95#13063313—22no—
96#13063313C2×C414yescomplemented
97#13063309—28no—
98#13063305—22no—
99#13063305C2×C414yes—
100#13063300—22no—
101#13063300C2×C414yescomplemented
102#13063299—28no—
103#13063295—28no—
104C4×D172C2×C414yes—
105C4×D172D414yes—
106#13063283—22no—
107#13063283—41no—
108C2×C4⋊Dic43—21no—
109C2×C4⋊Dic43D411yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×Dic43⋊C4—21no—
113C4⋊C4×D43—22no—
114C4⋊C4×D43—41no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—28no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4D411yescharacteristic
124C2×(C2×D43)⋊C4D411yescharacteristic
125C2×C4×Dic43—21no—
126C2×C4×Dic43—21no—
127#13063250—22no—
128#13063250—41no—
129#13063248—22no—
130#13063248—41no—
131#13063247—22no—
132#13063247—41no—
133#13063246—22no—
134#13063246D414yescomplemented
135#13063245—22no—
136#13063245—41no—
137(C2×D43)⋊C8—22no—
138(C2×D43)⋊C8—22no—
139C4×C43⋊C8—22no—
140C43⋊#95—21no—
141C43⋊#95—21no—
142C43⋊#95—21no—
143C22×D4×C43C2311yescharacteristic
144C23×C4×C43—21no—
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C4×D4×C43—22no—
148C4×D4×C43C2×C414yescomplemented
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C22⋊C4×C43—21no—
153C2×C42×C43C2311yescharacteristic
154C4⋊C8×C43—22no—
155#102×C43—22no—
156#102×C43—22no—
157#95×C43—21no—
158#95×C43—21no—
159C24×C43—21no—
160C23×D43—21no—
161C23×D43—24no—
162C23×D43—42no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—81no—
167C23×D43—81no—
168C23×D43C2×D411yescharacteristic
169C23×D43C2×D411yescharacteristic
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43C22×C412yes—
174C2×D4×C43C2×D412yes—
175C2×D4×C43#4112yes—
176C22×C4×C43—24no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—81no—
181C22×C4×C43—81no—
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2411yescharacteristic
185C2×C22⋊D43—24no—
186C2×C22⋊D43—24no—
187C2×C22⋊D43—42no—
188C2×C22⋊D43—42no—
189C2×C22⋊D43—42no—
190C2×C22⋊D43—42no—
191C22×Dic43—24no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199#10621900—28no—
200#10621900—44no—
201#10621900—44no—
202#10621900—44no—
203D4×D43—28no—
204D4×D43—44no—
205D4×D43—44no—
206D4×D43—44no—
207C2×D172—21no—
208C2×D172—24no—
209C2×D172—22no—
210C2×D172—22no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—81no—
216C2×D172—81no—
217C2×D172C22⋊C414yes—
218C2×D172C22×C412yes—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—42no—
228C2×C4×D43—42no—
229C2×C4×D43—81no—
230C2×C4×D43C22×C412yes—
231C2×C4×D43C22×C412yes—
232C2×C4×D43C2×D412yes—
233C2×C4×D43C2×D412yes—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86C22×C412yes—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43C22×C412yes—
252C22⋊C4×C43—24no—
253C42×C43C22×C412yes—
254C42×C43C2×D412yes—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—42no—
260(C2×D43)⋊C4—42no—
261(C2×D43)⋊C4—81no—
262(C2×D43)⋊C4C22⋊C414yes—
263(C2×D43)⋊C4C22⋊C414yes—
264C4⋊Dic43—21no—
265C4⋊Dic43—24no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43C22⋊C414yes—
269C4⋊Dic43C2×D412yes—
270Dic43⋊C4—42no—
271C4×Dic43—42no—
272C4×Dic43—81no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8C2×D412yes—
279C8×D43—44no—
280C8×D43—44no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43C22×D411yescharacteristic
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—21no—
292C22×D43—21no—
293C22×D43—21no—
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—22no—
300C22×D43—48no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—48no—
308C22×D43—84no—
309C22×D43—84no—
310C22×D43—84no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43C2×C22⋊C412yes—
314C22×D43C2×C22⋊C412yes—
315C22×D43#13512yes—
316C22×D43#13512yes—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43C4×D414yes—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—22no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—84no—
335C2×C4×C43C2×C22⋊C412yes—
336C2×C4×C43C2×C22⋊C412yes—
337C2×C4×C43C23×C411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43H(5,𝔽2)11yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C22⋊D43—48no—
344C22⋊D43—48no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—48no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43C2×C22⋊C412yes—
360C2×Dic43C2×C22⋊C412yes—
361D172—28no—
362D172—22no—
363D172—22no—
364D172—41no—
365D172—41no—
366D172—84no—
367C4×D43—22no—
368C4×D43—22no—
369C4×D43—22no—
370C4×D43—22no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—84no—
376Dic86—22no—
377Dic86—22no—
378Dic86—41no—
379Dic86—41no—
380C8×C43—41no—
381C8×C43—41no—
382C43⋊C8—22no—
383C43⋊C8—41no—
384#22414—431nomaximal, Sylow
385C22×C43—24no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—42no—
392C22×C43C22×C22⋊C411yescharacteristic
393C22×C43D4211yescharacteristic
394C22×C43#54611yescharacteristic
395C22×C43C2×#13511yescharacteristic
396C22×C43C2×#13511yescharacteristic
397C22×C43#57611yescharacteristic
398C22×C43#57711yescharacteristic
399C2×D43—22no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—41no—
409C2×D43—41no—
410C2×D43—41no—
411C2×D43—41no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—816no—
416C2×D43—81no—
417C2×D43—81no—
418C2×D43—81no—
419C2×D43—81no—
420C2×D43#41614yescomplemented
421C4×C43—22no—
422C4×C43—22no—
423C4×C43—42no—
424C4×C43—81no—
425C4×C43—81no—
426C4×C43C2×C4×D411yescharacteristic
427C4×C43#51811yescharacteristic
428C4×C43D4211yescharacteristic
429C4×C43#54611yescharacteristic
430Dic43—22no—
431Dic43—22no—
432Dic43—42no—
433Dic43—42no—
434Dic43—81no—
435C2×#546—431no—
436C2×C8×D4—431no—
437C2×#416—431no—
438C22×#102—431no—
439#2352—431no—
440#1983—431no—
441#1958—431no—
442#1893—431no—
443#1892—431no—
444#1875—431no—
445#1872—431no—
446#1804D4311yescharacteristic, complemented
447#1788—431no—
448#1786—431no—
449C4×#102—431no—
450C2×C43—44no—
451C2×C43D4×C22⋊C411yescharacteristic
452C2×C43C2×#41611yescharacteristic
453C2×C43#289711yescharacteristic
454C2×C43#328011yescharacteristic
455C2×C43#328211yescharacteristic
456C2×C43#329611yescharacteristic
457C2×C43#329711yescharacteristic
458D43—24no—
459D43—42no—
460D43—82no—
461C22×#41—431no—
462C23×D4—431no—
463C23×C8—431no—
464C23×C8—431no—
465#546—438no—
466#546—864no—
467C2×#124—431no—
468C2×#123—861no—
469C2×C22⋊Q8—431no—
470C2×#121—431no—
471C2×#121—861no—
472C2×#120—861no—
473C2×C4×D4—431no—
474C2×C4×D4C2×D4311yescharacteristic
475C2×#117—431no—
476C22×C4⋊C4—431no—
477C22×C22⋊C4—861no—
478C8×D4—864no—
479C2×C4⋊C8C2×D4311yescharacteristic, complemented
480#416—864no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—864no—
492C2×#102C2×D4311yescharacteristic
493C2×#102C2×D4311yescharacteristic
494C2×C22⋊C8—431no—
495C2×C22⋊C8—431no—
496C2×C4×C8—431no—
497#388—861no—
498#387—861no—
499#386—861no—
500#382C2×D4311yescharacteristic, complemented
501#380—431no—
502#380—431no—
503C4×C4⋊C4—431no—
504C4×C22⋊C4—861no—
505#340—431no—
506#340—431no—
507#340C2×D4311yescharacteristic, complemented
508#340C2×D4311yescharacteristic, complemented
509C43#2241411yescharacteristic, complemented, Sylow
510C25—861no—
511C2×#41—434no—
512C2×#41—862no—
513C2×#41—862no—
514C2×#41—862no—
515C2×#41—1721no—
516C2×#41—1721no—
517C22×Q8—431no—
518C22×D4—434no—
519C22×D4—431no—
520C22×D4—431no—
521C22×D4—861no—
522C22×D4—862no—
523C22×D4—861no—
524C22×D4—862no—
525C22×D4—862no—
526C22×D4—861no—
527C22×D4—1721no—
528C22×D4—1721no—
529C22×D4C22×D4311yescharacteristic
530C23×C4—21no—
531C23×C4—431no—
532C23×C4—431no—
533C23×C4—861no—
534C23×C4—861no—
535C22×C8—431no—
536C22×C8—431no—
537C22×C8—862no—
538C22×C8—862no—
539C22×C8—862no—
540C22×C8—862no—
541C22×C8—1721no—
542C22×C8—1721no—
543C22×C8C22×D4311yescharacteristic
544C22×C8C22×D4311yescharacteristic
545#124—434no—
546#124—862no—
547#123—868no—
548C22⋊Q8—434no—
549C22⋊Q8—862no—
550#121—434no—
551#121—868no—
552#121—862no—
553#120—868no—
554C4×D4—22no—
555C4×D4—434no—
556C4×D4—434no—
557C4×D4C4×D4314yescomplemented
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—862no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—1721no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—868no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C42—861no—
582C2×C42—861no—
583C2×C42C22×D4311yescharacteristic
584C4⋊C8—22no—
585#103—862no—
586#103—862no—
587#103—1721no—
588#103—1721no—
589#102—22no—
590#102—22no—
591#102—434no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—1721no—
596#102—1721no—
597C22⋊C8—862no—
598C22⋊C8—862no—
599C4×C8—862no—
600#95—21no—
601#95—21no—
602#95—861no—
603#95—861no—
604#95—861no—
605C24—21no—
606C24—431no—
607C24—431no—
608C24—864no—
609C24—861no—
610C24—3441no—
611C24—3441no—
612C24—1722no—
613C24—1722no—
614C24—1722no—
615C24—1722no—
616#41—868no—
617#41—1724no—
618#41—1724no—
619#41—1724no—
620C2×Q8—432no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—434no—
630C2×D4—432no—
631C2×D4—862no—
632C2×D4—862no—
633C2×D4—864no—
634C2×D4—864no—
635C2×D4—868no—
636C2×D4—864no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—3441no—
643C2×D4—3441no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4—1724no—
647C2×D4—1722no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4—1722no—
651C2×D4C2×C4×D4312yes—
652C2×D4D4×D4312yes—
653C2×D4#1062190212yes—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—432no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—432no—
666C22×C4—864no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—3441no—
679C22×C4—1722no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4—1722no—
683C22×C4D4×D4311yescharacteristic
684C22×C4D4×D4311yescharacteristic
685C22×C4C23×D4311yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—432no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—1724no—
699C2×C8—1724no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—434no—
706C4⋊C4—432no—
707C4⋊C4—864no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—1722no—
712C4⋊C4C2×C4×D4312yes—
713C22⋊C4—24no—
714C22⋊C4—434no—
715C22⋊C4—434no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—3441no—
721C22⋊C4—1722no—
722C22⋊C4—1722no—
723C42—3441no—
724C42—1722no—
725C42C2×C4×D4312yes—
726C42D4×D4312yes—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—432no—
735C23—432no—
736C23—432no—
737C23—432no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—861no—
742C23—861no—
743C23—861no—
744C23—861no—
745C23—861no—
746C23—861no—
747C23—861no—
748C23—862no—
749C23—3444no—
750C23—3444no—
751C23—3444no—
752C23—3444no—
753C23—3444no—
754C23—1728no—
755C23—1728no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23—1721no—
761C23—1721no—
762C23C2×D4×D4311yescharacteristic
763Q8—862no—
764Q8—862no—
765Q8—1721no—
766Q8—1721no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—868no—
771D4—862no—
772D4—862no—
773D4—3444no—
774D4—1728no—
775D4—1728no—
776D4—1721no—
777D4—1721no—
778D4#1306328714yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—84no—
793C2×C4—432no—
794C2×C4—432no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—3444no—
810C2×C4—1728no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4C22⋊C4×D4312yes—
819C2×C4C22⋊C4×D4312yes—
820C2×C4C22×C4×D4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C2×D4×D4311yescharacteristic
823C2×C4C2×#1062190211yescharacteristic
824C2×C4#1306337111yescharacteristic
825C2×C4#1306337111yescharacteristic
826C8—41no—
827C8—41no—
828C8—862no—
829C8—1721no—
830C22—24no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—434no—
838C22—862no—
839C22—862no—
840C22—862no—
841C22—862no—
842C22—862no—
843C22—862no—
844C22—862no—
845C22—862no—
846C22—862no—
847C22—34416no—
848C22—3441no—
849C22—3441no—
850C22—3441no—
851C22—3441no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1721no—
856C22—1721no—
857C22—1721no—
858C22—1721no—
859C22C2×C22⋊C4×D4311yescharacteristic
860C22#1458353311yescharacteristic
861C22#1458354011yescharacteristic
862C22#135×D4311yescharacteristic
863C22#135×D4311yescharacteristic
864C22#1458370311yescharacteristic
865C22#1458370911yescharacteristic
866C4—22no—
867C4—22no—
868C4—42no—
869C4—81no—
870C4—81no—
871C4—862no—
872C4—862no—
873C4—3441no—
874C4—1722no—
875C4—1722no—
876C4C2×#1306328711yescharacteristic
877C4#1458337311yescharacteristic
878C4#1458353311yescharacteristic
879C4#1458354011yescharacteristic
880C2—44no—
881C2—864no—
882C2—3442no—
883C2—1722no—
884C2#1913741511yescharacteristic
885C2#416×D4311yescharacteristic
886C2#1914312011yescharacteristic
887C2#1914627511yescharacteristic
888C2#1914630811yescharacteristic
889C2#1914642711yescharacteristic
890C2#1914644211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1804C2
socleC23×C43C22×D4
prime radicalC2×#14583544C2
cosocleC22×C4×C43C24
hypercenter#1804D43
hypocenterC43#22414
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#14582964C2semidirect
3. C2×#14582892C2semidirect
4. C2×#102×D43C2semidirect
5. #19137521C2semidirect
6. #19135525C2semidirect
7. #19135404C2semidirect
8. #19135022C2semidirect
9. #19135017C2semidirect
10. #19134916C2semidirect
11. #19134901C2semidirect
12. #19134532C2semidirect
13. #19134524C2semidirect
14. C4×#13063246C2semidirect
15. C43×#1804C2semidirect
19. C22×C8×D43C22semidirect
21. #14583544C4semidirect
29. C2×#13063283C22semidirect
34. C2×#13063250C22semidirect
35. C2×#13063250C22semidirect
36. C2×#13063248C22semidirect
37. C2×#13063248C22semidirect
46. C2×(C2×D43)⋊C8C22semidirect
47. C2×C4×C43⋊C8C22semidirect
52. #14582756C22semidirect
53. C4×C4⋊Dic43C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
58. C2×C4⋊C8×C43C22semidirect
61. C43×#382C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
70. C2×#10621900C2×C4semidirect
96. #13063313C2×C4semidirect
101. #13063300C2×C4semidirect
134. #13063246D4semidirect
148. C4×D4×C43C2×C4semidirect
420. C2×D43#416semidirect
446. #1804D43semidirect
479. C2×C4⋊C8C2×D43semidirect
500. #382C2×D43semidirect
507. #340C2×D43semidirect
508. #340C2×D43semidirect
509. C43#22414semidirect
557. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835442
C2×#145829642
C2×#145828922
C2×#102×D432
#191375212
#191355252
#191354042
#191350222
#191350172
#191349162
#191349012
#191345322
#191345242
C4×#130632462
C43×#18042
#2241443