Finite Group Databasebeta

← #25112203

Subgroups — #25112203

Order 11008.

1606 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×#14583540C211yesmaximal, characteristic
2C2×#14582975C211yesmaximal, characteristic, complemented
3C2×#14582899C211yesmaximal, characteristic, complemented
4C2×#14582905C211yesmaximal, characteristic, complemented
5#19137517C211yesmaximal, characteristic, complemented
6#19135524C211yesmaximal, characteristic, complemented
7#19135403C211yesmaximal, characteristic, complemented
8#19135032C211yesmaximal, characteristic, complemented
9#19134911C211yesmaximal, characteristic, complemented
10#19134908C211yesmaximal, characteristic, complemented
11#19134604C211yesmaximal, characteristic, complemented
12#19134534C211yesmaximal, characteristic, complemented
13#19134525C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1894C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C23×D172C2211yescharacteristic
18C22×#10621872C2211yescharacteristic, complemented
19#14583540—24no—
20#14583540C418yescomplemented
21C2×#13063314C2211yescharacteristic
22C2×#13063310—21no—
23C2×#13063300—21no—
24C2×#13063300C2211yescharacteristic
25C2×#13063295—21no—
26C2×#13063287C2211yescharacteristic
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic, complemented
30C2×C22⋊C4×D43—21no—
31#14582975—24no—
32C2×Dic43⋊C8C2211yescharacteristic, complemented
33#14582905—24no—
34#14582899—24no—
35C2×#13063249C2211yescharacteristic, complemented
36C2×#13063249C2211yescharacteristic, complemented
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
47C2×C8×Dic43C2211yescharacteristic, complemented
48#14582787—21no—
49#14582781—21no—
50#14582775—21no—
51#14582764C2211yescharacteristic, complemented
52#14582756C2211yescharacteristic, complemented
53C4⋊C4×Dic43C2211yescharacteristic, complemented
54#14582746—21no—
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C22×M16×C43C2211yescharacteristic
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic, complemented
60C2×#103×C43C2211yescharacteristic, complemented
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902—41no—
69C2×#10621902—41no—
70C2×#10621902C2×C414yes—
71C22×D172—22no—
72C22×D172—22no—
73C22×D172—21no—
74C22×D172—21no—
75C22×D172—22no—
76C22×D172—21no—
77C22×D172—41no—
78C22×D172—41no—
79C22×D172C2×C414yescomplemented
80C22×D172C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43D411yescharacteristic
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87C2×#10621872—22no—
88C2×#10621872—22no—
89C2×#10621872—41no—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92#13063314—22no—
93#13063314C2×C414yescomplemented
94#13063310—28no—
95#13063300—22no—
96#13063300—28no—
97#13063300C2×C414yes—
98#13063295—28no—
99#13063287—22no—
100#13063287C2×C414yescomplemented
101C4×C22⋊D43C2×C414yes—
102C4×C22⋊D43D414yes—
103#13063284—22no—
104#13063284—41no—
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4D411yescharacteristic
109C4⋊C4×D43—22no—
110C4⋊C4×D43—41no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43D411yescharacteristic
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4D411yescharacteristic
119C22⋊C4×D43—28no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123Dic43⋊C8—22no—
124#13063249—22no—
125#13063249—41no—
126#13063247—22no—
127#13063247—22no—
128#13063247—22no—
129#13063247D414yescomplemented
130#13063245—22no—
131#13063245—22no—
132#13063245—41no—
133#13063245—41no—
134C22⋊(C43⋊C8)—22no—
135(C2×D43)⋊C8—22no—
136C8×Dic43—22no—
137C43⋊#95—21no—
138C43⋊#95—21no—
139C43⋊#95—21no—
140C43⋊#95—21no—
141C22×Q8×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C2×M16×C43—22no—
144C2×M16×C43—22no—
145C2×M16×C43—41no—
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C22⋊Q8×C43—22no—
149C22⋊Q8×C43C2×C414yescomplemented
150C2×C4⋊C4×C43—21no—
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—21no—
156#103×C43—22no—
157#103×C43—41no—
158#95×C43—21no—
159C24×C43C2×D411yescharacteristic
160C23×D43—21no—
161C23×D43—21no—
162C23×D43—24no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—81no—
168C23×D43—81no—
169C23×D43C2×D411yescharacteristic
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43C22×C412yes—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43C22×C412yes—
185C22×C4×C43C2×D412yes—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C2×C22⋊D43—41no—
189C2×C22⋊D43—41no—
190C2×C22⋊D43C22⋊C414yes—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196#10621902—28no—
197#10621902—44no—
198#10621902—44no—
199#10621902—44no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172—24no—
204C2×D172—21no—
205C2×D172—24no—
206C2×D172—24no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—28no—
212C2×D172—42no—
213C2×D172—42no—
214C2×D172—42no—
215C2×D172—42no—
216C2×D172—44no—
217C2×D172—44no—
218C2×D172—44no—
219C2×D172—81no—
220C2×D172—81no—
221C2×D172C22×C412yes—
222C2×D172C22×C412yes—
223C2×D172C2×D412yes—
224C2×D172#4112yes—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43—42no—
234C2×C4×D43—42no—
235C2×C4×D43—81no—
236C2×C4×D43—81no—
237C2×C4×D43—81no—
238C2×C4×D43C22×C412yes—
239C2×C4×D43C2×D412yes—
240M16×C43—44no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43C2×D412yes—
247C4⋊C4×C43—24no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43C22×C412yes—
254C22⋊C4×C43—24no—
255C22⋊C4×C43—81no—
256C22⋊Dic43—42no—
257C22⋊Dic43C22⋊C414yes—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—42no—
263(C2×D43)⋊C4C22⋊C414yes—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43C2×D412yes—
268Dic43⋊C4—42no—
269Dic43⋊C4C22⋊C414yes—
270C4×Dic43—42no—
271C4×Dic43—81no—
272C4×Dic43C22×C412yes—
273C4×Dic43C2×D412yes—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280#10621872—44no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43C2×C22⋊C412yes—
288C23×C43C22×D411yescharacteristic
289C22×D43—22no—
290C22×D43—21no—
291C22×D43—22no—
292C22×D43—21no—
293C22×D43—22no—
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—22no—
299C22×D43—48no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—48no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43—84no—
316C22×D43C2×C22⋊C412yes—
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—41no—
320Q8×C43—41no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43C2×C22⋊C412yes—
340C2×C4×C43C23×C411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C2×#4111yescharacteristic
344C2×C4×C43H(5,𝔽2)11yescharacteristic
345C2×C4×C43H(5,𝔽2)11yescharacteristic
346C22⋊D43—44no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—22no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43C2×C22⋊C412yes—
360C2×Dic43C2×C22⋊C412yes—
361C2×Dic43C2×C22⋊C412yes—
362D172—22no—
363D172—22no—
364D172—22no—
365D172—22no—
366D172—22no—
367D172—48no—
368D172—48no—
369D172—41no—
370D172—41no—
371D172—84no—
372D172C4×D414yes—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—48no—
378C4×D43—84no—
379C4×D43—84no—
380C8×C43—22no—
381C8×C43—41no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384#22427—431nomaximal, Sylow
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43C22×C22⋊C411yescharacteristic
393C22×C43D4211yescharacteristic
394C22×C43#54611yescharacteristic
395C22×C43#57511yescharacteristic
396C22×C43#57511yescharacteristic
397C22×C43#57611yescharacteristic
398C22×C43#57711yescharacteristic
399C2×D43—24no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—42no—
404C2×D43—42no—
405C2×D43—41no—
406C2×D43—42no—
407C2×D43—41no—
408C2×D43—42no—
409C2×D43—41no—
410C2×D43—42no—
411C2×D43—41no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—816no—
417C2×D43—81no—
418C2×D43—81no—
419C2×D43—81no—
420C2×D43—81no—
421C4×C43—22no—
422C4×C43—42no—
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—22no—
433Dic43—42no—
434Dic43—81no—
435C2×#546—431no—
436C2×#436—431no—
437C2×#417—431no—
438C2×#418—431no—
439#2352—431no—
440#1983—431no—
441#1958—431no—
442#1895—431no—
443#1894D4311yescharacteristic, complemented
444#1874—431no—
445#1873—431no—
446#1804—431no—
447#1788—431no—
448#1786—431no—
449C4×#102—431no—
450C2×C43—42no—
451C2×C43D4×C22⋊C411yescharacteristic
452C2×C43#289611yescharacteristic
453C2×C43#289711yescharacteristic
454C2×C43#327311yescharacteristic
455C2×C43#327511yescharacteristic
456C2×C43#332211yescharacteristic
457C2×C43#332311yescharacteristic
458D43—42no—
459D43—44no—
460D43—82no—
461C22×#41—431no—
462C23×D4—431no—
463C22×M16—431no—
464C22×M16C2×D4311yescharacteristic
465#546—438no—
466#546—864no—
467C2×#124—431no—
468C2×#123—861no—
469C2×C22⋊Q8C2×D4311yescharacteristic
470C2×#121—431no—
471C2×#121—861no—
472C2×#120—861no—
473C2×C4×D4—431no—
474C2×C4×D4—431no—
475C2×#117—431no—
476C22×C4⋊C4—431no—
477C22×C22⋊C4—861no—
478#436—864no—
479C2×C4⋊C8—431no—
480#418—864no—
481#417—864no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103C2×D4311yescharacteristic, complemented
485C2×#103C2×D4311yescharacteristic, complemented
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—431no—
492C2×#102—431no—
493C2×#102—431no—
494C2×C22⋊C8—431no—
495C2×C22⋊C8—431no—
496C2×C4×C8—431no—
497#388—861no—
498#387—861no—
499#386—861no—
500#382—431no—
501#380—431no—
502#380C2×D4311yescharacteristic
503C4×C4⋊C4—431no—
504C4×C22⋊C4—861no—
505#340—431no—
506#340—431no—
507#340C2×D4311yescharacteristic, complemented
508#340C2×D4311yescharacteristic, complemented
509C43#2242711yescharacteristic, complemented, Sylow
510C25—861no—
511C2×#41—434no—
512C2×#41—862no—
513C2×#41—862no—
514C2×#41—862no—
515C2×#41—1721no—
516C2×#41—1721no—
517C22×Q8C22×D4311yescharacteristic
518C22×D4—431no—
519C22×D4—434no—
520C22×D4—431no—
521C22×D4—431no—
522C22×D4—862no—
523C22×D4—862no—
524C22×D4—861no—
525C22×D4—861no—
526C22×D4—861no—
527C22×D4—862no—
528C22×D4—1721no—
529C22×D4—1721no—
530C23×C4—431no—
531C23×C4—861no—
532C23×C4—861no—
533C23×C4—861no—
534C23×C4C22×D4311yescharacteristic
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—862no—
539C2×M16—862no—
540C2×M16—1721no—
541C22×C8—431no—
542C22×C8—431no—
543C22×C8C22×D4311yescharacteristic
544C22×C8C22×D4311yescharacteristic
545#124—434no—
546#124—862no—
547#123—868no—
548C22⋊Q8—22no—
549C22⋊Q8C4×D4314yescomplemented
550#121—434no—
551#121—868no—
552#121—862no—
553#120—868no—
554C4×D4—434no—
555C4×D4—434no—
556C4×D4—434no—
557C4×D4—862no—
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—862no—
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—21no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—431no—
574C2×C22⋊C4—868no—
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—431no—
582C2×C42—861no—
583C2×C42—861no—
584C4⋊C8—862no—
585#103—22no—
586#103—41no—
587#103—862no—
588#103—1721no—
589#102—434no—
590#102—862no—
591#102—862no—
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—861no—
602#95—861no—
603#95—861no—
604#95—861no—
605C24—431no—
606C24—861no—
607C24—864no—
608C24—861no—
609C24—3441no—
610C24—3441no—
611C24—1722no—
612C24—1722no—
613C24—1722no—
614C24—1722no—
615C24D4×D4311yescharacteristic
616#41—868no—
617#41—1724no—
618#41—1724no—
619#41—1724no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C2×C4×D4312yes—
626C2×D4—434no—
627C2×D4—432no—
628C2×D4—432no—
629C2×D4—432no—
630C2×D4—432no—
631C2×D4—868no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—864no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—3441no—
644C2×D4—3441no—
645C2×D4—1724no—
646C2×D4—1724no—
647C2×D4—1724no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4—1722no—
651C2×D4—1722no—
652C2×D4—1721no—
653C2×D4—1721no—
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—431no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—432no—
666C22×C4—432no—
667C22×C4—864no—
668C22×C4—864no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—3441no—
676C22×C4—3441no—
677C22×C4—3441no—
678C22×C4—1722no—
679C22×C4—1722no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4C2×C4×D4312yes—
683C22×C4D4×D4311yescharacteristic
684C22×C4D4×D4312yes—
685C22×C4C23×D4311yescharacteristic
686M16—44no—
687M16—1724no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—861no—
699C2×C8D4×D4312yes—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—434no—
707C4⋊C4—432no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—1722no—
712C4⋊C4C2×C4×D4312yes—
713C22⋊C4—24no—
714C22⋊C4—81no—
715C22⋊C4—434no—
716C22⋊C4—434no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—864no—
721C22⋊C4—1722no—
722C22⋊C4—1722no—
723C42—432no—
724C42—432no—
725C42—3441no—
726C42—1722no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—432no—
734C23—862no—
735C23—861no—
736C23—861no—
737C23—861no—
738C23—861no—
739C23—861no—
740C23—862no—
741C23—861no—
742C23—862no—
743C23—862no—
744C23—3444no—
745C23—3444no—
746C23—3444no—
747C23—3444no—
748C23—3444no—
749C23—1728no—
750C23—1728no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23—1721no—
761C23C22⋊C4×D4312yes—
762C23C2×D4×D4311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—434no—
768D4—862no—
769D4—862no—
770D4—862no—
771D4—862no—
772D4—862no—
773D4—3444no—
774D4—1728no—
775D4—1728no—
776D4—1724no—
777D4—1721no—
778D4—1721no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—432no—
798C2×C4—432no—
799C2×C4—432no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—3444no—
812C2×C4—3444no—
813C2×C4—1728no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4C22⋊C4×D4312yes—
820C2×C4C22×C4×D4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C2×D4×D4311yescharacteristic
823C2×C4#41×D4311yescharacteristic
824C2×C4#1306337011yescharacteristic
825C2×C4#1306337111yescharacteristic
826C8—22no—
827C8—41no—
828C8—1721no—
829C8—1721no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—862no—
838C22—864no—
839C22—862no—
840C22—862no—
841C22—34416no—
842C22—3441no—
843C22—3441no—
844C22—3441no—
845C22—3441no—
846C22—1722no—
847C22—1722no—
848C22—1722no—
849C22—1721no—
850C22—1722no—
851C22—1721no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1721no—
856C22—1722no—
857C22—1721no—
858C22—1722no—
859C22C2×C22⋊C4×D4311yescharacteristic
860C22#1458353311yescharacteristic
861C22#1458353811yescharacteristic
862C22#1458369811yescharacteristic
863C22#1458369811yescharacteristic
864C22#1458370311yescharacteristic
865C22#1458370811yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—81no—
870C4—81no—
871C4—862no—
872C4—862no—
873C4—862no—
874C4—3441no—
875C4—1722no—
876C4C4×D4×D4311yescharacteristic
877C4#1458337111yescharacteristic
878C4#1458353111yescharacteristic
879C4#1458354111yescharacteristic
880C2—42no—
881C2—3442no—
882C2—1722no—
883C2—1724no—
884C2#1913741311yescharacteristic
885C2#1914311311yescharacteristic
886C2#1914311911yescharacteristic
887C2#1914620311yescharacteristic
888C2#1914622311yescharacteristic
889C2#1914680211yescharacteristic
890C2#1914681711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1894C2
socleC23×C43C22×D4
prime radicalC2×#14583540C2
cosocleC22×C4×C43C24
hypercenter#1894D43
hypocenterC43#22427
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
2. C2×#14582975C2semidirect
3. C2×#14582899C2semidirect
4. C2×#14582905C2semidirect
5. #19137517C2semidirect
6. #19135524C2semidirect
7. #19135403C2semidirect
8. #19135032C2semidirect
9. #19134911C2semidirect
10. #19134908C2semidirect
11. #19134604C2semidirect
12. #19134534C2semidirect
13. #19134525C2semidirect
14. #19134409C2semidirect
15. C43×#1894C2semidirect
18. C22×#10621872C22semidirect
20. #14583540C4semidirect
29. C2×C4⋊C4×D43C22semidirect
32. C2×Dic43⋊C8C22semidirect
35. C2×#13063249C22semidirect
36. C2×#13063249C22semidirect
46. C2×(C2×D43)⋊C8C22semidirect
47. C2×C8×Dic43C22semidirect
51. #14582764C22semidirect
52. #14582756C22semidirect
53. C4⋊C4×Dic43C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
59. C2×#103×C43C22semidirect
60. C2×#103×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
79. C22×D172C2×C4semidirect
93. #13063314C2×C4semidirect
100. #13063287C2×C4semidirect
129. #13063247D4semidirect
149. C22⋊Q8×C43C2×C4semidirect
443. #1894D43semidirect
484. C2×#103C2×D43semidirect
485. C2×#103C2×D43semidirect
507. #340C2×D43semidirect
508. #340C2×D43semidirect
509. C43#22427semidirect
549. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835402
C2×#145829752
C2×#145828992
C2×#145829052
#191375172
#191355242
#191354032
#191350322
#191349112
#191349082
#191346042
#191345342
#191345252
#191344092
C43×#18942
#2242743