Finite Group Databasebeta

← #25112157

Subgroups — #25112157

Order 11008.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583544C211yesmaximal, characteristic
2C2×#14582972C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic, complemented
4C2×#14582892C211yesmaximal, characteristic, complemented
5#19137542C211yesmaximal, characteristic, complemented
6#19135527C211yesmaximal, characteristic, complemented
7#19135411C211yesmaximal, characteristic, complemented
8#19135027C211yesmaximal, characteristic, complemented
9#19135022C211yesmaximal, characteristic, complemented
10#19134916C211yesmaximal, characteristic, complemented
11#19134906C211yesmaximal, characteristic, complemented
12#19134595C211yesmaximal, characteristic, complemented
13#19134532C211yesmaximal, characteristic, complemented
14#19134524C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
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
30C2×#13063283C2211yescharacteristic, complemented
31C22×(C2×D43)⋊C4—21no—
32#14582972—24no—
33C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
34#14582902—24no—
35#14582892—24no—
36C2×#13063250C2211yescharacteristic, complemented
37C2×#13063250C2211yescharacteristic, complemented
38C2×#13063248C2211yescharacteristic, complemented
39C2×#13063248C2211yescharacteristic, complemented
40C2×#13063247C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063246C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45C2×#13063245C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
48#14582801—21no—
49#14582791—21no—
50#14582791—21no—
51#14582769C2211yescharacteristic, complemented
52#14582756C2211yescharacteristic
53#14582756C2211yescharacteristic, complemented
54C4×C4⋊Dic43—21no—
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C2×C4×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic, complemented
61C4×C4⋊C4×C43C2211yescharacteristic, 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×C414yes—
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×D43C2311yescharacteristic
85C22×C4×D43C2311yescharacteristic
86C2×#10621872—22no—
87C2×#10621872—22no—
88C2×#10621872—41no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C2×C8×D43—22no—
92C2×C8×D43—22no—
93C2×C8×D43—41no—
94#13063313—22no—
95#13063313C2×C414yes—
96#13063309—28no—
97#13063305—22no—
98#13063305C2×C414yes—
99#13063300—22no—
100#13063300C2×C414yes—
101#13063299—28no—
102#13063295—28no—
103C4×D172C2×C414yes—
104C4×D172D414yes—
105#13063283—22no—
106#13063283—22no—
107#13063283—41no—
108#13063283—41no—
109C2×C4⋊Dic43—21no—
110C2×C4⋊Dic43—21no—
111C2×C4⋊Dic43—21no—
112C2×C4⋊Dic43D411yescharacteristic
113C2×C4⋊Dic43C2311yescharacteristic
114C2×C4⋊Dic43C2311yescharacteristic
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)⋊C4—21no—
124C2×(C2×D43)⋊C4D411yescharacteristic
125C2×(C2×D43)⋊C4D411yescharacteristic
126C2×C4×Dic43—21no—
127C2×C4×Dic43—21no—
128C4⋊(C43⋊C8)—22no—
129#13063250—22no—
130#13063250—41no—
131#13063248—22no—
132#13063248—41no—
133#13063247—22no—
134#13063247—41no—
135#13063246—22no—
136#13063246—22no—
137#13063245—22no—
138#13063245—41no—
139(C2×D43)⋊C8—22no—
140(C2×D43)⋊C8—22no—
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×C414yes—
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C22⋊C4×C43—21no—
153C2×C42×C43—21no—
154C2×C42×C43C2311yescharacteristic
155#102×C43—22no—
156#102×C43D414yescomplemented
157#97×C43—22no—
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—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—41no—
214C2×D172—41no—
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×D43C22×C412yes—
228C2×C4×D43C22×C412yes—
229C2×C4×D43C2×D412yes—
230C2×C4×D43C2×D412yes—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86C22×C412yes—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43C2×D412yes—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43C22×C412yes—
248C4⋊C4×C43C2×D412yes—
249C22⋊C4×C43—24no—
250C42×C43—42no—
251C42×C43C22×C412yes—
252C42×C43C2×D412yes—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—42no—
258(C2×D43)⋊C4—42no—
259(C2×D43)⋊C4—81no—
260(C2×D43)⋊C4—81no—
261(C2×D43)⋊C4C22⋊C414yes—
262(C2×D43)⋊C4C22⋊C414yes—
263C4⋊Dic43—24no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—42no—
269C4⋊Dic43—81no—
270C4⋊Dic43C22⋊C414yes—
271C4×Dic43—42no—
272C4×Dic43—42no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279#10621872—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—21no—
300C22×D43—21no—
301C22×D43—22no—
302C22×D43—48no—
303C22×D43—48no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—84no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43C2×C22⋊C412yes—
316C22×D43C2×C22⋊C412yes—
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—22no—
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—48no—
351C2×Dic43—41no—
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—22no—
362D172—22no—
363D172—44no—
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—
375Dic86—22no—
376Dic86—22no—
377Dic86—41no—
378Dic86—41no—
379C8×C43—22no—
380C8×C43—41no—
381C43⋊C8—41no—
382C43⋊C8—41no—
383#22424—431nomaximal, Sylow
384C22×C43—24no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43C22×C22⋊C411yescharacteristic
392C22×C43D4211yescharacteristic
393C22×C43#54611yescharacteristic
394C22×C43#57511yescharacteristic
395C22×C43#57511yescharacteristic
396C22×C43#57611yescharacteristic
397C22×C43#57711yescharacteristic
398C2×D43—22no—
399C2×D43—22no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
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—
420C4×C43—22no—
421C4×C43—22no—
422C4×C43—42no—
423C4×C43—42no—
424C4×C43—81no—
425C4×C43C2×C4×D411yescharacteristic
426C4×C43#51811yescharacteristic
427C4×C43D4211yescharacteristic
428C4×C43#54611yescharacteristic
429Dic43—22no—
430Dic43—22no—
431Dic43—42no—
432Dic43—81no—
433Dic43—81no—
434C2×#546—431no—
435C2×#435—431no—
436C2×#418—431no—
437C2×#416—431no—
438#2354—431no—
439#1983—431no—
440#1959—431no—
441#1894—431no—
442#1893—431no—
443#1875—431no—
444#1873—431no—
445#1802—431no—
446#1788—431no—
447#1786—431no—
448#1762D4311yescharacteristic, complemented
449C2×C43—44no—
450C2×C43D4×C22⋊C411yescharacteristic
451C2×C43#289611yescharacteristic
452C2×C43#289711yescharacteristic
453C2×C43#326711yescharacteristic
454C2×C43#326811yescharacteristic
455C2×C43#331111yescharacteristic
456C2×C43#331911yescharacteristic
457D43—42no—
458D43—42no—
459D43—82no—
460C22×#41—431no—
461C23×D4—431no—
462C22×M16—431no—
463C23×C8—431no—
464#546—438no—
465#546—864no—
466C2×#124—431no—
467C2×#123—861no—
468C2×C22⋊Q8—431no—
469C2×#121—431no—
470C2×#121—861no—
471C2×#120—861no—
472C2×C4×D4—431no—
473C2×C4×D4C2×D4311yescharacteristic
474C2×#117—431no—
475C2×#117—431no—
476C22×C22⋊C4—861no—
477#435—864no—
478C2×C4⋊C8—431no—
479#418—864no—
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×#102C2×D4311yescharacteristic
492C2×#102C2×D4311yescharacteristic
493C2×C22⋊C8—431no—
494C2×C22⋊C8—431no—
495C2×#97C2×D4311yescharacteristic, complemented
496#390—861no—
497#388—861no—
498#388—861no—
499#384—431no—
500#380—431no—
501#380—431no—
502C4×C4⋊C4—861no—
503C4×C4⋊C4C2×D4311yescharacteristic, complemented
504#340—431no—
505#340—431no—
506#340C2×D4311yescharacteristic, complemented
507#340C2×D4311yescharacteristic, complemented
508C43#2242411yescharacteristic, complemented, Sylow
509C25—861no—
510C2×#41—434no—
511C2×#41—862no—
512C2×#41—862no—
513C2×#41—862no—
514C2×#41—1721no—
515C2×#41—1721no—
516C22×Q8—431no—
517C22×D4—434no—
518C22×D4—431no—
519C22×D4—431no—
520C22×D4—861no—
521C22×D4—862no—
522C22×D4—861no—
523C22×D4—862no—
524C22×D4—862no—
525C22×D4—861no—
526C22×D4—1721no—
527C22×D4—1721no—
528C22×D4C22×D4311yescharacteristic
529C23×C4—21no—
530C23×C4—431no—
531C23×C4—431no—
532C23×C4—861no—
533C2×M16—862no—
534C2×M16—862no—
535C2×M16—1721no—
536C22×C8—431no—
537C22×C8—431no—
538C22×C8—862no—
539C22×C8—862no—
540C22×C8—1721no—
541C22×C8C22×D4311yescharacteristic
542C22×C8C22×D4311yescharacteristic
543#124—434no—
544#124—862no—
545#123—868no—
546C22⋊Q8—434no—
547C22⋊Q8—862no—
548#121—434no—
549#121—868no—
550#121—862no—
551#120—868no—
552C4×D4—22no—
553C4×D4—434no—
554C4×D4—434no—
555C4×D4C4×D4314yes—
556#117—862no—
557#117—862no—
558#117—1721no—
559#117—1721no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4C22×D4311yescharacteristic
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—868no—
573C2×C22⋊C4—861no—
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—21no—
582C2×C42—861no—
583C2×C42—861no—
584C2×C42C22×D4311yescharacteristic
585C4⋊C8—862no—
586#103—862no—
587#103—862no—
588#103—1721no—
589#103—1721no—
590#102—22no—
591#102—862no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—1721no—
596#102—1721no—
597#102D17214yescomplemented
598C22⋊C8—862no—
599C22⋊C8—862no—
600#97—22no—
601#95—21no—
602#95—861no—
603#95—861no—
604C24—21no—
605C24—431no—
606C24—431no—
607C24—864no—
608C24—861no—
609C24—3441no—
610C24—3441no—
611C24—1722no—
612C24—1722no—
613C24—1722no—
614C24—1722no—
615#41—868no—
616#41—1724no—
617#41—1724no—
618#41—1724no—
619C2×Q8—432no—
620C2×Q8—861no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—434no—
629C2×D4—432no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—868no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—3441no—
640C2×D4—3441no—
641C2×D4—1721no—
642C2×D4—1721no—
643C2×D4—1724no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4—1722no—
647C2×D4—1722no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4C2×C4×D4312yes—
651C2×D4C2×D17212yes—
652C2×D4#1062189812yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—81no—
658C22×C4—81no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—432no—
662C22×C4—432no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—864no—
666C22×C4—861no—
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—1722no—
678C22×C4—1722no—
679C22×C4D4×D4311yescharacteristic
680C22×C4D4×D4311yescharacteristic
681C22×C4C23×D4311yescharacteristic
682M16—1724no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—1724no—
695C2×C8C2×D17212yes—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—434no—
701C4⋊C4—864no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—3441no—
707C4⋊C4—1722no—
708C4⋊C4C2×C4×D4312yes—
709C4⋊C4C2×D17212yes—
710C22⋊C4—24no—
711C22⋊C4—434no—
712C22⋊C4—434no—
713C22⋊C4—864no—
714C22⋊C4—864no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—3441no—
718C22⋊C4—3441no—
719C22⋊C4—1722no—
720C22⋊C4—1722no—
721C42—42no—
722C42—1722no—
723C42—1722no—
724C42C2×C4×D4312yes—
725C42D4×D4312yes—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—432no—
734C23—432no—
735C23—861no—
736C23—861no—
737C23—861no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—861no—
742C23—861no—
743C23—861no—
744C23—861no—
745C23—861no—
746C23—861no—
747C23—862no—
748C23—3444no—
749C23—3444no—
750C23—3444no—
751C23—3444no—
752C23—3444no—
753C23—1728no—
754C23—1728no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23—1721no—
761C23C2×D4×D4311yescharacteristic
762Q8—862no—
763Q8—862no—
764Q8—1721no—
765Q8—1721no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—862no—
770D4—862no—
771D4—3444no—
772D4—1724no—
773D4—1728no—
774D4—1728no—
775D4—1721no—
776D4—1721no—
777D4C4×D17214yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
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—84no—
792C2×C4—432no—
793C2×C4—432no—
794C2×C4—861no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—861no—
798C2×C4—862no—
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—1728no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4C22⋊C4×D4312yes—
817C2×C4C22⋊C4×D4312yes—
818C2×C4C22×C4×D4311yescharacteristic
819C2×C4C2×D4×D4311yescharacteristic
820C2×C4C22×D17211yescharacteristic
821C2×C4C2×#1062189811yescharacteristic
822C2×C4#1306337111yescharacteristic
823C2×C4#1306337111yescharacteristic
824C8—22no—
825C8—41no—
826C8—1721no—
827C8—1721no—
828C22—24no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—862no—
836C22—862no—
837C22—862no—
838C22—862no—
839C22—862no—
840C22—862no—
841C22—34416no—
842C22—3441no—
843C22—3441no—
844C22—3441no—
845C22—3441no—
846C22—1722no—
847C22—1722no—
848C22—1722no—
849C22—1721no—
850C22—1721no—
851C22—1721no—
852C22—1721no—
853C22—1721no—
854C22—1721no—
855C22—1721no—
856C22—1721no—
857C22C2×C22⋊C4×D4311yescharacteristic
858C22D4×D17211yescharacteristic
859C22#1458354511yescharacteristic
860C22#1458369511yescharacteristic
861C22#1458369811yescharacteristic
862C22#1458370311yescharacteristic
863C22#1458370911yescharacteristic
864C4—22no—
865C4—22no—
866C4—42no—
867C4—42no—
868C4—81no—
869C4—862no—
870C4—862no—
871C4—3441no—
872C4—3441no—
873C4—1722no—
874C4C2×C4×D17211yescharacteristic
875C4#1458337311yescharacteristic
876C4D4×D17211yescharacteristic
877C4#1458354511yescharacteristic
878C2—44no—
879C2—3442no—
880C2—1722no—
881C2—1722no—
882C2C22⋊C4×D17211yescharacteristic
883C2#1914311111yescharacteristic
884C2#1914312011yescharacteristic
885C2#1914612211yescharacteristic
886C2#1914613711yescharacteristic
887C2#1914663611yescharacteristic
888C2#1914675611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC2×#14583544C2
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#22424
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#14582972C2semidirect
3. C2×#14582902C2semidirect
4. C2×#14582892C2semidirect
5. #19137542C2semidirect
6. #19135527C2semidirect
7. #19135411C2semidirect
8. #19135027C2semidirect
9. #19135022C2semidirect
10. #19134916C2semidirect
11. #19134906C2semidirect
12. #19134595C2semidirect
13. #19134532C2semidirect
14. #19134524C2semidirect
15. C43×#1762C2semidirect
19. C22×C8×D43C22semidirect
21. #14583544C4semidirect
30. C2×#13063283C22semidirect
33. C2×C4⋊(C43⋊C8)C22semidirect
36. C2×#13063250C22semidirect
37. C2×#13063250C22semidirect
38. C2×#13063248C22semidirect
39. C2×#13063248C22semidirect
47. C2×(C2×D43)⋊C8C22semidirect
51. #14582769C22semidirect
53. #14582756C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
60. C2×#97×C43C22semidirect
61. C4×C4⋊C4×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
156. #102×C43D4semidirect
448. #1762D43semidirect
495. C2×#97C2×D43semidirect
503. C4×C4⋊C4C2×D43semidirect
506. #340C2×D43semidirect
507. #340C2×D43semidirect
508. C43#22424semidirect
597. #102D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145835442
C2×#145829722
C2×#145829022
C2×#145828922
#191375422
#191355272
#191354112
#191350272
#191350222
#191349162
#191349062
#191345952
#191345322
#191345242
C43×#17622
#2242443