Finite Group Databasebeta

← #25112116

Subgroups — #25112116

Order 11008.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583570C211yesmaximal, characteristic
2C2×#14582971C211yesmaximal, characteristic, complemented
3C2×#14582898C211yesmaximal, characteristic, complemented
4C2×#14582893C211yesmaximal, characteristic, complemented
5#19135522C211yesmaximal, characteristic, complemented
6#19135418C211yesmaximal, characteristic, complemented
7#19135031C211yesmaximal, characteristic, complemented
8#19135021C211yesmaximal, characteristic, complemented
9#19134917C211yesmaximal, characteristic, complemented
10#19134912C211yesmaximal, characteristic, complemented
11#19134607C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic, complemented
13#19134533C211yesmaximal, characteristic, complemented
14#19134428C211yesmaximal, characteristic, complemented
15C43×#2352C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621898C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20#14583570—24no—
21#14583570C418yescomplemented
22C2×#13063322C2211yescharacteristic
23C2×#13063321—21no—
24C2×#13063299C2211yescharacteristic
25C2×#13063299C2211yescharacteristic
26C2×#13063298—21no—
27C2×#13063298—21no—
28C2×C4×Dic86C2211yescharacteristic
29C2×#13063287—21no—
30#14582971—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32#14582898—24no—
33#14582893—24no—
34C2×#13063248C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45C2×#13063245C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47C2×C22⋊(C43⋊C8)C2211yescharacteristic
48C2×#13063236C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C43×#388—21no—
57C43×#387—21no—
58C43×#386—21no—
59C43×#382C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C4×C4⋊C4×C43C2211yescharacteristic
63C4×C22⋊C4×C43—21no—
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898—22no—
70C2×#10621898—41no—
71C2×#10621898—41no—
72C2×#10621898—41no—
73C2×#10621898—41no—
74C2×#10621898C2×C414yes—
75C2×#10621898C2×C414yescomplemented
76C22×Dic86C2311yescharacteristic
77C22×D172—21no—
78C22×D172—21no—
79C22×D172C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C2×#10621877—22no—
88C2×#10621877—22no—
89C2×#10621877—41no—
90C22×C43⋊C8—22no—
91C22×C43⋊C8—22no—
92C22×C43⋊C8—41no—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97#13063322—22no—
98#13063322C2×C414yescomplemented
99#13063321—28no—
100#13063299—22no—
101#13063299—22no—
102#13063299C2×C414yes—
103#13063299C2×C414yescomplemented
104#13063298—28no—
105#13063298—28no—
106C4×Dic86—22no—
107C4×Dic86C2×C414yescomplemented
108#13063287—28no—
109C2×C4⋊Dic43C2311yescharacteristic
110C2×Dic43⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×C4×Dic43—21no—
114C4⋊(C43⋊C8)—22no—
115#13063248—22no—
116#13063248—22no—
117#13063248—22no—
118#13063248D414yescomplemented
119#13063245—22no—
120#13063245—22no—
121#13063245—22no—
122#13063245—22no—
123#13063245—41no—
124#13063245—41no—
125#13063245—41no—
126#13063245—41no—
127C22⋊(C43⋊C8)—22no—
128C22⋊(C43⋊C8)—22no—
129#13063236—22no—
130C22×D4×C43D411yescharacteristic
131C23×C4×C43—21no—
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C4×D4×C43C2×C414yes—
135C4×D4×C43D414yes—
136#117×C43—22no—
137#117×C43—41no—
138C2×C4⋊C4×C43—22no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—41no—
141C2×C4⋊C4×C43D411yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43D411yescharacteristic
150C2×C22⋊C4×C43D411yescharacteristic
151C2×C42×C43—21no—
152C2×C42×C43—21no—
153C2×C42×C43C2311yescharacteristic
154#95×C43—21no—
155#95×C43—21no—
156#95×C43—21no—
157#95×C43—21no—
158#95×C43—21no—
159C24×C43C2×D411yescharacteristic
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C23×D43—21no—
163C2×D4×C43—41no—
164C2×D4×C43—41no—
165C2×D4×C43C22⋊C414yes—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—42no—
179C22×C4×C43—42no—
180C22×C4×C43—81no—
181C22×C4×C43C22×C412yes—
182C22×C4×C43C22×C412yes—
183C22×C4×C43C2×D412yes—
184C22×C4×C43C2×D412yes—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—24no—
191C2×C22⋊D43—24no—
192C2×C22⋊D43—24no—
193C2×C22⋊D43—24no—
194C2×C22⋊D43—42no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43—81no—
199C2×C22⋊D43—81no—
200C2×C22⋊D43—81no—
201C2×C22⋊D43—81no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204#10621898—28no—
205#10621898—28no—
206#10621898—44no—
207#10621898—44no—
208#10621898—44no—
209#10621898—44no—
210#10621898—44no—
211#10621898—44no—
212C2×D172—24no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—24no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172—21no—
224C2×D172—42no—
225C2×D172—42no—
226C2×D172—81no—
227C2×D172—81no—
228C2×D172C22×C412yes—
229C2×D172C22×C412yes—
230C2×C4×D43—24no—
231C2×C4×D43—24no—
232C2×C4×D43—42no—
233C2×C4×D43—42no—
234C2×C4×D43—42no—
235C2×C4×D43—42no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86C22×C412yes—
240C2×Dic86C2×D412yes—
241C2×Dic86#4112yes—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—42no—
250C4⋊C4×C43C22⋊C414yes—
251C4⋊C4×C43C2×D412yes—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—42no—
254C22⋊C4×C43—81no—
255C22⋊C4×C43C22⋊C414yes—
256C22⋊C4×C43C22⋊C414yes—
257C42×C43—42no—
258C42×C43—81no—
259C42×C43C22×C412yes—
260C42×C43C2×D412yes—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263C4⋊Dic43—21no—
264C4⋊Dic43C22×C412yes—
265Dic43⋊C4—24no—
266C4×Dic43—24no—
267#10621877—44no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—44no—
280C2×C43⋊C8C2×D412yes—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43C2×C22⋊C412yes—
294C23×C43C2×C22⋊C412yes—
295C23×C43C22×D411yescharacteristic
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—41no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310D4×C43—44no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
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—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—84no—
340C2×C4×C43C2×C22⋊C412yes—
341C2×C4×C43C2×C22⋊C412yes—
342C2×C4×C43C2×C22⋊C412yes—
343C2×C4×C43C2×C22⋊C412yes—
344C2×C4×C43C23×C411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C2×#4111yescharacteristic
348C2×C4×C43H(5,𝔽2)11yescharacteristic
349C2×C4×C43H(5,𝔽2)11yescharacteristic
350C22⋊D43—48no—
351C22⋊D43—48no—
352C22⋊D43—84no—
353C22⋊D43—84no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360D172—22no—
361D172—22no—
362D172—22no—
363D172—22no—
364D172—48no—
365D172—41no—
366D172—41no—
367D172—41no—
368D172—41no—
369D172—84no—
370C4×D43—48no—
371C4×D43—48no—
372Dic86—22no—
373Dic86—22no—
374Dic86—22no—
375Dic86C4×D414yes—
376C43⋊C8—22no—
377C43⋊C8—41no—
378C43⋊C8—41no—
379C43⋊C8—41no—
380#22422—431nomaximal, Sylow
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43C22×C22⋊C411yescharacteristic
396C22×C43D4211yescharacteristic
397C22×C43#54611yescharacteristic
398C22×C43#57511yescharacteristic
399C22×C43#57511yescharacteristic
400C22×C43#57611yescharacteristic
401C22×C43#57711yescharacteristic
402C2×D43—42no—
403C2×D43—42no—
404C2×D43—42no—
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—81no—
409C2×D43—81no—
410C2×D43—81no—
411C2×D43—81no—
412C2×D43—81no—
413C2×D43—81no—
414C2×D43—81no—
415C2×D43—81no—
416C4×C43—22no—
417C4×C43—22no—
418C4×C43—22no—
419C4×C43—22no—
420C4×C43—42no—
421C4×C43—81no—
422C4×C43—81no—
423C4×C43—81no—
424C4×C43C2×C4×D411yescharacteristic
425C4×C43#51811yescharacteristic
426C4×C43D4211yescharacteristic
427C4×C43#54611yescharacteristic
428Dic43—24no—
429Dic43—42no—
430C2×#550—431no—
431C2×#435—431no—
432C2×#417—431no—
433C2×#416—431no—
434#2352D4311yescharacteristic, complemented
435#1982—431no—
436#1961—431no—
437#1895—431no—
438#1893—431no—
439#1875—431no—
440#1874—431no—
441#1805—431no—
442#1788—431no—
443#1788—431no—
444#1763—431no—
445C2×C43—42no—
446C2×C43—42no—
447C2×C43D4×C22⋊C411yescharacteristic
448C2×C43#289611yescharacteristic
449C2×C43#289711yescharacteristic
450C2×C43#326811yescharacteristic
451C2×C43#327111yescharacteristic
452C2×C43#330911yescharacteristic
453C2×C43#331711yescharacteristic
454D43—82no—
455D43—82no—
456C22×#41—431no—
457C22×#41—431no—
458C22×M16—431no—
459C23×C8—431no—
460#550—438no—
461#550—864no—
462C2×#127—431no—
463C2×#127—861no—
464C2×#121—431no—
465C2×#121—431no—
466C2×#121—861no—
467C2×#121—861no—
468C2×C4×Q8—431no—
469C2×C4×D4—861no—
470C2×C4×D4C2×D4311yescharacteristic
471C2×#117C2×D4311yescharacteristic
472C22×C4⋊C4C2×D4311yescharacteristic
473#435—864no—
474C2×C4⋊C8—431no—
475#417—864no—
476#416—864no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103—431no—
480C2×#103—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×#102—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×C22⋊C8—431no—
490C2×C22⋊C8—431no—
491C2×#97—431no—
492#388—21no—
493#387—21no—
494#386—21no—
495#382C2×D4311yescharacteristic
496#380C2×D4311yescharacteristic
497#380C2×D4311yescharacteristic
498C4×C4⋊C4C2×D4311yescharacteristic
499C4×C22⋊C4—21no—
500#340—431no—
501#340—431no—
502#340—431no—
503#340—431no—
504C43#2242211yescharacteristic, complemented, Sylow
505C2×#41—434no—
506C2×#41—434no—
507C2×#41—862no—
508C2×#41—862no—
509C2×#41—862no—
510C2×#41—862no—
511C2×#41—862no—
512C2×#41—862no—
513C2×#41—1721no—
514C2×#41—1721no—
515C2×#41—1721no—
516C2×#41—1721no—
517C22×Q8—431no—
518C22×D4—431no—
519C22×D4—431no—
520C22×D4—861no—
521C22×D4—861no—
522C22×D4—861no—
523C22×D4—861no—
524C22×D4—861no—
525C22×D4—861no—
526C22×D4C22⋊D4311yescharacteristic
527C23×C4—21no—
528C23×C4—861no—
529C23×C4—861no—
530C23×C4C22×D4311yescharacteristic
531C23×C4C22×D4311yescharacteristic
532C2×M16—862no—
533C2×M16—862no—
534C2×M16—1721no—
535C22×C8—431no—
536C22×C8—431no—
537C22×C8—431no—
538C22×C8—431no—
539C22×C8—862no—
540C22×C8—862no—
541C22×C8—1721no—
542#127—434no—
543#127—868no—
544#127—862no—
545#121—434no—
546#121—434no—
547#121—862no—
548#121—862no—
549#121—868no—
550#121—868no—
551C4×Q8—434no—
552C4×Q8—862no—
553C4×D4—868no—
554C4×D4C4×D4314yes—
555C4×D4D17214yes—
556#117—22no—
557#117—41no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4C22⋊D4311yescharacteristic
564C2×C4⋊C4C22×D4311yescharacteristic
565C2×C4⋊C4C22×D4311yescharacteristic
566C2×C4⋊C4C22×D4311yescharacteristic
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4C22⋊D4311yescharacteristic
574C2×C22⋊C4C22⋊D4311yescharacteristic
575C2×C42—21no—
576C2×C42—21no—
577C2×C42—861no—
578C2×C42C22×D4311yescharacteristic
579C4⋊C8—862no—
580#103—434no—
581#103—862no—
582#103—862no—
583#103—862no—
584#102—862no—
585#102—862no—
586#102—862no—
587#102—862no—
588#102—1721no—
589#102—1721no—
590#102—1721no—
591#102—1721no—
592C22⋊C8—862no—
593C22⋊C8—862no—
594#97—862no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599#95—21no—
600C24—861no—
601C24—861no—
602C24C2×C22⋊D4311yescharacteristic
603C24C2×C22⋊D4311yescharacteristic
604#41—868no—
605#41—868no—
606#41—1724no—
607#41—1724no—
608#41—1724no—
609#41—1724no—
610#41—1724no—
611#41—1724no—
612C2×Q8—432no—
613C2×Q8—432no—
614C2×Q8—432no—
615C2×Q8—861no—
616C2×Q8—861no—
617C2×Q8—861no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—432no—
621C2×D4—432no—
622C2×D4—864no—
623C2×D4—864no—
624C2×D4—864no—
625C2×D4—864no—
626C2×D4—864no—
627C2×D4—864no—
628C2×D4—861no—
629C2×D4—861no—
630C2×D4—861no—
631C2×D4—861no—
632C2×D4—861no—
633C2×D4—861no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—3441no—
639C2×D4—3441no—
640C2×D4—3441no—
641C2×D4—3441no—
642C2×D4—3441no—
643C2×D4—3441no—
644C2×D4—1722no—
645C2×D4—1722no—
646C2×D4—1722no—
647C2×D4—1722no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4(C2×D43)⋊C414yes—
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—21no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—81no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—864no—
669C22×C4—864no—
670C22×C4—1722no—
671C22×C4—1722no—
672C22×C4—1722no—
673C22×C4—1722no—
674C22×C4C2×C4×D4312yes—
675C22×C4C2×C4×D4312yes—
676C22×C4C2×D17212yes—
677C22×C4C2×D17212yes—
678C22×C4C2×C22⋊D4311yescharacteristic
679C22×C4C2×C22⋊D4311yescharacteristic
680C22×C4C2×C22⋊D4311yescharacteristic
681C22×C4C2×C22⋊D4311yescharacteristic
682C22×C4C23×D4311yescharacteristic
683M16—1724no—
684C2×C8—432no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—1724no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—42no—
705C4⋊C4—432no—
706C4⋊C4—864no—
707C4⋊C4—861no—
708C4⋊C4(C2×D43)⋊C414yes—
709C4⋊C4D4×D4312yes—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—864no—
714C22⋊C4—864no—
715C22⋊C4(C2×D43)⋊C414yes—
716C22⋊C4(C2×D43)⋊C414yes—
717C42—42no—
718C42—81no—
719C42—864no—
720C42C2×C4×D4312yes—
721C42C2×D17212yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—862no—
735C23—862no—
736C23—1721no—
737C23—1721no—
738C23—1721no—
739C23—1721no—
740C23—1721no—
741C23—1721no—
742C23—1721no—
743C23—1721no—
744C23—1721no—
745C23—1721no—
746C23—1721no—
747C23—1721no—
748C23C2×(C2×D43)⋊C412yes—
749C23C2×(C2×D43)⋊C412yes—
750C23C22×C22⋊D4311yescharacteristic
751Q8—434no—
752Q8—862no—
753Q8—862no—
754Q8—862no—
755D4—44no—
756D4—862no—
757D4—862no—
758D4—862no—
759D4—862no—
760D4—3444no—
761D4—3444no—
762D4—3444no—
763D4—1728no—
764D4—1728no—
765D4—1728no—
766D4—1721no—
767D4—1721no—
768D4—1721no—
769D4—1721no—
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—22no—
779C2×C4—22no—
780C2×C4—22no—
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—41no—
798C2×C4—84no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—1728no—
804C2×C4—1728no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4C2×(C2×D43)⋊C412yes—
808C2×C4C2×(C2×D43)⋊C412yes—
809C2×C4C2×(C2×D43)⋊C412yes—
810C2×C4C2×(C2×D43)⋊C412yes—
811C2×C4C22×C4×D4311yescharacteristic
812C2×C4C2×D4×D4311yescharacteristic
813C2×C4C22×D17211yescharacteristic
814C2×C4#41×D4311yescharacteristic
815C2×C4#1306337011yescharacteristic
816C2×C4#1306337111yescharacteristic
817C8—862no—
818C8—1721no—
819C8—1721no—
820C8—1721no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—3441no—
836C22—3441no—
837C22—3441no—
838C22—3441no—
839C22—3441no—
840C22—3441no—
841C22—3441no—
842C22—3441no—
843C22—1722no—
844C22—1722no—
845C22—1722no—
846C22—1722no—
847C22—1722no—
848C22—1722no—
849C22C22×(C2×D43)⋊C411yescharacteristic
850C22D4×C22⋊D4311yescharacteristic
851C22#1458353711yescharacteristic
852C22#1458369711yescharacteristic
853C22#1458369711yescharacteristic
854C22#1458370211yescharacteristic
855C22#1458370711yescharacteristic
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—42no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4—864no—
865C4—1722no—
866C4C4×D4×D4311yescharacteristic
867C4#1458337111yescharacteristic
868C4D4×D17211yescharacteristic
869C4#1458354411yescharacteristic
870C2—42no—
871C2—42no—
872C2—3442no—
873C2—3442no—
874C2D4×(C2×D43)⋊C411yescharacteristic
875C2#1914311211yescharacteristic
876C2#1914311811yescharacteristic
877C2#1914613111yescharacteristic
878C2#1914618111yescharacteristic
879C2#1914659511yescharacteristic
880C2#1914671511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2352C2
socleC23×C43C22×D4
prime radicalC2×#14583570C2
cosocleC22×C4×C43C24
hypercenter#2352D43
hypocenterC43#22422
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#14582971C2semidirect
3. C2×#14582898C2semidirect
4. C2×#14582893C2semidirect
5. #19135522C2semidirect
6. #19135418C2semidirect
7. #19135031C2semidirect
8. #19135021C2semidirect
9. #19134917C2semidirect
10. #19134912C2semidirect
11. #19134607C2semidirect
12. #19134533C2semidirect
13. #19134533C2semidirect
14. #19134428C2semidirect
15. C43×#2352C2semidirect
21. #14583570C4semidirect
75. C2×#10621898C2×C4semidirect
98. #13063322C2×C4semidirect
103. #13063299C2×C4semidirect
107. C4×Dic86C2×C4semidirect
118. #13063248D4semidirect
434. #2352D43semidirect
504. C43#22422semidirect

Maximal subgroups

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

subgroupindex
C2×#145835702
C2×#145829712
C2×#145828982
C2×#145828932
#191355222
#191354182
#191350312
#191350212
#191349172
#191349122
#191346072
#191345332
#191344282
C43×#23522
#2242243