Finite Group Databasebeta

← #25112146

Subgroups — #25112146

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×#14583545C211yesmaximal, characteristic
2C2×#14582971C211yesmaximal, characteristic, complemented
3C2×#14582903C211yesmaximal, characteristic, complemented
4C2×#14582893C211yesmaximal, characteristic, complemented
5#19135527C211yesmaximal, characteristic, complemented
6#19135409C211yesmaximal, characteristic, complemented
7#19135026C211yesmaximal, characteristic, complemented
8#19135021C211yesmaximal, characteristic, complemented
9#19134917C211yesmaximal, characteristic, complemented
10#19134907C211yesmaximal, characteristic, complemented
11#19134592C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic, complemented
13#19134525C211yesmaximal, characteristic, complemented
14#19134423C211yesmaximal, characteristic, complemented
15C43×#2354C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×D172C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic, complemented
20#14583545—24no—
21#14583545C418yescomplemented
22C2×#13063313C2211yescharacteristic
23C2×#13063310—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063299C2211yescharacteristic
26C2×#13063298—21no—
27C2×#13063293—21no—
28C2×C4×D172C2211yescharacteristic
29C2×C22⋊C4×D43—21no—
30#14582971—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
32#14582903—24no—
33#14582893—24no—
34C2×#13063248C2211yescharacteristic, complemented
35C2×#13063248C2211yescharacteristic, complemented
36C2×#13063248C2211yescharacteristic, complemented
37C2×#13063248C2211yescharacteristic, complemented
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, complemented
48C2×#13063236C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53C2×C4×D4×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic, complemented
56C43×#390—21no—
57C43×#388—21no—
58C43×#388—21no—
59C43×#384C2211yescharacteristic, complemented
60C43×#380C2211yescharacteristic
61C43×#380C2211yescharacteristic, complemented
62C4×C4⋊C4×C43—21no—
63C4×C4⋊C4×C43C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—41no—
69C2×#10621898—41no—
70C2×#10621898C2×C414yes—
71C22×Dic86C2311yescharacteristic
72C22×D172—22no—
73C22×D172—22no—
74C22×D172—21no—
75C22×D172—22no—
76C22×D172—41no—
77C22×D172—41no—
78C22×D172C2×C414yes—
79C22×D172C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C2×#10621877—22no—
86C2×#10621877—22no—
87C2×#10621877—41no—
88C22×C43⋊C8—22no—
89C22×C43⋊C8—22no—
90C22×C43⋊C8—41no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95#13063313—22no—
96#13063313C2×C414yes—
97#13063310—28no—
98#13063304—22no—
99#13063304C2×C414yes—
100#13063299—22no—
101#13063299C2×C414yes—
102#13063298—28no—
103#13063293—28no—
104C4×D172—22no—
105C4×D172C2×C414yes—
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×C22⋊Dic43—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C22⋊C4×D43—28no—
114C4⋊(C43⋊C8)—22no—
115#13063248—22no—
116#13063248—22no—
117#13063248—41no—
118#13063248—41no—
119#13063245—22no—
120#13063245—22no—
121#13063245—22no—
122#13063245—22no—
123#13063245—22no—
124#13063245—41no—
125#13063245—41no—
126#13063245D414yescomplemented
127C22⋊(C43⋊C8)—22no—
128C22⋊(C43⋊C8)—22no—
129#13063236—22no—
130C22×D4×C43D411yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C4×D4×C43C2×C414yes—
134C4×D4×C43D414yes—
135#117×C43—22no—
136#117×C43—22no—
137#117×C43—41no—
138#117×C43—41no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—21no—
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×C43—21no—
150C2×C22⋊C4×C43D411yescharacteristic
151C2×C22⋊C4×C43D411yescharacteristic
152C2×C42×C43—21no—
153C2×C42×C43—21no—
154C2×C42×C43—21no—
155C2×C42×C43C2311yescharacteristic
156#95×C43—21no—
157#95×C43—21no—
158#95×C43—21no—
159C24×C43C2×D411yescharacteristic
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C23×D43—21no—
163C23×D43—24no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—42no—
168C23×D43—81no—
169C23×D43—81no—
170C2×D4×C43—41no—
171C2×D4×C43—41no—
172C2×D4×C43C22⋊C414yes—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
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×C43—21no—
185C22×C4×C43C22×C412yes—
186C22×C4×C43C22×C412yes—
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2×D412yes—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—24no—
195C2×C22⋊D43—24no—
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43—81no—
199C2×C22⋊D43—81no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202#10621898—28no—
203#10621898—44no—
204#10621898—44no—
205#10621898—44no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—24no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—28no—
216C2×D172—42no—
217C2×D172—42no—
218C2×D172—44no—
219C2×D172—44no—
220C2×D172—44no—
221C2×D172C22×C412yes—
222C2×D172C22×C412yes—
223C2×D172C2×D412yes—
224C2×D172#4112yes—
225C2×C4×D43—24no—
226C2×C4×D43—24no—
227C2×C4×D43—42no—
228C2×C4×D43—42no—
229C2×C4×D43—81no—
230C2×C4×D43—81no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86C22×C412yes—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—42no—
245C4⋊C4×C43—81no—
246C4⋊C4×C43C22⋊C414yes—
247C4⋊C4×C43C2×D412yes—
248C22⋊C4×C43—42no—
249C22⋊C4×C43—42no—
250C22⋊C4×C43—81no—
251C22⋊C4×C43—81no—
252C22⋊C4×C43C22⋊C414yes—
253C22⋊C4×C43C22⋊C414yes—
254C42×C43—42no—
255C42×C43—42no—
256C42×C43—42no—
257C42×C43C22×C412yes—
258C42×C43C2×D412yes—
259C22⋊Dic43—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264C4⋊Dic43—21no—
265C4⋊Dic43C22×C412yes—
266Dic43⋊C4—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—22no—
299C22×D43—22no—
300C22×D43—48no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—48no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43—84no—
316C22×D43—84no—
317D4×C43—44no—
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—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43C2×C22⋊C412yes—
347C2×C4×C43C2×C22⋊C412yes—
348C2×C4×C43C2×C22⋊C412yes—
349C2×C4×C43C2×C22⋊C412yes—
350C2×C4×C43C23×C411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C2×#4111yescharacteristic
354C2×C4×C43H(5,𝔽2)11yescharacteristic
355C2×C4×C43H(5,𝔽2)11yescharacteristic
356C22⋊D43—48no—
357C22⋊D43—84no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364D172—22no—
365D172—22no—
366D172—22no—
367D172—22no—
368D172—22no—
369D172—48no—
370D172—41no—
371D172—41no—
372D172C4×D414yes—
373C4×D43—48no—
374C4×D43—84no—
375Dic86—22no—
376Dic86—22no—
377Dic86—41no—
378Dic86—41no—
379C43⋊C8—22no—
380C43⋊C8—41no—
381C43⋊C8—41no—
382C43⋊C8—41no—
383#22424—431nomaximal, Sylow
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43C22×C22⋊C411yescharacteristic
399C22×C43D4211yescharacteristic
400C22×C43#54611yescharacteristic
401C22×C43#57511yescharacteristic
402C22×C43#57511yescharacteristic
403C22×C43#57611yescharacteristic
404C22×C43#57711yescharacteristic
405C2×D43—24no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
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—22no—
423C4×C43—22no—
424C4×C43—42no—
425C4×C43—81no—
426C4×C43—81no—
427C4×C43—81no—
428C4×C43C2×C4×D411yescharacteristic
429C4×C43#51811yescharacteristic
430C4×C43D4211yescharacteristic
431C4×C43#54611yescharacteristic
432Dic43—42no—
433Dic43—42no—
434C2×#546—431no—
435C2×#435—431no—
436C2×#418—431no—
437C2×#416—431no—
438#2354D4311yescharacteristic, complemented
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#1762—431no—
449C2×C43—42no—
450C2×C43—42no—
451C2×C43D4×C22⋊C411yescharacteristic
452C2×C43#289611yescharacteristic
453C2×C43#289711yescharacteristic
454C2×C43#326711yescharacteristic
455C2×C43#326811yescharacteristic
456C2×C43#331111yescharacteristic
457C2×C43#331911yescharacteristic
458D43—44no—
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×#117C2×D4311yescharacteristic
475C2×#117C2×D4311yescharacteristic, complemented
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×#102—431no—
492C2×#102—431no—
493C2×C22⋊C8—431no—
494C2×C22⋊C8—431no—
495C2×#97—431no—
496#390—21no—
497#388—21no—
498#388—21no—
499#384C2×D4311yescharacteristic, complemented
500#380C2×D4311yescharacteristic
501#380C2×D4311yescharacteristic, complemented
502C4×C4⋊C4—21no—
503C4×C4⋊C4C2×D4311yescharacteristic, complemented
504#340—431no—
505#340—431no—
506#340—431no—
507#340—431no—
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—862no—
521C22×D4—862no—
522C22×D4—861no—
523C22×D4—861no—
524C22×D4—862no—
525C22×D4—861no—
526C22×D4—1721no—
527C22×D4—1721no—
528C22×D4C22⋊D4311yescharacteristic
529C23×C4—861no—
530C23×C4—861no—
531C23×C4C22×D4311yescharacteristic
532C23×C4C22×D4311yescharacteristic
533C2×M16—862no—
534C2×M16—862no—
535C2×M16—1721no—
536C22×C8—431no—
537C22×C8—431no—
538C22×C8—431no—
539C22×C8—431no—
540C22×C8—862no—
541C22×C8—862no—
542C22×C8—1721no—
543#124—434no—
544#124—862no—
545#123—868no—
546C22⋊Q8—434no—
547C22⋊Q8—862no—
548#121—434no—
549#121—862no—
550#121—868no—
551#120—868no—
552C4×D4—434no—
553C4×D4—862no—
554C4×D4C4×D4314yes—
555C4×D4D17214yes—
556#117—22no—
557#117—22no—
558#117—41no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4C22⋊D4311yescharacteristic
565C2×C4⋊C4C22×D4311yescharacteristic
566C2×C4⋊C4C22×D4311yescharacteristic
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—868no—
579C2×C22⋊C4C22⋊D4311yescharacteristic
580C2×C22⋊C4C22⋊D4311yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C22×D4311yescharacteristic
585C4⋊C8—862no—
586#103—862no—
587#103—862no—
588#103—1721no—
589#103—1721no—
590#102—434no—
591#102—862no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—862no—
596#102—1721no—
597#102—1721no—
598C22⋊C8—862no—
599C22⋊C8—862no—
600#97—862no—
601#95—21no—
602#95—21no—
603#95—21no—
604C24—861no—
605C24—864no—
606C24—861no—
607C24—3441no—
608C24—3441no—
609C24—1722no—
610C24—1722no—
611C24—1722no—
612C24—1722no—
613C24C2×C22⋊D4311yescharacteristic
614C24C2×C22⋊D4311yescharacteristic
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—41no—
626C2×D4—41no—
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(C2×D43)⋊C414yes—
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—21no—
664C22×C4—21no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—864no—
668C22×C4—864no—
669C22×C4—3441no—
670C22×C4—3441no—
671C22×C4—1722no—
672C22×C4—1722no—
673C22×C4C2×C4×D4312yes—
674C22×C4C2×C4×D4312yes—
675C22×C4C2×D17212yes—
676C22×C4C2×D17212yes—
677C22×C4C2×C22⋊D4311yescharacteristic
678C22×C4C2×C22⋊D4311yescharacteristic
679C22×C4C2×C22⋊D4311yescharacteristic
680C22×C4C2×C22⋊D4311yescharacteristic
681C22×C4C23×D4311yescharacteristic
682M16—1724no—
683C2×C8—432no—
684C2×C8—861no—
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—1724no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—42no—
704C4⋊C4—81no—
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—81no—
714C22⋊C4—864no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4(C2×D43)⋊C414yes—
720C22⋊C4(C2×D43)⋊C414yes—
721C42—42no—
722C42—42no—
723C42—42no—
724C42C2×C4×D4312yes—
725C42C2×D17212yes—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—862no—
739C23—862no—
740C23—862no—
741C23—862no—
742C23—3444no—
743C23—3444no—
744C23—3444no—
745C23—3444no—
746C23—3444no—
747C23—1728no—
748C23—1728no—
749C23—1721no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23C2×(C2×D43)⋊C412yes—
760C23C2×(C2×D43)⋊C412yes—
761C23C22×C22⋊D4311yescharacteristic
762Q8—862no—
763Q8—862no—
764Q8—1721no—
765Q8—1721no—
766D4—44no—
767D4—434no—
768D4—862no—
769D4—862no—
770D4—862no—
771D4—862no—
772D4—862no—
773D4—3444no—
774D4—1728no—
775D4—1728no—
776D4—1721no—
777D4—1721no—
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—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—3444no—
809C2×C4—1728no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4C2×(C2×D43)⋊C412yes—
815C2×C4C2×(C2×D43)⋊C412yes—
816C2×C4C2×(C2×D43)⋊C412yes—
817C2×C4C2×(C2×D43)⋊C412yes—
818C2×C4C22×C4×D4311yescharacteristic
819C2×C4C2×D4×D4311yescharacteristic
820C2×C4C22×D17211yescharacteristic
821C2×C4#41×D4311yescharacteristic
822C2×C4#1306337011yescharacteristic
823C2×C4#1306337111yescharacteristic
824C8—862no—
825C8—1721no—
826C8—1721no—
827C8—1721no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—864no—
843C22—34416no—
844C22—3441no—
845C22—3441no—
846C22—3441no—
847C22—3441no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1722no—
856C22—1722no—
857C22C22×(C2×D43)⋊C411yescharacteristic
858C22D4×C22⋊D4311yescharacteristic
859C22#1458353711yescharacteristic
860C22#1458369711yescharacteristic
861C22#1458369711yescharacteristic
862C22#1458370211yescharacteristic
863C22#1458370711yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4—1722no—
873C4—1722no—
874C4C4×D4×D4311yescharacteristic
875C4#1458337111yescharacteristic
876C4D4×D17211yescharacteristic
877C4#1458354411yescharacteristic
878C2—42no—
879C2—42no—
880C2—3442no—
881C2—1724no—
882C2D4×(C2×D43)⋊C411yescharacteristic
883C2#1914311211yescharacteristic
884C2#1914311811yescharacteristic
885C2#1914612111yescharacteristic
886C2#1914613611yescharacteristic
887C2#1914662511yescharacteristic
888C2#1914674511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2354C2
socleC23×C43C22×D4
prime radicalC2×#14583545C2
cosocleC22×C4×C43C24
hypercenter#2354D43
hypocenterC43#22424
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. C2×#14582971C2semidirect
3. C2×#14582903C2semidirect
4. C2×#14582893C2semidirect
5. #19135527C2semidirect
6. #19135409C2semidirect
7. #19135026C2semidirect
8. #19135021C2semidirect
9. #19134917C2semidirect
10. #19134907C2semidirect
11. #19134592C2semidirect
12. #19134533C2semidirect
13. #19134525C2semidirect
14. #19134423C2semidirect
15. C43×#2354C2semidirect
19. C23×C43⋊C8C22semidirect
21. #14583545C4semidirect
31. C2×C4⋊(C43⋊C8)C22semidirect
34. C2×#13063248C22semidirect
35. C2×#13063248C22semidirect
36. C2×#13063248C22semidirect
37. C2×#13063248C22semidirect
47. C2×C22⋊(C43⋊C8)C22semidirect
48. C2×#13063236C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
55. C2×#117×C43C22semidirect
59. C43×#384C22semidirect
61. C43×#380C22semidirect
63. C4×C4⋊C4×C43C22semidirect
126. #13063245D4semidirect
438. #2354D43semidirect
475. C2×#117C2×D43semidirect
499. #384C2×D43semidirect
501. #380C2×D43semidirect
503. C4×C4⋊C4C2×D43semidirect
508. C43#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#145835452
C2×#145829712
C2×#145829032
C2×#145828932
#191355272
#191354092
#191350262
#191350212
#191349172
#191349072
#191345922
#191345332
#191345252
#191344232
C43×#23542
#2242443