Finite Group Databasebeta

← #25112130

Subgroups — #25112130

Order 11008.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D43C211yesmaximal, characteristic
2C2×#14582973C211yesmaximal, characteristic, complemented
3C2×#14582904C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5#19137517C211yesmaximal, characteristic, complemented
6#19135520C211yesmaximal, characteristic, complemented
7#19135417C211yesmaximal, characteristic, complemented
8#19135031C211yesmaximal, characteristic, complemented
9#19135020C211yesmaximal, characteristic, complemented
10#19134915C211yesmaximal, characteristic, complemented
11#19134909C211yesmaximal, characteristic, complemented
12#19134603C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C23×C22⋊D43—21no—
17C22×D4×D43C2211yescharacteristic
18C22×#10621877C2211yescharacteristic, complemented
19C22×C8×D43C2211yescharacteristic, complemented
20D4×C22⋊D43—24no—
21D4×C22⋊D43C418yescomplemented
22C2×#13063321C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063297—21no—
25C2×#13063296C2211yescharacteristic
26C2×#13063294—21no—
27C2×#13063293—21no—
28C2×D4×Dic43C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×#13063284C2211yescharacteristic, complemented
31C2×C4⋊C4×D43C2211yescharacteristic, complemented
32#14582973—24no—
33C2×Dic43⋊C8C2211yescharacteristic, complemented
34#14582904—24no—
35C2×#13063247C2211yescharacteristic, complemented
36C2×#13063247C2211yescharacteristic, complemented
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic, complemented
40C2×#13063246C2211yescharacteristic, complemented
41C2×#13063245C2211yescharacteristic, complemented
42C2×#13063245C2211yescharacteristic, complemented
43#102×D43—24no—
44C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
45C2×#13063235C2211yescharacteristic, complemented
46#14582787—21no—
47#14582781—21no—
48#14582775—21no—
49#14582764C2211yescharacteristic, complemented
50#14582756C2211yescharacteristic, complemented
51C4⋊C4×Dic43C2211yescharacteristic, complemented
52#14582746—21no—
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C23×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic, complemented
61C2×#102×C43C2211yescharacteristic, complemented
62C2×C22⋊C8×C43C2211yescharacteristic, complemented
63C43×#380C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C22×C22⋊D43—28no—
69C22×C22⋊D43—21no—
70C22×C22⋊D43—21no—
71C22×C22⋊D43—21no—
72C22×C22⋊D43—44no—
73C22×C22⋊D43—44no—
74C22×C22⋊D43D411yescharacteristic
75C2×D4×D43—22no—
76C2×D4×D43—22no—
77C2×D4×D43—22no—
78C2×D4×D43—41no—
79C2×D4×D43—41no—
80C2×D4×D43C2×C414yes—
81C23×Dic43—21no—
82C22×C4×D43—21no—
83C22×C4×D43C2311yescharacteristic
84C2×#10621877—22no—
85C2×#10621877—22no—
86C2×#10621877—41no—
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C2×C8×D43—22no—
90C2×C8×D43—22no—
91C2×C8×D43—41no—
92#13063321—22no—
93#13063321C2×C414yescomplemented
94#13063299—22no—
95#13063299C2×C414yescomplemented
96#13063297—28no—
97#13063296—22no—
98#13063296C2×C414yes—
99#13063294—28no—
100#13063293—28no—
101D4×Dic43—22no—
102D4×Dic43C2×C414yescomplemented
103C4×C22⋊D43C2×C414yes—
104C4×C22⋊D43D414yes—
105#13063284—22no—
106#13063284—41no—
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4D411yescharacteristic
112C4⋊C4×D43—22no—
113C4⋊C4×D43—41no—
114C2×C22⋊Dic43—21no—
115C2×C22⋊Dic43—21no—
116C2×C22⋊Dic43—21no—
117C2×C22⋊Dic43D411yescharacteristic
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4D411yescharacteristic
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123C2×C4×Dic43C2311yescharacteristic
124Dic43⋊C8—22no—
125#13063247—22no—
126#13063247—41no—
127#13063246—22no—
128#13063246—22no—
129#13063246—22no—
130#13063246D414yescomplemented
131#13063245—22no—
132#13063245—41no—
133(C2×D43)⋊C8—22no—
134#13063235—22no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C43⋊#95—21no—
139C25×C43—21no—
140C22×D4×C43—22no—
141C22×D4×C43—22no—
142C22×D4×C43—21no—
143C22×D4×C43—22no—
144C22×D4×C43—41no—
145C22×D4×C43—41no—
146C22×D4×C43C2×C414yescomplemented
147C22×D4×C43C2311yescharacteristic
148C22×D4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151C22×C8×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C22⋊C4×C43—21no—
155#102×C43—22no—
156#102×C43—22no—
157#102×C43—41no—
158#102×C43—41no—
159C22⋊C8×C43—22no—
160#95×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—24no—
164C24×C43—42no—
165C24×C43—42no—
166C24×C43—42no—
167C24×C43—42no—
168C24×C43—81no—
169C24×C43—81no—
170C24×C43C2×D411yescharacteristic
171C23×D43—21no—
172C23×D43—24no—
173C23×D43—42no—
174C23×D43—42no—
175C23×D43—42no—
176C23×D43—42no—
177C23×D43—81no—
178C23×D43—81no—
179C23×D43C2×D411yescharacteristic
180C2×D4×C43—24no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—28no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—42no—
191C2×D4×C43—42no—
192C2×D4×C43—44no—
193C2×D4×C43—44no—
194C2×D4×C43—44no—
195C2×D4×C43C22×C412yes—
196C2×D4×C43C22×C412yes—
197C2×D4×C43C2×D412yes—
198C2×D4×C43#4112yes—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43C22×C412yes—
206C22×C4×C43C2×D412yes—
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43—22no—
215C2×C22⋊D43—22no—
216C2×C22⋊D43—42no—
217C2×C22⋊D43—42no—
218C2×C22⋊D43—42no—
219C2×C22⋊D43—42no—
220C2×C22⋊D43—42no—
221C2×C22⋊D43—42no—
222C2×C22⋊D43—432no—
223C2×C22⋊D43—42no—
224C2×C22⋊D43—42no—
225C2×C22⋊D43—81no—
226C2×C22⋊D43—81no—
227C2×C22⋊D43C22⋊C414yes—
228C22×Dic43—24no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—42no—
233C22×Dic43—42no—
234C22×Dic43C2×D411yescharacteristic
235C22×Dic43C2×D411yescharacteristic
236C22×Dic43C2×D411yescharacteristic
237D4×D43—28no—
238D4×D43—44no—
239D4×D43—44no—
240D4×D43—44no—
241C2×D172—21no—
242C2×D172—21no—
243C2×D172—21no—
244C2×D172—21no—
245C2×D172—21no—
246C2×D172C22×C412yes—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—42no—
252C2×C4×D43—42no—
253C2×C4×D43—81no—
254C2×C4×D43C22×C412yes—
255C2×C4×D43C2×D412yes—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C22⋊C4×C43—81no—
267C22⋊Dic43—24no—
268C22⋊Dic43—24no—
269C22⋊Dic43—42no—
270C22⋊Dic43C22⋊C414yes—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—42no—
273(C2×D43)⋊C4C22⋊C414yes—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43C22×C412yes—
279C4⋊Dic43C2×D412yescomplemented
280Dic43⋊C4—42no—
281Dic43⋊C4C22⋊C414yes—
282C4×Dic43—42no—
283C4×Dic43—81no—
284C4×Dic43C22×C412yes—
285C4×Dic43C2×D412yes—
286#10621877—44no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8C2×D412yescomplemented
293C8×D43—44no—
294C23×C43—22no—
295C23×C43—21no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—22no—
304C23×C43—48no—
305C23×C43—48no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—84no—
317C23×C43—84no—
318C23×C43—84no—
319C23×C43—84no—
320C23×C43—84no—
321C23×C43C2×C22⋊C412yes—
322C23×C43C22×D411yescharacteristic
323C22×D43—21no—
324C22×D43—21no—
325C22×D43—21no—
326C22×D43—21no—
327C22×D43—22no—
328C22×D43—48no—
329C22×D43—41no—
330C22×D43—41no—
331C22×D43—41no—
332C22×D43—41no—
333C22×D43—41no—
334C22×D43—41no—
335C22×D43—48no—
336C22×D43—84no—
337C22×D43—84no—
338C22×D43—84no—
339C22×D43—84no—
340C22×D43—84no—
341C22×D43C2×C22⋊C412yes—
342C22×D43AGL(1,ℤ/8)12yes—
343C22×D43AGL(1,ℤ/8)12yes—
344D4×C43—22no—
345D4×C43—22no—
346D4×C43—22no—
347D4×C43—22no—
348D4×C43—22no—
349D4×C43—48no—
350D4×C43—41no—
351D4×C43—41no—
352D4×C43C4×D414yes—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43C2×C22⋊C412yes—
366C2×C4×C43C23×C411yescharacteristic
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C2×#4111yescharacteristic
370C2×C4×C43H(5,𝔽2)11yescharacteristic
371C2×C4×C43H(5,𝔽2)11yescharacteristic
372C22⋊D43—28no—
373C22⋊D43—48no—
374C22⋊D43—48no—
375C22⋊D43—48no—
376C22⋊D43—48no—
377C22⋊D43—84no—
378C2×Dic43—21no—
379C2×Dic43—21no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—48no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43C2×C22⋊C412yes—
395C2×Dic43C2×C22⋊C412yes—
396C2×Dic43C2×C22⋊C412yes—
397D172—22no—
398D172—22no—
399D172—41no—
400D172—41no—
401C4×D43—22no—
402C4×D43—22no—
403C4×D43—22no—
404C4×D43—22no—
405C4×D43—84no—
406C8×C43—41no—
407C8×C43—41no—
408C43⋊C8—22no—
409C43⋊C8—41no—
410#22423—431nomaximal, Sylow
411C22×C43—24no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—42no—
416C22×C43—42no—
417C22×C43—42no—
418C22×C43—41no—
419C22×C43—42no—
420C22×C43—41no—
421C22×C43—42no—
422C22×C43—41no—
423C22×C43—42no—
424C22×C43—41no—
425C22×C43—42no—
426C22×C43—42no—
427C22×C43—42no—
428C22×C43—816no—
429C22×C43—81no—
430C22×C43—81no—
431C22×C43—81no—
432C22×C43—81no—
433C22×C43C22×C22⋊C411yescharacteristic
434C22×C43D4211yescharacteristic
435C22×C43#54611yescharacteristic
436C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
437C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
438C22×C43#57611yescharacteristic
439C22×C43#57711yescharacteristic
440C2×D43—22no—
441C2×D43—22no—
442C2×D43—22no—
443C2×D43—22no—
444C2×D43—22no—
445C2×D43—22no—
446C2×D43—42no—
447C2×D43—42no—
448C2×D43—42no—
449C2×D43—816no—
450C2×D43—81no—
451C2×D43—81no—
452C2×D43—81no—
453C2×D43—81no—
454C2×D43#41814yescomplemented
455C4×C43—22no—
456C4×C43—81no—
457C4×C43—81no—
458C4×C43C2×C4×D411yescharacteristic
459C4×C43#51811yescharacteristic
460C4×C43D4211yescharacteristic
461C4×C43#54611yescharacteristic
462Dic43—22no—
463Dic43—22no—
464Dic43—22no—
465Dic43—42no—
466Dic43—42no—
467Dic43—81no—
468C2×D42—431no—
469C2×#435—431no—
470C2×#418—431no—
471C22×#102—431no—
472#2352—431no—
473#1982—431no—
474#1961—431no—
475#1895—431no—
476#1893—431no—
477#1875—431no—
478#1874—431no—
479#1804—431no—
480#1786—431no—
481#1786D4311yescharacteristic, complemented
482#1762—431no—
483C2×C43—44no—
484C2×C43—42no—
485C2×C43—82no—
486C2×C43D4×C22⋊C411yescharacteristic
487C2×C43C2×#41811yescharacteristic
488C2×C43#289711yescharacteristic
489C2×C43#326411yescharacteristic
490C2×C43#326511yescharacteristic
491C2×C43#331011yescharacteristic
492C2×C43#331811yescharacteristic
493D43—24no—
494D43—82no—
495C23×D4—431no—
496C23×D4—861no—
497C23×D4C2×D4311yescharacteristic
498C22×M16—431no—
499C23×C8—431no—
500D42—438no—
501D42—864no—
502C2×#127—431no—
503C2×#121—431no—
504C2×#121—431no—
505C2×#121—861no—
506C2×#120—861no—
507C2×#120—861no—
508C2×C4×D4—431no—
509C2×C4×D4—431no—
510C2×#117—431no—
511C22×C4⋊C4—431no—
512#435—864no—
513C2×C4⋊C8—431no—
514#418—864no—
515C2×#102—431no—
516C2×#102—431no—
517C2×#102—431no—
518C2×#102—431no—
519C2×#102—431no—
520C2×#102—431no—
521C2×#102—431no—
522C2×#102—431no—
523C2×#102—864no—
524C2×#102C2×D4311yescharacteristic
525C2×#102C2×D4311yescharacteristic
526C2×#102C2×D4311yescharacteristic, complemented
527C2×#102C2×D4311yescharacteristic, complemented
528C2×C22⋊C8—431no—
529C2×C22⋊C8C2×D4311yescharacteristic, complemented
530C2×#97—431no—
531#388—861no—
532#387—861no—
533#386—861no—
534#382—431no—
535#380—431no—
536#380C2×D4311yescharacteristic, complemented
537C4×C4⋊C4—431no—
538C4×C22⋊C4—861no—
539#340—431no—
540#340—431no—
541#340—431no—
542#340—431no—
543C43#2242311yescharacteristic, complemented, Sylow
544C25—21no—
545C25—861no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—21no—
549C22×D4—22no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—431no—
553C22×D4—434no—
554C22×D4—431no—
555C22×D4—862no—
556C22×D4—861no—
557C22×D4—861no—
558C22×D4—861no—
559C22×D4—868no—
560C22×D4—862no—
561C22×D4—862no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4—1721no—
565C22×D4—1721no—
566C22×D4—1724no—
567C22×D4—1724no—
568C22×D4C4×D4314yescomplemented
569C22×D4C22×D4311yescharacteristic
570C22×D4C22×D4311yescharacteristic
571C23×C4—431no—
572C23×C4—861no—
573C23×C4—861no—
574C23×C4C22×D4311yescharacteristic
575C2×M16—862no—
576C2×M16—862no—
577C2×M16—1721no—
578C22×C8—431no—
579C22×C8—431no—
580C22×C8—862no—
581C22×C8—862no—
582C22×C8—1721no—
583C22×C8C22×D4311yescharacteristic
584C22×C8C22×D4311yescharacteristic
585#127—434no—
586#127—862no—
587#121—434no—
588#121—434no—
589#121—868no—
590#121—862no—
591#121—862no—
592#120—868no—
593#120—868no—
594C4×D4—434no—
595C4×D4—434no—
596C4×D4—434no—
597C4×D4—862no—
598#117—862no—
599#117—1721no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—431no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—862no—
605C2×C4⋊C4—861no—
606C2×C4⋊C4—1721no—
607C2×C4⋊C4C22×D4311yescharacteristic
608C2×C4⋊C4C22×D4311yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—431no—
611C2×C22⋊C4—431no—
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4—861no—
616C2×C22⋊C4—861no—
617C2×C42—431no—
618C2×C42—861no—
619C2×C42—861no—
620C4⋊C8—862no—
621#102—22no—
622#102—22no—
623#102—41no—
624#102—41no—
625#102—434no—
626#102—862no—
627#102—862no—
628#102—862no—
629#102—862no—
630#102—862no—
631#102—1721no—
632#102—1721no—
633C22⋊C8—22no—
634C22⋊C8—862no—
635#97—862no—
636#95—21no—
637#95—861no—
638#95—861no—
639#95—861no—
640#95—861no—
641C24—21no—
642C24—21no—
643C24—24no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—42no—
648C24—81no—
649C24—81no—
650C24—431no—
651C24—864no—
652C24—861no—
653C24—3441no—
654C24—3441no—
655C24—1722no—
656C24—1722no—
657C24—1722no—
658C24—1722no—
659C24D4×D4311yescharacteristic
660C2×D4—28no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—434no—
676C2×D4—432no—
677C2×D4—864no—
678C2×D4—864no—
679C2×D4—864no—
680C2×D4—862no—
681C2×D4—862no—
682C2×D4—868no—
683C2×D4—864no—
684C2×D4—864no—
685C2×D4—861no—
686C2×D4—861no—
687C2×D4—861no—
688C2×D4—861no—
689C2×D4—861no—
690C2×D4—3441no—
691C2×D4—3441no—
692C2×D4—1724no—
693C2×D4—1724no—
694C2×D4—1724no—
695C2×D4—1722no—
696C2×D4—1722no—
697C2×D4—1722no—
698C2×D4—1722no—
699C2×D4—17232no—
700C2×D4—1722no—
701C2×D4—1722no—
702C2×D4—1722no—
703C2×D4—1722no—
704C2×D4C2×C4×D4312yes—
705C2×D4C2×C4×D4312yes—
706C2×D4D4×D4312yes—
707C2×D4#1062190012yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—431no—
717C22×C4—432no—
718C22×C4—432no—
719C22×C4—864no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—3441no—
728C22×C4—1722no—
729C22×C4—1722no—
730C22×C4—1722no—
731C22×C4—1722no—
732C22×C4C2×C4×D4312yes—
733C22×C4D4×D4311yescharacteristic
734C22×C4D4×D4312yes—
735C22×C4C23×D4311yescharacteristic
736M16—1724no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—432no—
744C2×C8—861no—
745C2×C8—861no—
746C2×C8—861no—
747C2×C8—861no—
748C2×C8—861no—
749C2×C8—1724no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—434no—
755C4⋊C4—432no—
756C4⋊C4—432no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—1722no—
762C22⋊C4—81no—
763C22⋊C4—434no—
764C22⋊C4—434no—
765C22⋊C4—864no—
766C22⋊C4—864no—
767C22⋊C4—864no—
768C22⋊C4—1722no—
769C22⋊C4—1722no—
770C42—432no—
771C42—432no—
772C42—3441no—
773C42—1722no—
774C23—22no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—48no—
785C23—48no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—432no—
802C23—432no—
803C23—432no—
804C23—861no—
805C23—861no—
806C23—861no—
807C23—861no—
808C23—862no—
809C23—3444no—
810C23—3444no—
811C23—3444no—
812C23—3444no—
813C23—3444no—
814C23—1728no—
815C23—1728no—
816C23—1721no—
817C23—1721no—
818C23—1721no—
819C23—1721no—
820C23—1721no—
821C23—1721no—
822C23C22⋊C4×D4312yes—
823C23C2×D4×D4311yescharacteristic
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—48no—
830D4—41no—
831D4—41no—
832D4—868no—
833D4—862no—
834D4—862no—
835D4—3444no—
836D4—1728no—
837D4—1728no—
838D4—1728no—
839D4—1728no—
840D4—1721no—
841D4—1721no—
842D4(C22⋊D43)⋊C414yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—432no—
856C2×C4—432no—
857C2×C4—432no—
858C2×C4—861no—
859C2×C4—861no—
860C2×C4—861no—
861C2×C4—861no—
862C2×C4—861no—
863C2×C4—861no—
864C2×C4—862no—
865C2×C4—862no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—862no—
869C2×C4—862no—
870C2×C4—3444no—
871C2×C4—1728no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4—1721no—
877C2×C4—1721no—
878C2×C4—1721no—
879C2×C4C22⋊C4×D4312yes—
880C2×C4C22×C4×D4311yescharacteristic
881C2×C4C2×D4×D4311yescharacteristic
882C2×C4C2×D4×D4311yescharacteristic
883C2×C4C2×#1062190011yescharacteristic
884C2×C4#1306337011yescharacteristic
885C2×C4#1306337011yescharacteristic
886C8—41no—
887C8—41no—
888C8—862no—
889C8—1721no—
890C22—22no—
891C22—24no—
892C22—22no—
893C22—22no—
894C22—41no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—434no—
913C22—862no—
914C22—862no—
915C22—862no—
916C22—862no—
917C22—862no—
918C22—862no—
919C22—34416no—
920C22—3441no—
921C22—3441no—
922C22—3441no—
923C22—3441no—
924C22—1722no—
925C22—1722no—
926C22—1722no—
927C22C2×C22⋊C4×D4311yescharacteristic
928C22#1458353111yescharacteristic
929C22#1458353611yescharacteristic
930C22AGL(1,ℤ/8)×D4311yescharacteristic
931C22AGL(1,ℤ/8)×D4311yescharacteristic
932C22#1458370011yescharacteristic
933C22#1458370511yescharacteristic
934C4—22no—
935C4—81no—
936C4—81no—
937C4—862no—
938C4—862no—
939C4—862no—
940C4—3441no—
941C4—1722no—
942C4—1722no—
943C4C2×(C22⋊D43)⋊C411yescharacteristic
944C4#1458337211yescharacteristic
945C4#1458353111yescharacteristic
946C4#1458353611yescharacteristic
947C2—42no—
948C2—44no—
949C2—82no—
950C2—864no—
951C2—3442no—
952C2#1913741111yescharacteristic
953C2#418×D4311yescharacteristic
954C2#1914311611yescharacteristic
955C2#1914607311yescharacteristic
956C2#1914608811yescharacteristic
957C2#1914660911yescharacteristic
958C2#1914672911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radicalC2×D4×C22⋊D43C2
cosocleC22×C4×C43C24
hypercenter#1786D43
hypocenterC43#22423
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#14582973C2semidirect
3. C2×#14582904C2semidirect
4. C2×#102×D43C2semidirect
5. #19137517C2semidirect
6. #19135520C2semidirect
7. #19135417C2semidirect
8. #19135031C2semidirect
9. #19135020C2semidirect
10. #19134915C2semidirect
11. #19134909C2semidirect
12. #19134603C2semidirect
13. #19134524C2semidirect
14. #19134422C2semidirect
15. C43×#1786C2semidirect
18. C22×#10621877C22semidirect
19. C22×C8×D43C22semidirect
21. D4×C22⋊D43C4semidirect
30. C2×#13063284C22semidirect
31. C2×C4⋊C4×D43C22semidirect
33. C2×Dic43⋊C8C22semidirect
35. C2×#13063247C22semidirect
36. C2×#13063247C22semidirect
39. C2×#13063246C22semidirect
40. C2×#13063246C22semidirect
41. C2×#13063245C22semidirect
42. C2×#13063245C22semidirect
44. C2×(C2×D43)⋊C8C22semidirect
45. C2×#13063235C22semidirect
49. #14582764C22semidirect
50. #14582756C22semidirect
51. C4⋊C4×Dic43C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
60. C2×#102×C43C22semidirect
61. C2×#102×C43C22semidirect
62. C2×C22⋊C8×C43C22semidirect
63. C43×#380C22semidirect
93. #13063321C2×C4semidirect
95. #13063299C2×C4semidirect
102. D4×Dic43C2×C4semidirect
130. #13063246D4semidirect
146. C22×D4×C43C2×C4semidirect
279. C4⋊Dic43C2×D4semidirect
292. C2×C43⋊C8C2×D4semidirect
454. C2×D43#418semidirect
481. #1786D43semidirect
526. C2×#102C2×D43semidirect
527. C2×#102C2×D43semidirect
529. C2×C22⋊C8C2×D43semidirect
536. #380C2×D43semidirect
543. C43#22423semidirect
568. C22×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊D432
C2×#145829732
C2×#145829042
C2×#102×D432
#191375172
#191355202
#191354172
#191350312
#191350202
#191349152
#191349092
#191346032
#191345242
#191344222
C43×#17862
#2242343