Finite Group Databasebeta

← #25112208

Subgroups — #25112208

Order 11008.

1910 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D43C211yesmaximal, characteristic
2C2×#14582975C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic, complemented
4#19137545C211yesmaximal, characteristic, complemented
5#19135520C211yesmaximal, characteristic, complemented
6#19135399C211yesmaximal, characteristic, complemented
7#19135033C211yesmaximal, characteristic, complemented
8#19135030C211yesmaximal, characteristic, complemented
9#19134917C211yesmaximal, characteristic, complemented
10#19134914C211yesmaximal, characteristic, complemented
11#19134593C211yesmaximal, characteristic, complemented
12#19134526C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#418C211yesmaximal, characteristic, complemented
16C23×C22⋊D43—21no—
17C22×D4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic, complemented
19D4×C22⋊D43—24no—
20D4×C22⋊D43C418yescomplemented
21C2×#13063321C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23C2×#13063297—21no—
24C2×#13063296C2211yescharacteristic
25C2×#13063294—21no—
26C2×#13063293—21no—
27C2×D4×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063283C2211yescharacteristic, complemented
30#14582975—24no—
31C2×Dic43⋊C8C2211yescharacteristic, complemented
32#14582902—24no—
33C2×#13063247C2211yescharacteristic, complemented
34C2×#13063247C2211yescharacteristic, complemented
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic, complemented
38C2×#13063246C2211yescharacteristic, complemented
39C2×#13063245C2211yescharacteristic, complemented
40C2×#13063245C2211yescharacteristic, complemented
41C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
42C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
43C2×C8×Dic43C2211yescharacteristic, complemented
44#14582799—21no—
45#14582790—21no—
46#14582787—21no—
47#14582768C2211yescharacteristic, complemented
48#14582759C2211yescharacteristic, complemented
49#14582756C2211yescharacteristic, complemented
50C4⋊C4×Dic43C2211yescharacteristic, complemented
51C4×Dic43⋊C4—21no—
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C23×D4×C43C2211yescharacteristic
57C22×M16×C43C2211yescharacteristic, complemented
58C2×#117×C43C2211yescharacteristic, complemented
59C43×#418—24no—
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic, complemented
63C2×#102×C43C2211yescharacteristic, 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×D43C2311yescharacteristic
83C2×#10621872—22no—
84C2×#10621872—22no—
85C2×#10621872—41no—
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063321—22no—
89#13063321C2×C414yes—
90#13063299—22no—
91#13063299C2×C414yes—
92#13063297—28no—
93#13063296—22no—
94#13063296C2×C414yes—
95#13063294—28no—
96#13063293—28no—
97D4×Dic43—22no—
98D4×Dic43C2×C414yes—
99C4×C22⋊D43C2×C414yes—
100C4×C22⋊D43D414yes—
101#13063283—22no—
102#13063283—41no—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4D411yescharacteristic
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
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)⋊C4D411yescharacteristic
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43C2311yescharacteristic
120Dic43⋊C8—22no—
121#13063247—22no—
122#13063247—41no—
123#13063246—22no—
124#13063246—22no—
125#13063246—41no—
126#13063246—41no—
127#13063245—22no—
128#13063245—41no—
129C22⋊(C43⋊C8)—22no—
130(C2×D43)⋊C8—22no—
131C8×Dic43—22no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C25×C43—21no—
136C22×D4×C43—22no—
137C22×D4×C43—22no—
138C22×D4×C43—21no—
139C22×D4×C43—22no—
140C22×D4×C43—41no—
141C22×D4×C43—41no—
142C22×D4×C43C2×C414yes—
143C22×D4×C43C2311yescharacteristic
144C22×D4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C2×M16×C43—22no—
147C2×M16×C43—22no—
148C2×M16×C43—41no—
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151#117×C43—22no—
152#117×C43—41no—
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C22⋊C4×C43—21no—
156C2×C42×C43—21no—
157#102×C43—22no—
158#102×C43—22no—
159#102×C43—22no—
160#102×C43D414yescomplemented
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—22no—
213C2×C22⋊D43—22no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—24no—
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×D43C22×C412yes—
252C2×C4×D43C2×D412yes—
253M16×C43—44no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43C2×D412yescomplemented
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43C2×D412yescomplemented
264C22⋊C4×C43—42no—
265C42×C43—42no—
266C22⋊Dic43—24no—
267C22⋊Dic43—24no—
268C22⋊Dic43—81no—
269C22⋊Dic43C22⋊C414yes—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—42no—
272(C2×D43)⋊C4—81no—
273(C2×D43)⋊C4C22⋊C414yes—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43C22×C412yes—
280Dic43⋊C4—42no—
281Dic43⋊C4—81no—
282Dic43⋊C4C22⋊C414yes—
283C4×Dic43—42no—
284C4×Dic43—42no—
285C4×Dic43C22×C412yes—
286C4×Dic43C2×D412yes—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293#10621872—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—21no—
328C22×D43—21no—
329C22×D43—22no—
330C22×D43—48no—
331C22×D43—48no—
332C22×D43—41no—
333C22×D43—41no—
334C22×D43—41no—
335C22×D43—41no—
336C22×D43—41no—
337C22×D43—41no—
338C22×D43—84no—
339C22×D43—84no—
340C22×D43—84no—
341C22×D43—84no—
342C22×D43—84no—
343C22×D43C2×C22⋊C412yes—
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—22no—
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—22no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—48no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43C2×C22⋊C412yes—
393C2×Dic43C2×C22⋊C412yes—
394C2×Dic43C2×C22⋊C412yes—
395C2×Dic43AGL(1,ℤ/8)12yes—
396C2×Dic43AGL(1,ℤ/8)12yes—
397D172—22no—
398D172—22no—
399D172—41no—
400D172—41no—
401C4×D43—22no—
402C4×D43—22no—
403C4×D43—22no—
404C4×D43—22no—
405C8×C43—22no—
406C8×C43—41no—
407C43⋊C8—41no—
408C43⋊C8—41no—
409#22428—431nomaximal, Sylow
410C22×C43—24no—
411C22×C43—22no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—42no—
415C22×C43—42no—
416C22×C43—42no—
417C22×C43—41no—
418C22×C43—42no—
419C22×C43—41no—
420C22×C43—42no—
421C22×C43—41no—
422C22×C43—42no—
423C22×C43—41no—
424C22×C43—42no—
425C22×C43—42no—
426C22×C43—42no—
427C22×C43—816no—
428C22×C43—81no—
429C22×C43—81no—
430C22×C43—81no—
431C22×C43—81no—
432C22×C43C22×C22⋊C411yescharacteristic
433C22×C43D4211yescharacteristic
434C22×C43#54611yescharacteristic
435C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
436C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
437C22×C43#57611yescharacteristic
438C22×C43#57711yescharacteristic
439C2×D43—22no—
440C2×D43—22no—
441C2×D43—22no—
442C2×D43—41no—
443C2×D43—41no—
444C2×D43—41no—
445C2×D43—41no—
446C2×D43—42no—
447C2×D43—42no—
448C2×D43—42no—
449C2×D43—816no—
450C2×D43—81no—
451C2×D43—81no—
452C2×D43—81no—
453C2×D43—81no—
454C4×C43—22no—
455C4×C43—42no—
456C4×C43—81no—
457C4×C43C2×C4×D411yescharacteristic
458C4×C43#51811yescharacteristic
459C4×C43D4211yescharacteristic
460C4×C43#54611yescharacteristic
461Dic43—22no—
462Dic43—22no—
463Dic43—42no—
464Dic43—81no—
465Dic43—81no—
466Dic43#41814yescomplemented
467C2×D42—431no—
468C2×#436—431no—
469C2×#418—431no—
470C2×#418D4311yescharacteristic, complemented
471#2354—431no—
472#1982—431no—
473#1957—431no—
474#1895—431no—
475#1895—431no—
476#1875—431no—
477#1875—431no—
478#1802—431no—
479#1786—431no—
480#1786—431no—
481C4×#102—431no—
482C2×C43—44no—
483C2×C43—42no—
484C2×C43—82no—
485C2×C43D4×C22⋊C411yescharacteristic
486C2×C43C2×#41811yescharacteristic
487C2×C43#289711yescharacteristic
488C2×C43#327211yescharacteristic
489C2×C43#327411yescharacteristic
490C2×C43#332411yescharacteristic
491C2×C43#332511yescharacteristic
492D43—42no—
493D43—82no—
494C23×D4—431no—
495C23×D4—861no—
496C23×D4C2×D4311yescharacteristic
497C22×M16—431no—
498C22×M16C2×D4311yescharacteristic, complemented
499D42—438no—
500D42—864no—
501C2×#127—431no—
502C2×#121—431no—
503C2×#121—431no—
504C2×#121—861no—
505C2×#120—861no—
506C2×#120—861no—
507C2×C4×D4—431no—
508C2×C4×D4—431no—
509C2×#117—431no—
510C2×#117C2×D4311yescharacteristic, complemented
511#436—864no—
512C2×C4⋊C8—431no—
513#418—24no—
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×#102C2×D4311yescharacteristic
524C2×#102C2×D4311yescharacteristic
525C2×#102C2×D4311yescharacteristic, complemented
526C2×#102C2×D4311yescharacteristic, complemented
527C2×C22⋊C8—431no—
528C2×C22⋊C8—431no—
529C2×C4×C8—431no—
530#390—861no—
531#388—861no—
532#388—861no—
533#384—431no—
534#380—431no—
535#380—431no—
536C4×C4⋊C4—431no—
537C4×C4⋊C4—861no—
538#340—431no—
539#340—431no—
540#340—431no—
541#340—431no—
542C43#2242811yescharacteristic, complemented, Sylow
543C25—21no—
544C25—861no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—41no—
550C22×D4—41no—
551C22×D4—431no—
552C22×D4—434no—
553C22×D4—431no—
554C22×D4—862no—
555C22×D4—861no—
556C22×D4—861no—
557C22×D4—861no—
558C22×D4—868no—
559C22×D4—862no—
560C22×D4—862no—
561C22×D4—861no—
562C22×D4—861no—
563C22×D4—1721no—
564C22×D4—1721no—
565C22×D4—1724no—
566C22×D4—1724no—
567C22×D4C4×D4314yes—
568C22×D4C22×D4311yescharacteristic
569C22×D4C22×D4311yescharacteristic
570C23×C4—431no—
571C23×C4—861no—
572C23×C4C22×D4311yescharacteristic
573C2×M16—22no—
574C2×M16—22no—
575C2×M16—41no—
576C2×M16—862no—
577C2×M16—862no—
578C2×M16—1721no—
579C22×C8—431no—
580C22×C8—431no—
581C22×C8C22×D4311yescharacteristic
582C22×C8C22×D4311yescharacteristic
583#127—434no—
584#127—862no—
585#121—434no—
586#121—434no—
587#121—868no—
588#121—862no—
589#121—862no—
590#120—868no—
591#120—868no—
592C4×D4—434no—
593C4×D4—434no—
594C4×D4—434no—
595C4×D4—862no—
596#117—22no—
597#117—41no—
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—861no—
605C2×C4⋊C4—861no—
606C2×C4⋊C4C22×D4311yescharacteristic
607C2×C4⋊C4C22×D4311yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—431no—
610C2×C22⋊C4—431no—
611C2×C22⋊C4—861no—
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4—861no—
616C2×C22⋊C4—861no—
617C2×C42—21no—
618C2×C42—431no—
619C2×C42—861no—
620C2×C42—861no—
621C4⋊C8—862no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—862no—
626#102—862no—
627#102—862no—
628#102—862no—
629#102—1721no—
630#102—1721no—
631#102—1721no—
632#102—1721no—
633#102C22⋊D4314yescomplemented
634C22⋊C8—862no—
635C22⋊C8—862no—
636C4×C8—862no—
637#95—861no—
638#95—861no—
639#95—861no—
640C24—21no—
641C24—21no—
642C24—24no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—81no—
648C24—81no—
649C24—431no—
650C24—864no—
651C24—861no—
652C24—3441no—
653C24—3441no—
654C24—1722no—
655C24—1722no—
656C24—1722no—
657C24—1722no—
658C24D4×D4311yescharacteristic
659C2×D4—28no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—434no—
675C2×D4—432no—
676C2×D4—862no—
677C2×D4—862no—
678C2×D4—864no—
679C2×D4—864no—
680C2×D4—864no—
681C2×D4—868no—
682C2×D4—864no—
683C2×D4—864no—
684C2×D4—861no—
685C2×D4—861no—
686C2×D4—861no—
687C2×D4—861no—
688C2×D4—861no—
689C2×D4—3441no—
690C2×D4—3441no—
691C2×D4—1722no—
692C2×D4—1722no—
693C2×D4—1724no—
694C2×D4—1724no—
695C2×D4—1724no—
696C2×D4—1722no—
697C2×D4—1722no—
698C2×D4—17232no—
699C2×D4—1722no—
700C2×D4—1722no—
701C2×D4—1722no—
702C2×D4—1722no—
703C2×D4C2×C4×D4312yes—
704C2×D4C2×C4×D4312yes—
705C2×D4#1062189812yes—
706C2×D4C2×C22⋊D4312yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—432no—
717C22×C4—432no—
718C22×C4—864no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—1722no—
727C22×C4—1722no—
728C22×C4C2×C4×D4312yes—
729C22×C4D4×D4311yescharacteristic
730C22×C4D4×D4312yes—
731C22×C4C23×D4311yescharacteristic
732M16—44no—
733M16—1724no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—861no—
740C2×C8—861no—
741C2×C8—861no—
742C2×C8—861no—
743C2×C8—861no—
744C2×C8—861no—
745C2×C8C2×C22⋊D4312yescomplemented
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—434no—
750C4⋊C4—432no—
751C4⋊C4—861no—
752C4⋊C4—861no—
753C4⋊C4—861no—
754C4⋊C4—861no—
755C4⋊C4—861no—
756C4⋊C4—3441no—
757C4⋊C4—1722no—
758C4⋊C4C2×C22⋊D4312yescomplemented
759C22⋊C4—42no—
760C22⋊C4—434no—
761C22⋊C4—434no—
762C22⋊C4—864no—
763C22⋊C4—864no—
764C22⋊C4—864no—
765C22⋊C4—3441no—
766C22⋊C4—3441no—
767C22⋊C4—1722no—
768C42—42no—
769C42—432no—
770C42—432no—
771C42—1722no—
772C42—1722no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—48no—
784C23—48no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—432no—
801C23—861no—
802C23—861no—
803C23—861no—
804C23—861no—
805C23—861no—
806C23—861no—
807C23—862no—
808C23—3444no—
809C23—3444no—
810C23—3444no—
811C23—3444no—
812C23—3444no—
813C23—1728no—
814C23—1728no—
815C23—1721no—
816C23—1721no—
817C23—1721no—
818C23—1721no—
819C23—1721no—
820C23—1721no—
821C23C22⋊C4×D4312yes—
822C23C2×D4×D4311yescharacteristic
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—868no—
832D4—862no—
833D4—862no—
834D4—3444no—
835D4—1728no—
836D4—1728no—
837D4—1728no—
838D4—1728no—
839D4—1721no—
840D4—1721no—
841D4C4×C22⋊D4314yes—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
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—432no—
855C2×C4—432no—
856C2×C4—432no—
857C2×C4—432no—
858C2×C4—432no—
859C2×C4—861no—
860C2×C4—861no—
861C2×C4—861no—
862C2×C4—861no—
863C2×C4—862no—
864C2×C4—862no—
865C2×C4—862no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—1728no—
869C2×C4—1721no—
870C2×C4—1721no—
871C2×C4—1721no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4—1721no—
877C2×C4C22⋊C4×D4312yes—
878C2×C4C22×C4×D4311yescharacteristic
879C2×C4C2×D4×D4311yescharacteristic
880C2×C4C22×C22⋊D4311yescharacteristic
881C2×C4C2×#1062189811yescharacteristic
882C2×C4#1306337011yescharacteristic
883C2×C4#1306337011yescharacteristic
884C8—22no—
885C8—41no—
886C8—1721no—
887C8—1721no—
888C22—22no—
889C22—24no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—42no—
894C22—41no—
895C22—42no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—816no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—862no—
911C22—862no—
912C22—862no—
913C22—34416no—
914C22—3441no—
915C22—3441no—
916C22—3441no—
917C22—3441no—
918C22—1722no—
919C22—1722no—
920C22—1722no—
921C22—1721no—
922C22—1721no—
923C22—1721no—
924C22—1721no—
925C22C2×C22⋊C4×D4311yescharacteristic
926C22D4×C22⋊D4311yescharacteristic
927C22#1458353911yescharacteristic
928C22AGL(1,ℤ/8)×D4311yescharacteristic
929C22AGL(1,ℤ/8)×D4311yescharacteristic
930C22#1458370311yescharacteristic
931C22#1458370911yescharacteristic
932C4—22no—
933C4—42no—
934C4—81no—
935C4—434no—
936C4—862no—
937C4—862no—
938C4—3441no—
939C4—3441no—
940C4—1722no—
941C4C2×C4×C22⋊D4311yescharacteristic
942C4#1458337211yescharacteristic
943C4D4×C22⋊D4311yescharacteristic
944C4#1458353911yescharacteristic
945C2—42no—
946C2—44no—
947C2—82no—
948C2—3442no—
949C2—1722no—
950C2C22⋊C4×C22⋊D4311yescharacteristic
951C2#418×D4311yescharacteristic
952C2#1914312011yescharacteristic
953C2#1914618911yescharacteristic
954C2#1914620911yescharacteristic
955C2#1914682211yescharacteristic
956C2#1914683311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#418C2
socleC23×C43C22×D4
prime radicalC2×D4×C22⋊D43C2
cosocleC22×C4×C43C24
hypercenterC2×#418D43
hypocenterC43#22428
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#14582975C2semidirect
3. C2×#14582902C2semidirect
4. #19137545C2semidirect
5. #19135520C2semidirect
6. #19135399C2semidirect
7. #19135033C2semidirect
8. #19135030C2semidirect
9. #19134917C2semidirect
10. #19134914C2semidirect
11. #19134593C2semidirect
12. #19134526C2semidirect
13. #19134524C2semidirect
14. #102×Dic43C2semidirect
15. C2×C43×#418C2semidirect
18. C22×#10621872C22semidirect
20. D4×C22⋊D43C4semidirect
29. C2×#13063283C22semidirect
31. C2×Dic43⋊C8C22semidirect
33. C2×#13063247C22semidirect
34. C2×#13063247C22semidirect
37. C2×#13063246C22semidirect
38. C2×#13063246C22semidirect
39. C2×#13063245C22semidirect
40. C2×#13063245C22semidirect
41. C2×C22⋊(C43⋊C8)C22semidirect
42. C2×(C2×D43)⋊C8C22semidirect
43. C2×C8×Dic43C22semidirect
47. #14582768C22semidirect
48. #14582759C22semidirect
49. #14582756C22semidirect
50. C4⋊C4×Dic43C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
57. C22×M16×C43C22semidirect
58. C2×#117×C43C22semidirect
62. C2×#102×C43C22semidirect
63. C2×#102×C43C22semidirect
160. #102×C43D4semidirect
259. C2×C8×C43C2×D4semidirect
263. C4⋊C4×C43C2×D4semidirect
466. Dic43#418semidirect
470. C2×#418D43semidirect
498. C22×M16C2×D43semidirect
510. C2×#117C2×D43semidirect
525. C2×#102C2×D43semidirect
526. C2×#102C2×D43semidirect
542. C43#22428semidirect
633. #102C22⋊D43semidirect
745. C2×C8C2×C22⋊D43semidirect
758. C4⋊C4C2×C22⋊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×#145829752
C2×#145829022
#191375452
#191355202
#191353992
#191350332
#191350302
#191349172
#191349142
#191345932
#191345262
#191345242
#102×Dic432
C2×C43×#4182
#2242843