Finite Group Databasebeta

← #25112133

Subgroups — #25112133

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×#14582970C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic, complemented
4#19137520C211yesmaximal, characteristic, complemented
5#19135520C211yesmaximal, characteristic, complemented
6#19135417C211yesmaximal, characteristic, complemented
7#19135030C211yesmaximal, characteristic, complemented
8#19135023C211yesmaximal, characteristic, complemented
9#19134914C211yesmaximal, characteristic, complemented
10#19134912C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic, complemented
12#19134526C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic, complemented
15C22×#102×C43C211yesmaximal, 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#14582970—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×#13063235C2211yescharacteristic, complemented
44#14582789—21no—
45#14582780—21no—
46#14582778—21no—
47#14582764C2211yescharacteristic, complemented
48#14582759C2211yescharacteristic, complemented
49#14582756C2211yescharacteristic, complemented
50C4⋊C4×Dic43C2211yescharacteristic, complemented
51C4×C22⋊Dic43—21no—
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C23×D4×C43C2211yescharacteristic
57C23×C8×C43C2211yescharacteristic, complemented
58C22×C4⋊C4×C43C2211yescharacteristic, complemented
59C2×#102×C43—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×C414yescomplemented
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×C414yescomplemented
90#13063299—22no—
91#13063299C2×C414yes—
92#13063297—28no—
93#13063296—22no—
94#13063296C2×C414yescomplemented
95#13063294—28no—
96#13063293—28no—
97D4×Dic43—22no—
98D4×Dic43C2×C414yescomplemented
99C4×C22⋊D43C2×C414yes—
100C4×C22⋊D43D414yes—
101#13063283—22no—
102#13063283—41no—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×Dic43⋊C4D411yescharacteristic
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43D411yescharacteristic
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4D411yescharacteristic
115C2×C4×Dic43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43C2311yescharacteristic
118Dic43⋊C8—22no—
119#13063247—22no—
120#13063247—41no—
121#13063246—22no—
122#13063246—22no—
123#13063246—41no—
124#13063246—41no—
125#13063245—22no—
126#13063245—41no—
127C22⋊(C43⋊C8)—22no—
128(C2×D43)⋊C8—22no—
129#13063235—22no—
130C43⋊#95—21no—
131C43⋊#95—21no—
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×C43—21no—
146C23×C4×C43C2311yescharacteristic
147C22×C8×C43—22no—
148C22×C8×C43—22no—
149C22×C8×C43—41no—
150C22×C8×C43C2311yescharacteristic
151C22×C8×C43C2311yescharacteristic
152C2×C4⋊C4×C43—22no—
153C2×C4⋊C4×C43—21no—
154C2×C4⋊C4×C43—41no—
155C2×C4⋊C4×C43C2311yescharacteristic
156C2×C4⋊C4×C43C2311yescharacteristic
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×C43—42no—
206C22×C4×C43—42no—
207C22×C4×C43—81no—
208C22×C4×C43C22×C412yes—
209C22×C4×C43C2×D412yes—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2411yescharacteristic
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—24no—
216C2×C22⋊D43—22no—
217C2×C22⋊D43—22no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—42no—
220C2×C22⋊D43—42no—
221C2×C22⋊D43—42no—
222C2×C22⋊D43—42no—
223C2×C22⋊D43—42no—
224C2×C22⋊D43—42no—
225C2×C22⋊D43—432no—
226C2×C22⋊D43—42no—
227C2×C22⋊D43—42no—
228C2×C22⋊D43—81no—
229C2×C22⋊D43—81no—
230C2×C22⋊D43C22⋊C414yes—
231C22×Dic43—24no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—42no—
236C22×Dic43—42no—
237C22×Dic43C2×D411yescharacteristic
238C22×Dic43C2×D411yescharacteristic
239C22×Dic43C2×D411yescharacteristic
240D4×D43—28no—
241D4×D43—44no—
242D4×D43—44no—
243D4×D43—44no—
244C2×D172—21no—
245C2×D172—21no—
246C2×D172—21no—
247C2×D172—21no—
248C2×D172—21no—
249C2×D172C22×C412yes—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—21no—
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—44no—
262C2×C8×C43C2×D412yescomplemented
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—42no—
267C4⋊C4×C43C2×D412yescomplemented
268C22⋊Dic43—24no—
269C22⋊Dic43—24no—
270C22⋊Dic43—42no—
271C22⋊Dic43C22⋊C414yes—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—42no—
274(C2×D43)⋊C4—81no—
275(C2×D43)⋊C4C22⋊C414yes—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43C22×C412yes—
282Dic43⋊C4C22⋊C414yes—
283C4×Dic43—42no—
284C4×Dic43—81no—
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—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—22no—
302C23×C43—48no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—48no—
314C23×C43—84no—
315C23×C43—84no—
316C23×C43—84no—
317C23×C43—84no—
318C23×C43—84no—
319C23×C43C2×C22⋊C412yes—
320C23×C43AGL(1,ℤ/8)12yes—
321C23×C43AGL(1,ℤ/8)12yes—
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×C43—84no—
366C2×C4×C43C2×C22⋊C412yes—
367C2×C4×C43C23×C411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C22×D411yescharacteristic
370C2×C4×C43C2×#4111yescharacteristic
371C2×C4×C43H(5,𝔽2)11yescharacteristic
372C2×C4×C43H(5,𝔽2)11yescharacteristic
373C22⋊D43—28no—
374C22⋊D43—48no—
375C22⋊D43—48no—
376C22⋊D43—48no—
377C22⋊D43—48no—
378C22⋊D43—84no—
379C2×Dic43—21no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—21no—
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×Dic43—41no—
395C2×Dic43C2×C22⋊C412yes—
396C2×Dic43C2×C22⋊C412yes—
397C2×Dic43C2×C22⋊C412yes—
398D172—22no—
399D172—22no—
400D172—41no—
401D172—41no—
402C4×D43—22no—
403C4×D43—22no—
404C4×D43—22no—
405C4×D43—22no—
406C8×C43—22no—
407C8×C43—41no—
408C43⋊C8—41no—
409C43⋊C8—41no—
410#22423—431nomaximal, Sylow
411C22×C43—22no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—22no—
416C22×C43—22no—
417C22×C43—24no—
418C22×C43—42no—
419C22×C43—42no—
420C22×C43—42no—
421C22×C43—42no—
422C22×C43—42no—
423C22×C43—42no—
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×C43#41814yescomplemented
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—41no—
444C2×D43—41no—
445C2×D43—41no—
446C2×D43—41no—
447C2×D43—42no—
448C2×D43—42no—
449C2×D43—42no—
450C2×D43—816no—
451C2×D43—81no—
452C2×D43—81no—
453C2×D43—81no—
454C2×D43—81no—
455C4×C43—22no—
456C4×C43—42no—
457C4×C43—81no—
458C4×C43C2×C4×D411yescharacteristic
459C4×C43#51811yescharacteristic
460C4×C43D4211yescharacteristic
461C4×C43#54611yescharacteristic
462Dic43—22no—
463Dic43—22no—
464Dic43—22no—
465Dic43—42no—
466Dic43—81no—
467Dic43—81no—
468C2×D42—431no—
469C2×#435—431no—
470C2×#418—431no—
471C22×#102D4311yescharacteristic, complemented
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#1786—431no—
482#1762—431no—
483C2×C43—24no—
484C2×C43—44no—
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—42no—
494D43—82no—
495C23×D4—431no—
496C23×D4—861no—
497C23×D4C2×D4311yescharacteristic
498C22×M16—431no—
499C23×C8C2×D4311yescharacteristic, complemented
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⋊C4C2×D4311yescharacteristic, complemented
512#435—864no—
513C2×C4⋊C8—431no—
514#418—864no—
515C2×#102—24no—
516C2×#102—431no—
517C2×#102—431no—
518C2×#102—431no—
519C2×#102—431no—
520C2×#102—431no—
521C2×#102—431no—
522C2×#102—431no—
523C2×#102—431no—
524C2×#102C2×D4311yescharacteristic
525C2×#102C2×D4311yescharacteristic
526C2×#102C2×D4311yescharacteristic, complemented
527C2×#102C2×D4311yescharacteristic, complemented
528C2×C22⋊C8—431no—
529C2×C22⋊C8—431no—
530C2×#97—431no—
531#388—861no—
532#387—861no—
533#386—861no—
534#382—431no—
535#380—431no—
536#380—431no—
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×D4314yes—
569C22×D4C22×D4311yescharacteristic
570C22×D4C22×D4311yescharacteristic
571C23×C4—21no—
572C23×C4—431no—
573C23×C4—861no—
574C23×C4C22×D4311yescharacteristic
575C2×M16—862no—
576C2×M16—862no—
577C2×M16—1721no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8—431no—
582C22×C8—431no—
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—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—431no—
605C2×C4⋊C4—431no—
606C2×C4⋊C4—431no—
607C2×C4⋊C4C22×D4311yescharacteristic
608C2×C4⋊C4C22×D4311yescharacteristic
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—431no—
618C2×C42—861no—
619C2×C42—861no—
620C4⋊C8—862no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—862no—
625#102—862no—
626#102—862no—
627#102—862no—
628#102—1721no—
629#102—1721no—
630#102—1721no—
631#102—1721no—
632#102C22⋊D4314yescomplemented
633C22⋊C8—862no—
634C22⋊C8—862no—
635#97—862no—
636#95—861no—
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×D4#1062189812yes—
707C2×D4C2×C22⋊D4312yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—81no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—431no—
720C22×C4—432no—
721C22×C4—432no—
722C22×C4—864no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—861no—
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—44no—
743C2×C8—861no—
744C2×C8—861no—
745C2×C8—861no—
746C2×C8—861no—
747C2×C8—861no—
748C2×C8—861no—
749C2×C8C2×C22⋊D4312yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—42no—
754C4⋊C4—434no—
755C4⋊C4—432no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4C2×C22⋊D4312yescomplemented
762C22⋊C4—434no—
763C22⋊C4—434no—
764C22⋊C4—864no—
765C22⋊C4—864no—
766C22⋊C4—864no—
767C22⋊C4—3441no—
768C22⋊C4—1722no—
769C22⋊C4—1722no—
770C42—432no—
771C42—432no—
772C42—3441no—
773C42—1722no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—48no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—48no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—432no—
800C23—861no—
801C23—861no—
802C23—861no—
803C23—861no—
804C23—861no—
805C23—861no—
806C23—862no—
807C23—3444no—
808C23—3444no—
809C23—3444no—
810C23—3444no—
811C23—3444no—
812C23—1728no—
813C23—1728no—
814C23—1721no—
815C23—1721no—
816C23—1721no—
817C23—1721no—
818C23—1721no—
819C23—1721no—
820C23C22⋊C4×D4312yes—
821C23#1306334912yes—
822C23#1306335212yes—
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—
842D4C4×C22⋊D4314yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—84no—
856C2×C4—432no—
857C2×C4—432no—
858C2×C4—432no—
859C2×C4—861no—
860C2×C4—861no—
861C2×C4—861no—
862C2×C4—861no—
863C2×C4—861no—
864C2×C4—861no—
865C2×C4—862no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—862no—
869C2×C4—862no—
870C2×C4—1728no—
871C2×C4—1721no—
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×C4C22×C22⋊D4311yescharacteristic
883C2×C4C2×#1062189811yescharacteristic
884C2×C4#1306337011yescharacteristic
885C2×C4#1306337011yescharacteristic
886C8—22no—
887C8—41no—
888C8—1721no—
889C8—1721no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—24no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—816no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—862no—
912C22—862no—
913C22—862no—
914C22—34416no—
915C22—3441no—
916C22—3441no—
917C22—3441no—
918C22—3441no—
919C22—1722no—
920C22—1722no—
921C22—1722no—
922C22—1721no—
923C22—1721no—
924C22—1721no—
925C22—1721no—
926C22#1458290214yescomplemented
927C22C2×C22⋊C4×D4311yescharacteristic
928C22D4×C22⋊D4311yescharacteristic
929C22#1458353911yescharacteristic
930C22C2×#1306334911yescharacteristic
931C22C2×#1306335211yescharacteristic
932C22#1458370011yescharacteristic
933C22#1458370511yescharacteristic
934C4—22no—
935C4—42no—
936C4—81no—
937C4—862no—
938C4—862no—
939C4—862no—
940C4—3441no—
941C4—3441no—
942C4—1722no—
943C4C2×C4×C22⋊D4311yescharacteristic
944C4#1458337211yescharacteristic
945C4D4×C22⋊D4311yescharacteristic
946C4#1458353911yescharacteristic
947C2—24no—
948C2—44no—
949C2—82no—
950C2—3442no—
951C2—1722no—
952C2C22⋊C4×C22⋊D4311yescharacteristic
953C2C2×#1458290211yescharacteristic
954C2#1914311611yescharacteristic
955C2#1914607511yescharacteristic
956C2#1914609011yescharacteristic
957C2#1914661211yescharacteristic
958C2#1914673211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×D4×C22⋊D43C2
cosocleC22×C4×C43C24
hypercenterC22×#102D43
hypocenterC43#22423
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14582970C2semidirect
3. C2×#14582902C2semidirect
4. #19137520C2semidirect
5. #19135520C2semidirect
6. #19135417C2semidirect
7. #19135030C2semidirect
8. #19135023C2semidirect
9. #19134914C2semidirect
10. #19134912C2semidirect
11. #19134603C2semidirect
12. #19134526C2semidirect
13. #19134524C2semidirect
14. #19134422C2semidirect
15. C22×#102×C43C2semidirect
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×#13063235C22semidirect
47. #14582764C22semidirect
48. #14582759C22semidirect
49. #14582756C22semidirect
50. C4⋊C4×Dic43C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
57. C23×C8×C43C22semidirect
58. C22×C4⋊C4×C43C22semidirect
62. C2×#102×C43C22semidirect
63. C2×#102×C43C22semidirect
80. C2×D4×D43C2×C4semidirect
89. #13063321C2×C4semidirect
94. #13063296C2×C4semidirect
98. D4×Dic43C2×C4semidirect
160. #102×C43D4semidirect
262. C2×C8×C43C2×D4semidirect
267. C4⋊C4×C43C2×D4semidirect
432. C22×C43#418semidirect
471. C22×#102D43semidirect
499. C23×C8C2×D43semidirect
511. C22×C4⋊C4C2×D43semidirect
526. C2×#102C2×D43semidirect
527. C2×#102C2×D43semidirect
543. C43#22423semidirect
632. #102C22⋊D43semidirect
749. C2×C8C2×C22⋊D43semidirect
761. C4⋊C4C2×C22⋊D43semidirect
926. C22#14582902semidirect

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×#145829702
C2×#145829022
#191375202
#191355202
#191354172
#191350302
#191350232
#191349142
#191349122
#191346032
#191345262
#191345242
#191344222
C22×#102×C432
#2242343