Finite Group Databasebeta

← #25112191

Subgroups — #25112191

Order 11008.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583545C211yesmaximal, characteristic
2C2×#14582977C211yesmaximal, characteristic, complemented
3C2×#14582898C211yesmaximal, characteristic, complemented
4C2×#14582903C211yesmaximal, characteristic, complemented
5#19135527C211yesmaximal, characteristic, complemented
6#19135404C211yesmaximal, characteristic, complemented
7#19135031C211yesmaximal, characteristic, complemented
8#19135026C211yesmaximal, characteristic, complemented
9#19134912C211yesmaximal, characteristic, complemented
10#19134907C211yesmaximal, characteristic, complemented
11#19134602C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic, complemented
13#19134525C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic, complemented
15C43×#2352C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×D172C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C22×#10621877C2211yescharacteristic, 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#14582977—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
32#14582903—24no—
33#14582898—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×C4×C43⋊C8C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53C2×C4×D4×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic, complemented
56C43×#388—21no—
57C43×#387—21no—
58C43×#386—21no—
59C43×#382C2211yescharacteristic, complemented
60C43×#380C2211yescharacteristic
61C43×#380C2211yescharacteristic, complemented
62C4×C4⋊C4×C43C2211yescharacteristic, complemented
63C4×C22⋊C4×C43—21no—
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×C414yescomplemented
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—22no—
88C2×#10621877—22no—
89C2×#10621877—41no—
90C2×#10621877—41no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95#13063313—22no—
96#13063313C2×C414yescomplemented
97#13063310—28no—
98#13063304—22no—
99#13063304C2×C414yescomplemented
100#13063299—22no—
101#13063299C2×C414yes—
102#13063298—28no—
103#13063293—28no—
104C4×D172—22no—
105C4×D172C2×C414yescomplemented
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—
129C4×C43⋊C8—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—
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×C43—42no—
186C22×C4×C43—42no—
187C22×C4×C43—81no—
188C22×C4×C43C22×C412yes—
189C22×C4×C43C22×C412yes—
190C22×C4×C43C2×D412yes—
191C22×C4×C43C2×D412yes—
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—24no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—42no—
200C2×C22⋊D43—42no—
201C2×C22⋊D43—81no—
202C2×C22⋊D43—81no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205#10621898—28no—
206#10621898—44no—
207#10621898—44no—
208#10621898—44no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—24no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—28no—
219C2×D172—42no—
220C2×D172—42no—
221C2×D172—44no—
222C2×D172—44no—
223C2×D172—44no—
224C2×D172C22×C412yes—
225C2×D172C22×C412yes—
226C2×D172C2×D412yes—
227C2×D172#4112yes—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—81no—
233C2×C4×D43—81no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86C22×C412yes—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—42no—
248C4⋊C4×C43C22⋊C414yes—
249C4⋊C4×C43C2×D412yes—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—81no—
253C22⋊C4×C43C22⋊C414yes—
254C22⋊C4×C43C22⋊C414yes—
255C42×C43—42no—
256C42×C43—81no—
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—
268#10621877—44no—
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—21no—
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×C43—84no—
347C2×C4×C43C2×C22⋊C412yes—
348C2×C4×C43C2×C22⋊C412yes—
349C2×C4×C43C2×C22⋊C412yes—
350C2×C4×C43C2×C22⋊C412yes—
351C2×C4×C43C23×C411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C2×#4111yescharacteristic
355C2×C4×C43H(5,𝔽2)11yescharacteristic
356C2×C4×C43H(5,𝔽2)11yescharacteristic
357C22⋊D43—48no—
358C22⋊D43—84no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365D172—22no—
366D172—22no—
367D172—22no—
368D172—22no—
369D172—22no—
370D172—48no—
371D172—41no—
372D172—41no—
373D172C4×D414yes—
374C4×D43—48no—
375C4×D43—84no—
376Dic86—22no—
377Dic86—22no—
378Dic86—41no—
379Dic86—41no—
380C43⋊C8—22no—
381C43⋊C8—41no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384#22427—431nomaximal, Sylow
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43C22×C22⋊C411yescharacteristic
400C22×C43D4211yescharacteristic
401C22×C43#54611yescharacteristic
402C22×C43#57511yescharacteristic
403C22×C43#57511yescharacteristic
404C22×C43#57611yescharacteristic
405C22×C43#57711yescharacteristic
406C2×D43—24no—
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—42no—
416C2×D43—816no—
417C2×D43—81no—
418C2×D43—81no—
419C2×D43—81no—
420C2×D43—81no—
421C4×C43—22no—
422C4×C43—22no—
423C4×C43—22no—
424C4×C43—22no—
425C4×C43—42no—
426C4×C43—81no—
427C4×C43—81no—
428C4×C43—81no—
429C4×C43C2×C4×D411yescharacteristic
430C4×C43#51811yescharacteristic
431C4×C43D4211yescharacteristic
432C4×C43#54611yescharacteristic
433Dic43—42no—
434Dic43—42no—
435C2×#546—431no—
436C2×#436—431no—
437C2×#417—431no—
438C2×#418—431no—
439#2352D4311yescharacteristic, complemented
440#1983—431no—
441#1958—431no—
442#1895—431no—
443#1894—431no—
444#1874—431no—
445#1873—431no—
446#1804—431no—
447#1788—431no—
448#1786—431no—
449C4×#102—431no—
450C2×C43—42no—
451C2×C43—42no—
452C2×C43D4×C22⋊C411yescharacteristic
453C2×C43#289611yescharacteristic
454C2×C43#289711yescharacteristic
455C2×C43#327311yescharacteristic
456C2×C43#327511yescharacteristic
457C2×C43#332211yescharacteristic
458C2×C43#332311yescharacteristic
459D43—44no—
460D43—82no—
461C22×#41—431no—
462C23×D4—431no—
463C22×M16—431no—
464C22×M16—431no—
465#546—438no—
466#546—864no—
467C2×#124—431no—
468C2×#123—861no—
469C2×C22⋊Q8—431no—
470C2×#121—431no—
471C2×#121—861no—
472C2×#120—861no—
473C2×C4×D4—431no—
474C2×C4×D4C2×D4311yescharacteristic
475C2×#117C2×D4311yescharacteristic
476C22×C4⋊C4C2×D4311yescharacteristic, complemented
477C22×C22⋊C4—861no—
478#436—864no—
479C2×C4⋊C8—431no—
480#418—864no—
481#417—864no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#103—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—431no—
492C2×#102—431no—
493C2×#102—431no—
494C2×C22⋊C8—431no—
495C2×C22⋊C8—431no—
496C2×C4×C8—431no—
497#388—21no—
498#387—21no—
499#386—21no—
500#382C2×D4311yescharacteristic, complemented
501#380C2×D4311yescharacteristic
502#380C2×D4311yescharacteristic, complemented
503C4×C4⋊C4C2×D4311yescharacteristic, complemented
504C4×C22⋊C4—21no—
505#340—431no—
506#340—431no—
507#340—431no—
508#340—431no—
509C43#2242711yescharacteristic, complemented, Sylow
510C25—861no—
511C2×#41—434no—
512C2×#41—862no—
513C2×#41—862no—
514C2×#41—862no—
515C2×#41—1721no—
516C2×#41—1721no—
517C22×Q8—431no—
518C22×D4—434no—
519C22×D4—431no—
520C22×D4—431no—
521C22×D4—862no—
522C22×D4—862no—
523C22×D4—861no—
524C22×D4—861no—
525C22×D4—862no—
526C22×D4—861no—
527C22×D4—1721no—
528C22×D4—1721no—
529C22×D4C22⋊D4311yescharacteristic
530C23×C4—21no—
531C23×C4—861no—
532C23×C4—861no—
533C23×C4C22×D4311yescharacteristic
534C23×C4C22×D4311yescharacteristic
535C2×M16—862no—
536C2×M16—862no—
537C2×M16—862no—
538C2×M16—862no—
539C2×M16—1721no—
540C2×M16—1721no—
541C22×C8—431no—
542C22×C8—431no—
543C22×C8—431no—
544C22×C8—431no—
545#124—434no—
546#124—862no—
547#123—868no—
548C22⋊Q8—434no—
549C22⋊Q8—862no—
550#121—434no—
551#121—862no—
552#121—868no—
553#120—868no—
554C4×D4—434no—
555C4×D4—862no—
556C4×D4C4×D4314yes—
557C4×D4D17214yes—
558#117—22no—
559#117—41no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4C22⋊D4311yescharacteristic
566C2×C4⋊C4C22×D4311yescharacteristic
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C4⋊C4C22×D4311yescharacteristic
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×C42C22×D4311yescharacteristic
584C4⋊C8—862no—
585#103—862no—
586#103—862no—
587#103—1721no—
588#103—1721no—
589#102—434no—
590#102—862no—
591#102—862no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—1721no—
596#102—1721no—
597C22⋊C8—862no—
598C22⋊C8—862no—
599C4×C8—862no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605C24—861no—
606C24—864no—
607C24—861no—
608C24—3441no—
609C24—3441no—
610C24—1722no—
611C24—1722no—
612C24—1722no—
613C24—1722no—
614C24C2×C22⋊D4311yescharacteristic
615C24C2×C22⋊D4311yescharacteristic
616#41—868no—
617#41—1724no—
618#41—1724no—
619#41—1724no—
620C2×Q8—432no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4—432no—
629C2×D4—432no—
630C2×D4—432no—
631C2×D4—432no—
632C2×D4—868no—
633C2×D4—864no—
634C2×D4—864no—
635C2×D4—864no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—3441no—
645C2×D4—3441no—
646C2×D4—1724no—
647C2×D4—1724no—
648C2×D4—1724no—
649C2×D4—1722no—
650C2×D4—1722no—
651C2×D4—1722no—
652C2×D4—1722no—
653C2×D4(C2×D43)⋊C414yes—
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—21no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—864no—
672C22×C4—864no—
673C22×C4—3441no—
674C22×C4—3441no—
675C22×C4—1722no—
676C22×C4—1722no—
677C22×C4C2×C4×D4312yes—
678C22×C4C2×C4×D4312yes—
679C22×C4C2×D17212yes—
680C22×C4C2×D17212yes—
681C22×C4C2×C22⋊D4311yescharacteristic
682C22×C4C2×C22⋊D4311yescharacteristic
683C22×C4C2×C22⋊D4311yescharacteristic
684C22×C4C2×C22⋊D4311yescharacteristic
685C22×C4C23×D4311yescharacteristic
686M16—1724no—
687M16—1724no—
688C2×C8—432no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—861no—
699C2×C8—861no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4—432no—
709C4⋊C4—864no—
710C4⋊C4—861no—
711C4⋊C4(C2×D43)⋊C414yes—
712C4⋊C4D4×D4312yes—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—81no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—864no—
721C22⋊C4(C2×D43)⋊C414yes—
722C22⋊C4(C2×D43)⋊C414yes—
723C42—42no—
724C42—81no—
725C42C2×C4×D4312yes—
726C42C2×D17212yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—862no—
740C23—862no—
741C23—862no—
742C23—862no—
743C23—3444no—
744C23—3444no—
745C23—3444no—
746C23—3444no—
747C23—3444no—
748C23—1728no—
749C23—1728no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23C2×(C2×D43)⋊C412yes—
761C23C2×(C2×D43)⋊C412yes—
762C23C22×C22⋊D4311yescharacteristic
763Q8—862no—
764Q8—862no—
765Q8—1721no—
766Q8—1721no—
767D4—44no—
768D4—434no—
769D4—862no—
770D4—862no—
771D4—862no—
772D4—862no—
773D4—862no—
774D4—3444no—
775D4—1728no—
776D4—1728no—
777D4—1721no—
778D4—1721no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
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—22no—
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—41no—
807C2×C4—84no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—3444no—
811C2×C4—1728no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4C2×(C2×D43)⋊C412yes—
817C2×C4C2×(C2×D43)⋊C412yes—
818C2×C4C2×(C2×D43)⋊C412yes—
819C2×C4C2×(C2×D43)⋊C412yes—
820C2×C4C22×C4×D4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C22×D17211yescharacteristic
823C2×C4#41×D4311yescharacteristic
824C2×C4#1306337011yescharacteristic
825C2×C4#1306337111yescharacteristic
826C8—862no—
827C8—1721no—
828C8—1721no—
829C8—1721no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—864no—
845C22—34416no—
846C22—3441no—
847C22—3441no—
848C22—3441no—
849C22—3441no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1722no—
856C22—1722no—
857C22—1722no—
858C22—1722no—
859C22C22×(C2×D43)⋊C411yescharacteristic
860C22D4×C22⋊D4311yescharacteristic
861C22#1458353711yescharacteristic
862C22#1458369711yescharacteristic
863C22#1458369711yescharacteristic
864C22#1458370211yescharacteristic
865C22#1458370711yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—1722no—
875C4—1722no—
876C4C4×D4×D4311yescharacteristic
877C4#1458337111yescharacteristic
878C4D4×D17211yescharacteristic
879C4#1458354411yescharacteristic
880C2—42no—
881C2—42no—
882C2—3442no—
883C2—1724no—
884C2D4×(C2×D43)⋊C411yescharacteristic
885C2#1914311211yescharacteristic
886C2#1914311811yescharacteristic
887C2#1914620211yescharacteristic
888C2#1914622711yescharacteristic
889C2#1914679011yescharacteristic
890C2#1914680511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2352C2
socleC23×C43C22×D4
prime radicalC2×#14583545C2
cosocleC22×C4×C43C24
hypercenter#2352D43
hypocenterC43#22427
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×#14582977C2semidirect
3. C2×#14582898C2semidirect
4. C2×#14582903C2semidirect
5. #19135527C2semidirect
6. #19135404C2semidirect
7. #19135031C2semidirect
8. #19135026C2semidirect
9. #19134912C2semidirect
10. #19134907C2semidirect
11. #19134602C2semidirect
12. #19134533C2semidirect
13. #19134525C2semidirect
14. C4×#13063245C2semidirect
15. C43×#2352C2semidirect
19. C22×#10621877C22semidirect
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×C4×C43⋊C8C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
55. C22×C4⋊C4×C43C22semidirect
59. C43×#382C22semidirect
61. C43×#380C22semidirect
62. C4×C4⋊C4×C43C22semidirect
78. C22×D172C2×C4semidirect
96. #13063313C2×C4semidirect
99. #13063304C2×C4semidirect
105. C4×D172C2×C4semidirect
126. #13063245D4semidirect
439. #2352D43semidirect
476. C22×C4⋊C4C2×D43semidirect
500. #382C2×D43semidirect
502. #380C2×D43semidirect
503. C4×C4⋊C4C2×D43semidirect
509. C43#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#145835452
C2×#145829772
C2×#145828982
C2×#145829032
#191355272
#191354042
#191350312
#191350262
#191349122
#191349072
#191346022
#191345332
#191345252
C4×#130632452
C43×#23522
#2242743