Finite Group Databasebeta

← C2×#19145461 #25967266

Subgroups — C2×#19145461 #25967266

Order 11008.

2314 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583472C211yesmaximal, characteristic, complemented
2C2×#14583465C211yesmaximal, characteristic
3#19145461C2116yesmaximal, direct product factor
4C2×#14583243C211yesmaximal, characteristic, complemented
5C2×#14583238C211yesmaximal, characteristic, complemented
6C2×#14583225C211yesmaximal, characteristic, complemented
7C2×#14583222C211yesmaximal, characteristic, complemented
8C2×#14583147C211yesmaximal, characteristic, complemented
9C2×#14583143C211yesmaximal, characteristic, complemented
10C2×#14583128C211yesmaximal, characteristic, complemented
11C2×#14583039C211yesmaximal, characteristic, complemented
12C2×#14583036C211yesmaximal, characteristic, complemented
13C2×#14583051C211yesmaximal, characteristic, complemented
14C2×#14583048C211yesmaximal, characteristic, complemented
15C2×#14582865C211yesmaximal, characteristic, complemented
16C2×C43×#465C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic, complemented
19C22×D4×D43C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621884C2211yescharacteristic
23C22×#10621877C2211yescharacteristic, complemented
24#14583472—24no—
25#14583472C2218yescomplemented
26#14583465—24no—
27#14583465C2218yes—
28C2×#13063324—21no—
29C2×#13063321—21no—
30C2×#13063311—21no—
31C2×#13063311—21no—
32C2×#13063310—21no—
33C2×#13063307—21no—
34C2×#13063305C2211yescharacteristic
35C2×#13063304C2211yescharacteristic, complemented
36C2×#13063301C2211yescharacteristic
37C2×#13063300C2211yescharacteristic
38C2×#13063299C2211yescharacteristic
39C2×#13063296C2211yescharacteristic
40C2×#13063295—21no—
41C2×#13063293—21no—
42C2×#13063283C2211yescharacteristic
43C2×#13063283C2211yescharacteristic, complemented
44#14583243C2218yescomplemented
45#14583238C2218yescomplemented
46#14583225C2218yescomplemented
47#14583222C2218yescomplemented
48#14583147C2218yescomplemented
49#14583143C2218yescomplemented
50#14583128C2218yescomplemented
51#14583051C2218yescomplemented
52#14583048C2218yescomplemented
53#14583039C2218yescomplemented
54#14583036C2218yescomplemented
55C2×#13063258C2211yescharacteristic, complemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063257C2211yescharacteristic, complemented
58C2×#13063250C2211yescharacteristic, complemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063248C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64#14582865C2218yescomplemented
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic, complemented
71C2×C22⋊Q8×C43C2211yescharacteristic, complemented
72C2×#121×C43C2211yescharacteristic
73C43×#465C2218yescomplemented
74C2×#106×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×#102×C43C2211yescharacteristic
77C24×D43—21no—
78C2×#10621898—42no—
79C2×#10621898—42no—
80C2×#10621898D414yes—
81C2×#10621898C2314yes—
82C22×Dic86—21no—
83C22×Dic86D411yescharacteristic
84C22×Dic86C2311yescharacteristic
85C2×Q8×D43—22no—
86C2×Q8×D43—42no—
87C2×Q8×D43—42no—
88C2×Q8×D43C2314yescomplemented
89C22×D172—21no—
90C22×D172D411yescharacteristic
91C22×D172C2311yescharacteristic
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C22⋊D43—21no—
95C22×C22⋊D43D411yescharacteristic
96C22×C22⋊D43D411yescharacteristic
97C2×D4×D43—22no—
98C2×D4×D43—42no—
99C2×D4×D43—42no—
100C2×D4×D43C2314yes—
101C22×C4×D43—21no—
102C22×C4×D43C2311yescharacteristic
103C22×C4×D43C2311yescharacteristic
104C2×#10621873—42no—
105C2×#10621873C2314yes—
106C2×#10621883—42no—
107C2×#10621883C2314yes—
108C2×#10621884—42no—
109C2×#10621884C2314yes—
110C2×#10621877—42no—
111C2×#10621877C2314yescomplemented
112C22×C43⋊C8C2311yescharacteristic
113C22×C43⋊C8C2311yescharacteristic
114#13063324—28no—
115#13063321—28no—
116#13063311—28no—
117#13063311—28no—
118#13063310—28no—
119#13063307—28no—
120#13063305—22no—
121#13063305C2314yes—
122#13063304—22no—
123#13063304C2314yescomplemented
124#13063301—22no—
125#13063301C2314yes—
126#13063300—22no—
127#13063300C2314yes—
128#13063299—22no—
129#13063299C2314yes—
130#13063296—22no—
131#13063296C2314yes—
132#13063295—28no—
133#13063293—28no—
134#13063283—22no—
135#13063283—22no—
136#13063283C2314yes—
137#13063283C2314yescomplemented
138C2×C4⋊Dic43—21no—
139C2×C4⋊Dic43C2311yescharacteristic
140C2×C4⋊Dic43C2311yescharacteristic
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4—21no—
143C2×C22⋊Dic43—21no—
144C2×C22⋊Dic43—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×C4×Dic43—21no—
152C2×C4×Dic43—21no—
153#13063258C2314yescomplemented
154#13063258C2314yescomplemented
155#13063257C2314yescomplemented
156#13063250C2314yescomplemented
157#13063249C2314yescomplemented
158#13063248C2314yescomplemented
159#13063247C2314yes—
160#13063246C2314yes—
161#13063245C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164(C2×D43)⋊C8C2314yescomplemented
165(C2×D43)⋊C8C2314yescomplemented
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43—21no—
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43C2311yescharacteristic
170C2×SD16×C43—42no—
171C2×SD16×C43C2314yes—
172C22×C8×C43—42no—
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2314yescomplemented
176C22⋊Q8×C43—22no—
177C22⋊Q8×C43C2314yescomplemented
178#121×C43—22no—
179#121×C43C2314yes—
180C2×C4⋊C4×C43—21no—
181C2×C4⋊C4×C43C2311yescharacteristic
182C2×C4⋊C4×C43C2311yescharacteristic
183C2×C22⋊C4×C43—21no—
184C2×C22⋊C4×C43—21no—
185#106×C43C2314yescomplemented
186#103×C43C2314yescomplemented
187#102×C43C2314yes—
188C24×C43—21no—
189C24×C43C2×D411yescharacteristic
190C23×D43—21no—
191C23×D43—24no—
192C23×D43—44no—
193C23×D43—82no—
194C23×D43—82no—
195C23×D43C2×D411yescharacteristic
196C23×D43C2×D411yescharacteristic
197C2×Q8×C43—21no—
198C2×Q8×C43—22no—
199C2×Q8×C43—22no—
200C2×Q8×C43C2412yes—
201C2×D4×C43—21no—
202C2×D4×C43—24no—
203C2×D4×C43—22no—
204C2×D4×C43—22no—
205C2×D4×C43—82no—
206C2×D4×C43C2412yes—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2412yes—
215C22×C4×C43C2411yescharacteristic
216C2×C22⋊D43—24no—
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—42no—
220C2×C22⋊D43—42no—
221C2×C22⋊D43—44no—
222C2×C22⋊D43—82no—
223C2×C22⋊D43—82no—
224C2×C22⋊D43C2×D414yes—
225C2×C22⋊D43C2×D414yes—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231Q8×D43—44no—
232Q8×D43—44no—
233Q8×D43—48no—
234D4×D43—44no—
235D4×D43—44no—
236D4×D43—48no—
237#10621898—48no—
238#10621898—44no—
239#10621898—44no—
240C2×D172—21no—
241C2×D172—24no—
242C2×D172—22no—
243C2×D172—22no—
244C2×D172—42no—
245C2×D172—82no—
246C2×D172C2×D414yes—
247C2×D172C2412yes—
248C2×C4×D43—22no—
249C2×C4×D43—22no—
250C2×C4×D43—22no—
251C2×C4×D43—22no—
252C2×C4×D43—24no—
253C2×C4×D43—44no—
254C2×C4×D43C2×D412yes—
255C2×C4×D43C2×D412yes—
256C2×C4×D43C2412yes—
257C2×C4×D43C2412yes—
258C2×Dic86—22no—
259C2×Dic86—22no—
260C2×Dic86—21no—
261C2×Dic86—24no—
262C2×Dic86—42no—
263C2×Dic86—44no—
264C2×Dic86C2×D414yes—
265C2×Dic86C2412yes—
266SD16×C43—44no—
267C2×C8×C43—22no—
268C2×C8×C43—22no—
269C2×C8×C43—44no—
270C2×C8×C43C2412yes—
271C2×C8×C43C2412yes—
272C4⋊C4×C43—24no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43C2412yes—
276C4⋊C4×C43C2412yes—
277C22⋊C4×C43—24no—
278C22⋊C4×C43—24no—
279C22⋊Dic43—24no—
280C22⋊Dic43—24no—
281#10621884—44no—
282#10621883—44no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4—24no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—24no—
287(C2×D43)⋊C4—24no—
288(C2×D43)⋊C4—24no—
289C4⋊Dic43—21no—
290C4⋊Dic43—21no—
291C4⋊Dic43—24no—
292C4⋊Dic43C2412yes—
293C4⋊Dic43C2412yes—
294Dic43⋊C4—24no—
295Dic43⋊C4—24no—
296C4×Dic43—24no—
297C4×Dic43—24no—
298#10621877—44no—
299C2×C43⋊C8—22no—
300C2×C43⋊C8—22no—
301C2×C43⋊C8C2412yes—
302C2×C43⋊C8C2412yes—
303#10621873—44no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—42no—
309C23×C43—42no—
310C23×C43—42no—
311C23×C43C22×D412yes—
312C23×C43C22×D411yescharacteristic
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—48no—
321C22×D43—42no—
322C22×D43—42no—
323C22×D43—42no—
324C22×D43—84no—
325C22×D43—84no—
326C22×D43—816no—
327C22×D43C22×D412yes—
328C22×D43C22×D412yes—
329Q8×C43—22no—
330Q8×C43—22no—
331Q8×C43—42no—
332D4×C43—22no—
333D4×C43—22no—
334D4×C43—42no—
335D4×C43—84no—
336C2×C4×C43—22no—
337C2×C4×C43—24no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—42no—
344C2×C4×C43—42no—
345C2×C4×C43—42no—
346C2×C4×C43C22×D412yes—
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43H(5,𝔽2)12yes—
349C2×C4×C43H(5,𝔽2)12yes—
350C2×C4×C43C2511yescharacteristic
351C22⋊D43—44no—
352C22⋊D43—44no—
353C22⋊D43—48no—
354C22⋊D43—84no—
355C22⋊D43—84no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—42no—
362C2×Dic43—42no—
363C2×Dic43—42no—
364C2×Dic43C22×D412yes—
365C2×Dic43C22×D412yes—
366D172—22no—
367D172—22no—
368D172—44no—
369D172—42no—
370D172—84no—
371C4×D43—24no—
372C4×D43—24no—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—48no—
378Dic86—22no—
379Dic86—22no—
380Dic86—44no—
381Dic86—48no—
382Dic86—42no—
383C8×C43—22no—
384C8×C43—22no—
385C43⋊C8—22no—
386C43⋊C8—22no—
387C2×#3200—431nomaximal, Sylow
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—44no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—84no—
396C22×C43#53412yes—
397C22×C43#57712yes—
398C22×C43#57712yes—
399C22×C43C23×D411yescharacteristic
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—22no—
406C2×D43—44no—
407C2×D43—44no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—816no—
412C2×D43—84no—
413C4×C43—22no—
414C4×C43—42no—
415C4×C43—42no—
416C4×C43—42no—
417C4×C43#53412yes—
418C4×C43C2×H(5,𝔽2)11yescharacteristic
419C4×C43C2×H(5,𝔽2)11yescharacteristic
420Dic43—22no—
421Dic43—22no—
422Dic43—42no—
423Dic43—42no—
424Dic43—42no—
425C2×#536—431no—
426C2×#535—431no—
427#3200—4316no—
428C2×#485—431no—
429C2×#485—431no—
430C2×#482—431no—
431C2×#482—431no—
432C2×#468—431no—
433C2×#468—431no—
434C2×#465—431no—
435C2×#465D4311yescharacteristic, complemented
436C2×#448—431no—
437C2×#448—431no—
438C2×#450—431no—
439C2×#450—431no—
440C2×#408—431no—
441C2×C43—42no—
442C2×C43—82no—
443C2×C43#320014yescomplemented
444C2×C43C2×#53411yescharacteristic
445C2×C43C2×#57711yescharacteristic
446C2×C43C2×#57711yescharacteristic
447D43—42no—
448D43—42no—
449D43—82no—
450C22×#41—431no—
451C23×Q8—431no—
452C23×D4—431no—
453C22×SD16—431no—
454C22×SD16—431no—
455C22×SD16—431no—
456C22×SD16C2×D4311yescharacteristic
457C22×M16—431no—
458C23×C8C2×D4311yescharacteristic, complemented
459#536—438no—
460#536—864no—
461#535—438no—
462#535—864no—
463C2×C4⋊Q8—861no—
464C2×#127—861no—
465C2×#124—861no—
466C2×#124—861no—
467C2×#123—861no—
468C2×#123—861no—
469C2×C22⋊Q8—431no—
470C2×C22⋊Q8—431no—
471C2×C22⋊Q8—431no—
472C2×C22⋊Q8C2×D4311yescharacteristic, complemented
473C2×#121—431no—
474C2×#121—431no—
475C2×#121—431no—
476C2×#121C2×D4311yescharacteristic
477C2×#120—861no—
478C2×#120—861no—
479C2×#117—431no—
480C2×#117—431no—
481#485—438no—
482#485—438no—
483#482—438no—
484#482—438no—
485#468—438no—
486#468—438no—
487#465—438no—
488#465C2×D4318yescomplemented
489#450—438no—
490#450—438no—
491#448—438no—
492#448—438no—
493C2×#107—431no—
494C2×#107—431no—
495C2×#106—431no—
496C2×#106C2×D4311yescharacteristic, complemented
497C2×#103—431no—
498C2×#103—431no—
499C2×#103—431no—
500C2×#103C2×D4311yescharacteristic, complemented
501C2×#102—431no—
502C2×#102—431no—
503C2×#102—431no—
504C2×#102C2×D4311yescharacteristic
505#408—438no—
506C2×C22⋊C8—431no—
507C2×C22⋊C8—431no—
508C2×C22⋊C8—431no—
509C2×C22⋊C8—431no—
510C43C2×#320011yescharacteristic, complemented, Sylow
511C25—861no—
512C2×#41—434no—
513C2×#41—434no—
514C2×#41—1722no—
515C2×#41—1722no—
516C22×Q8—431no—
517C22×Q8—434no—
518C22×Q8—431no—
519C22×Q8—861no—
520C22×Q8—862no—
521C22×Q8—1722no—
522C22×Q8—1722no—
523C22×Q8C22×D4311yescharacteristic
524C22×D4—21no—
525C22×D4—431no—
526C22×D4—431no—
527C22×D4—434no—
528C22×D4—431no—
529C22×D4—431no—
530C22×D4—861no—
531C22×D4—862no—
532C22×D4—861no—
533C22×D4—861no—
534C22×D4—861no—
535C22×D4—1722no—
536C22×D4—1722no—
537C22×D4C22×D4311yescharacteristic
538C23×C4—431no—
539C23×C4—431no—
540C23×C4—861no—
541C23×C4C22×D4311yescharacteristic
542C2×SD16—42no—
543C2×SD16—434no—
544C2×SD16—434no—
545C2×SD16—434no—
546C2×SD16—1722no—
547C2×SD16—1722no—
548C2×SD16—1722no—
549C2×SD16C22×D4314yes—
550C2×M16—434no—
551C2×M16—1722no—
552C22×C8—42no—
553C22×C8—431no—
554C22×C8—431no—
555C22×C8C22×D4311yescharacteristic
556C22×C8C22×D4311yescharacteristic
557C22×C8C22×D4314yescomplemented
558C4⋊Q8—868no—
559#127—868no—
560#124—868no—
561#124—868no—
562#123—868no—
563#123—868no—
564C22⋊Q8—22no—
565C22⋊Q8—434no—
566C22⋊Q8—434no—
567C22⋊Q8—434no—
568C22⋊Q8—862no—
569C22⋊Q8—862no—
570C22⋊Q8—862no—
571C22⋊Q8C22×D4314yescomplemented
572#121—22no—
573#121—434no—
574#121—434no—
575#121—434no—
576#121—862no—
577#121—862no—
578#121—862no—
579#121C22×D4314yes—
580#120—868no—
581#120—868no—
582#117—434no—
583#117—434no—
584#117—862no—
585#117—862no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—431no—
589C2×C4⋊C4—861no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4C22×D4311yescharacteristic
593C2×C4⋊C4C22×D4311yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—861no—
597C2×C22⋊C4—861no—
598C2×C22⋊C4—861no—
599C2×C22⋊C4—861no—
600C2×C22⋊C4—861no—
601C2×C22⋊C4—861no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C42—861no—
605C2×C42—861no—
606#107—434no—
607#107—434no—
608#106—434no—
609#106C22×D4314yescomplemented
610#103—434no—
611#103—434no—
612#103—434no—
613#103C22×D4314yescomplemented
614#102—434no—
615#102—434no—
616#102—434no—
617#102C22×D4314yes—
618C22⋊C8—434no—
619C22⋊C8—434no—
620C22⋊C8—434no—
621C22⋊C8—434no—
622C24—21no—
623C24—431no—
624C24—431no—
625C24—864no—
626C24—861no—
627C24—3442no—
628C24—3442no—
629C24—1724no—
630C24D4×D4311yescharacteristic
631#41—1728no—
632#41—1724no—
633#41—1724no—
634C2×Q8—21no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—434no—
638C2×Q8—432no—
639C2×Q8—864no—
640C2×Q8—861no—
641C2×Q8—862no—
642C2×Q8—862no—
643C2×Q8—1722no—
644C2×Q8—1724no—
645C2×Q8—1724no—
646C2×Q8—1724no—
647C2×Q8—1728no—
648C2×Q8C23×D4312yes—
649C2×D4—24no—
650C2×D4—21no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—82no—
654C2×D4—434no—
655C2×D4—434no—
656C2×D4—434no—
657C2×D4—432no—
658C2×D4—864no—
659C2×D4—864no—
660C2×D4—864no—
661C2×D4—864no—
662C2×D4—861no—
663C2×D4—862no—
664C2×D4—862no—
665C2×D4—3442no—
666C2×D4—3442no—
667C2×D4—3442no—
668C2×D4—1722no—
669C2×D4—1724no—
670C2×D4—1724no—
671C2×D4—1728no—
672C2×D4—1722no—
673C2×D4—1722no—
674C2×D4—1724no—
675C2×D4C23×D4312yes—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—431no—
682C22×C4—431no—
683C22×C4—432no—
684C22×C4—432no—
685C22×C4—432no—
686C22×C4—432no—
687C22×C4—864no—
688C22×C4—862no—
689C22×C4—862no—
690C22×C4—862no—
691C22×C4—862no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4—861no—
695C22×C4—1724no—
696C22×C4D4×D4312yes—
697C22×C4D4×D4311yescharacteristic
698C22×C4C23×D4312yes—
699C22×C4C23×D4311yescharacteristic
700SD16—44no—
701SD16—1724no—
702SD16—1724no—
703SD16—1724no—
704M16—1724no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—44no—
708C2×C8—432no—
709C2×C8—432no—
710C2×C8—862no—
711C2×C8—862no—
712C2×C8C23×D4312yes—
713C2×C8C23×D4312yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—432no—
718C4⋊C4—432no—
719C4⋊C4—864no—
720C4⋊C4—864no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4—864no—
724C4⋊C4C23×D4312yes—
725C4⋊C4C23×D4312yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—864no—
729C22⋊C4—864no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C42—864no—
737C42—864no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—432no—
746C23—432no—
747C23—862no—
748C23—862no—
749C23—862no—
750C23—862no—
751C23—862no—
752C23—862no—
753C23—862no—
754C23—3444no—
755C23—3444no—
756C23—34416no—
757C23—1728no—
758C23—1722no—
759C23—1722no—
760C23—1722no—
761C23C2×D4×D4312yes—
762C23C2×D4×D4311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—862no—
767Q8—862no—
768Q8—1724no—
769Q8—1728no—
770Q8—1722no—
771D4—22no—
772D4—22no—
773D4—42no—
774D4—84no—
775D4—862no—
776D4—862no—
777D4—3444no—
778D4—3444no—
779D4—3444no—
780D4—1724no—
781D4—1724no—
782D4—1724no—
783D4—1728no—
784D4—1722no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—432no—
796C2×C4—432no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—864no—
800C2×C4—864no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—1728no—
809C2×C4—1722no—
810C2×C4—1722no—
811C2×C4—1722no—
812C2×C4C2×D4×D4312yes—
813C2×C4C2×D4×D4311yescharacteristic
814C2×C4#1306337012yes—
815C2×C4#1306337112yes—
816C2×C4C24×D4311yescharacteristic
817C8—22no—
818C8—22no—
819C8—862no—
820C8—862no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—84no—
829C22—862no—
830C22—862no—
831C22—862no—
832C22—862no—
833C22—862no—
834C22—862no—
835C22—34416no—
836C22—3444no—
837C22—1722no—
838C22—1722no—
839C22—1722no—
840C22—1724no—
841C22—1724no—
842C22#1458345712yes—
843C22#1458370512yes—
844C22#1458370612yes—
845C22C22×D4×D4311yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—862no—
851C4—862no—
852C4—1722no—
853C4—1722no—
854C4—1722no—
855C4#1458345712yes—
856C4C2×#1306337011yescharacteristic
857C4C2×#1306337111yescharacteristic
858C2—42no—
859C2—82no—
860C2—3442no—
861C2—1722no—
862C2—1722no—
863C2#1914546114yesdirect product factor
864C2C2×#1458345711yescharacteristic
865C2C2×#1458370511yescharacteristic
866C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#465C2
socleC23×C43C22×D4
prime radicalC2×#14583465C2
hypercenterC2×#465D43
hypocenterC43C2×#3200
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#14583472C2semidirect
3. #19145461C2direct (N × H)
4. C2×#14583243C2semidirect
5. C2×#14583238C2semidirect
6. C2×#14583225C2semidirect
7. C2×#14583222C2semidirect
8. C2×#14583147C2semidirect
9. C2×#14583143C2semidirect
10. C2×#14583128C2semidirect
11. C2×#14583039C2semidirect
12. C2×#14583036C2semidirect
13. C2×#14583051C2semidirect
14. C2×#14583048C2semidirect
15. C2×#14582865C2semidirect
16. C2×C43×#465C2semidirect
18. C22×Q8×D43C22semidirect
23. C22×#10621877C22semidirect
25. #14583472C22semidirect
35. C2×#13063304C22semidirect
43. C2×#13063283C22semidirect
44. #14583243C22semidirect
45. #14583238C22semidirect
46. #14583225C22semidirect
47. #14583222C22semidirect
48. #14583147C22semidirect
49. #14583143C22semidirect
50. #14583128C22semidirect
51. #14583051C22semidirect
52. #14583048C22semidirect
53. #14583039C22semidirect
54. #14583036C22semidirect
55. C2×#13063258C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063257C22semidirect
58. C2×#13063250C22semidirect
59. C2×#13063249C22semidirect
60. C2×#13063248C22semidirect
64. #14582865C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
70. C23×C8×C43C22semidirect
71. C2×C22⋊Q8×C43C22semidirect
73. C43×#465C22semidirect
74. C2×#106×C43C22semidirect
75. C2×#103×C43C22semidirect
88. C2×Q8×D43C23semidirect
111. C2×#10621877C23semidirect
123. #13063304C23semidirect
137. #13063283C23semidirect
153. #13063258C23semidirect
154. #13063258C23semidirect
155. #13063257C23semidirect
156. #13063250C23semidirect
157. #13063249C23semidirect
158. #13063248C23semidirect
164. (C2×D43)⋊C8C23semidirect
165. (C2×D43)⋊C8C23semidirect
175. C22×C8×C43C23semidirect
177. C22⋊Q8×C43C23semidirect
185. #106×C43C23semidirect
186. #103×C43C23semidirect
435. C2×#465D43semidirect
443. C2×C43#3200semidirect
458. C23×C8C2×D43semidirect
472. C2×C22⋊Q8C2×D43semidirect
488. #465C2×D43semidirect
496. C2×#106C2×D43semidirect
500. C2×#103C2×D43semidirect
510. C43C2×#3200semidirect
557. C22×C8C22×D43semidirect
571. C22⋊Q8C22×D43semidirect
609. #106C22×D43semidirect
613. #103C22×D43semidirect
863. C2#19145461direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834722
C2×#145834652
#191454612
C2×#145832432
C2×#145832382
C2×#145832252
C2×#145832222
C2×#145831472
C2×#145831432
C2×#145831282
C2×#145830392
C2×#145830362
C2×#145830512
C2×#145830482
C2×#145828652
C2×C43×#4652
C2×#320043