Finite Group Databasebeta

← C2×#19145387 #25967161

Subgroups — C2×#19145387 #25967161

Order 11008.

2394 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×#14583412C211yesmaximal, characteristic, complemented
2C2×#14583406C211yesmaximal, characteristic, complemented
3#19145387C2116yesmaximal, direct product factor
4C2×#14583238C211yesmaximal, characteristic, complemented
5C2×#14583237C211yesmaximal, characteristic, complemented
6C2×#14583224C211yesmaximal, characteristic, complemented
7C2×#14583221C211yesmaximal, characteristic, complemented
8C2×#14583137C211yesmaximal, characteristic, complemented
9C2×#14583134C211yesmaximal, characteristic, complemented
10C2×#14583131C211yesmaximal, characteristic, complemented
11C2×#14583125C211yesmaximal, characteristic, complemented
12C2×#14583060C211yesmaximal, characteristic, complemented
13C2×#14583044C211yesmaximal, characteristic, complemented
14C2×#14583043C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D43C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×#10621884C2211yescharacteristic, complemented
20C22×#10621882C2211yescharacteristic, complemented
21C22×C8×D43C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23#14583412—24no—
24#14583412C2218yescomplemented
25#14583406—24no—
26#14583406C2218yescomplemented
27C2×#13063310—21no—
28C2×#13063306—21no—
29C2×#13063301C2211yescharacteristic
30C2×#13063301C2211yescharacteristic
31C2×#13063301C2211yescharacteristic
32C2×#13063300C2211yescharacteristic
33C2×#13063299C2211yescharacteristic
34C2×#13063296C2211yescharacteristic
35C2×#13063296C2211yescharacteristic
36C2×#13063295—21no—
37C2×#13063293—21no—
38C2×#13063287—21no—
39C2×C4×C22⋊D43—21no—
40C2×C4×C22⋊D43—21no—
41C2×(C22⋊D43)⋊C4—21no—
42C2×#13063284C2211yescharacteristic
43C2×#13063283C2211yescharacteristic
44#14583238C2218yescomplemented
45#14583237C2218yescomplemented
46#14583224C2218yescomplemented
47#14583221C2218yescomplemented
48#14583137C2218yescomplemented
49#14583134C2218yescomplemented
50#14583131C2218yescomplemented
51#14583125C2218yescomplemented
52#14583060C2218yescomplemented
53#14583044C2218yescomplemented
54#14583043C2218yescomplemented
55C2×#13063259C2211yescharacteristic, complemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063257C2211yescharacteristic, complemented
58C2×#13063256C2211yescharacteristic, complemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063249C2211yescharacteristic, complemented
61C2×#13063249C2211yescharacteristic, complemented
62C2×#13063247C2211yescharacteristic, complemented
63C2×#13063247C2211yescharacteristic, complemented
64C2×#13063246C2211yescharacteristic, complemented
65C2×C22⋊(C43⋊C8)C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C22⋊C8×D43C2218yescomplemented
69C22×#41×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic, complemented
71C22×SD16×C43C2211yescharacteristic, complemented
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#452C2218yescomplemented
74C2×#103×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic, complemented
76C2×C22⋊C8×C43C2211yescharacteristic
77C24×D43D411yescharacteristic
78C2×#10621902—22no—
79C2×#10621902—42no—
80C2×#10621902—42no—
81C2×#10621902C2314yes—
82C22×D172—21no—
83C22×D172—21no—
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C23×Dic43D411yescharacteristic
89C22×C4×D43—21no—
90C22×C4×D43—42no—
91C22×C4×D43—42no—
92C22×C4×D43D411yescharacteristic
93C22×C4×D43D411yescharacteristic
94C22×C4×D43D414yes—
95C22×C4×D43C2311yescharacteristic
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2314yes—
98C2×#10621884—42no—
99C2×#10621884C2314yescomplemented
100C2×#10621882—42no—
101C2×#10621882C2314yescomplemented
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104C2×C8×D43—42no—
105C2×C8×D43—42no—
106C2×C8×D43C2314yes—
107C2×C8×D43C2314yes—
108#13063310—28no—
109#13063306—28no—
110#13063301—22no—
111#13063301—22no—
112#13063301—22no—
113#13063301C2314yes—
114#13063301C2314yes—
115#13063301C2314yes—
116#13063300—22no—
117#13063300C2314yes—
118#13063299—22no—
119#13063299C2314yes—
120#13063296—22no—
121#13063296—22no—
122#13063296C2314yes—
123#13063296C2314yes—
124#13063295—28no—
125#13063293—28no—
126#13063287—28no—
127C4×C22⋊D43—28no—
128C4×C22⋊D43—28no—
129(C22⋊D43)⋊C4—28no—
130#13063284—22no—
131#13063284C2314yes—
132#13063283—22no—
133#13063283C2314yes—
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151#13063259C2314yescomplemented
152#13063258C2314yescomplemented
153#13063257C2314yescomplemented
154#13063256C2314yescomplemented
155#13063249C2314yescomplemented
156#13063249C2314yescomplemented
157#13063249C2314yescomplemented
158#13063247C2314yescomplemented
159#13063247C2314yescomplemented
160#13063246C2314yescomplemented
161C22⋊(C43⋊C8)C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164C2×#41×C43—22no—
165C2×#41×C43—42no—
166C2×#41×C43—42no—
167C2×#41×C43C2314yes—
168C22×Q8×C43C2311yescharacteristic
169C22×Q8×C43C2311yescharacteristic
170C22×D4×C43—21no—
171C22×D4×C43C2311yescharacteristic
172C23×C4×C43—21no—
173C23×C4×C43C2311yescharacteristic
174C2×Q16×C43—42no—
175C2×Q16×C43C2314yescomplemented
176C2×SD16×C43—42no—
177C2×SD16×C43C2314yescomplemented
178C22×C8×C43C2311yescharacteristic
179C22×C8×C43C2311yescharacteristic
180C22⋊Q8×C43—22no—
181C22⋊Q8×C43C2314yes—
182C2×C4⋊C4×C43—21no—
183C2×C4⋊C4×C43C2311yescharacteristic
184C2×C22⋊C4×C43—21no—
185#103×C43C2314yescomplemented
186#102×C43C2314yescomplemented
187C22⋊C8×C43C2314yes—
188C24×C43—21no—
189C24×C43C2×D411yescharacteristic
190C23×D43—24no—
191C23×D43—21no—
192C23×D43—42no—
193C23×D43—42no—
194C23×D43C2×D411yescharacteristic
195C23×D43C2×D411yescharacteristic
196C23×D43C2×D414yes—
197#41×C43—44no—
198#41×C43—44no—
199#41×C43—48no—
200C2×Q8×C43—21no—
201C2×Q8×C43—21no—
202C2×Q8×C43—22no—
203C2×Q8×C43—22no—
204C2×Q8×C43—22no—
205C2×Q8×C43—22no—
206C2×Q8×C43C2412yes—
207C2×Q8×C43C2412yes—
208C2×D4×C43—21no—
209C2×D4×C43—24no—
210C2×D4×C43—22no—
211C2×D4×C43—22no—
212C2×D4×C43—44no—
213C2×D4×C43C2412yes—
214C22×C4×C43—22no—
215C22×C4×C43—22no—
216C22×C4×C43—24no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—44no—
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D412yes—
223C22×C4×C43C2412yes—
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—24no—
226C2×C22⋊D43—24no—
227C2×C22⋊D43—24no—
228C2×C22⋊D43—44no—
229C2×C22⋊D43—44no—
230C2×C22⋊D43—44no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—42no—
235C22×Dic43C2×D411yescharacteristic
236C22×Dic43C2×D411yescharacteristic
237C22×Dic43C2×D414yes—
238#10621902—44no—
239#10621902—44no—
240#10621902—48no—
241C2×D172—21no—
242C2×D172—24no—
243C2×D172—24no—
244C2×D172—22no—
245C2×D172—22no—
246C2×D172—44no—
247C2×D172—44no—
248C2×D172C2412yes—
249C2×C4×D43—22no—
250C2×C4×D43—22no—
251C2×C4×D43—22no—
252C2×C4×D43—22no—
253C2×C4×D43—24no—
254C2×C4×D43—42no—
255C2×C4×D43—42no—
256C2×C4×D43—48no—
257C2×C4×D43—44no—
258C2×C4×D43—44no—
259C2×C4×D43—44no—
260C2×C4×D43C2×D412yes—
261C2×C4×D43C2×D412yes—
262C2×C4×D43C2×D414yes—
263C2×C4×D43C2×D414yes—
264C2×C4×D43C2412yes—
265C2×C4×D43C2412yes—
266Q16×C43—44no—
267SD16×C43—44no—
268C2×C8×C43—22no—
269C2×C8×C43—22no—
270C2×C8×C43C2412yes—
271C2×C8×C43C2412yes—
272C4⋊C4×C43—24no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43C2412yes—
275C22⋊C4×C43—24no—
276C22⋊Dic43—24no—
277C22⋊Dic43—24no—
278C22⋊Dic43—24no—
279#10621884—44no—
280#10621882—44no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4—24no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—24no—
287C4⋊Dic43—21no—
288C4⋊Dic43—21no—
289C4⋊Dic43—21no—
290C4⋊Dic43C2412yes—
291C4⋊Dic43C2412yes—
292C4⋊Dic43C2412yes—
293Dic43⋊C4—24no—
294Dic43⋊C4—24no—
295Dic43⋊C4—24no—
296C4×Dic43—24no—
297C4×Dic43—24no—
298C2×C43⋊C8—22no—
299C2×C43⋊C8—22no—
300C2×C43⋊C8C2412yes—
301C2×C43⋊C8C2412yes—
302C8×D43—44no—
303C8×D43—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—28no—
319C22×D43—22no—
320C22×D43—44no—
321C22×D43—44no—
322C22×D43—416no—
323C22×D43—42no—
324C22×D43—42no—
325C22×D43—42no—
326C22×D43#13514yes—
327C22×D43C22×D412yes—
328C22×D43C22×D412yes—
329Q8×C43—22no—
330Q8×C43—22no—
331Q8×C43—22no—
332Q8×C43—22no—
333Q8×C43—42no—
334Q8×C43—42no—
335D4×C43—22no—
336D4×C43—22no—
337D4×C43—48no—
338D4×C43—42no—
339C2×C4×C43—22no—
340C2×C4×C43—24no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—48no—
347C2×C4×C43—42no—
348C2×C4×C43—42no—
349C2×C4×C43—42no—
350C2×C4×C43C22×D412yes—
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43H(5,𝔽2)12yes—
353C2×C4×C43H(5,𝔽2)12yes—
354C2×C4×C43C2511yescharacteristic
355C22⋊D43—48no—
356C22⋊D43—48no—
357C22⋊D43—48no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—44no—
364C2×Dic43—42no—
365C2×Dic43—42no—
366C2×Dic43—42no—
367C2×Dic43C22×D412yes—
368C2×Dic43C22×D412yes—
369D172—22no—
370D172—22no—
371D172—48no—
372D172—48no—
373D172—42no—
374C4×D43—24no—
375C4×D43—24no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—44no—
381C4×D43—44no—
382C4×D43—48no—
383C8×C43—22no—
384C8×C43—22no—
385C43⋊C8—22no—
386C43⋊C8—22no—
387C2×#3191—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×C43C2×#13512yes—
398C22×C43#57512yes—
399C22×C43C23×D411yescharacteristic
400C2×D43—22no—
401C2×D43—28no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—22no—
406C2×D43—416no—
407C2×D43—44no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—84no—
412C2×D43C2×#13514yes—
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×#525—431no—
426C2×#525—431no—
427#3191—4316no—
428C2×#485—431no—
429C2×#485—431no—
430C2×#482—431no—
431C2×#482—431no—
432C2×#467—431no—
433C2×#466—431no—
434C2×#465—431no—
435C2×#465—431no—
436C2×#452—431no—
437C2×#452D4311yescharacteristic, complemented
438C2×#449—431no—
439C2×#449—431no—
440C22×C22⋊C8—431no—
441C2×C43—42no—
442C2×C43—82no—
443C2×C43#319114yescomplemented
444C2×C43C2×#53411yescharacteristic
445C2×C43C22×#13511yescharacteristic
446C2×C43C2×#57511yescharacteristic
447D43—24no—
448D43—42no—
449D43—82no—
450C22×#41—431no—
451C22×#41C2×D4311yescharacteristic
452C24×C4—431no—
453C22×Q16C2×D4311yescharacteristic, complemented
454C22×SD16—431no—
455C22×SD16C2×D4311yescharacteristic, complemented
456C22×D8—431no—
457C23×C8—431no—
458C23×C8—431no—
459#525—438no—
460#525—438no—
461#525—864no—
462#525—864no—
463C2×#123—861no—
464C2×#123—861no—
465C2×C22⋊Q8—431no—
466C2×C22⋊Q8—431no—
467C2×C22⋊Q8—431no—
468C2×C22⋊Q8C2×D4311yescharacteristic
469C2×#121—431no—
470C2×#121—431no—
471C2×#121—431no—
472C2×#121—431no—
473C2×#120—861no—
474C2×#120—861no—
475C2×C4×D4—861no—
476C2×C4×D4—861no—
477C2×C4×D4—861no—
478C2×C4×D4—861no—
479C2×#117—431no—
480C2×#117—431no—
481#485—438no—
482#485—438no—
483#482—438no—
484#482—438no—
485#467—438no—
486#466—438no—
487#465—438no—
488#465—438no—
489#452—438no—
490#452C2×D4318yescomplemented
491#449—438no—
492#449—438no—
493C2×#107—431no—
494C2×#107—431no—
495C2×#106—431no—
496C2×#106—431no—
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, complemented
505C2×C22⋊C8—431no—
506C2×C22⋊C8—431no—
507C2×C22⋊C8—431no—
508C2×C22⋊C8—438no—
509C2×C22⋊C8C2×D4311yescharacteristic
510C43C2×#319111yescharacteristic, complemented, Sylow
511C25—431no—
512C2×#41—22no—
513C2×#41—42no—
514C2×#41—42no—
515C2×#41—434no—
516C2×#41—862no—
517C2×#41—1722no—
518C2×#41—1722no—
519C2×#41C22×D4314yes—
520C22×Q8C22×D4311yescharacteristic
521C22×Q8C22×D4311yescharacteristic
522C22×D4—21no—
523C22×D4—431no—
524C22×D4—861no—
525C22×D4—861no—
526C22×D4—861no—
527C22×D4—861no—
528C22×D4—861no—
529C22×D4C22×D4311yescharacteristic
530C23×C4—21no—
531C23×C4—431no—
532C23×C4—431no—
533C23×C4—431no—
534C23×C4—431no—
535C23×C4—431no—
536C23×C4—434no—
537C23×C4—434no—
538C23×C4—861no—
539C23×C4—1722no—
540C23×C4—1722no—
541C23×C4C22×D4311yescharacteristic
542C2×Q16—42no—
543C2×Q16C22×D4314yescomplemented
544C2×SD16—42no—
545C2×SD16—434no—
546C2×SD16—1722no—
547C2×SD16C22×D4314yescomplemented
548C2×D8—434no—
549C2×D8—1722no—
550C22×C8—431no—
551C22×C8—431no—
552C22×C8—434no—
553C22×C8—434no—
554C22×C8—1722no—
555C22×C8—1722no—
556C22×C8C22×D4311yescharacteristic
557C22×C8C22×D4311yescharacteristic
558#123—868no—
559#123—868no—
560C22⋊Q8—22no—
561C22⋊Q8—434no—
562C22⋊Q8—434no—
563C22⋊Q8—434no—
564C22⋊Q8—862no—
565C22⋊Q8—862no—
566C22⋊Q8—862no—
567C22⋊Q8C22×D4314yes—
568#121—434no—
569#121—434no—
570#121—434no—
571#121—434no—
572#121—862no—
573#121—862no—
574#121—862no—
575#121—862no—
576#120—868no—
577#120—868no—
578C4×D4—868no—
579C4×D4—868no—
580C4×D4—868no—
581C4×D4—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—431no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4C22×D4311yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—861no—
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#106—434no—
610#103—434no—
611#103—434no—
612#103—434no—
613#103C22×D4314yescomplemented
614#102—434no—
615#102—434no—
616#102—434no—
617#102C22×D4314yescomplemented
618C22⋊C8—434no—
619C22⋊C8—434no—
620C22⋊C8—434no—
621C22⋊C8C22×D4314yes—
622C24—21no—
623C24—431no—
624C24—431no—
625C24—434no—
626C24—864no—
627C24—861no—
628C24—1722no—
629C24—1722no—
630C24D4×D4311yescharacteristic
631#41—44no—
632#41—44no—
633#41—48no—
634#41—1724no—
635#41—1724no—
636#41—1728no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—22no—
643C2×Q8C23×D4312yes—
644C2×Q8C23×D4312yes—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—44no—
650C2×D4—432no—
651C2×D4—864no—
652C2×D4—864no—
653C2×D4—864no—
654C2×D4—864no—
655C2×D4—864no—
656C2×D4—861no—
657C2×D4—862no—
658C2×D4—862no—
659C2×D4—1724no—
660C2×D4—1724no—
661C2×D4—1724no—
662C2×D4—1724no—
663C2×D4—1724no—
664C2×D4C23×D4312yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—24no—
671C22×C4—44no—
672C22×C4—431no—
673C22×C4—431no—
674C22×C4—434no—
675C22×C4—432no—
676C22×C4—432no—
677C22×C4—432no—
678C22×C4—432no—
679C22×C4—434no—
680C22×C4—434no—
681C22×C4—864no—
682C22×C4—862no—
683C22×C4—862no—
684C22×C4—862no—
685C22×C4—862no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—1728no—
690C22×C4—1724no—
691C22×C4—1724no—
692C22×C4—1722no—
693C22×C4—1722no—
694C22×C4—1724no—
695C22×C4—1722no—
696C22×C4D4×D4312yes—
697C22×C4D4×D4311yescharacteristic
698C22×C4C23×D4312yes—
699C22×C4C23×D4311yescharacteristic
700Q16—44no—
701SD16—44no—
702SD16—1724no—
703D8—1724no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—432no—
707C2×C8—432no—
708C2×C8—862no—
709C2×C8—862no—
710C2×C8—1724no—
711C2×C8—1724no—
712C2×C8C23×D4312yes—
713C2×C8C23×D4312yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—432no—
717C4⋊C4—432no—
718C4⋊C4—432no—
719C4⋊C4—864no—
720C4⋊C4—864no—
721C4⋊C4—864no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4C23×D4312yes—
726C22⋊C4—24no—
727C22⋊C4—864no—
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—434no—
746C23—432no—
747C23—432no—
748C23—868no—
749C23—862no—
750C23—862no—
751C23—862no—
752C23—862no—
753C23—862no—
754C23—862no—
755C23—1724no—
756C23—1724no—
757C23—17216no—
758C23—1722no—
759C23—1722no—
760C23—1722no—
761C23C2×D4×D4312yes—
762C23C2×D4×D4311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—42no—
768Q8—42no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—42no—
773D4—862no—
774D4—862no—
775D4—1728no—
776D4—1728no—
777D4—1728no—
778D4—1728no—
779D4—1728no—
780D4—1722no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—48no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—432no—
793C2×C4—432no—
794C2×C4—862no—
795C2×C4—862no—
796C2×C4—864no—
797C2×C4—864no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—1724no—
806C2×C4—1724no—
807C2×C4—1728no—
808C2×C4—1724no—
809C2×C4—1722no—
810C2×C4—1722no—
811C2×C4—1722no—
812C2×C4C2×D4×D4312yes—
813C2×C4C2×D4×D4311yescharacteristic
814C2×C4#1306337012yes—
815C2×C4#1306337012yes—
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—434no—
830C22—862no—
831C22—862no—
832C22—868no—
833C22—862no—
834C22—862no—
835C22—862no—
836C22—3444no—
837C22—17216no—
838C22—1722no—
839C22—1722no—
840C22—1722no—
841C22—1724no—
842C22#1458345912yes—
843C22#135×D4312yes—
844C22#1458369812yes—
845C22C22×D4×D4311yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—862no—
851C4—862no—
852C4—1722no—
853C4—1722no—
854C4—1722no—
855C4#1458345912yes—
856C4C2×#1306337011yescharacteristic
857C4C2×#1306337011yescharacteristic
858C2—42no—
859C2—82no—
860C2—864no—
861C2—3442no—
862C2—1722no—
863C2#1914538714yesdirect product factor
864C2C2×#1458345911yescharacteristic
865C2C2×#135×D4311yescharacteristic
866C2C2×#1458369811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
hypercenterC2×#452D43
hypocenterC43C2×#3191
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#14583412C2semidirect
2. C2×#14583406C2semidirect
3. #19145387C2direct (N × H)
4. C2×#14583238C2semidirect
5. C2×#14583237C2semidirect
6. C2×#14583224C2semidirect
7. C2×#14583221C2semidirect
8. C2×#14583137C2semidirect
9. C2×#14583134C2semidirect
10. C2×#14583131C2semidirect
11. C2×#14583125C2semidirect
12. C2×#14583060C2semidirect
13. C2×#14583044C2semidirect
14. C2×#14583043C2semidirect
15. C2×C22⋊C8×D43C2semidirect
16. C2×C43×#452C2semidirect
19. C22×#10621884C22semidirect
20. C22×#10621882C22semidirect
24. #14583412C22semidirect
26. #14583406C22semidirect
44. #14583238C22semidirect
45. #14583237C22semidirect
46. #14583224C22semidirect
47. #14583221C22semidirect
48. #14583137C22semidirect
49. #14583134C22semidirect
50. #14583131C22semidirect
51. #14583125C22semidirect
52. #14583060C22semidirect
53. #14583044C22semidirect
54. #14583043C22semidirect
55. C2×#13063259C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063257C22semidirect
58. C2×#13063256C22semidirect
59. C2×#13063249C22semidirect
60. C2×#13063249C22semidirect
61. C2×#13063249C22semidirect
62. C2×#13063247C22semidirect
63. C2×#13063247C22semidirect
64. C2×#13063246C22semidirect
68. C22⋊C8×D43C22semidirect
70. C22×Q16×C43C22semidirect
71. C22×SD16×C43C22semidirect
73. C43×#452C22semidirect
74. C2×#103×C43C22semidirect
75. C2×#102×C43C22semidirect
99. C2×#10621884C23semidirect
101. C2×#10621882C23semidirect
151. #13063259C23semidirect
152. #13063258C23semidirect
153. #13063257C23semidirect
154. #13063256C23semidirect
155. #13063249C23semidirect
156. #13063249C23semidirect
157. #13063249C23semidirect
158. #13063247C23semidirect
159. #13063247C23semidirect
160. #13063246C23semidirect
175. C2×Q16×C43C23semidirect
177. C2×SD16×C43C23semidirect
185. #103×C43C23semidirect
186. #102×C43C23semidirect
437. C2×#452D43semidirect
443. C2×C43#3191semidirect
453. C22×Q16C2×D43semidirect
455. C22×SD16C2×D43semidirect
490. #452C2×D43semidirect
500. C2×#103C2×D43semidirect
504. C2×#102C2×D43semidirect
510. C43C2×#3191semidirect
543. C2×Q16C22×D43semidirect
547. C2×SD16C22×D43semidirect
613. #103C22×D43semidirect
617. #102C22×D43semidirect
863. C2#19145387direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834122
C2×#145834062
#191453872
C2×#145832382
C2×#145832372
C2×#145832242
C2×#145832212
C2×#145831372
C2×#145831342
C2×#145831312
C2×#145831252
C2×#145830602
C2×#145830442
C2×#145830432
C2×C22⋊C8×D432
C2×C43×#4522
C2×#319143