Finite Group Databasebeta

← C2×#19145993 #25969482

Subgroups — C2×#19145993 #25969482

Order 11008.

1930 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583431C211yesmaximal, characteristic, complemented
2C2×#14583428C211yesmaximal, characteristic, complemented
3#19145993C2116yesmaximal, direct product factor
4C2×#14583207C211yesmaximal, characteristic, complemented
5C2×#14583204C211yesmaximal, characteristic, complemented
6C2×#14583199C211yesmaximal, characteristic, complemented
7C2×#14583197C211yesmaximal, characteristic, complemented
8C2×#14583156C211yesmaximal, characteristic, complemented
9C2×#14583149C211yesmaximal, characteristic
10C2×#14583144C211yesmaximal, characteristic, complemented
11C2×#14583142C211yesmaximal, characteristic, complemented
12C2×#14583119C211yesmaximal, characteristic, complemented
13C2×#14583118C211yesmaximal, characteristic, complemented
14C2×#14583112C211yesmaximal, characteristic, complemented
15C2×#14582921C211yesmaximal, characteristic, complemented
16C2×C43×#463C211yesmaximal, characteristic, complemented
17C22×#10621885C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21#14583431—24no—
22#14583431C2218yescomplemented
23#14583428—24no—
24#14583428C2218yescomplemented
25C2×#13063318—21no—
26C2×#13063318—21no—
27C2×#13063317C2211yescharacteristic
28C2×#13063316C2211yescharacteristic
29C2×#13063312C2211yescharacteristic
30C2×#13063307—21no—
31C2×#13063307—21no—
32C2×#13063305C2211yescharacteristic
33C2×#13063301C2211yescharacteristic
34C2×#13063296C2211yescharacteristic
35C2×#13063296C2211yescharacteristic
36C2×Q8×Dic43C2211yescharacteristic
37C2×C4×Dic86C2211yescharacteristic
38C2×D4×Dic43C2211yescharacteristic
39C2×C4×C22⋊D43—21no—
40C2×(C22⋊D43)⋊C4—21no—
41C2×#13063284—21no—
42C2×#13063281—21no—
43C2×C42×D43C2211yescharacteristic
44#14583207C2218yescomplemented
45#14583204C2218yescomplemented
46#14583199C2218yescomplemented
47#14583197C2218yescomplemented
48#14583156C2218yescomplemented
49#14583149C2218yes—
50#14583144C2218yescomplemented
51#14583142C2218yescomplemented
52#14583119C2218yescomplemented
53#14583118C2218yescomplemented
54#14583112C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59#14582921C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063249C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×#13063246C2211yescharacteristic
68C2×#13063246C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C22×D8×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×D4×C43C2211yescharacteristic
73C43×#463C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×C22⋊D43—21no—
79C22×C22⋊D43—21no—
80C23×Dic43—21no—
81C22×C4×D43D411yescharacteristic
82C22×C4×D43D411yescharacteristic
83C22×C4×D43C2311yescharacteristic
84C2×#10621885—42no—
85C2×#10621885C2314yes—
86C2×#10621883—42no—
87C2×#10621883C2314yes—
88C2×#10621872—42no—
89C2×#10621872—42no—
90C2×#10621872C2314yes—
91C2×#10621872C2314yes—
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94#13063318—28no—
95#13063318—28no—
96#13063317—22no—
97#13063317C2314yes—
98#13063316—22no—
99#13063316C2314yes—
100#13063312—22no—
101#13063312C2314yes—
102#13063307—28no—
103#13063307—28no—
104#13063305—22no—
105#13063305C2314yes—
106#13063301—22no—
107#13063301C2314yes—
108#13063296—22no—
109#13063296—22no—
110#13063296C2314yes—
111#13063296C2314yes—
112Q8×Dic43—22no—
113Q8×Dic43C2314yes—
114C4×Dic86—22no—
115C4×Dic86C2314yes—
116D4×Dic43—22no—
117D4×Dic43C2314yes—
118C4×C22⋊D43—28no—
119(C22⋊D43)⋊C4—28no—
120#13063284—28no—
121#13063281—28no—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×C22⋊Dic43—21no—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43C2311yescharacteristic
145C42×D43D414yes—
146C42×D43C2314yes—
147#13063259C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063256C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152Dic43⋊C8C2314yes—
153Dic43⋊C8C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063249C2314yes—
157#13063246C2314yes—
158#13063246C2314yes—
159#13063246C2314yes—
160C22×Q8×C43C2311yescharacteristic
161C22×D4×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C2×SD16×C43—42no—
165C2×SD16×C43C2314yes—
166C2×D8×C43—42no—
167C2×D8×C43C2314yes—
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170#124×C43—22no—
171#124×C43C2314yes—
172C4×D4×C43—22no—
173C4×D4×C43C2314yes—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43—21no—
178C2×C42×C43C2311yescharacteristic
179C4⋊C8×C43C2314yes—
180#103×C43C2314yes—
181#102×C43C2314yes—
182C24×C43—21no—
183C24×C43—21no—
184C23×D43C2×D411yescharacteristic
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43C2412yes—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—22no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43C2412yes—
196C2×D4×C43C2412yes—
197C22×C4×C43—24no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—44no—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2411yescharacteristic
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—44no—
207C2×C22⋊D43—44no—
208C22×Dic43—24no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—44no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—42no—
220C2×C4×D43—42no—
221C2×C4×D43C2×D412yes—
222C2×C4×D43C2×D414yes—
223C2×C4×D43C2×D414yes—
224C2×C4×D43C2412yes—
225C2×Dic86—22no—
226C2×Dic86—22no—
227C2×Dic86—21no—
228C2×Dic86C2412yes—
229SD16×C43—44no—
230D8×C43—44no—
231C2×C8×C43—22no—
232C2×C8×C43—22no—
233C2×C8×C43C2412yes—
234C2×C8×C43C2412yes—
235C4⋊C4×C43—21no—
236C4⋊C4×C43C2412yes—
237C22⋊C4×C43—24no—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—24no—
240C42×C43C2×D412yes—
241C42×C43C2412yes—
242C22⋊Dic43—24no—
243C22⋊Dic43—24no—
244C22⋊Dic43—24no—
245C22⋊Dic43—24no—
246C22⋊Dic43—24no—
247#10621885—44no—
248#10621883—44no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—24no—
255C4⋊Dic43—24no—
256C4⋊Dic43—24no—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259C4⋊Dic43C2412yes—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265C4×Dic43—24no—
266C4×Dic43—24no—
267C4×Dic43C2×D412yes—
268C4×Dic43C2×D414yes—
269C4×Dic43C2×D414yes—
270C4×Dic43C2412yes—
271C2×C43⋊C8—22no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8C2412yes—
274C2×C43⋊C8C2412yes—
275#10621872—44no—
276#10621872—44no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43—42no—
282C23×C43—42no—
283C23×C43—42no—
284C23×C43—42no—
285C23×C43C22×D411yescharacteristic
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43C22×D412yes—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—42no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—42no—
298D4×C43—42no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—48no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43C22×D412yes—
307C2×C4×C43C22×D412yes—
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43H(5,𝔽2)12yes—
310C2×C4×C432−1+412yes—
311C2×C4×C43C2511yescharacteristic
312C22⋊D43—48no—
313C22⋊D43—48no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—48no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43C22×D412yes—
327C2×Dic43C22×D412yes—
328C2×Dic43C22×D412yes—
329C4×D43—24no—
330C4×D43—22no—
331C4×D43—22no—
332C4×D43—44no—
333C4×D43—44no—
334Dic86—22no—
335Dic86—22no—
336Dic86—42no—
337C8×C43—22no—
338C8×C43—22no—
339C43⋊C8—22no—
340C43⋊C8—22no—
341C2×#3256—431nomaximal, Sylow
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—84no—
349C22×C43—84no—
350C22×C43#53712yes—
351C22×C43#57512yes—
352C22×C43#57512yes—
353C22×C43C23×D411yescharacteristic
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—44no—
358C4×C43—22no—
359C4×C43—22no—
360C4×C43—42no—
361C4×C43—42no—
362C4×C43#53712yes—
363C4×C43C2×H(5,𝔽2)11yescharacteristic
364C4×C43C2×2−1+411yescharacteristic
365Dic43—22no—
366Dic43—22no—
367Dic43—22no—
368Dic43—42no—
369Dic43—42no—
370Dic43—42no—
371Dic43—42no—
372C2×#529—431no—
373C2×#529—431no—
374#3256—4316no—
375C2×#479—431no—
376C2×#479—431no—
377C2×#478—431no—
378C2×#478—431no—
379C2×#470—431no—
380C2×#469—431no—
381C2×#468—431no—
382C2×#468—431no—
383C2×#464—431no—
384C2×#464—431no—
385C2×#463—431no—
386C2×#463D4311yescharacteristic, complemented
387C2×#423—431no—
388C2×C43—82no—
389C2×C43—82no—
390C2×C43#325614yescomplemented
391C2×C43C2×#53711yescharacteristic
392C2×C43C2×#57511yescharacteristic
393C2×C43C2×#57511yescharacteristic
394D43—42no—
395C22×Q16—431no—
396C22×SD16—431no—
397C22×SD16C2×D4311yescharacteristic
398C22×D8C2×D4311yescharacteristic
399C22×M16—431no—
400C22×M16—431no—
401#529—438no—
402#529—438no—
403#529—864no—
404#529—864no—
405C2×#126—861no—
406C2×#126—861no—
407C2×#125—431no—
408C2×#125—431no—
409C2×#124—431no—
410C2×#124C2×D4311yescharacteristic
411C2×#123—861no—
412C2×#123—861no—
413C2×C22⋊Q8—431no—
414C2×C22⋊Q8—431no—
415C2×#121—431no—
416C2×#121—431no—
417C2×C4×Q8—431no—
418C2×C4×Q8—431no—
419C2×C4×D4—431no—
420C2×C4×D4—861no—
421C2×C4×D4—861no—
422C2×C4×D4C2×D4311yescharacteristic
423C2×#117—861no—
424C2×#117—861no—
425C22×C42—431no—
426#479—438no—
427#479—438no—
428#478—438no—
429#478—438no—
430#470—438no—
431#469—438no—
432#468—438no—
433#468—438no—
434#464—438no—
435#464—438no—
436#463—438no—
437#463C2×D4318yescomplemented
438C2×#107—431no—
439C2×#107—431no—
440C2×#106—431no—
441C2×#106—431no—
442#423—438no—
443C2×C4⋊C8—431no—
444C2×C4⋊C8—431no—
445C2×C4⋊C8—431no—
446C2×C4⋊C8C2×D4311yescharacteristic
447C2×#103—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103C2×D4311yescharacteristic
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102C2×D4311yescharacteristic
455C43C2×#325611yescharacteristic, complemented, Sylow
456C22×Q8—431no—
457C22×Q8C22×D4311yescharacteristic
458C22×D4—861no—
459C22×D4—861no—
460C22×D4C22×D4311yescharacteristic
461C22×D4C22×D4311yescharacteristic
462C23×C4—21no—
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—861no—
467C2×Q16—434no—
468C2×Q16—1722no—
469C2×SD16—42no—
470C2×SD16—434no—
471C2×SD16—1722no—
472C2×SD16C22×D4314yes—
473C2×D8—42no—
474C2×D8C22×D4314yes—
475C2×M16—434no—
476C2×M16—434no—
477C2×M16—1722no—
478C2×M16—1722no—
479C22×C8—431no—
480C22×C8—431no—
481C22×C8C22×D4311yescharacteristic
482C22×C8C22×D4311yescharacteristic
483#126—868no—
484#126—868no—
485#125—434no—
486#125—434no—
487#125—862no—
488#125—862no—
489#124—22no—
490#124—434no—
491#124—862no—
492#124C22×D4314yes—
493#123—868no—
494#123—868no—
495C22⋊Q8—434no—
496C22⋊Q8—434no—
497C22⋊Q8—862no—
498C22⋊Q8—862no—
499#121—434no—
500#121—434no—
501#121—862no—
502#121—862no—
503C4×Q8—434no—
504C4×Q8—434no—
505C4×Q8—862no—
506C4×Q8—862no—
507C4×D4—22no—
508C4×D4—434no—
509C4×D4—862no—
510C4×D4—868no—
511C4×D4—868no—
512C4×D4C22×D4314yes—
513#117—868no—
514#117—868no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C42—431no—
538C2×C42—431no—
539C2×C42—431no—
540C2×C42—434no—
541C2×C42—434no—
542C2×C42—861no—
543C2×C42—861no—
544C2×C42C22×D4311yescharacteristic
545#107—434no—
546#107—434no—
547#106—434no—
548#106—434no—
549C4⋊C8—434no—
550C4⋊C8—434no—
551C4⋊C8—434no—
552C4⋊C8C22×D4314yes—
553#103—434no—
554#103—434no—
555#103—434no—
556#103C22×D4314yes—
557#102—434no—
558#102—434no—
559#102—434no—
560#102C22×D4314yes—
561C24—21no—
562C24—21no—
563C24—431no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—432no—
568C2×Q8—861no—
569C2×Q8—862no—
570C2×Q8—862no—
571C2×Q8C23×D4312yes—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—864no—
579C2×D4—864no—
580C2×D4—1724no—
581C2×D4—1724no—
582C2×D4C23×D4312yes—
583C2×D4C23×D4312yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—431no—
589C22×C4—431no—
590C22×C4—431no—
591C22×C4—432no—
592C22×C4—432no—
593C22×C4—434no—
594C22×C4—434no—
595C22×C4—864no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—1722no—
603C22×C4—1722no—
604C22×C4—1724no—
605C22×C4D4×D4311yescharacteristic
606C22×C4D4×D4311yescharacteristic
607C22×C4C23×D4311yescharacteristic
608Q16—1724no—
609SD16—44no—
610SD16—1724no—
611D8—44no—
612M16—1724no—
613M16—1724no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—432no—
617C2×C8—432no—
618C2×C8—862no—
619C2×C8—862no—
620C2×C8C23×D4312yes—
621C2×C8C23×D4312yes—
622C4⋊C4—21no—
623C4⋊C4—432no—
624C4⋊C4—432no—
625C4⋊C4—432no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—864no—
635C4⋊C4—864no—
636C4⋊C4—864no—
637C4⋊C4C23×D4312yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C42—434no—
649C42—432no—
650C42—434no—
651C42—432no—
652C42—864no—
653C42—864no—
654C42D4×D4312yes—
655C42C23×D4312yes—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—432no—
665C23—862no—
666C23—862no—
667C23—862no—
668C23C2×D4×D4311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—862no—
673Q8—862no—
674Q8—1722no—
675D4—22no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—42no—
681D4—1728no—
682D4—1728no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—432no—
691C2×C4—432no—
692C2×C4—432no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—864no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—1724no—
704C2×C4—1724no—
705C2×C4—1728no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4C2×D4×D4312yes—
711C2×C4C2×D4×D4312yes—
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4#1306337012yes—
714C2×C4#1306337212yes—
715C2×C4C24×D4311yescharacteristic
716C8—22no—
717C8—22no—
718C8—862no—
719C8—862no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—84no—
728C22—862no—
729C22—862no—
730C22—862no—
731C22—1724no—
732C22#1458347812yes—
733C22#1458369512yes—
734C22#1458369612yes—
735C22C22×D4×D4311yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—862no—
741C4—862no—
742C4—862no—
743C4—1722no—
744C4—1722no—
745C4—1722no—
746C4—1722no—
747C4#1458347812yes—
748C4C2×#1306337011yescharacteristic
749C4C2×#1306337211yescharacteristic
750C2—82no—
751C2—82no—
752C2—1722no—
753C2#1914599314yesdirect product factor
754C2C2×#1458347811yescharacteristic
755C2C2×#1458369511yescharacteristic
756C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#463C2
socleC23×C43C22×D4
prime radicalC2×#14583149C2
hypercenterC2×#463D43
hypocenterC43C2×#3256
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#14583431C2semidirect
2. C2×#14583428C2semidirect
3. #19145993C2direct (N × H)
4. C2×#14583207C2semidirect
5. C2×#14583204C2semidirect
6. C2×#14583199C2semidirect
7. C2×#14583197C2semidirect
8. C2×#14583156C2semidirect
10. C2×#14583144C2semidirect
11. C2×#14583142C2semidirect
12. C2×#14583119C2semidirect
13. C2×#14583118C2semidirect
14. C2×#14583112C2semidirect
15. C2×#14582921C2semidirect
16. C2×C43×#463C2semidirect
22. #14583431C22semidirect
24. #14583428C22semidirect
44. #14583207C22semidirect
45. #14583204C22semidirect
46. #14583199C22semidirect
47. #14583197C22semidirect
48. #14583156C22semidirect
50. #14583144C22semidirect
51. #14583142C22semidirect
52. #14583119C22semidirect
53. #14583118C22semidirect
54. #14583112C22semidirect
59. #14582921C22semidirect
73. C43×#463C22semidirect
386. C2×#463D43semidirect
390. C2×C43#3256semidirect
437. #463C2×D43semidirect
455. C43C2×#3256semidirect
753. C2#19145993direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834312
C2×#145834282
#191459932
C2×#145832072
C2×#145832042
C2×#145831992
C2×#145831972
C2×#145831562
C2×#145831492
C2×#145831442
C2×#145831422
C2×#145831192
C2×#145831182
C2×#145831122
C2×#145829212
C2×C43×#4632
C2×#325643