Finite Group Databasebeta

← C2×#19146064 #25969571

Subgroups — C2×#19146064 #25969571

Order 11008.

1882 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×#14583523C211yesmaximal, characteristic, complemented
2C2×#14583521C211yesmaximal, characteristic, complemented
3#19146064C2116yesmaximal, direct product factor
4C2×#14583183C211yesmaximal, characteristic, complemented
5C2×#14583188C211yesmaximal, characteristic, complemented
6C2×#14583186C211yesmaximal, characteristic, complemented
7C2×#14583156C211yesmaximal, characteristic, complemented
8C2×#14583153C211yesmaximal, characteristic
9C2×#14583131C211yesmaximal, characteristic, complemented
10C2×#14583129C211yesmaximal, characteristic, complemented
11C2×#14583124C211yesmaximal, characteristic, complemented
12C2×#14583121C211yesmaximal, characteristic, complemented
13C2×#14583117C211yesmaximal, characteristic, complemented
14C2×#14583115C211yesmaximal, characteristic, complemented
15C2×#14582924C211yesmaximal, characteristic, complemented
16C2×C43×#475C211yesmaximal, characteristic, complemented
17C22×#10621885C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×D344C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23#14583523—24no—
24#14583523C2218yescomplemented
25#14583521—24no—
26#14583521C2218yescomplemented
27C2×#13063324C2211yescharacteristic
28C2×#13063320—21no—
29C2×#13063319—21no—
30C2×#13063314—21no—
31C2×#13063314C2211yescharacteristic
32C2×#13063313—21no—
33C2×#13063313C2211yescharacteristic
34C2×#13063310—21no—
35C2×#13063310—21no—
36C2×#13063305C2211yescharacteristic
37C2×#13063303—21no—
38C2×#13063301—21no—
39C2×#13063301C2211yescharacteristic
40C2×#13063300C2211yescharacteristic
41C2×#13063300C2211yescharacteristic
42C2×#13063290C2211yescharacteristic
43C2×C4×D172C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063282C2211yescharacteristic
46#14583188C2218yescomplemented
47#14583186C2218yescomplemented
48#14583183C2218yescomplemented
49#14583156C2218yescomplemented
50#14583153C2218yes—
51#14583131C2218yescomplemented
52#14583129C2218yescomplemented
53#14583124C2218yescomplemented
54#14583121C2218yescomplemented
55#14583117C2218yescomplemented
56#14583115C2218yescomplemented
57C2×#13063256C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59#14582924C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×#13063245C2211yescharacteristic
68C2×#13063245C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#475C2218yescomplemented
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×D172—21no—
80C22×D172—21no—
81C22×D172C2311yescharacteristic
82C22×D172C2311yescharacteristic
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C2×#10621885—42no—
87C2×#10621885C2314yes—
88C2×#10621873—42no—
89C2×#10621873C2314yes—
90C2×#10621884—42no—
91C2×#10621884C2314yes—
92C2×D344—42no—
93C2×D344C2314yes—
94C2×#10621872—42no—
95C2×#10621872C2314yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C2×C8×D43—42no—
99C2×C8×D43C2314yes—
100#13063324—22no—
101#13063324C2314yes—
102#13063320—28no—
103#13063319—28no—
104#13063314—28no—
105#13063314—22no—
106#13063314C2314yes—
107#13063313—22no—
108#13063313—28no—
109#13063313C2314yes—
110#13063310—28no—
111#13063310—28no—
112#13063305—22no—
113#13063305C2314yes—
114#13063303—28no—
115#13063301—22no—
116#13063301—28no—
117#13063301C2314yes—
118#13063300—22no—
119#13063300—22no—
120#13063300C2314yes—
121#13063300C2314yes—
122#13063290—22no—
123#13063290C2314yes—
124C4×D172—22no—
125C4×D172C2314yes—
126#13063287—22no—
127#13063287C2314yes—
128#13063282D414yes—
129#13063282C2314yes—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4D411yescharacteristic
136C2×Dic43⋊C4D411yescharacteristic
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4D411yescharacteristic
148C2×(C2×D43)⋊C4D411yescharacteristic
149C2×C4×Dic43—21no—
150C2×C4×Dic43C2311yescharacteristic
151#13063256C2314yes—
152#13063256C2314yes—
153C4⋊(C43⋊C8)C2314yes—
154Dic43⋊C8C2314yes—
155Dic43⋊C8C2314yes—
156#13063250C2314yes—
157#13063248C2314yes—
158#13063247C2314yes—
159#13063245C2314yes—
160#13063245C2314yes—
161#13063245C2314yes—
162C22×Q8×C43—21no—
163C22×Q8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C4⋊Q8×C43—22no—
167C4⋊Q8×C43C2314yes—
168C4×Q8×C43—22no—
169C4×Q8×C43C2314yes—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C42×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#106×C43C2314yes—
178#106×C43C2314yes—
179C4⋊C8×C43C2314yes—
180#103×C43C2314yes—
181#103×C43C2314yes—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43C2×D411yescharacteristic
185C2×Q8×C43—21no—
186C2×Q8×C43—24no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43—82no—
190C2×Q8×C43C2412yes—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—24no—
206C2×D172—24no—
207C2×D172—22no—
208C2×D172—22no—
209C2×D172—22no—
210C2×D172—22no—
211C2×D172—82no—
212C2×D172—82no—
213C2×D172C2412yes—
214C2×D172C2412yes—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
217C2×C4×D43—24no—
218C2×C4×D43—24no—
219C2×C4×D43—82no—
220C2×C4×D43—82no—
221C2×C4×D43C2×D412yes—
222C2×C4×D43C2412yes—
223C2×Dic86—22no—
224C2×Dic86—22no—
225C2×Dic86—21no—
226C2×Dic86—24no—
227C2×Dic86—82no—
228C2×Dic86C2412yes—
229C2×C8×C43—22no—
230C2×C8×C43—22no—
231C2×C8×C43C2412yes—
232C2×C8×C43C2412yes—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43C2412yes—
239C4⋊C4×C43C2412yes—
240C4⋊C4×C43C2412yes—
241C42×C43—24no—
242C42×C43C2×D412yes—
243C42×C43C2412yes—
244#10621885—44no—
245#10621884—44no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4C2×D414yes—
257(C2×D43)⋊C4C2×D414yes—
258C4⋊Dic43—21no—
259C4⋊Dic43—24no—
260C4⋊Dic43C2412yes—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4C2×D414yes—
265Dic43⋊C4C2×D414yes—
266C4×Dic43—24no—
267C4×Dic43C2×D412yes—
268C4×Dic43C2412yes—
269C2×C43⋊C8—22no—
270C2×C43⋊C8—22no—
271C2×C43⋊C8C2412yes—
272C2×C43⋊C8C2412yes—
273D344—44no—
274#10621873—44no—
275#10621872—44no—
276C8×D43—44no—
277C23×C43C22×D411yescharacteristic
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43—42no—
288C22×D43—42no—
289C22×D43C22×D412yes—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—42no—
293Q8×C43—84no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43C22×D412yes—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43H(5,𝔽2)12yes—
308C2×C4×C432−1+412yes—
309C2×C4×C43C2511yescharacteristic
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43C22×D412yes—
318C2×Dic43C22×D412yes—
319C2×Dic43C22×D412yes—
320D172—22no—
321D172—22no—
322D172—22no—
323D172—22no—
324D172—42no—
325D172—42no—
326D172—84no—
327D172—84no—
328C4×D43—24no—
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—84no—
332C4×D43—84no—
333Dic86—22no—
334Dic86—22no—
335Dic86—42no—
336Dic86—84no—
337C8×C43—22no—
338C8×C43—22no—
339C43⋊C8—22no—
340C43⋊C8—22no—
341C2×#3263—431nomaximal, Sylow
342C22×C43#53712yes—
343C22×C43#57712yes—
344C22×C43#57712yes—
345C22×C43C23×D411yescharacteristic
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—44no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—84no—
357C2×D43—84no—
358C4×C43—22no—
359C4×C43—22no—
360C4×C43—42no—
361C4×C43—42no—
362C4×C43—42no—
363C4×C43—42no—
364C4×C43#53712yes—
365C4×C43C2×H(5,𝔽2)11yescharacteristic
366C4×C43C2×2−1+411yescharacteristic
367Dic43—22no—
368Dic43—22no—
369Dic43—22no—
370Dic43—42no—
371Dic43—42no—
372C2×#542—431no—
373C2×#542—431no—
374#3263—4316no—
375C2×#475—431no—
376C2×#475D4311yescharacteristic, complemented
377C2×#476—431no—
378C2×#476—431no—
379C2×#470—431no—
380C2×#469—431no—
381C2×#465—431no—
382C2×#465—431no—
383C2×#464—431no—
384C2×#464—431no—
385C2×#463—431no—
386C2×#463—431no—
387C2×#424—431no—
388C2×C43#326314yescomplemented
389C2×C43C2×#53711yescharacteristic
390C2×C43C2×#57711yescharacteristic
391C2×C43C2×#57711yescharacteristic
392D43—42no—
393D43—82no—
394D43—82no—
395C22×Q16—431no—
396C22×SD16—431no—
397C22×SD16—431no—
398C22×D8—431no—
399C22×M16—431no—
400C23×C8—431no—
401#542—438no—
402#542—438no—
403#542—864no—
404#542—864no—
405C2×C4⋊Q8—431no—
406C2×C4⋊Q8C2×D4311yescharacteristic
407C2×#126—861no—
408C2×#126—861no—
409C2×#124—431no—
410C2×#124—431no—
411C2×#124—861no—
412C2×#124—861no—
413C2×#123—861no—
414C2×#123—861no—
415C2×C22⋊Q8—431no—
416C2×C22⋊Q8—431no—
417C2×C22⋊Q8—861no—
418C2×C22⋊Q8—861no—
419C2×#121—431no—
420C2×#121—431no—
421C2×C4×Q8—431no—
422C2×C4×Q8C2×D4311yescharacteristic
423C2×C4×D4—431no—
424C2×C4×D4—431no—
425C2×#117—431no—
426#476—438no—
427#476—438no—
428#475—438no—
429#475C2×D4318yescomplemented
430#470—438no—
431#469—438no—
432#465—438no—
433#465—438no—
434#464—438no—
435#464—438no—
436#463—438no—
437#463—438no—
438C2×#106—431no—
439C2×#106—431no—
440C2×#106C2×D4311yescharacteristic
441C2×#106C2×D4311yescharacteristic
442#424—438no—
443C2×C4⋊C8—431no—
444C2×C4⋊C8—431no—
445C2×C4⋊C8—431no—
446C2×C4⋊C8C2×D4311yescharacteristic
447C2×#103—431no—
448C2×#103—431no—
449C2×#103C2×D4311yescharacteristic
450C2×#103C2×D4311yescharacteristic
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C43C2×#326311yescharacteristic, complemented, Sylow
456C22×Q8—21no—
457C22×Q8—431no—
458C22×Q8—861no—
459C22×Q8C22×D4311yescharacteristic
460C22×D4—431no—
461C22×D4—431no—
462C22×D4—861no—
463C22×D4—861no—
464C23×C4—431no—
465C23×C4—861no—
466C23×C4—861no—
467C2×Q16—434no—
468C2×Q16—1722no—
469C2×SD16—434no—
470C2×SD16—434no—
471C2×SD16—1722no—
472C2×SD16—1722no—
473C2×D8—434no—
474C2×D8—1722no—
475C2×M16—434no—
476C2×M16—1722no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8—434no—
480C22×C8—1722no—
481C22×C8C22×D4311yescharacteristic
482C22×C8C22×D4311yescharacteristic
483C4⋊Q8—22no—
484C4⋊Q8—434no—
485C4⋊Q8—862no—
486C4⋊Q8C22×D4314yes—
487#126—868no—
488#126—868no—
489#124—434no—
490#124—434no—
491#124—868no—
492#124—862no—
493#124—868no—
494#124—862no—
495#123—868no—
496#123—868no—
497C22⋊Q8—434no—
498C22⋊Q8—434no—
499C22⋊Q8—868no—
500C22⋊Q8—862no—
501C22⋊Q8—868no—
502C22⋊Q8—862no—
503#121—434no—
504#121—434no—
505#121—862no—
506#121—862no—
507C4×Q8—22no—
508C4×Q8—434no—
509C4×Q8—862no—
510C4×Q8C22×D4314yes—
511C4×D4—434no—
512C4×D4—434no—
513C4×D4—862no—
514C4×D4—862no—
515#117—434no—
516#117—434no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C22⋊C4—431no—
530C2×C22⋊C4—431no—
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×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C42—21no—
542C2×C42—431no—
543C2×C42—861no—
544C2×C42C22×D4311yescharacteristic
545#106—434no—
546#106—434no—
547#106C22×D4314yes—
548#106C22×D4314yes—
549C4⋊C8—434no—
550C4⋊C8—434no—
551C4⋊C8—434no—
552C4⋊C8C22×D4314yes—
553#103—434no—
554#103—434no—
555#103C22×D4314yes—
556#103C22×D4314yes—
557#102—434no—
558#102—434no—
559#102—434no—
560#102—434no—
561C24—431no—
562C24—861no—
563C24—861no—
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—432no—
570C2×Q8—864no—
571C2×Q8—861no—
572C2×Q8—862no—
573C2×Q8—862no—
574C2×Q8—3442no—
575C2×Q8C23×D4312yes—
576C2×D4—432no—
577C2×D4—432no—
578C2×D4—864no—
579C2×D4—864no—
580C2×D4—861no—
581C2×D4—861no—
582C2×D4—862no—
583C2×D4—862no—
584C2×D4—862no—
585C2×D4—862no—
586C2×D4—3442no—
587C2×D4—3442no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—431no—
593C22×C4—431no—
594C22×C4—431no—
595C22×C4—432no—
596C22×C4—432no—
597C22×C4—864no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—864no—
603C22×C4—3442no—
604C22×C4—3442no—
605C22×C4D4×D4311yescharacteristic
606C22×C4D4×D4311yescharacteristic
607C22×C4C23×D4311yescharacteristic
608Q16—1724no—
609SD16—1724no—
610SD16—1724no—
611D8—1724no—
612M16—1724no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—432no—
616C2×C8—432no—
617C2×C8—862no—
618C2×C8—862no—
619C2×C8—1724no—
620C2×C8C23×D4312yes—
621C2×C8C23×D4312yes—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—434no—
628C4⋊C4—434no—
629C4⋊C4—432no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4—861no—
635C4⋊C4C23×D4312yes—
636C4⋊C4C23×D4312yes—
637C4⋊C4C23×D4312yes—
638C22⋊C4—434no—
639C22⋊C4—434no—
640C22⋊C4—864no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C42—24no—
651C42—432no—
652C42—432no—
653C42—864no—
654C42D4×D4312yes—
655C42C23×D4312yes—
656C23—432no—
657C23—862no—
658C23—862no—
659C23—862no—
660C23—862no—
661C23—862no—
662C23—1722no—
663C23—1722no—
664C23—1722no—
665C23—1722no—
666C23—1722no—
667C23—1722no—
668C23C2×D4×D4311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—84no—
673Q8—862no—
674Q8—862no—
675Q8—3444no—
676Q8—1722no—
677D4—862no—
678D4—862no—
679D4—862no—
680D4—862no—
681D4—3444no—
682D4—3444no—
683D4—1722no—
684D4—1722no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—432no—
696C2×C4—432no—
697C2×C4—432no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—864no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—3444no—
707C2×C4—3444no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4C2×D4×D4312yes—
711C2×C4C2×D4×D4312yes—
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4#1306337112yes—
714C2×C4#1306337312yes—
715C2×C4C24×D4311yescharacteristic
716C8—22no—
717C8—22no—
718C8—862no—
719C8—862no—
720C22—862no—
721C22—862no—
722C22—862no—
723C22—3444no—
724C22—3444no—
725C22—1722no—
726C22—1722no—
727C22—1722no—
728C22—1722no—
729C22—1722no—
730C22—1722no—
731C22—1724no—
732C22#1458347912yes—
733C22#1458370512yes—
734C22#1458370812yes—
735C22C22×D4×D4311yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—862no—
743C4—862no—
744C4—862no—
745C4—1722no—
746C4—1722no—
747C4#1458347912yes—
748C4C2×#1306337111yescharacteristic
749C4C2×#1306337311yescharacteristic
750C2—3442no—
751C2—3442no—
752C2—1722no—
753C2#1914606414yesdirect product factor
754C2C2×#1458347911yescharacteristic
755C2C2×#1458370511yescharacteristic
756C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#475C2
socleC23×C43C22×D4
prime radicalC2×#14583153C2
hypercenterC2×#475D43
hypocenterC43C2×#3263
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#14583523C2semidirect
2. C2×#14583521C2semidirect
3. #19146064C2direct (N × H)
4. C2×#14583183C2semidirect
5. C2×#14583188C2semidirect
6. C2×#14583186C2semidirect
7. C2×#14583156C2semidirect
9. C2×#14583131C2semidirect
10. C2×#14583129C2semidirect
11. C2×#14583124C2semidirect
12. C2×#14583121C2semidirect
13. C2×#14583117C2semidirect
14. C2×#14583115C2semidirect
15. C2×#14582924C2semidirect
16. C2×C43×#475C2semidirect
24. #14583523C22semidirect
26. #14583521C22semidirect
46. #14583188C22semidirect
47. #14583186C22semidirect
48. #14583183C22semidirect
49. #14583156C22semidirect
51. #14583131C22semidirect
52. #14583129C22semidirect
53. #14583124C22semidirect
54. #14583121C22semidirect
55. #14583117C22semidirect
56. #14583115C22semidirect
59. #14582924C22semidirect
71. C43×#475C22semidirect
376. C2×#475D43semidirect
388. C2×C43#3263semidirect
429. #475C2×D43semidirect
455. C43C2×#3263semidirect
753. C2#19146064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835232
C2×#145835212
#191460642
C2×#145831832
C2×#145831882
C2×#145831862
C2×#145831562
C2×#145831532
C2×#145831312
C2×#145831292
C2×#145831242
C2×#145831212
C2×#145831172
C2×#145831152
C2×#145829242
C2×C43×#4752
C2×#326343