Finite Group Databasebeta

← C2×#19147094 #25975191

Subgroups — C2×#19147094 #25975191

Order 11008.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583615C211yesmaximal, characteristic, complemented
2C2×#14583602C211yesmaximal, characteristic, complemented
3#19147094C2116yesmaximal, direct product factor
4C2×#14583226C211yesmaximal, characteristic, complemented
5C2×#14583225C211yesmaximal, characteristic, complemented
6C2×#14583225C211yesmaximal, characteristic, complemented
7C2×#14583214C211yesmaximal, characteristic, complemented
8C2×#14583196C211yesmaximal, characteristic, complemented
9C2×#14583176C211yesmaximal, characteristic, complemented
10C2×#14583153C211yesmaximal, characteristic, complemented
11C2×#14583136C211yesmaximal, characteristic, complemented
12C2×#14583012C211yesmaximal, characteristic, complemented
13C2×#14582972C211yesmaximal, characteristic, complemented
14C2×#14582940C211yesmaximal, characteristic, complemented
15C2×#14582934C211yesmaximal, characteristic, complemented
16C2×C43×#501C211yesmaximal, characteristic, complemented
17C22×D344C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583615—24no—
21#14583615C2218yescomplemented
22#14583602—24no—
23#14583602C2218yescomplemented
24C2×#13063320—21no—
25C2×#13063314—21no—
26C2×#13063314—21no—
27C2×#13063310—21no—
28C2×#13063300—21no—
29C2×#13063300—21no—
30C2×#13063300C2211yescharacteristic
31C2×#13063300C2211yescharacteristic
32C2×#13063300C2211yescharacteristic
33C2×#13063300C2211yescharacteristic
34C2×C4×D172C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C2×#13063287—21no—
38C2×#13063283—21no—
39C2×#13063283C2211yescharacteristic
40C2×#13063283C2211yescharacteristic
41C2×#13063283C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583226C2218yescomplemented
44#14583225C2218yescomplemented
45#14583225C2218yescomplemented
46#14583214C2218yescomplemented
47#14583196C2218yescomplemented
48#14583176C2218yescomplemented
49#14583153C2218yescomplemented
50#14583136C2218yescomplemented
51#14583012C2218yescomplemented
52#14582972C2218yescomplemented
53#14582940C2218yescomplemented
54#14582934C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063256C2211yescharacteristic
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×#125×C43C2211yescharacteristic
71C43×#501C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#107×C43C2211yescharacteristic
74C2×#106×C43C2211yescharacteristic
75C2×#106×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C22×D172—21no—
78C22×D172—21no—
79C22×D172—21no—
80C22×D172—21no—
81C22×D172D411yescharacteristic
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43C2311yescharacteristic
88C22×C4×D43C2311yescharacteristic
89C2×D344—24no—
90C2×D344C2314yes—
91C2×#10621872—24no—
92C2×#10621872C2314yes—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95C2×C8×D43—24no—
96C2×C8×D43C2314yes—
97#13063320—28no—
98#13063314—28no—
99#13063314—28no—
100#13063310—28no—
101#13063300—28no—
102#13063300—28no—
103#13063300—22no—
104#13063300—22no—
105#13063300—22no—
106#13063300—22no—
107#13063300C2314yes—
108#13063300C2314yes—
109#13063300C2314yes—
110#13063300C2314yes—
111C4×D172—22no—
112C4×D172—22no—
113C4×D172D414yes—
114C4×D172C2314yes—
115C4×D172C2314yes—
116C4×D172C2314yes—
117#13063287—28no—
118#13063283—22no—
119#13063283—22no—
120#13063283—22no—
121#13063283—28no—
122#13063283C2314yes—
123#13063283C2314yes—
124#13063283C2314yes—
125C2×C4⋊Dic43D411yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4—21no—
129C4⋊C4×D43—22no—
130C4⋊C4×D43C2314yes—
131C2×(C2×D43)⋊C4—21no—
132C2×(C2×D43)⋊C4—21no—
133C2×(C2×D43)⋊C4—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4D411yescharacteristic
141C2×(C2×D43)⋊C4D411yescharacteristic
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145#13063258C2314yes—
146#13063258C2314yes—
147#13063258C2314yes—
148#13063257C2314yes—
149#13063256C2314yes—
150C4⋊(C43⋊C8)C2314yes—
151#13063247C2314yes—
152#13063247C2314yes—
153#13063245C2314yes—
154#13063245C2314yes—
155#13063245C2314yes—
156#13063245C2314yes—
157(C2×D43)⋊C8C2314yes—
158(C2×D43)⋊C8C2314yes—
159C22×Q8×C43—21no—
160C22×C8×C43C2311yescharacteristic
161C22×C8×C43C2311yescharacteristic
162C4⋊Q8×C43—22no—
163C4⋊Q8×C43C2314yes—
164#125×C43—22no—
165#125×C43C2314yes—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C42×C43C2311yescharacteristic
174#107×C43C2314yes—
175#107×C43C2314yes—
176#106×C43C2314yes—
177#106×C43C2314yes—
178#97×C43C2314yes—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43C2×D411yescharacteristic
182C23×D43C2×D411yescharacteristic
183C2×Q8×C43—24no—
184C2×Q8×C43—82no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2411yescharacteristic
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196C2×D172—21no—
197C2×D172—21no—
198C2×D172—24no—
199C2×D172—24no—
200C2×D172—24no—
201C2×D172—24no—
202C2×D172—22no—
203C2×D172—22no—
204C2×D172—22no—
205C2×D172—22no—
206C2×D172—42no—
207C2×D172—44no—
208C2×D172—82no—
209C2×D172—82no—
210C2×D172—82no—
211C2×D172C2×D414yes—
212C2×D172C2412yes—
213C2×D172C2412yes—
214C2×C4×D43—22no—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
217C2×C4×D43—22no—
218C2×C4×D43—24no—
219C2×C4×D43—24no—
220C2×C4×D43—24no—
221C2×C4×D43—44no—
222C2×C4×D43—82no—
223C2×C4×D43—82no—
224C2×C4×D43C2×D412yes—
225C2×C4×D43C2×D412yes—
226C2×C4×D43C2412yes—
227C2×C4×D43C2412yes—
228C2×C8×C43—22no—
229C2×C8×C43#4114yes—
230C2×C8×C43C2412yes—
231C2×C8×C43C2412yes—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43C2412yes—
240C4⋊C4×C43C2412yes—
241C4⋊C4×C43C2412yes—
242C4⋊C4×C43C2412yes—
243C42×C43C2×D412yes—
244C42×C43C2412yes—
245(C2×D43)⋊C4—24no—
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)⋊C4C2×D414yes—
255(C2×D43)⋊C4C2×D414yes—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43C2×D414yes—
259C4⋊Dic43C2412yes—
260C4⋊Dic43C2412yes—
261Dic43⋊C4—24no—
262C4×Dic43—24no—
263C4×Dic43—24no—
264C4×Dic43—24no—
265C2×C43⋊C8—22no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8C2412yes—
268C2×C43⋊C8C2412yes—
269D344—28no—
270#10621872—28no—
271C8×D43—28no—
272C23×C43C22×D411yescharacteristic
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43C22×D412yes—
288C22×D43C22×D412yes—
289Q8×C43—84no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43C22×D412yes—
301C2×C4×C43C22×D412yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C2×#4112yes—
304C2×C4×C432−1+412yes—
305C2×C4×C43C2511yescharacteristic
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43C22×D412yes—
313C2×Dic43C22×D412yes—
314D172—22no—
315D172—22no—
316D172—22no—
317D172—22no—
318D172—44no—
319D172—48no—
320D172—42no—
321D172—42no—
322D172—84no—
323D172—84no—
324D172—84no—
325C4×D43—24no—
326C4×D43—24no—
327C4×D43—22no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—48no—
332C4×D43—84no—
333C4×D43—84no—
334C8×C43—22no—
335C8×C43C2×#4114yes—
336C43⋊C8—22no—
337C43⋊C8—22no—
338C2×#3347—431nomaximal, Sylow
339C22×C43#54712yes—
340C22×C43#57512yes—
341C22×C43#57612yes—
342C22×C43C23×D411yescharacteristic
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—44no—
350C2×D43—44no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—84no—
358C2×D43—84no—
359C4×C43—22no—
360C4×C43—22no—
361C4×C43—42no—
362C4×C43—42no—
363C4×C43—42no—
364C4×C43—42no—
365C4×C43#54712yes—
366C4×C43C22×#4111yescharacteristic
367C4×C43C2×2−1+411yescharacteristic
368Dic43—22no—
369Dic43—22no—
370Dic43—42no—
371Dic43—42no—
372C2×#555—431no—
373C2×#553—431no—
374#3347—4316no—
375C2×#501D4311yescharacteristic, complemented
376C2×#482—431no—
377C2×#482—431no—
378C2×#482—431no—
379C2×#480—431no—
380C2×#478—431no—
381C2×#474—431no—
382C2×#469—431no—
383C2×#466—431no—
384C2×#442—431no—
385C2×#435—431no—
386C2×#428—431no—
387C2×#427—431no—
388C2×C43#334714yescomplemented
389C2×C43C2×#54711yescharacteristic
390C2×C43C2×#57511yescharacteristic
391C2×C43C2×#57611yescharacteristic
392D43—42no—
393D43—42no—
394D43—82no—
395D43—82no—
396C22×D8—431no—
397C22×M16—431no—
398C23×C8—431no—
399#555—438no—
400#555—864no—
401#553—438no—
402#553—864no—
403C2×C4⋊Q8C2×D4311yescharacteristic
404C2×#126—861no—
405C2×#125C2×D4311yescharacteristic
406C2×#124—861no—
407C2×#124—861no—
408C2×#123—861no—
409C2×#121—431no—
410C2×#121—431no—
411C2×#121—431no—
412C2×#121—431no—
413C2×#121—861no—
414C2×#121—861no—
415C2×C4×D4—431no—
416C2×C4×D4—431no—
417C2×C4×D4—431no—
418C2×C4×D4—861no—
419C2×#117—431no—
420C2×#117—431no—
421C2×#117—431no—
422C2×#117—861no—
423C22×C4⋊C4—431no—
424#501C2×D4318yescomplemented
425#482—438no—
426#482—438no—
427#482—438no—
428#480—438no—
429#478—438no—
430#474—438no—
431#469—438no—
432#466—438no—
433#442—438no—
434#435—438no—
435#428—438no—
436#427—438no—
437C2×#107—431no—
438C2×#107—431no—
439C2×#107—431no—
440C2×#107C2×D4311yescharacteristic
441C2×#107C2×D4311yescharacteristic
442C2×#106—431no—
443C2×#106—431no—
444C2×#106C2×D4311yescharacteristic
445C2×#106C2×D4311yescharacteristic
446C2×C4⋊C8—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×C22⋊C8—431no—
454C2×C22⋊C8—431no—
455C2×#97C2×D4311yescharacteristic
456C43C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—21no—
458C22×D4—431no—
459C22×D4—431no—
460C22×D4—431no—
461C22×D4—861no—
462C22×D4—861no—
463C22×D4—861no—
464C22×D4—861no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—861no—
468C23×C4—861no—
469C23×C4—861no—
470C2×D8—434no—
471C2×D8—864no—
472C2×M16—434no—
473C2×M16—864no—
474C22×C8—431no—
475C22×C8—431no—
476C22×C8—434no—
477C22×C8—864no—
478C22×C8C22×D4311yescharacteristic
479C22×C8C22×D4311yescharacteristic
480C4⋊Q8—22no—
481C4⋊Q8C22×D4314yes—
482#126—868no—
483#125—22no—
484#125C22×D4314yes—
485#124—868no—
486#124—868no—
487#123—868no—
488#121—434no—
489#121—434no—
490#121—434no—
491#121—434no—
492#121—862no—
493#121—862no—
494#121—862no—
495#121—862no—
496#121—868no—
497#121—868no—
498C4×D4—434no—
499C4×D4—434no—
500C4×D4—434no—
501C4×D4—434no—
502C4×D4—868no—
503C4×D4—862no—
504C4×D4—862no—
505#117—434no—
506#117—434no—
507#117—434no—
508#117—868no—
509#117—862no—
510#117—862no—
511#117—862no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—434no—
519C2×C4⋊C4—862no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4C22×D4311yescharacteristic
522C2×C4⋊C4C22×D4311yescharacteristic
523C2×C4⋊C4C22×D4311yescharacteristic
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C22⋊C4—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
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×C42—861no—
537C2×C42—861no—
538C2×C42—861no—
539C2×C42C22×D4311yescharacteristic
540#107—434no—
541#107—434no—
542#107—434no—
543#107C22×D4314yes—
544#107C22×D4314yes—
545#106—434no—
546#106—434no—
547#106C22×D4314yes—
548#106C22×D4314yes—
549C4⋊C8—434no—
550#102—434no—
551#102—434no—
552#102—434no—
553#102—434no—
554#102—434no—
555#102—434no—
556C22⋊C8—434no—
557C22⋊C8—434no—
558#97C22×D4314yes—
559C24—431no—
560C24—431no—
561C24—861no—
562C24—861no—
563C2×Q8—24no—
564C2×Q8—82no—
565C2×D4—434no—
566C2×D4—432no—
567C2×D4—432no—
568C2×D4—864no—
569C2×D4—864no—
570C2×D4—864no—
571C2×D4—864no—
572C2×D4—861no—
573C2×D4—861no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—862no—
578C2×D4—3442no—
579C2×D4—3442no—
580C2×D4—3442no—
581C2×D4—1722no—
582C2×D4—1724no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—431no—
588C22×C4—431no—
589C22×C4—432no—
590C22×C4—432no—
591C22×C4—432no—
592C22×C4—432no—
593C22×C4—864no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—864no—
601C22×C4—864no—
602C22×C4—3442no—
603C22×C4—3442no—
604C22×C4—1724no—
605C22×C4D4×D4311yescharacteristic
606C22×C4D4×D4311yescharacteristic
607C22×C4C23×D4311yescharacteristic
608D8—868no—
609M16—868no—
610C2×C8—22no—
611C2×C8—432no—
612C2×C8—432no—
613C2×C8—862no—
614C2×C8—862no—
615C2×C8—868no—
616C2×C8#1062190214yes—
617C2×C8C23×D4312yes—
618C2×C8C23×D4312yes—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—434no—
627C4⋊C4—432no—
628C4⋊C4—432no—
629C4⋊C4—864no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4C23×D4312yes—
633C4⋊C4C23×D4312yes—
634C4⋊C4C23×D4312yes—
635C4⋊C4C23×D4312yes—
636C22⋊C4—434no—
637C22⋊C4—434no—
638C22⋊C4—864no—
639C22⋊C4—864no—
640C22⋊C4—864no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C42—864no—
648C42—864no—
649C42—864no—
650C42D4×D4312yes—
651C42C23×D4312yes—
652C23—432no—
653C23—432no—
654C23—862no—
655C23—862no—
656C23—862no—
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—84no—
670D4—862no—
671D4—862no—
672D4—862no—
673D4—862no—
674D4—3444no—
675D4—3444no—
676D4—3444no—
677D4—1724no—
678D4—1728no—
679D4—1722no—
680D4—1722no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—432no—
692C2×C4—432no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—864no—
696C2×C4—864no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—3444no—
704C2×C4—3444no—
705C2×C4—1728no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4C2×D4×D4312yes—
709C2×C4C2×D4×D4312yes—
710C2×C4C2×D4×D4311yescharacteristic
711C2×C4C2×#1062190212yes—
712C2×C4#1306337312yes—
713C2×C4C24×D4311yescharacteristic
714C8—22no—
715C8—862no—
716C8—862no—
717C8C2×#1062190214yes—
718C22—862no—
719C22—862no—
720C22—862no—
721C22—862no—
722C22—862no—
723C22—862no—
724C22—3444no—
725C22—3444no—
726C22—1722no—
727C22—1722no—
728C22—1722no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1724no—
733C22—1724no—
734C22#1458355212yes—
735C22#1458369812yes—
736C22#1458370312yes—
737C22C22×D4×D4311yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—862no—
745C4—862no—
746C4—1722no—
747C4—1722no—
748C4#1458355212yes—
749C4C22×#1062190211yescharacteristic
750C4C2×#1306337311yescharacteristic
751C2—3442no—
752C2—3442no—
753C2—1722no—
754C2—1722no—
755C2#1914709414yesdirect product factor
756C2C2×#1458355211yescharacteristic
757C2C2×#1458369811yescharacteristic
758C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#501C2
socleC23×C43C22×D4
hypercenterC2×#501D43
hypocenterC43C2×#3347
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#14583615C2semidirect
2. C2×#14583602C2semidirect
3. #19147094C2direct (N × H)
4. C2×#14583226C2semidirect
5. C2×#14583225C2semidirect
6. C2×#14583225C2semidirect
7. C2×#14583214C2semidirect
8. C2×#14583196C2semidirect
9. C2×#14583176C2semidirect
10. C2×#14583153C2semidirect
11. C2×#14583136C2semidirect
12. C2×#14583012C2semidirect
13. C2×#14582972C2semidirect
14. C2×#14582940C2semidirect
15. C2×#14582934C2semidirect
16. C2×C43×#501C2semidirect
21. #14583615C22semidirect
23. #14583602C22semidirect
43. #14583226C22semidirect
44. #14583225C22semidirect
45. #14583225C22semidirect
46. #14583214C22semidirect
47. #14583196C22semidirect
48. #14583176C22semidirect
49. #14583153C22semidirect
50. #14583136C22semidirect
51. #14583012C22semidirect
52. #14582972C22semidirect
53. #14582940C22semidirect
54. #14582934C22semidirect
71. C43×#501C22semidirect
375. C2×#501D43semidirect
388. C2×C43#3347semidirect
424. #501C2×D43semidirect
456. C43C2×#3347semidirect
755. C2#19147094direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836152
C2×#145836022
#191470942
C2×#145832262
C2×#145832252
C2×#145832142
C2×#145831962
C2×#145831762
C2×#145831532
C2×#145831362
C2×#145830122
C2×#145829722
C2×#145829402
C2×#145829342
C2×C43×#5012
C2×#334743