Finite Group Databasebeta

← C2×#19147091 #25975188

Subgroups — C2×#19147091 #25975188

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×#14583612C211yesmaximal, characteristic, complemented
2C2×#14583593C211yesmaximal, characteristic, complemented
3#19147091C2116yesmaximal, direct product factor
4C2×#14583306C211yesmaximal, characteristic, complemented
5C2×#14583226C211yesmaximal, characteristic, complemented
6C2×#14583223C211yesmaximal, characteristic, complemented
7C2×#14583223C211yesmaximal, characteristic, complemented
8C2×#14583214C211yesmaximal, characteristic, complemented
9C2×#14583202C211yesmaximal, characteristic, complemented
10C2×#14583178C211yesmaximal, characteristic, complemented
11C2×#14583153C211yesmaximal, characteristic, complemented
12C2×#14583135C211yesmaximal, characteristic, complemented
13C2×#14583010C211yesmaximal, characteristic, complemented
14C2×#14582970C211yesmaximal, characteristic, complemented
15C2×#14582938C211yesmaximal, characteristic, complemented
16C2×C43×#427C211yesmaximal, characteristic, complemented
17C22×D344C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19#14583612—24no—
20#14583612C2218yescomplemented
21#14583593—24no—
22#14583593C2218yescomplemented
23C2×#13063324C2211yescharacteristic
24C2×#13063319—21no—
25C2×#13063316C2211yescharacteristic
26C2×#13063313—21no—
27C2×#13063311—21no—
28C2×#13063307—21no—
29C2×#13063300C2211yescharacteristic
30C2×#13063300C2211yescharacteristic
31C2×#13063299C2211yescharacteristic
32C2×#13063299C2211yescharacteristic
33C2×#13063298—21no—
34C2×#13063298—21no—
35C2×C4×D172—21no—
36C2×#13063287C2211yescharacteristic
37C2×#13063287C2211yescharacteristic
38C2×C4×C22⋊D43C2211yescharacteristic
39C2×#13063283C2211yescharacteristic
40C2×#13063282—21no—
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583306C2218yescomplemented
43#14583226C2218yescomplemented
44#14583223C2218yescomplemented
45#14583223C2218yescomplemented
46#14583214C2218yescomplemented
47#14583202C2218yescomplemented
48#14583178C2218yescomplemented
49#14583153C2218yescomplemented
50#14583135C2218yescomplemented
51#14583010C2218yescomplemented
52#14582970C2218yescomplemented
53#14582938C2218yescomplemented
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C23×C8×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C2×#117×C43C2211yescharacteristic
72C43×#427C2218yescomplemented
73C2×#107×C43C2211yescharacteristic
74C2×#107×C43C2211yescharacteristic
75C2×#106×C43C2211yescharacteristic
76C2×#106×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×D172—21no—
79C22×D172—21no—
80C22×D172C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C22×C22⋊D43D411yescharacteristic
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43C2311yescharacteristic
89C2×D344—24no—
90C2×D344C2314yes—
91C2×#10621872—24no—
92C2×#10621872C2314yes—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95#13063324—22no—
96#13063324C2314yes—
97#13063319—28no—
98#13063316—22no—
99#13063316C2314yes—
100#13063313—28no—
101#13063311—28no—
102#13063307—28no—
103#13063300—22no—
104#13063300—22no—
105#13063300C2314yes—
106#13063300C2314yes—
107#13063299—22no—
108#13063299—22no—
109#13063299C2314yes—
110#13063299C2314yes—
111#13063298—28no—
112#13063298—28no—
113C4×D172—28no—
114#13063287—22no—
115#13063287—22no—
116#13063287C2314yes—
117#13063287C2314yes—
118C4×C22⋊D43D414yes—
119C4×C22⋊D43C2314yes—
120#13063283—22no—
121#13063283C2314yes—
122#13063282—28no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4D411yescharacteristic
130C4⋊C4×D43—22no—
131C4⋊C4×D43C2314yes—
132C2×C22⋊Dic43D411yescharacteristic
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×C4×Dic43—21no—
142C2×C4×Dic43C2311yescharacteristic
143#13063259C2314yes—
144#13063258C2314yes—
145#13063258C2314yes—
146#13063256C2314yes—
147#13063256C2314yes—
148Dic43⋊C8C2314yes—
149#13063247C2314yes—
150#13063247C2314yes—
151#13063245C2314yes—
152#13063245C2314yes—
153#13063245C2314yes—
154#13063245C2314yes—
155C22⋊(C43⋊C8)C2314yes—
156(C2×D43)⋊C8C2314yes—
157#13063235C2314yes—
158C23×C4×C43C2311yescharacteristic
159C22×C8×C43—24no—
160C22×C8×C43C2311yescharacteristic
161C22×C8×C43C2314yes—
162C22×C8×C43C2311yescharacteristic
163#117×C43—22no—
164#117×C43—22no—
165#117×C43C2314yes—
166#117×C43C2314yes—
167C2×C4⋊C4×C43C2311yescharacteristic
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C22⋊C4×C43—21no—
172C2×C22⋊C4×C43—21no—
173C2×C42×C43—21no—
174C2×C42×C43—21no—
175#107×C43C2314yes—
176#107×C43C2314yes—
177#106×C43C2314yes—
178#106×C43C2314yes—
179C24×C43C2×D411yescharacteristic
180C23×D43—21no—
181C23×D43—21no—
182C23×D43C2×D411yescharacteristic
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2411yescharacteristic
193C2×C22⋊D43—24no—
194C2×C22⋊D43—24no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—82no—
197C2×C22⋊D43—82no—
198C2×C22⋊D43C2×D414yes—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—24no—
207C2×D172—24no—
208C2×D172—22no—
209C2×D172—22no—
210C2×D172—22no—
211C2×D172—22no—
212C2×D172—44no—
213C2×D172—82no—
214C2×D172C2412yes—
215C2×D172C2412yes—
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×D43C2412yes—
226C2×Dic86—24no—
227C2×Dic86—82no—
228C2×C8×C43—22no—
229C2×C8×C43—28no—
230C2×C8×C43#4114yes—
231C2×C8×C43C2412yes—
232C2×C8×C43C2412yes—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C4⋊C4×C43C2412yes—
240C4⋊C4×C43C2412yes—
241C22⋊C4×C43—24no—
242C22⋊C4×C43—24no—
243C42×C43—24no—
244C42×C43—24no—
245C22⋊Dic43C2×D414yes—
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)⋊C4C2×D414yes—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—24no—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4C2×D414yes—
263C4×Dic43—24no—
264C4×Dic43C2×D412yes—
265C4×Dic43C2412yes—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—22no—
268C2×C43⋊C8C2412yes—
269C2×C43⋊C8C2412yes—
270D344—28no—
271#10621872—28no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43C22×D412yes—
276C23×C43C22×D411yescharacteristic
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43—42no—
288C22×D43C22×D412yes—
289C2×C4×C43—22no—
290C2×C4×C43—24no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43C22×D412yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C2×#4112yes—
304C2×C4×C432−1+412yes—
305C2×C4×C43C2511yescharacteristic
306C22⋊D43—44no—
307C22⋊D43—84no—
308C22⋊D43—84no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43C22×D412yes—
317C2×Dic43C22×D412yes—
318C2×Dic43C22×D412yes—
319D172—22no—
320D172—22no—
321D172—22no—
322D172—22no—
323D172—48no—
324D172—42no—
325D172—42no—
326D172—84no—
327C4×D43—24no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—48no—
331C4×D43—84no—
332C4×D43—84no—
333Dic86—84no—
334C8×C43—22no—
335C8×C43C2×#4114yes—
336C43⋊C8—22no—
337C43⋊C8—22no—
338C2×#3347—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—44no—
343C22×C43#54712yes—
344C22×C43#57512yes—
345C22×C43#57612yes—
346C22×C43C23×D411yescharacteristic
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
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—42no—
361C4×C43—42no—
362C4×C43—42no—
363C4×C43—42no—
364C4×C43#54712yes—
365C4×C43C22×#4111yescharacteristic
366C4×C43C2×2−1+411yescharacteristic
367Dic43—22no—
368Dic43—22no—
369Dic43—22no—
370Dic43—42no—
371Dic43—42no—
372C2×#555—431no—
373C2×#553—431no—
374#3347—4316no—
375C2×#501—431no—
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×#427D4311yescharacteristic, complemented
388C2×C43—42no—
389C2×C43#334714yescomplemented
390C2×C43C2×#54711yescharacteristic
391C2×C43C2×#57511yescharacteristic
392C2×C43C2×#57611yescharacteristic
393D43—42no—
394D43—82no—
395D43—82no—
396C22×D8—431no—
397C22×M16—431no—
398C23×C8C2×D4311yescharacteristic
399#555—438no—
400#555—864no—
401#553—438no—
402#553—864no—
403C2×C4⋊Q8—431no—
404C2×#126—861no—
405C2×#125—431no—
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—861no—
421C2×#117C2×D4311yescharacteristic
422C2×#117C2×D4311yescharacteristic
423C22×C4⋊C4—431no—
424#501—438no—
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#427C2×D4318yescomplemented
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×#97—431no—
456C43C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—861no—
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—861no—
467C23×C4—861no—
468C23×C4—861no—
469C23×C4C22×D4311yescharacteristic
470C2×D8—434no—
471C2×D8—864no—
472C2×M16—434no—
473C2×M16—864no—
474C22×C8—24no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4314yes—
479C22×C8C22×D4311yescharacteristic
480C4⋊Q8—434no—
481C4⋊Q8—862no—
482#126—868no—
483#125—434no—
484#125—862no—
485#124—868no—
486#124—868no—
487#123—868no—
488#121—434no—
489#121—434no—
490#121—434no—
491#121—434no—
492#121—868no—
493#121—868no—
494#121—862no—
495#121—862no—
496#121—862no—
497#121—862no—
498C4×D4—434no—
499C4×D4—434no—
500C4×D4—434no—
501C4×D4—434no—
502C4×D4—868no—
503C4×D4—862no—
504C4×D4—862no—
505#117—22no—
506#117—22no—
507#117—434no—
508#117—868no—
509#117—862no—
510#117C22×D4314yes—
511#117C22×D4314yes—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—434no—
516C2×C4⋊C4—862no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4C22×D4311yescharacteristic
522C2×C4⋊C4C22×D4311yescharacteristic
523C2×C4⋊C4C22×D4311yescharacteristic
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—431no—
528C2×C22⋊C4—431no—
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—21no—
537C2×C42—21no—
538C2×C42—431no—
539C2×C42—861no—
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#97—434no—
559C24—431no—
560C24—861no—
561C24—861no—
562C24D4×D4311yescharacteristic
563C2×Q8—864no—
564C2×Q8—3442no—
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—1724no—
582C2×D4—1722no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—431no—
590C22×C4—431no—
591C22×C4—431no—
592C22×C4—432no—
593C22×C4—432no—
594C22×C4—864no—
595C22×C4—864no—
596C22×C4—864no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—3442no—
602C22×C4—3442no—
603C22×C4—1724no—
604C22×C4D4×D4312yes—
605C22×C4D4×D4311yescharacteristic
606C22×C4C23×D4312yes—
607C22×C4C23×D4311yescharacteristic
608D8—868no—
609M16—868no—
610C2×C8—22no—
611C2×C8—28no—
612C2×C8—432no—
613C2×C8—432no—
614C2×C8—862no—
615C2×C8—862no—
616C2×C8#1062189814yes—
617C2×C8C23×D4312yes—
618C2×C8C23×D4312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—434no—
624C4⋊C4—432no—
625C4⋊C4—432no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4C23×D4312yes—
633C4⋊C4C23×D4312yes—
634C4⋊C4C23×D4312yes—
635C4⋊C4C23×D4312yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
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—
647C42—24no—
648C42—24no—
649C42—432no—
650C42—432no—
651C42—864no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—432no—
656C23—862no—
657C23—862no—
658C23—862no—
659C23—862no—
660C23—862no—
661C23—1722no—
662C23—1722no—
663C23—1722no—
664C23—1722no—
665C23—1722no—
666C23—1722no—
667C23C2×D4×D4312yes—
668C23C2×D4×D4311yescharacteristic
669Q8—3444no—
670D4—862no—
671D4—862no—
672D4—862no—
673D4—862no—
674D4—3444no—
675D4—3444no—
676D4—3444no—
677D4—1728no—
678D4—1724no—
679D4—1722no—
680D4—1722no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—432no—
694C2×C4—432no—
695C2×C4—432no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—864no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—3444no—
705C2×C4—3444no—
706C2×C4—1728no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4C2×D4×D4312yes—
710C2×C4C2×D4×D4311yescharacteristic
711C2×C4C2×#1062189812yes—
712C2×C4#1306337312yes—
713C2×C4C24×D4311yescharacteristic
714C8—22no—
715C8—862no—
716C8—862no—
717C8C2×#1062189814yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—862no—
723C22—862no—
724C22—862no—
725C22—3444no—
726C22—3444no—
727C22—1722no—
728C22—1722no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1722no—
733C22—1724no—
734C22#1458355012yes—
735C22#1458369612yes—
736C22#1458370112yes—
737C22C22×D4×D4311yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—862no—
744C4—862no—
745C4—862no—
746C4—1722no—
747C4—1722no—
748C4#1458355012yes—
749C4C22×#1062189811yescharacteristic
750C4C2×#1306337311yescharacteristic
751C2—42no—
752C2—3442no—
753C2—3442no—
754C2—1722no—
755C2#1914709114yesdirect product factor
756C2C2×#1458355011yescharacteristic
757C2C2×#1458369611yescharacteristic
758C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#427C2
socleC23×C43C22×D4
hypercenterC2×#427D43
hypocenterC43C2×#3347
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
1. C2×#14583612C2semidirect
2. C2×#14583593C2semidirect
3. #19147091C2direct (N × H)
4. C2×#14583306C2semidirect
5. C2×#14583226C2semidirect
6. C2×#14583223C2semidirect
7. C2×#14583223C2semidirect
8. C2×#14583214C2semidirect
9. C2×#14583202C2semidirect
10. C2×#14583178C2semidirect
11. C2×#14583153C2semidirect
12. C2×#14583135C2semidirect
13. C2×#14583010C2semidirect
14. C2×#14582970C2semidirect
15. C2×#14582938C2semidirect
16. C2×C43×#427C2semidirect
20. #14583612C22semidirect
22. #14583593C22semidirect
42. #14583306C22semidirect
43. #14583226C22semidirect
44. #14583223C22semidirect
45. #14583223C22semidirect
46. #14583214C22semidirect
47. #14583202C22semidirect
48. #14583178C22semidirect
49. #14583153C22semidirect
50. #14583135C22semidirect
51. #14583010C22semidirect
52. #14582970C22semidirect
53. #14582938C22semidirect
72. C43×#427C22semidirect
387. C2×#427D43semidirect
389. C2×C43#3347semidirect
436. #427C2×D43semidirect
456. C43C2×#3347semidirect
755. C2#19147091direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836122
C2×#145835932
#191470912
C2×#145833062
C2×#145832262
C2×#145832232
C2×#145832142
C2×#145832022
C2×#145831782
C2×#145831532
C2×#145831352
C2×#145830102
C2×#145829702
C2×#145829382
C2×C43×#4272
C2×#334743