Finite Group Databasebeta

← C2×#19145275 #25966478

Subgroups — C2×#19145275 #25966478

Order 11008.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583518C211yesmaximal, characteristic, complemented
2C2×#14583503C211yesmaximal, characteristic, complemented
3#19145275C2116yesmaximal, direct product factor
4C2×#14583308C211yesmaximal, characteristic, complemented
5C2×#14583253C211yesmaximal, characteristic, complemented
6C2×#14583245C211yesmaximal, characteristic, complemented
7C2×#14583149C211yesmaximal, characteristic, complemented
8C2×#14583142C211yesmaximal, characteristic, complemented
9C2×#14583132C211yesmaximal, characteristic, complemented
10C2×#14583125C211yesmaximal, characteristic, complemented
11C2×#14583011C211yesmaximal, characteristic, complemented
12C2×#14583000C211yesmaximal, characteristic, complemented
13C2×SD16×Dic43C211yesmaximal, characteristic, complemented
14C2×D8×Dic43C211yesmaximal, characteristic, complemented
15C2×#14582856C211yesmaximal, characteristic, complemented
16C2×C43×#496C211yesmaximal, characteristic, complemented
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583518—24no—
20#14583518C2218yescomplemented
21#14583503—24no—
22#14583503C2218yescomplemented
23C2×#13063325C2211yescharacteristic
24C2×#13063318—21no—
25C2×#13063317C2211yescharacteristic
26C2×#13063311—21no—
27C2×#13063309—21no—
28C2×#13063306—21no—
29C2×#13063306—21no—
30C2×#13063302—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063297—21no—
33C2×#13063297—21no—
34C2×#13063296C2211yescharacteristic
35C2×#13063296C2211yescharacteristic
36C2×#13063296C2211yescharacteristic
37C2×Q8×Dic43C2211yescharacteristic
38C2×D4×Dic43C2211yescharacteristic
39C2×D4×Dic43C2211yescharacteristic
40C2×D4×Dic43C2211yescharacteristic
41C2×#13063282C2211yescharacteristic
42#14583308C2218yescomplemented
43#14583253C2218yescomplemented
44#14583245C2218yescomplemented
45#14583149C2218yescomplemented
46#14583142C2218yescomplemented
47#14583132C2218yescomplemented
48#14583125C2218yescomplemented
49#14583011C2218yescomplemented
50#14583000C2218yescomplemented
51SD16×Dic43C2218yescomplemented
52D8×Dic43C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063257C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063249C2211yescharacteristic
58C2×#13063249C2211yescharacteristic
59C2×#13063246C2211yescharacteristic
60C2×#13063246C2211yescharacteristic
61C2×#13063246C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65#14582856C2218yescomplemented
66C2×#13063235C2211yescharacteristic
67C2×C4×C43⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C22×D8×C43C2211yescharacteristic
72C22×D8×C43C2211yescharacteristic
73C2×#127×C43C2211yescharacteristic
74C2×#124×C43C2211yescharacteristic
75C43×#496C2218yescomplemented
76C2×#97×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×C22⋊D43—21no—
79C22×C22⋊D43—21no—
80C22×C22⋊D43—21no—
81C23×Dic43—21no—
82C23×Dic43—21no—
83C23×Dic43—21no—
84C22×C4×D43C2311yescharacteristic
85C2×#10621872—24no—
86C2×#10621872C2314yes—
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C2×C8×D43—24no—
90C2×C8×D43C2314yes—
91#13063325—22no—
92#13063325C2314yes—
93#13063318—28no—
94#13063317—22no—
95#13063317C2314yes—
96#13063311—28no—
97#13063309—28no—
98#13063306—28no—
99#13063306—28no—
100#13063302—28no—
101#13063301—22no—
102#13063301C2314yes—
103#13063297—28no—
104#13063297—28no—
105#13063296—22no—
106#13063296—22no—
107#13063296—22no—
108#13063296C2314yes—
109#13063296C2314yes—
110#13063296C2314yes—
111Q8×Dic43—22no—
112Q8×Dic43C2314yes—
113D4×Dic43—22no—
114D4×Dic43—22no—
115D4×Dic43—22no—
116D4×Dic43C2314yes—
117D4×Dic43C2314yes—
118D4×Dic43C2314yes—
119#13063282D414yes—
120#13063282C2314yes—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4D411yescharacteristic
131C2×Dic43⋊C4D411yescharacteristic
132C2×C22⋊Dic43—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)⋊C4D411yescharacteristic
140C2×(C2×D43)⋊C4D411yescharacteristic
141C2×C4×Dic43—21no—
142C2×C4×Dic43C2311yescharacteristic
143#13063259C2314yes—
144#13063259C2314yes—
145#13063257C2314yes—
146#13063257C2314yes—
147#13063249C2314yes—
148#13063249C2314yes—
149#13063246C2314yes—
150#13063246C2314yes—
151#13063246C2314yes—
152#13063246C2314yes—
153#13063246C2314yes—
154#13063246C2314yes—
155#13063235C2314yes—
156C4×C43⋊C8C2314yes—
157C8×Dic43C2314yes—
158C22×Q8×C43C2311yescharacteristic
159C22×D4×C43—21no—
160C22×D4×C43—21no—
161C22×D4×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C22×D4×C43C2311yescharacteristic
164C2×SD16×C43—24no—
165C2×SD16×C43—24no—
166C2×SD16×C43C2314yes—
167C2×SD16×C43C2314yes—
168C2×D8×C43—24no—
169C2×D8×C43—24no—
170C2×D8×C43C2314yes—
171C2×D8×C43C2314yes—
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174#127×C43—22no—
175#127×C43C2314yes—
176#124×C43—22no—
177#124×C43C2314yes—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#97×C43C2314yes—
182C24×C43—21no—
183C24×C43—21no—
184C24×C43—21no—
185C23×D43C2×D411yescharacteristic
186C2×Q8×C43—21no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43C2412yes—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—24no—
194C2×D4×C43—24no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—22no—
201C2×D4×C43—82no—
202C2×D4×C43—82no—
203C2×D4×C43C2412yes—
204C2×D4×C43C2412yes—
205C2×D4×C43C2412yes—
206C22×C4×C43—21no—
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2411yescharacteristic
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—82no—
214C2×C22⋊D43—82no—
215C2×C22⋊D43—82no—
216C22×Dic43—24no—
217C22×Dic43—24no—
218C22×Dic43—24no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—82no—
224C22×Dic43—82no—
225C22×Dic43—82no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43C2×D412yes—
232C2×C4×D43C2412yes—
233C2×Dic86—24no—
234C2×Dic86—82no—
235SD16×C43—28no—
236SD16×C43—28no—
237D8×C43—28no—
238D8×C43—28no—
239C2×C8×C43#4114yes—
240C2×C8×C43#4114yes—
241C2×C8×C43C2412yes—
242C2×C8×C43C2412yes—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—24no—
245C42×C43C2×D412yes—
246C42×C43C2412yes—
247C22⋊Dic43—24no—
248C22⋊Dic43—24no—
249C22⋊Dic43—24no—
250C22⋊Dic43—24no—
251C22⋊Dic43—24no—
252C22⋊Dic43—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4C2×D414yes—
255(C2×D43)⋊C4C2×D414yes—
256C4⋊Dic43—24no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—24no—
262C4⋊Dic43C2412yes—
263C4⋊Dic43C2412yes—
264C4⋊Dic43C2412yes—
265C4⋊Dic43C2412yes—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269Dic43⋊C4C2×D414yes—
270Dic43⋊C4C2×D414yes—
271C4×Dic43—24no—
272C4×Dic43C2×D412yes—
273C4×Dic43C2412yes—
274C2×C43⋊C8—22no—
275C2×C43⋊C8—22no—
276C2×C43⋊C8C2412yes—
277C2×C43⋊C8C2412yes—
278#10621872—28no—
279C8×D43—28no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—42no—
284C23×C43—42no—
285C23×C43—42no—
286C23×C43—42no—
287C23×C43—42no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43—42no—
292C23×C43C22×D411yescharacteristic
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43C22×D412yes—
297Q8×C43—22no—
298Q8×C43—22no—
299Q8×C43—42no—
300D4×C43—22no—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—22no—
304D4×C43—22no—
305D4×C43—22no—
306D4×C43—42no—
307D4×C43—42no—
308D4×C43—42no—
309D4×C43—84no—
310D4×C43—84no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—42no—
315C2×C4×C43C22×D412yes—
316C2×C4×C43C22×D412yes—
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C2×#4112yes—
319C2×C4×C43C2×#4112yes—
320C2×C4×C43C2511yescharacteristic
321C22⋊D43—84no—
322C22⋊D43—84no—
323C22⋊D43—84no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—84no—
336C2×Dic43—84no—
337C2×Dic43—84no—
338C2×Dic43C22×D412yes—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341C4×D43—24no—
342C4×D43—22no—
343C4×D43—22no—
344Dic86—84no—
345C8×C43C2×#4114yes—
346C8×C43C2×#4114yes—
347C43⋊C8—22no—
348C43⋊C8—22no—
349C2×#3179—431nomaximal, Sylow
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—84no—
360C22×C43—84no—
361C22×C43—84no—
362C22×C43#53212yes—
363C22×C43#57612yes—
364C22×C43#57712yes—
365C22×C43C23×D411yescharacteristic
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—44no—
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—42no—
373C4×C43#53212yes—
374C4×C43C22×#4111yescharacteristic
375C4×C43C22×#4111yescharacteristic
376Dic43—22no—
377Dic43—22no—
378Dic43—22no—
379Dic43—42no—
380Dic43—42no—
381Dic43—42no—
382Dic43—42no—
383C2×#542—431no—
384C2×#540—431no—
385#3179—4316no—
386C2×#501—431no—
387C2×#496D4311yescharacteristic, complemented
388C2×#488—431no—
389C2×#486—431no—
390C2×#469—431no—
391C2×#468—431no—
392C2×#466—431no—
393C2×#465—431no—
394C2×#442—431no—
395C2×#440—431no—
396C2×C4×SD16—431no—
397C2×C4×D8—431no—
398C2×#405—431no—
399C2×C43—82no—
400C2×C43—82no—
401C2×C43—82no—
402C2×C43#317914yescomplemented
403C2×C43C2×#53211yescharacteristic
404C2×C43C2×#57611yescharacteristic
405C2×C43C2×#57711yescharacteristic
406D43—42no—
407C22×SD16C2×D4311yescharacteristic
408C22×SD16C2×D4311yescharacteristic
409C22×D8C2×D4311yescharacteristic
410C22×D8C2×D4311yescharacteristic
411C22×M16—431no—
412C23×C8—431no—
413#542—438no—
414#542—864no—
415#540—438no—
416#540—864no—
417C2×C4⋊Q8—431no—
418C2×#127C2×D4311yescharacteristic
419C2×#126—861no—
420C2×#125—431no—
421C2×#124—861no—
422C2×#124C2×D4311yescharacteristic
423C2×#123—861no—
424C2×#123—861no—
425C2×#123—861no—
426C2×C22⋊Q8—431no—
427C2×C22⋊Q8—861no—
428C2×#121—431no—
429C2×#121—431no—
430C2×#121—431no—
431C2×#121—861no—
432C2×#121—861no—
433C2×C4×Q8—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—431no—
437C2×#117—431no—
438#501—438no—
439#496C2×D4318yescomplemented
440#488—438no—
441#486—438no—
442#469—438no—
443#468—438no—
444#466—438no—
445#465—438no—
446#442—438no—
447#440—438no—
448C4×SD16—438no—
449C4×D8—438no—
450C2×#107—431no—
451C2×#107—431no—
452C2×#106—431no—
453C2×#106—431no—
454C2×#103—431no—
455C2×#103—431no—
456C2×#102—431no—
457C2×#102—431no—
458C2×#102—431no—
459C2×#102—431no—
460C2×#102—431no—
461C2×#102—431no—
462#405—438no—
463C2×#97—431no—
464C2×#97C2×D4311yescharacteristic
465C2×C4×C8—431no—
466C2×C4×C8—431no—
467C43C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—861no—
469C22×Q8C22×D4311yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—861no—
473C22×D4—861no—
474C22×D4—861no—
475C22×D4C22×D4311yescharacteristic
476C22×D4C22×D4311yescharacteristic
477C22×D4C22×D4311yescharacteristic
478C23×C4—431no—
479C23×C4—861no—
480C23×C4—861no—
481C23×C4—861no—
482C2×SD16—24no—
483C2×SD16—24no—
484C2×SD16C22×D4314yes—
485C2×SD16C22×D4314yes—
486C2×D8—24no—
487C2×D8—24no—
488C2×D8C22×D4314yes—
489C2×D8C22×D4314yes—
490C2×M16—434no—
491C2×M16—864no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8—434no—
495C22×C8—864no—
496C22×C8C22×D4311yescharacteristic
497C22×C8C22×D4311yescharacteristic
498C4⋊Q8—434no—
499C4⋊Q8—862no—
500#127—22no—
501#127C22×D4314yes—
502#126—868no—
503#125—434no—
504#125—862no—
505#124—22no—
506#124—868no—
507#124C22×D4314yes—
508#123—868no—
509#123—868no—
510#123—868no—
511C22⋊Q8—434no—
512C22⋊Q8—868no—
513C22⋊Q8—862no—
514#121—434no—
515#121—434no—
516#121—434no—
517#121—868no—
518#121—868no—
519#121—862no—
520#121—862no—
521#121—862no—
522C4×Q8—434no—
523C4×Q8—862no—
524C4×D4—434no—
525C4×D4—434no—
526C4×D4—434no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4—862no—
530#117—434no—
531#117—434no—
532C2×C4⋊C4—431no—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—431no—
546C2×C22⋊C4—431no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C42—431no—
555C2×C42—861no—
556C2×C42C22×D4311yescharacteristic
557#107—434no—
558#107—434no—
559#106—434no—
560#106—434no—
561#103—434no—
562#103—434no—
563#102—434no—
564#102—434no—
565#102—434no—
566#102—434no—
567#102—434no—
568#102—434no—
569#97—434no—
570#97C22×D4314yes—
571C4×C8—434no—
572C4×C8—434no—
573C24—21no—
574C24—21no—
575C24—21no—
576C24—431no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—864no—
581C2×Q8—3442no—
582C2×Q8C23×D4312yes—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—24no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—82no—
595C2×D4—82no—
596C2×D4—864no—
597C2×D4—864no—
598C2×D4—864no—
599C2×D4—3442no—
600C2×D4—3442no—
601C2×D4—3442no—
602C2×D4C23×D4312yes—
603C2×D4C23×D4312yes—
604C2×D4C23×D4312yes—
605C22×C4—21no—
606C22×C4—431no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—432no—
610C22×C4—432no—
611C22×C4—864no—
612C22×C4—864no—
613C22×C4—864no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—3442no—
621C22×C4—3442no—
622C22×C4—3442no—
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4C23×D4311yescharacteristic
626SD16—28no—
627SD16—28no—
628D8—28no—
629D8—28no—
630M16—868no—
631C2×C8—432no—
632C2×C8—432no—
633C2×C8—862no—
634C2×C8—862no—
635C2×C8—868no—
636C2×C8#1062190014yes—
637C2×C8#1062190014yes—
638C2×C8C23×D4312yes—
639C2×C8C23×D4312yes—
640C4⋊C4—434no—
641C4⋊C4—434no—
642C4⋊C4—432no—
643C4⋊C4—432no—
644C4⋊C4—432no—
645C4⋊C4—432no—
646C4⋊C4—864no—
647C4⋊C4—864no—
648C4⋊C4—861no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—864no—
653C4⋊C4—864no—
654C4⋊C4—864no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—434no—
658C22⋊C4—434no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C22⋊C4—864no—
662C22⋊C4—864no—
663C22⋊C4—864no—
664C22⋊C4—864no—
665C22⋊C4—864no—
666C42—432no—
667C42—432no—
668C42—864no—
669C42D4×D4312yes—
670C42C23×D4312yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—432no—
684C23—862no—
685C23—862no—
686C23—862no—
687C23C2×D4×D4311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—3444no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—84no—
702D4—84no—
703D4—3444no—
704D4—3444no—
705D4—3444no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—432no—
711C2×C4—432no—
712C2×C4—432no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—864no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—3444no—
724C2×C4—3444no—
725C2×C4—3444no—
726C2×C4—1722no—
727C2×C4—1722no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4C2×D4×D4312yes—
731C2×C4C2×D4×D4312yes—
732C2×C4C2×D4×D4311yescharacteristic
733C2×C4C2×#1062190012yes—
734C2×C4C2×#1062190012yes—
735C2×C4C24×D4311yescharacteristic
736C8—862no—
737C8—862no—
738C8C2×#1062190014yes—
739C8C2×#1062190014yes—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—84no—
750C22—84no—
751C22—84no—
752C22—862no—
753C22—862no—
754C22—862no—
755C22—1724no—
756C22#1458344712yes—
757C22#1458370312yes—
758C22#1458370912yes—
759C22C22×D4×D4311yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—862no—
764C4—862no—
765C4—862no—
766C4—1722no—
767C4—1722no—
768C4—1722no—
769C4—1722no—
770C4#1458344712yes—
771C4C22×#1062190011yescharacteristic
772C4C22×#1062190011yescharacteristic
773C2—82no—
774C2—82no—
775C2—82no—
776C2—1722no—
777C2#1914527514yesdirect product factor
778C2C2×#1458344711yescharacteristic
779C2C2×#1458370311yescharacteristic
780C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#496C2
socleC23×C43C22×D4
hypercenterC2×#496D43
hypocenterC43C2×#3179
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#14583518C2semidirect
2. C2×#14583503C2semidirect
3. #19145275C2direct (N × H)
4. C2×#14583308C2semidirect
5. C2×#14583253C2semidirect
6. C2×#14583245C2semidirect
7. C2×#14583149C2semidirect
8. C2×#14583142C2semidirect
9. C2×#14583132C2semidirect
10. C2×#14583125C2semidirect
11. C2×#14583011C2semidirect
12. C2×#14583000C2semidirect
13. C2×SD16×Dic43C2semidirect
14. C2×D8×Dic43C2semidirect
15. C2×#14582856C2semidirect
16. C2×C43×#496C2semidirect
20. #14583518C22semidirect
22. #14583503C22semidirect
42. #14583308C22semidirect
43. #14583253C22semidirect
44. #14583245C22semidirect
45. #14583149C22semidirect
46. #14583142C22semidirect
47. #14583132C22semidirect
48. #14583125C22semidirect
49. #14583011C22semidirect
50. #14583000C22semidirect
51. SD16×Dic43C22semidirect
52. D8×Dic43C22semidirect
65. #14582856C22semidirect
75. C43×#496C22semidirect
387. C2×#496D43semidirect
402. C2×C43#3179semidirect
439. #496C2×D43semidirect
467. C43C2×#3179semidirect
777. C2#19145275direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835182
C2×#145835032
#191452752
C2×#145833082
C2×#145832532
C2×#145832452
C2×#145831492
C2×#145831422
C2×#145831322
C2×#145831252
C2×#145830112
C2×#145830002
C2×SD16×Dic432
C2×D8×Dic432
C2×#145828562
C2×C43×#4962
C2×#317943