Finite Group Databasebeta

← C2×#19146155 #25971631

Subgroups — C2×#19146155 #25971631

Order 11008.

2774 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063358C211yesmaximal, characteristic, complemented
2C22×#13063347C211yesmaximal, characteristic, complemented
3C2×#14583558C211yesmaximal, characteristic, complemented
4C2×#14583554C211yesmaximal, characteristic, complemented
5#19146155C2116yesmaximal, direct product factor
6C2×#14583293C211yesmaximal, characteristic, complemented
7C2×#14583145C211yesmaximal, characteristic, complemented
8C2×#14583140C211yesmaximal, characteristic, complemented
9C2×#14583110C211yesmaximal, characteristic, complemented
10C2×#14583115C211yesmaximal, characteristic, complemented
11C2×#14583063C211yesmaximal, characteristic, complemented
12C2×#14583063C211yesmaximal, characteristic, complemented
13C2×#14583046C211yesmaximal, characteristic, complemented
14C2×#14583057C211yesmaximal, characteristic, complemented
15C2×#14583001C211yesmaximal, characteristic, complemented
16C2×C43×#435C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621898C2211yescharacteristic
19C22×#10621898C2211yescharacteristic
20C23×Dic86C2211yescharacteristic
21C2×#13063358—28no—
22C2×#13063358C2218yescomplemented
23C2×#13063347—28no—
24C2×#13063347C2218yescomplemented
25C22×Dic172C2211yescharacteristic
26C22×Dic172C2211yescharacteristic
27C22×Dic172C2211yescharacteristic
28C22×Dic172C2211yescharacteristic
29C22×#10621873C2211yescharacteristic
30C22×#10621873C2211yescharacteristic
31C22×#10621873C2211yescharacteristic
32C22×#10621873C2211yescharacteristic
33C22×D344C2211yescharacteristic
34#14583558—24no—
35#14583558C2218yescomplemented
36#14583554—24no—
37#14583554C2218yescomplemented
38C2×#13063325C2211yescharacteristic
39C2×#13063313C2211yescharacteristic
40C2×#13063311—21no—
41C2×#13063307—21no—
42C2×#13063307—21no—
43C2×#13063304C2211yescharacteristic
44C2×#13063304C2211yescharacteristic
45C2×#13063304C2211yescharacteristic
46C2×#13063303—21no—
47C2×#13063299C2211yescharacteristic
48C2×#13063297—21no—
49C2×#13063296—21no—
50C2×C4×Dic86C2211yescharacteristic
51C2×C4×D172C2211yescharacteristic
52C2×(C22⋊D43)⋊C4—21no—
53C2×C4⋊C4×D43—21no—
54#14583293C2218yescomplemented
55#14583145C2218yescomplemented
56#14583140C2218yescomplemented
57#14583115C2218yescomplemented
58#14583110C2218yescomplemented
59#14583063C2218yescomplemented
60#14583063C2218yescomplemented
61#14583057C2218yescomplemented
62#14583046C2218yescomplemented
63#14583001C2218yescomplemented
64C2×#13063259C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063250C2211yescharacteristic
67C2×#13063250C2211yescharacteristic
68C2×#13063250C2211yescharacteristic
69C2×#13063247C2211yescharacteristic
70C2×#13063247C2211yescharacteristic
71C22×M16×C43C2211yescharacteristic
72C23×C8×C43C2211yescharacteristic
73C2×C4×D4×C43C2211yescharacteristic
74C43×#435C2218yescomplemented
75C2×C4⋊C8×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×C22⋊C8×C43C2211yescharacteristic
78C2×#97×C43C2211yescharacteristic
79C2×#10621898—22no—
80C2×#10621898—22no—
81C2×#10621898—22no—
82C2×#10621898—24no—
83C2×#10621898—24no—
84C2×#10621898—24no—
85C2×#10621898—42no—
86C2×#10621898—42no—
87C2×#10621898—42no—
88C2×#10621898C2314yes—
89C2×#10621898C2314yes—
90C2×#10621898C2314yes—
91C22×Dic86—24no—
92C22×Dic86—22no—
93C22×Dic86—21no—
94C22×Dic86—42no—
95C22×Dic86C2311yescharacteristic
96C22×Dic86C2311yescharacteristic
97C22×Dic86C2311yescharacteristic
98C22×Dic86C2314yes—
99C22×Dic86C2311yescharacteristic
100C22×D172C2311yescharacteristic
101C22×D172C2311yescharacteristic
102C22×C22⋊D43—21no—
103C22×C22⋊D43—21no—
104C22×C22⋊D43—21no—
105C22×C22⋊D43—21no—
106C23×Dic43—21no—
107C22×C4×D43—21no—
108C22×C4×D43—21no—
109C22×C4×D43—21no—
110C22×C4×D43—21no—
111#13063358—232no—
112#13063347—232no—
113C2×Dic172—24no—
114C2×Dic172—24no—
115C2×Dic172—24no—
116C2×Dic172—42no—
117C2×Dic172C2314yes—
118C2×Dic172C2314yes—
119C2×Dic172C2314yes—
120C2×Dic172C2314yes—
121C2×#10621873—24no—
122C2×#10621873—24no—
123C2×#10621873—42no—
124C2×#10621873D418yescomplemented
125C2×#10621873C2314yes—
126C2×#10621873C2314yes—
127C2×#10621873C2314yes—
128C2×#10621873C2314yes—
129C2×D344—24no—
130C2×D344C2314yes—
131#13063325—22no—
132#13063325C2314yes—
133#13063313—22no—
134#13063313C2314yes—
135#13063311—28no—
136#13063307—28no—
137#13063307—28no—
138#13063304—22no—
139#13063304—22no—
140#13063304—22no—
141#13063304C2314yes—
142#13063304C2314yes—
143#13063304C2314yes—
144#13063303—28no—
145#13063299—22no—
146#13063299C2314yes—
147#13063297—28no—
148#13063296—28no—
149C4×Dic86—22no—
150C4×Dic86C2314yes—
151C4×D172—22no—
152C4×D172C2314yes—
153(C22⋊D43)⋊C4—28no—
154C2×C4⋊Dic43—21no—
155C2×C4⋊Dic43—21no—
156C2×C4⋊Dic43C2311yescharacteristic
157C2×C4⋊Dic43C2311yescharacteristic
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4—21no—
162C4⋊C4×D43—28no—
163C2×C22⋊Dic43—21no—
164C2×C22⋊Dic43—21no—
165C2×C22⋊Dic43—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4—21no—
169C2×(C2×D43)⋊C4—21no—
170C2×C4×Dic43—21no—
171#13063259C2314yes—
172#13063250C2314yes—
173#13063250C2314yes—
174#13063250C2314yes—
175#13063250C2314yes—
176#13063247C2314yes—
177#13063247C2314yes—
178C22×D4×C43D411yescharacteristic
179C23×C4×C43C2311yescharacteristic
180C23×C4×C43C2311yescharacteristic
181C2×M16×C43—24no—
182C2×M16×C43C2314yes—
183C22×C8×C43—24no—
184C22×C8×C43C2314yes—
185C22×C8×C43C2311yescharacteristic
186C22×C8×C43C2311yescharacteristic
187C22×C8×C43C2311yescharacteristic
188C22×C8×C43C2311yescharacteristic
189C4×D4×C43D414yes—
190C4×D4×C43C2314yes—
191C2×C4⋊C4×C43D411yescharacteristic
192C2×C22⋊C4×C43D411yescharacteristic
193C2×C22⋊C4×C43D411yescharacteristic
194C2×C42×C43C2311yescharacteristic
195C4⋊C8×C43C2314yes—
196C22⋊C8×C43C2314yes—
197C22⋊C8×C43C2314yes—
198#97×C43C2314yes—
199C24×C43C2×D411yescharacteristic
200C24×C43C2×D411yescharacteristic
201C23×D43—21no—
202C23×D43—21no—
203C2×D4×C43—42no—
204C2×D4×C43C2×D414yes—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2412yes—
217C22×C4×C43C2411yescharacteristic
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—24no—
222C2×C22⋊D43—44no—
223C2×C22⋊D43—44no—
224C2×C22⋊D43—44no—
225C2×C22⋊D43—44no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—24no—
233C22×Dic43—44no—
234#10621898—28no—
235#10621898—28no—
236#10621898—28no—
237#10621898—44no—
238#10621898—44no—
239#10621898—44no—
240#10621898—48no—
241#10621898—48no—
242#10621898—48no—
243C2×D172—21no—
244C2×D172—22no—
245C2×D172—21no—
246C2×D172—22no—
247C2×D172—22no—
248C2×D172C2×D414yes—
249C2×D172C2412yes—
250C2×D172C2412yes—
251C2×C4×D43—24no—
252C2×C4×D43—24no—
253C2×C4×D43—24no—
254C2×C4×D43—24no—
255C2×C4×D43—44no—
256C2×C4×D43—44no—
257C2×C4×D43—44no—
258C2×C4×D43—44no—
259C2×Dic86—21no—
260C2×Dic86—22no—
261C2×Dic86—22no—
262C2×Dic86—22no—
263C2×Dic86—22no—
264C2×Dic86—22no—
265C2×Dic86—22no—
266C2×Dic86—22no—
267C2×Dic86—28no—
268C2×Dic86—24no—
269C2×Dic86—21no—
270C2×Dic86—21no—
271C2×Dic86—21no—
272C2×Dic86—44no—
273C2×Dic86—48no—
274C2×Dic86—44no—
275C2×Dic86C2×D414yes—
276C2×Dic86C2412yes—
277C2×Dic86C2412yes—
278C2×Dic86C2412yes—
279C2×Dic86C2412yes—
280M16×C43—28no—
281C2×C8×C43—22no—
282C2×C8×C43—22no—
283C2×C8×C43—22no—
284C2×C8×C43—28no—
285C2×C8×C43C2×D414yes—
286C2×C8×C43C2412yes—
287C2×C8×C43C2412yes—
288C2×C8×C43C2412yes—
289C2×C8×C43C2412yes—
290C4⋊C4×C43C2×D414yes—
291C22⋊C4×C43C2×D414yes—
292C22⋊C4×C43C2×D414yes—
293C42×C43C2×D412yes—
294C42×C43C2412yes—
295C22⋊Dic43—24no—
296C22⋊Dic43—24no—
297C22⋊Dic43—24no—
298(C2×D43)⋊C4—24no—
299(C2×D43)⋊C4—24no—
300(C2×D43)⋊C4—24no—
301(C2×D43)⋊C4—24no—
302C4⋊Dic43—24no—
303C4⋊Dic43—24no—
304C4⋊Dic43—21no—
305C4⋊Dic43—21no—
306C4⋊Dic43C2412yes—
307C4⋊Dic43C2412yes—
308Dic43⋊C4—24no—
309Dic43⋊C4—24no—
310Dic43⋊C4—24no—
311Dic43⋊C4—24no—
312C4×Dic43—24no—
313Dic172—28no—
314Dic172—28no—
315Dic172—28no—
316Dic172—44no—
317D344—28no—
318#10621873—28no—
319#10621873—28no—
320#10621873—44no—
321#10621873C2×D4116yescomplemented
322C23×C43—22no—
323C23×C43—22no—
324C23×C43—22no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43C22×D412yes—
329C23×C43C22×D412yes—
330C23×C43C22×D411yescharacteristic
331C22×D43—24no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—42no—
335C22×D43—42no—
336C22×D43—42no—
337C22×D43—42no—
338C22×D43—42no—
339D4×C43—44no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—24no—
345C2×C4×C43—24no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43C22×D412yes—
351C2×C4×C43C22×D412yes—
352C2×C4×C43C22×D412yes—
353C2×C4×C43C22×D412yes—
354C2×C4×C43C22×D412yes—
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43H(5,𝔽2)12yes—
357C2×C4×C43C2511yescharacteristic
358C22⋊D43—48no—
359C22⋊D43—48no—
360C22⋊D43—48no—
361C22⋊D43—48no—
362C2×Dic43—24no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—48no—
370C2×Dic43—42no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43—42no—
374C2×Dic43—42no—
375D172—24no—
376D172—22no—
377D172—22no—
378D172—22no—
379D172—42no—
380D172C22×D414yes—
381C4×D43—48no—
382C4×D43—48no—
383C4×D43—48no—
384C4×D43—48no—
385Dic86—24no—
386Dic86—22no—
387Dic86—22no—
388Dic86—22no—
389Dic86—22no—
390Dic86—22no—
391Dic86—22no—
392Dic86—22no—
393Dic86—48no—
394Dic86—42no—
395Dic86—42no—
396Dic86—42no—
397Dic86C22×D414yes—
398C8×C43—22no—
399C8×C43—22no—
400C8×C43—22no—
401C8×C43C22×D414yes—
402C2×#3269—431nomaximal, Sylow
403C22×C43—22no—
404C22×C43—22no—
405C22×C43—22no—
406C22×C43—22no—
407C22×C43—22no—
408C22×C43—22no—
409C22×C43—44no—
410C22×C43—44no—
411C22×C43D4212yes—
412C22×C43#57512yes—
413C22×C43#57812yes—
414C22×C43C23×D411yescharacteristic
415C2×D43—24no—
416C2×D43—48no—
417C2×D43—42no—
418C2×D43—42no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—84no—
423C4×C43—22no—
424C4×C43—22no—
425C4×C43—22no—
426C4×C43—22no—
427C4×C43D4212yes—
428C4×C43C23×D411yescharacteristic
429C4×C43C2×H(5,𝔽2)11yescharacteristic
430Dic43—24no—
431Dic43—42no—
432Dic43—42no—
433Dic43—42no—
434Dic43—42no—
435Dic43—42no—
436C22×#137—431no—
437C22×#135—431no—
438C2×#548—431no—
439C2×#547—431no—
440#3269—4316no—
441C2×#497—431no—
442C2×#468—431no—
443C2×#467—431no—
444C2×#462—431no—
445C2×#463—431no—
446C2×#452—431no—
447C2×#452—431no—
448C2×#449—431no—
449C2×#451—431no—
450C2×#440—431no—
451C2×#435D4311yescharacteristic, complemented
452C2×C43—42no—
453C2×C43—42no—
454C2×C43#326914yescomplemented
455C2×C43C2×D4211yescharacteristic
456C2×C43C2×#57511yescharacteristic
457C2×C43C2×#57811yescharacteristic
458D43—44no—
459D43—82no—
460C22×#41—431no—
461C22×#41—431no—
462C22×#41—431no—
463C23×Q8—431no—
464C2×#137—438no—
465C2×#137—868no—
466C2×#135—438no—
467C2×#135—868no—
468C22×Q16—431no—
469C22×Q16—431no—
470C22×Q16—431no—
471C22×Q16—431no—
472C22×SD16—431no—
473C22×SD16—431no—
474C22×SD16—431no—
475C22×SD16—431no—
476C22×D8—431no—
477C22×M16C2×D4311yescharacteristic
478C23×C8C2×D4311yescharacteristic
479#548—438no—
480#548—864no—
481#547—438no—
482#547—864no—
483C2×C4⋊Q8—431no—
484C2×#124—431no—
485C2×#124—861no—
486C2×#123—861no—
487C2×#123—861no—
488C2×C22⋊Q8—431no—
489C2×C22⋊Q8—431no—
490C2×C22⋊Q8—431no—
491C2×C22⋊Q8—861no—
492C2×#121—431no—
493C2×#121—861no—
494C2×#121—861no—
495C2×C4×Q8—431no—
496C2×C4×D4—431no—
497C2×C4×D4—861no—
498C2×C4×D4C2×D4311yescharacteristic
499C22×C4⋊C4—861no—
500#497—438no—
501#468—438no—
502#467—438no—
503#463—438no—
504#462—438no—
505#452—438no—
506#452—438no—
507#451—438no—
508#449—438no—
509#440—438no—
510#435C2×D4318yescomplemented
511C2×#107—431no—
512C2×C4⋊C8C2×D4311yescharacteristic
513C2×#103—431no—
514C2×#103—431no—
515C2×#103—431no—
516C2×#103—431no—
517C2×#102—431no—
518C2×#102—431no—
519C2×C22⋊C8C2×D4311yescharacteristic
520C2×C22⋊C8C2×D4311yescharacteristic
521C2×#97C2×D4311yescharacteristic
522C43C2×#326911yescharacteristic, complemented, Sylow
523C2×#41—434no—
524C2×#41—434no—
525C2×#41—434no—
526C2×#41—864no—
527C2×#41—864no—
528C2×#41—864no—
529C2×#41—862no—
530C2×#41—862no—
531C2×#41—862no—
532C2×#41—1722no—
533C2×#41—1722no—
534C2×#41—1722no—
535C22×Q8—431no—
536C22×Q8—431no—
537C22×Q8—431no—
538C22×Q8—431no—
539C22×Q8—434no—
540C22×Q8—864no—
541C22×Q8—861no—
542C22×Q8—862no—
543C22×Q8—1722no—
544C22×D4—431no—
545C22×D4—431no—
546C22×D4—861no—
547C22×D4—861no—
548C22×D4—861no—
549C22×D4—861no—
550C22×D4D17211yescharacteristic
551C23×C4—861no—
552C23×C4—861no—
553C23×C4—861no—
554C23×C4—861no—
555C23×C4—861no—
556C23×C4C22×D4311yescharacteristic
557C23×C4C22×D4311yescharacteristic
558#137—8632no—
559#135—8632no—
560C2×Q16—434no—
561C2×Q16—434no—
562C2×Q16—434no—
563C2×Q16—434no—
564C2×Q16—864no—
565C2×Q16—864no—
566C2×Q16—864no—
567C2×Q16—1722no—
568C2×SD16—438no—
569C2×SD16—434no—
570C2×SD16—434no—
571C2×SD16—434no—
572C2×SD16—434no—
573C2×SD16—864no—
574C2×SD16—864no—
575C2×SD16—1722no—
576C2×D8—434no—
577C2×D8—864no—
578C2×M16—24no—
579C2×M16C22×D4314yes—
580C22×C8—24no—
581C22×C8C22×D4311yescharacteristic
582C22×C8C22×D4314yes—
583C22×C8C22×D4311yescharacteristic
584C22×C8C22×D4311yescharacteristic
585C22×C8C22×D4311yescharacteristic
586C4⋊Q8—434no—
587C4⋊Q8—862no—
588#124—434no—
589#124—868no—
590#124—862no—
591#123—868no—
592#123—868no—
593C22⋊Q8—434no—
594C22⋊Q8—434no—
595C22⋊Q8—434no—
596C22⋊Q8—862no—
597C22⋊Q8—862no—
598C22⋊Q8—862no—
599C22⋊Q8—868no—
600#121—434no—
601#121—868no—
602#121—868no—
603#121—862no—
604C4×Q8—434no—
605C4×Q8—862no—
606C4×D4—434no—
607C4×D4—868no—
608C4×D4—862no—
609C4×D4D17214yes—
610C4×D4C22×D4314yes—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—861no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4—861no—
617C2×C4⋊C4—861no—
618C2×C4⋊C4—861no—
619C2×C4⋊C4—868no—
620C2×C4⋊C4D17211yescharacteristic
621C2×C22⋊C4—861no—
622C2×C22⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C22⋊C4D17211yescharacteristic
629C2×C22⋊C4D17211yescharacteristic
630C2×C42—861no—
631C2×C42C22×D4311yescharacteristic
632#107—434no—
633C4⋊C8C22×D4314yes—
634#103—434no—
635#103—434no—
636#103—434no—
637#103—434no—
638#102—434no—
639#102—434no—
640C22⋊C8C22×D4314yes—
641C22⋊C8C22×D4314yes—
642#97C22×D4314yes—
643C24—861no—
644C24—861no—
645C24C2×D17211yescharacteristic
646C24C2×D17211yescharacteristic
647#41—868no—
648#41—868no—
649#41—868no—
650#41—1724no—
651#41—1724no—
652#41—1724no—
653#41—1728no—
654#41—1728no—
655#41—1728no—
656C2×Q8—434no—
657C2×Q8—432no—
658C2×Q8—432no—
659C2×Q8—432no—
660C2×Q8—432no—
661C2×Q8—868no—
662C2×Q8—861no—
663C2×Q8—864no—
664C2×Q8—861no—
665C2×Q8—861no—
666C2×Q8—861no—
667C2×Q8—862no—
668C2×Q8—862no—
669C2×Q8—862no—
670C2×Q8—862no—
671C2×Q8—862no—
672C2×Q8—862no—
673C2×Q8—862no—
674C2×Q8—1724no—
675C2×Q8—1724no—
676C2×Q8—1728no—
677C2×D4—42no—
678C2×D4—434no—
679C2×D4—432no—
680C2×D4—432no—
681C2×D4—864no—
682C2×D4—864no—
683C2×D4—864no—
684C2×D4—864no—
685C2×D4—862no—
686C2×D4—861no—
687C2×D4—861no—
688C2×D4—862no—
689C2×D4—862no—
690C2×D4—1724no—
691C2×D4—1724no—
692C2×D4—1724no—
693C2×D4—1724no—
694C2×D4C2×D17214yes—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—861no—
700C22×C4—864no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4—861no—
706C22×C4—864no—
707C22×C4—864no—
708C22×C4—864no—
709C22×C4—864no—
710C22×C4—1724no—
711C22×C4—1724no—
712C22×C4—1724no—
713C22×C4—1724no—
714C22×C4—1724no—
715C22×C4C2×D17212yes—
716C22×C4C2×D17212yes—
717C22×C4C2×D17211yescharacteristic
718C22×C4C2×D17211yescharacteristic
719C22×C4C2×D17211yescharacteristic
720C22×C4C2×D17211yescharacteristic
721C22×C4C23×D4312yes—
722C22×C4C23×D4312yes—
723C22×C4C23×D4311yescharacteristic
724Q16—868no—
725Q16—868no—
726Q16—868no—
727Q16—1724no—
728SD16—4316no—
729SD16—868no—
730SD16—868no—
731SD16—1724no—
732D8—868no—
733M16—28no—
734C2×C8—22no—
735C2×C8—22no—
736C2×C8—22no—
737C2×C8—28no—
738C2×C8D4×D4314yes—
739C2×C8C23×D4312yes—
740C2×C8C23×D4312yes—
741C2×C8C23×D4312yes—
742C2×C8C23×D4312yes—
743C4⋊C4—432no—
744C4⋊C4—432no—
745C4⋊C4—861no—
746C4⋊C4—861no—
747C4⋊C4—864no—
748C4⋊C4—864no—
749C4⋊C4—864no—
750C4⋊C4—864no—
751C4⋊C4—864no—
752C4⋊C4—864no—
753C4⋊C4C2×D17214yes—
754C22⋊C4—864no—
755C22⋊C4—864no—
756C22⋊C4—864no—
757C22⋊C4—864no—
758C22⋊C4—864no—
759C22⋊C4—864no—
760C22⋊C4—864no—
761C22⋊C4C2×D17214yes—
762C22⋊C4C2×D17214yes—
763C42—864no—
764C42C2×D17212yes—
765C42C23×D4312yes—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—862no—
773C23—864no—
774C23—862no—
775C23—1722no—
776C23—1722no—
777C23—1722no—
778C23—1722no—
779C23—1722no—
780C23C22×D17212yes—
781C23C22×D17212yes—
782C23C22×D17211yescharacteristic
783Q8—434no—
784Q8—862no—
785Q8—864no—
786Q8—862no—
787Q8—862no—
788Q8—862no—
789Q8—862no—
790Q8—862no—
791Q8—862no—
792Q8—1728no—
793Q8—1722no—
794Q8—1722no—
795Q8—1722no—
796D4—44no—
797D4—434no—
798D4—862no—
799D4—862no—
800D4—862no—
801D4—864no—
802D4—1728no—
803D4—1728no—
804D4—1728no—
805D4—1728no—
806D4—1722no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—862no—
818C2×C4—864no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—1728no—
825C2×C4—1728no—
826C2×C4—1728no—
827C2×C4—1728no—
828C2×C4—1728no—
829C2×C4—1722no—
830C2×C4—1722no—
831C2×C4—1722no—
832C2×C4—1722no—
833C2×C4—1722no—
834C2×C4C2×D4×D4312yes—
835C2×C4C22×D17212yes—
836C2×C4C22×D17212yes—
837C2×C4C22×D17212yes—
838C2×C4C22×D17212yes—
839C2×C4C22×D17211yescharacteristic
840C2×C4#1306337112yes—
841C2×C4C24×D4311yescharacteristic
842C8—22no—
843C8—22no—
844C8—22no—
845C8C2×D4×D4314yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—44no—
854C22—864no—
855C22—3444no—
856C22—1722no—
857C22—1722no—
858C22—1722no—
859C22—1722no—
860C22—1722no—
861C22—1728no—
862C22D4×D17212yes—
863C22#1458369912yes—
864C22#1458371612yes—
865C22C23×D17211yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—864no—
871C4—1722no—
872C4—1722no—
873C4—1722no—
874C4—1722no—
875C4—1722no—
876C4D4×D17212yes—
877C4C22×D4×D4311yescharacteristic
878C4C2×#1306337111yescharacteristic
879C2—42no—
880C2—42no—
881C2—3442no—
882C2—1724no—
883C2#1914615514yesdirect product factor
884C2C2×D4×D17211yescharacteristic
885C2C2×#1458369911yescharacteristic
886C2C2×#1458371611yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
hypercenterC2×#435D43
hypocenterC43C2×#3269
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×#13063358C2semidirect
2. C22×#13063347C2semidirect
3. C2×#14583558C2semidirect
4. C2×#14583554C2semidirect
5. #19146155C2direct (N × H)
6. C2×#14583293C2semidirect
7. C2×#14583145C2semidirect
8. C2×#14583140C2semidirect
9. C2×#14583110C2semidirect
10. C2×#14583115C2semidirect
11. C2×#14583063C2semidirect
12. C2×#14583063C2semidirect
13. C2×#14583046C2semidirect
14. C2×#14583057C2semidirect
15. C2×#14583001C2semidirect
16. C2×C43×#435C2semidirect
22. C2×#13063358C22semidirect
24. C2×#13063347C22semidirect
35. #14583558C22semidirect
37. #14583554C22semidirect
54. #14583293C22semidirect
55. #14583145C22semidirect
56. #14583140C22semidirect
57. #14583115C22semidirect
58. #14583110C22semidirect
59. #14583063C22semidirect
60. #14583063C22semidirect
61. #14583057C22semidirect
62. #14583046C22semidirect
63. #14583001C22semidirect
74. C43×#435C22semidirect
124. C2×#10621873D4semidirect
321. #10621873C2×D4semidirect
451. C2×#435D43semidirect
454. C2×C43#3269semidirect
510. #435C2×D43semidirect
522. C43C2×#3269semidirect
883. C2#19146155direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633582
C22×#130633472
C2×#145835582
C2×#145835542
#191461552
C2×#145832932
C2×#145831452
C2×#145831402
C2×#145831102
C2×#145831152
C2×#145830632
C2×#145830462
C2×#145830572
C2×#145830012
C2×C43×#4352
C2×#326943