Finite Group Databasebeta

← C2×#19146154 #25971630

Subgroups — C2×#19146154 #25971630

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×#13063354C211yesmaximal, characteristic, complemented
2C22×#13063345C211yesmaximal, characteristic, complemented
3C2×#14583559C211yesmaximal, characteristic, complemented
4C2×#14583548C211yesmaximal, characteristic, complemented
5#19146154C2116yesmaximal, direct product factor
6C2×#14583292C211yesmaximal, characteristic, complemented
7C2×#14583148C211yesmaximal, characteristic, complemented
8C2×#14583138C211yesmaximal, characteristic, complemented
9C2×#14583108C211yesmaximal, characteristic, complemented
10C2×#14583116C211yesmaximal, characteristic, complemented
11C2×#14583063C211yesmaximal, characteristic, complemented
12C2×#14583045C211yesmaximal, characteristic, complemented
13C2×#14583053C211yesmaximal, characteristic, complemented
14C2×#14582996C211yesmaximal, characteristic, complemented
15C2×#14582967C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic
20C2×#13063354—28no—
21C2×#13063354C2218yescomplemented
22C2×#13063345—28no—
23C2×#13063345C2218yescomplemented
24C22×Dic172C2211yescharacteristic
25C22×#10621885C2211yescharacteristic
26C22×#10621885C2211yescharacteristic
27C22×#10621873C2211yescharacteristic
28C22×#10621883C2211yescharacteristic
29C22×#10621884C2211yescharacteristic
30C22×#10621882C2211yescharacteristic
31C22×#10621872C2211yescharacteristic
32C23×C43⋊C8C2211yescharacteristic
33#14583559—24no—
34#14583559C2218yescomplemented
35#14583548—24no—
36#14583548C2218yescomplemented
37C2×#13063323C2211yescharacteristic
38C2×#13063314C2211yescharacteristic
39C2×#13063311—21no—
40C2×#13063308—21no—
41C2×#13063306—21no—
42C2×#13063304C2211yescharacteristic
43C2×#13063303—21no—
44C2×#13063301C2211yescharacteristic
45C2×#13063300C2211yescharacteristic
46C2×#13063298—21no—
47C2×#13063297—21no—
48C2×#13063290C2211yescharacteristic
49C2×D4×Dic43C2211yescharacteristic
50C2×#13063287—21no—
51C2×C4×C22⋊D43C2211yescharacteristic
52C22×Dic43⋊C4—21no—
53#14583292C2218yescomplemented
54#14583148C2218yescomplemented
55#14583138C2218yescomplemented
56#14583116C2218yescomplemented
57#14583108C2218yescomplemented
58#14583063C2218yescomplemented
59#14583053C2218yescomplemented
60#14583045C2218yescomplemented
61#14582996C2218yescomplemented
62#14582967C2218yescomplemented
63C2×#13063258C2211yescharacteristic
64C2×Dic43⋊C8C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063249C2211yescharacteristic
67C2×#13063248C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×#13063235C2211yescharacteristic
71C22×#41×C43C2211yescharacteristic
72C22×Q16×C43C2211yescharacteristic
73C22×SD16×C43C2211yescharacteristic
74C2×C22⋊Q8×C43C2211yescharacteristic
75C43×#452C2218yescomplemented
76C2×#103×C43C2211yescharacteristic
77C2×#102×C43C2211yescharacteristic
78C2×C22⋊C8×C43C2211yescharacteristic
79C2×#10621898—22no—
80C2×#10621898—24no—
81C2×#10621898—42no—
82C2×#10621898C2314yes—
83C2×#10621900—24no—
84C2×#10621900—22no—
85C2×#10621900—42no—
86C2×#10621900C2314yes—
87C22×Dic86—21no—
88C22×Dic86C2311yescharacteristic
89C22×Dic86C2311yescharacteristic
90C2×Q8×D43—22no—
91C2×Q8×D43—24no—
92C2×Q8×D43—42no—
93C2×Q8×D43C2314yes—
94C22×D172—21no—
95C22×D172C2311yescharacteristic
96C22×C22⋊D43—21no—
97C22×C22⋊D43—21no—
98C22×C22⋊D43D411yescharacteristic
99C23×Dic43—21no—
100C23×Dic43—21no—
101C22×C4×D43—21no—
102C22×C4×D43—21no—
103C22×C4×D43C2311yescharacteristic
104#13063354—232no—
105#13063345—232no—
106C2×Dic172—24no—
107C2×Dic172C2314yes—
108C2×#10621885—24no—
109C2×#10621885—24no—
110C2×#10621885C2314yes—
111C2×#10621885C2314yes—
112C2×#10621873—42no—
113C2×#10621873C2314yes—
114C2×#10621883D418yescomplemented
115C2×#10621883C2314yes—
116C2×#10621884—24no—
117C2×#10621884C2314yes—
118C2×#10621882—24no—
119C2×#10621882C2314yes—
120C2×#10621872—24no—
121C2×#10621872C2314yes—
122C22×C43⋊C8—24no—
123C22×C43⋊C8C2311yescharacteristic
124C22×C43⋊C8C2314yes—
125C22×C43⋊C8C2311yescharacteristic
126#13063323—22no—
127#13063323C2314yes—
128#13063314—22no—
129#13063314C2314yes—
130#13063311—28no—
131#13063308—28no—
132#13063306—28no—
133#13063304—22no—
134#13063304C2314yes—
135#13063303—28no—
136#13063301—22no—
137#13063301C2314yes—
138#13063300—22no—
139#13063300C2314yes—
140#13063298—28no—
141#13063297—28no—
142#13063290—22no—
143#13063290C2314yes—
144D4×Dic43—22no—
145D4×Dic43C2314yes—
146#13063287—28no—
147C4×C22⋊D43D414yes—
148C4×C22⋊D43C2314yes—
149C2×C4⋊Dic43C2311yescharacteristic
150C2×Dic43⋊C4—21no—
151C2×Dic43⋊C4—21no—
152C2×Dic43⋊C4—21no—
153C2×Dic43⋊C4—21no—
154C2×Dic43⋊C4—21no—
155C2×Dic43⋊C4—28no—
156C2×Dic43⋊C4D411yescharacteristic
157C2×C22⋊Dic43—21no—
158C2×C22⋊Dic43—21no—
159C2×C22⋊Dic43D411yescharacteristic
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4D411yescharacteristic
165C2×C4×Dic43—21no—
166C2×C4×Dic43C2311yescharacteristic
167#13063258C2314yes—
168Dic43⋊C8C2314yes—
169#13063250C2314yes—
170#13063249C2314yes—
171#13063248C2314yes—
172#13063247C2314yes—
173(C2×D43)⋊C8C2314yes—
174#13063235C2314yes—
175C2×#41×C43—22no—
176C2×#41×C43—24no—
177C2×#41×C43—42no—
178C2×#41×C43C2314yes—
179C22×Q8×C43C2311yescharacteristic
180C22×Q8×C43C2311yescharacteristic
181C22×D4×C43—21no—
182C22×D4×C43C2311yescharacteristic
183C23×C4×C43—21no—
184C23×C4×C43C2311yescharacteristic
185C2×Q16×C43—42no—
186C2×Q16×C43C2314yes—
187C2×SD16×C43—24no—
188C2×SD16×C43C2314yes—
189C22×C8×C43C2311yescharacteristic
190C22×C8×C43C2311yescharacteristic
191C22⋊Q8×C43—22no—
192C22⋊Q8×C43C2314yes—
193C2×C4⋊C4×C43—21no—
194C2×C4⋊C4×C43C2311yescharacteristic
195C2×C22⋊C4×C43—21no—
196#103×C43C2314yes—
197#102×C43C2314yes—
198C22⋊C8×C43C2314yes—
199C24×C43—21no—
200C24×C43C2×D411yescharacteristic
201C23×D43—21no—
202C23×D43C2×D411yescharacteristic
203#41×C43—28no—
204#41×C43—44no—
205#41×C43—48no—
206C2×Q8×C43—21no—
207C2×Q8×C43—21no—
208C2×Q8×C43—22no—
209C2×Q8×C43—22no—
210C2×Q8×C43—22no—
211C2×Q8×C43—22no—
212C2×Q8×C43C2412yes—
213C2×Q8×C43C2412yes—
214C2×D4×C43—21no—
215C2×D4×C43—22no—
216C2×D4×C43—24no—
217C2×D4×C43—44no—
218C2×D4×C43C2×D414yes—
219C2×D4×C43C2412yes—
220C22×C4×C43—22no—
221C22×C4×C43—22no—
222C22×C4×C43—24no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—44no—
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2412yes—
230C22×C4×C43C2411yescharacteristic
231C2×C22⋊D43—24no—
232C2×C22⋊D43—24no—
233C2×C22⋊D43—42no—
234C2×C22⋊D43—44no—
235C2×C22⋊D43—44no—
236C2×C22⋊D43C2×D414yes—
237C22×Dic43—24no—
238C22×Dic43—24no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—44no—
243C22×Dic43—44no—
244C22×Dic43C2×D411yescharacteristic
245C22×Dic43C2×D411yescharacteristic
246C22×Dic43C2×D411yescharacteristic
247Q8×D43—28no—
248Q8×D43—44no—
249Q8×D43—48no—
250#10621900—28no—
251#10621900—44no—
252#10621900—48no—
253#10621898—28no—
254#10621898—44no—
255#10621898—48no—
256C2×D172—21no—
257C2×D172—24no—
258C2×D172—22no—
259C2×D172—22no—
260C2×D172—44no—
261C2×D172C2412yes—
262C2×C4×D43—22no—
263C2×C4×D43—22no—
264C2×C4×D43—24no—
265C2×C4×D43—24no—
266C2×C4×D43—44no—
267C2×C4×D43—44no—
268C2×C4×D43C2×D412yes—
269C2×C4×D43C2412yes—
270C2×Dic86—21no—
271C2×Dic86—22no—
272C2×Dic86—22no—
273C2×Dic86—22no—
274C2×Dic86—21no—
275C2×Dic86—24no—
276C2×Dic86—44no—
277C2×Dic86C2×D414yes—
278C2×Dic86C2412yes—
279C2×Dic86C2412yes—
280Q16×C43—44no—
281SD16×C43—28no—
282C2×C8×C43—22no—
283C2×C8×C43—22no—
284C2×C8×C43C2412yes—
285C2×C8×C43C2412yes—
286C4⋊C4×C43—24no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43C2412yes—
289C22⋊C4×C43—24no—
290C22⋊Dic43—24no—
291C22⋊Dic43—24no—
292C22⋊Dic43C2×D414yes—
293#10621885—28no—
294#10621885—28no—
295#10621884—28no—
296#10621883C2×D4116yescomplemented
297#10621882—28no—
298(C2×D43)⋊C4—24no—
299(C2×D43)⋊C4—24no—
300(C2×D43)⋊C4—24no—
301(C2×D43)⋊C4—24no—
302(C2×D43)⋊C4C2×D414yes—
303C4⋊Dic43—21no—
304C4⋊Dic43C2412yes—
305Dic43⋊C4—24no—
306Dic43⋊C4—24no—
307Dic43⋊C4—24no—
308Dic43⋊C4—24no—
309Dic43⋊C4—24no—
310Dic43⋊C4C2×D414yes—
311C4×Dic43—24no—
312C4×Dic43C2×D412yes—
313C4×Dic43C2412yes—
314C2×C43⋊C8—22no—
315C2×C43⋊C8—28no—
316C2×C43⋊C8C2×D414yes—
317C2×C43⋊C8C2412yes—
318C2×C43⋊C8C2412yes—
319Dic172—28no—
320#10621873—44no—
321#10621872—28no—
322C23×C43—24no—
323C23×C43—22no—
324C23×C43—22no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—42no—
328C23×C43—42no—
329C23×C43C22×D412yes—
330C23×C43C22×D411yescharacteristic
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—42no—
336C22×D43—42no—
337C22×D43—42no—
338C22×D43C22×D412yes—
339Q8×C43—22no—
340Q8×C43—22no—
341Q8×C43—22no—
342Q8×C43—22no—
343Q8×C43—42no—
344Q8×C43—42no—
345D4×C43—24no—
346D4×C43—22no—
347D4×C43—48no—
348D4×C43C22×D414yes—
349C2×C4×C43—22no—
350C2×C4×C43—24no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—48no—
357C2×C4×C43—42no—
358C2×C4×C43—42no—
359C2×C4×C43—42no—
360C2×C4×C43C22×D412yes—
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×D412yes—
363C2×C4×C43H(5,𝔽2)12yes—
364C2×C4×C43C2511yescharacteristic
365C22⋊D43—44no—
366C22⋊D43—48no—
367C22⋊D43—48no—
368C2×Dic43—24no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—22no—
374C2×Dic43—22no—
375C2×Dic43—48no—
376C2×Dic43—48no—
377C2×Dic43—42no—
378C2×Dic43—42no—
379C2×Dic43C22×D412yes—
380C2×Dic43C22×D412yes—
381C2×Dic43C22×D412yes—
382D172—22no—
383D172—22no—
384D172—48no—
385D172—42no—
386C4×D43—24no—
387C4×D43—22no—
388C4×D43—22no—
389C4×D43—48no—
390C4×D43—48no—
391Dic86—24no—
392Dic86—22no—
393Dic86—22no—
394Dic86—22no—
395Dic86—48no—
396Dic86—42no—
397Dic86C22×D414yes—
398C8×C43—22no—
399C8×C43—22no—
400C43⋊C8—22no—
401C43⋊C8C22×D414yes—
402C2×#3269—431nomaximal, Sylow
403C22×C43—24no—
404C22×C43—22no—
405C22×C43—22no—
406C22×C43—22no—
407C22×C43—44no—
408C22×C43—48no—
409C22×C43—42no—
410C22×C43—42no—
411C22×C43D4212yes—
412C22×C43#57512yes—
413C22×C43#57812yes—
414C22×C43C23×D411yescharacteristic
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—44no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—84no—
423C4×C43—22no—
424C4×C43—42no—
425C4×C43—42no—
426C4×C43—42no—
427C4×C43D4212yes—
428C4×C43C23×D411yescharacteristic
429C4×C43C2×H(5,𝔽2)11yescharacteristic
430Dic43—24no—
431Dic43—22no—
432Dic43—22no—
433Dic43—22no—
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×#452D4311yescharacteristic, complemented
448C2×#449—431no—
449C2×#451—431no—
450C2×#440—431no—
451C2×#435—431no—
452C2×C43—42no—
453C2×C43—44no—
454C2×C43#326914yescomplemented
455C2×C43C2×D4211yescharacteristic
456C2×C43C2×#57511yescharacteristic
457C2×C43C2×#57811yescharacteristic
458D43—42no—
459D43—82no—
460C22×#41—431no—
461C22×#41—431no—
462C22×#41C2×D4311yescharacteristic
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×Q16C2×D4311yescharacteristic
472C22×SD16—431no—
473C22×SD16—431no—
474C22×SD16—431no—
475C22×SD16C2×D4311yescharacteristic
476C22×D8—431no—
477C22×M16—431no—
478C23×C8—431no—
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—861no—
491C2×C22⋊Q8C2×D4311yescharacteristic
492C2×#121—431no—
493C2×#121—861no—
494C2×#121—861no—
495C2×C4×Q8—431no—
496C2×C4×D4—431no—
497C2×C4×D4—431no—
498C2×C4×D4—861no—
499C22×C4⋊C4—861no—
500#497—438no—
501#468—438no—
502#467—438no—
503#463—438no—
504#462—438no—
505#452—438no—
506#452C2×D4318yescomplemented
507#451—438no—
508#449—438no—
509#440—438no—
510#435—438no—
511C2×#107—431no—
512C2×C4⋊C8—431no—
513C2×#103—431no—
514C2×#103—431no—
515C2×#103—431no—
516C2×#103C2×D4311yescharacteristic
517C2×#102—431no—
518C2×#102C2×D4311yescharacteristic
519C2×C22⋊C8—431no—
520C2×C22⋊C8C2×D4311yescharacteristic
521C2×#97—431no—
522C43C2×#326911yescharacteristic, complemented, Sylow
523C2×#41—22no—
524C2×#41—24no—
525C2×#41—42no—
526C2×#41—434no—
527C2×#41—434no—
528C2×#41—864no—
529C2×#41—862no—
530C2×#41—862no—
531C2×#41—864no—
532C2×#41—1722no—
533C2×#41—1722no—
534C2×#41C22×D4314yes—
535C22×Q8—434no—
536C22×Q8—431no—
537C22×Q8—431no—
538C22×Q8—861no—
539C22×Q8—862no—
540C22×Q8—864no—
541C22×Q8—1722no—
542C22×Q8C22×D4311yescharacteristic
543C22×Q8C22×D4311yescharacteristic
544C22×D4—21no—
545C22×D4—431no—
546C22×D4—431no—
547C22×D4—861no—
548C22×D4—861no—
549C22×D4—861no—
550C22×D4C22×D4311yescharacteristic
551C23×C4—21no—
552C23×C4—431no—
553C23×C4—861no—
554C23×C4—861no—
555C23×C4—861no—
556C23×C4—861no—
557C23×C4C22×D4311yescharacteristic
558#137—8632no—
559#135—8632no—
560C2×Q16—42no—
561C2×Q16—434no—
562C2×Q16—434no—
563C2×Q16—434no—
564C2×Q16—864no—
565C2×Q16—864no—
566C2×Q16—864no—
567C2×Q16C22×D4314yes—
568C2×SD16—24no—
569C2×SD16—438no—
570C2×SD16—434no—
571C2×SD16—434no—
572C2×SD16—434no—
573C2×SD16—864no—
574C2×SD16—1722no—
575C2×SD16C22×D4314yes—
576C2×D8—434no—
577C2×D8—864no—
578C2×M16—434no—
579C2×M16—864no—
580C22×C8—431no—
581C22×C8—431no—
582C22×C8—434no—
583C22×C8—864no—
584C22×C8C22×D4311yescharacteristic
585C22×C8C22×D4311yescharacteristic
586C4⋊Q8—434no—
587C4⋊Q8—862no—
588#124—434no—
589#124—862no—
590#124—868no—
591#123—868no—
592#123—868no—
593C22⋊Q8—22no—
594C22⋊Q8—434no—
595C22⋊Q8—434no—
596C22⋊Q8—868no—
597C22⋊Q8—862no—
598C22⋊Q8—862no—
599C22⋊Q8C22×D4314yes—
600#121—434no—
601#121—868no—
602#121—862no—
603#121—868no—
604C4×Q8—434no—
605C4×Q8—862no—
606C4×D4—434no—
607C4×D4—434no—
608C4×D4—434no—
609C4×D4—862no—
610C4×D4—868no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—431no—
614C2×C4⋊C4—868no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4—861no—
617C2×C4⋊C4—861no—
618C2×C4⋊C4—861no—
619C2×C4⋊C4—861no—
620C2×C4⋊C4C22×D4311yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—431no—
623C2×C22⋊C4—431no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C22⋊C4—861no—
629C2×C22⋊C4—861no—
630C2×C42—431no—
631C2×C42—861no—
632#107—434no—
633C4⋊C8—434no—
634#103—434no—
635#103—434no—
636#103—434no—
637#103C22×D4314yes—
638#102—434no—
639#102C22×D4314yes—
640C22⋊C8—434no—
641C22⋊C8C22×D4314yes—
642#97—434no—
643C24—21no—
644C24—431no—
645C24—861no—
646C24D4×D4311yescharacteristic
647#41—28no—
648#41—44no—
649#41—48no—
650#41—868no—
651#41—868no—
652#41—1724no—
653#41—1728no—
654#41—1724no—
655#41—1728no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—22no—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—22no—
662C2×Q8—434no—
663C2×Q8—432no—
664C2×Q8—432no—
665C2×Q8—864no—
666C2×Q8—861no—
667C2×Q8—861no—
668C2×Q8—862no—
669C2×Q8—868no—
670C2×Q8—862no—
671C2×Q8—862no—
672C2×Q8—1724no—
673C2×Q8—1724no—
674C2×Q8—1728no—
675C2×Q8C23×D4312yes—
676C2×Q8C23×D4312yes—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—44no—
681C2×D4—434no—
682C2×D4—432no—
683C2×D4—864no—
684C2×D4—864no—
685C2×D4—864no—
686C2×D4—862no—
687C2×D4—861no—
688C2×D4—862no—
689C2×D4—1724no—
690C2×D4—1722no—
691C2×D4—1724no—
692C2×D4—1724no—
693C2×D4D4×D4314yes—
694C2×D4C23×D4312yes—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—24no—
701C22×C4—44no—
702C22×C4—431no—
703C22×C4—431no—
704C22×C4—431no—
705C22×C4—432no—
706C22×C4—432no—
707C22×C4—864no—
708C22×C4—864no—
709C22×C4—864no—
710C22×C4—861no—
711C22×C4—862no—
712C22×C4—862no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—864no—
716C22×C4—1724no—
717C22×C4—1724no—
718C22×C4—1724no—
719C22×C4—1724no—
720C22×C4D4×D4312yes—
721C22×C4D4×D4311yescharacteristic
722C22×C4C23×D4312yes—
723C22×C4C23×D4311yescharacteristic
724Q16—44no—
725Q16—868no—
726Q16—868no—
727Q16—868no—
728SD16—28no—
729SD16—4316no—
730SD16—868no—
731SD16—1724no—
732D8—868no—
733M16—868no—
734C2×C8—22no—
735C2×C8—22no—
736C2×C8—434no—
737C2×C8—432no—
738C2×C8—432no—
739C2×C8—868no—
740C2×C8—862no—
741C2×C8C23×D4312yes—
742C2×C8C23×D4312yes—
743C4⋊C4—24no—
744C4⋊C4—21no—
745C4⋊C4—434no—
746C4⋊C4—432no—
747C4⋊C4—864no—
748C4⋊C4—864no—
749C4⋊C4—864no—
750C4⋊C4—864no—
751C4⋊C4—861no—
752C4⋊C4—864no—
753C4⋊C4C23×D4312yes—
754C22⋊C4—24no—
755C22⋊C4—434no—
756C22⋊C4—434no—
757C22⋊C4—864no—
758C22⋊C4—864no—
759C22⋊C4—864no—
760C22⋊C4—864no—
761C22⋊C4—864no—
762C22⋊C4—864no—
763C42—432no—
764C42—432no—
765C42—864no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—42no—
772C23—42no—
773C23—432no—
774C23—862no—
775C23—862no—
776C23—862no—
777C23—862no—
778C23—1722no—
779C23—1722no—
780C23—1722no—
781C23C2×D4×D4312yes—
782C23C2×D4×D4311yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—42no—
788Q8—42no—
789Q8—434no—
790Q8—862no—
791Q8—864no—
792Q8—862no—
793Q8—862no—
794Q8—1728no—
795Q8—1722no—
796D4—22no—
797D4—24no—
798D4—48no—
799D4—862no—
800D4—862no—
801D4—1728no—
802D4—1724no—
803D4—1728no—
804D4—1728no—
805D4—1722no—
806D4C2×D4×D4314yes—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—48no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—432no—
819C2×C4—432no—
820C2×C4—432no—
821C2×C4—862no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—864no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—864no—
829C2×C4—862no—
830C2×C4—862no—
831C2×C4—1728no—
832C2×C4—1728no—
833C2×C4—1728no—
834C2×C4—1728no—
835C2×C4—1722no—
836C2×C4—1722no—
837C2×C4C2×D4×D4312yes—
838C2×C4C2×D4×D4312yes—
839C2×C4C2×D4×D4311yescharacteristic
840C2×C4#1306337012yes—
841C2×C4C24×D4311yescharacteristic
842C8—22no—
843C8—22no—
844C8—434no—
845C8—862no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—42no—
851C22—42no—
852C22—44no—
853C22—48no—
854C22—862no—
855C22—862no—
856C22—862no—
857C22—3444no—
858C22—1722no—
859C22—1722no—
860C22—1722no—
861C22—1724no—
862C22#1458353112yes—
863C22#1458369612yes—
864C22#1458371512yes—
865C22C22×D4×D4311yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—862no—
871C4—862no—
872C4—862no—
873C4—864no—
874C4—1722no—
875C4—1722no—
876C4#1458353112yes—
877C4C22×D4×D4311yescharacteristic
878C4C2×#1306337011yescharacteristic
879C2—42no—
880C2—44no—
881C2—3442no—
882C2—1722no—
883C2#1914615414yesdirect product factor
884C2C2×#1458353111yescharacteristic
885C2C2×#1458369611yescharacteristic
886C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
hypercenterC2×#452D43
hypocenterC43C2×#3269
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C22×#13063354C2semidirect
2. C22×#13063345C2semidirect
3. C2×#14583559C2semidirect
4. C2×#14583548C2semidirect
5. #19146154C2direct (N × H)
6. C2×#14583292C2semidirect
7. C2×#14583148C2semidirect
8. C2×#14583138C2semidirect
9. C2×#14583108C2semidirect
10. C2×#14583116C2semidirect
11. C2×#14583063C2semidirect
12. C2×#14583045C2semidirect
13. C2×#14583053C2semidirect
14. C2×#14582996C2semidirect
15. C2×#14582967C2semidirect
16. C2×C43×#452C2semidirect
21. C2×#13063354C22semidirect
23. C2×#13063345C22semidirect
34. #14583559C22semidirect
36. #14583548C22semidirect
53. #14583292C22semidirect
54. #14583148C22semidirect
55. #14583138C22semidirect
56. #14583116C22semidirect
57. #14583108C22semidirect
58. #14583063C22semidirect
59. #14583053C22semidirect
60. #14583045C22semidirect
61. #14582996C22semidirect
62. #14582967C22semidirect
75. C43×#452C22semidirect
114. C2×#10621883D4semidirect
296. #10621883C2×D4semidirect
447. C2×#452D43semidirect
454. C2×C43#3269semidirect
506. #452C2×D43semidirect
522. C43C2×#3269semidirect
883. C2#19146154direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633542
C22×#130633452
C2×#145835592
C2×#145835482
#191461542
C2×#145832922
C2×#145831482
C2×#145831382
C2×#145831082
C2×#145831162
C2×#145830632
C2×#145830452
C2×#145830532
C2×#145829962
C2×#145829672
C2×C43×#4522
C2×#326943