Finite Group Databasebeta

← C2×#19146310 #25971834

Subgroups — C2×#19146310 #25971834

Order 11008.

2806 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×#13063346C211yesmaximal, characteristic, complemented
2C22×#13063345C211yesmaximal, characteristic, complemented
3C2×#14583551C211yesmaximal, characteristic, complemented
4C2×#14583548C211yesmaximal, characteristic, complemented
5#19146310C2116yesmaximal, direct product factor
6C2×#14583277C211yesmaximal, characteristic, complemented
7C2×#14583139C211yesmaximal, characteristic, complemented
8C2×#14583138C211yesmaximal, characteristic, complemented
9C2×#14583103C211yesmaximal, characteristic, complemented
10C2×#14583102C211yesmaximal, characteristic, complemented
11C2×#14583063C211yesmaximal, characteristic, complemented
12C2×#14583062C211yesmaximal, characteristic, complemented
13C2×#14583060C211yesmaximal, characteristic, complemented
14C2×#14582979C211yesmaximal, characteristic, complemented
15C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621898C2211yescharacteristic
19C22×#10621900C2211yescharacteristic
20C2×#13063346—28no—
21C2×#13063346C2218yescomplemented
22C2×#13063345—28no—
23C2×#13063345C2218yescomplemented
24C22×Dic172C2211yescharacteristic
25C22×#10621885C2211yescharacteristic
26C22×#10621885C2211yescharacteristic
27C22×#10621873C2211yescharacteristic
28C22×#10621883C2211yescharacteristic
29C22×#10621884C2211yescharacteristic
30C22×#10621882C2211yescharacteristic
31C23×C43⋊C8C2211yescharacteristic
32C22×C8×D43C2211yescharacteristic
33#14583551—24no—
34#14583551C2218yescomplemented
35#14583548—24no—
36#14583548C2218yescomplemented
37C2×#13063323C2211yescharacteristic
38C2×#13063323C2211yescharacteristic
39C2×#13063310—21no—
40C2×#13063308—21no—
41C2×#13063307—21no—
42C2×#13063306—21no—
43C2×#13063305C2211yescharacteristic
44C2×#13063304C2211yescharacteristic
45C2×#13063301C2211yescharacteristic
46C2×#13063298—21no—
47C2×#13063297—21no—
48C2×D4×Dic43C2211yescharacteristic
49C2×#13063287C2211yescharacteristic
50C2×C4×C22⋊D43C2211yescharacteristic
51C22×Dic43⋊C4—21no—
52C2×C4⋊C4×D43—21no—
53#14583277C2218yescomplemented
54#14583139C2218yescomplemented
55#14583138C2218yescomplemented
56#14583103C2218yescomplemented
57#14583102C2218yescomplemented
58#14583063C2218yescomplemented
59#14583062C2218yescomplemented
60#14583060C2218yescomplemented
61#14582979C2218yescomplemented
62(C22⋊D43)⋊C8C2218yescomplemented
63C2×#13063258C2211yescharacteristic
64C2×Dic43⋊C8C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063249C2211yescharacteristic
67C2×#13063248C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×C8×Dic43C2211yescharacteristic
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×#10621902—22no—
80C2×#10621902—24no—
81C2×#10621902—42no—
82C2×#10621902C2314yes—
83C2×#10621898—22no—
84C2×#10621898—24no—
85C2×#10621898—42no—
86C2×#10621898C2314yes—
87C2×#10621900—24no—
88C2×#10621900—22no—
89C2×#10621900—42no—
90C2×#10621900C2314yes—
91C22×Dic86C2311yescharacteristic
92C22×Dic86C2311yescharacteristic
93C22×D172—21no—
94C22×D172C2311yescharacteristic
95C22×C22⋊D43—21no—
96C22×C22⋊D43—21no—
97C22×C22⋊D43D411yescharacteristic
98C23×Dic43—21no—
99C23×Dic43—21no—
100C22×C4×D43—21no—
101C22×C4×D43—21no—
102C22×C4×D43—21no—
103C22×C4×D43C2311yescharacteristic
104#13063346—232no—
105#13063345—232no—
106C2×Dic172—42no—
107C2×Dic172C2314yes—
108C2×#10621885—24no—
109C2×#10621885—24no—
110C2×#10621885C2314yes—
111C2×#10621885C2314yes—
112C2×#10621873—24no—
113C2×#10621873C2314yes—
114C2×#10621883—24no—
115C2×#10621883C2314yes—
116C2×#10621884—24no—
117C2×#10621884C2314yes—
118C2×#10621882D418yescomplemented
119C2×#10621882C2314yes—
120C22×C43⋊C8—24no—
121C22×C43⋊C8C2311yescharacteristic
122C22×C43⋊C8C2314yes—
123C22×C43⋊C8C2311yescharacteristic
124C2×C8×D43—24no—
125C2×C8×D43C2314yes—
126#13063323—22no—
127#13063323—22no—
128#13063323C2314yes—
129#13063323C2314yes—
130#13063310—28no—
131#13063308—28no—
132#13063307—28no—
133#13063306—28no—
134#13063305—22no—
135#13063305C2314yes—
136#13063304—22no—
137#13063304C2314yes—
138#13063301—22no—
139#13063301C2314yes—
140#13063298—28no—
141#13063297—28no—
142D4×Dic43—22no—
143D4×Dic43C2314yes—
144#13063287—22no—
145#13063287C2314yes—
146C4×C22⋊D43D414yes—
147C4×C22⋊D43C2314yes—
148C2×C4⋊Dic43—21no—
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—21no—
156C2×Dic43⋊C4—28no—
157C2×Dic43⋊C4D411yescharacteristic
158C4⋊C4×D43—28no—
159C2×C22⋊Dic43—21no—
160C2×C22⋊Dic43—21no—
161C2×C22⋊Dic43D411yescharacteristic
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4D411yescharacteristic
166C2×C4×Dic43C2311yescharacteristic
167#13063258C2314yes—
168Dic43⋊C8C2314yes—
169#13063250C2314yes—
170#13063249C2314yes—
171#13063248C2314yes—
172#13063247C2314yes—
173(C2×D43)⋊C8C2314yes—
174C8×Dic43C2314yes—
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—24no—
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
247#10621902—28no—
248#10621902—44no—
249#10621902—48no—
250#10621900—28no—
251#10621900—44no—
252#10621900—48no—
253#10621898—28no—
254#10621898—44no—
255#10621898—48no—
256C2×D172—21no—
257C2×D172—22no—
258C2×D172—24no—
259C2×D172—44no—
260C2×D172C2×D414yes—
261C2×D172C2412yes—
262C2×C4×D43—22no—
263C2×C4×D43—22no—
264C2×C4×D43—24no—
265C2×C4×D43—24no—
266C2×C4×D43—24no—
267C2×C4×D43—44no—
268C2×C4×D43—44no—
269C2×C4×D43—44no—
270C2×C4×D43C2×D412yes—
271C2×C4×D43C2412yes—
272C2×Dic86—22no—
273C2×Dic86—22no—
274C2×Dic86—22no—
275C2×Dic86—22no—
276C2×Dic86—21no—
277C2×Dic86—21no—
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#10621883—28no—
297#10621882C2×D4116yescomplemented
298(C2×D43)⋊C4—24no—
299(C2×D43)⋊C4—24no—
300(C2×D43)⋊C4—24no—
301(C2×D43)⋊C4C2×D414yes—
302C4⋊Dic43—21no—
303C4⋊Dic43—24no—
304C4⋊Dic43C2412yes—
305Dic43⋊C4—24no—
306Dic43⋊C4—24no—
307Dic43⋊C4—24no—
308Dic43⋊C4—24no—
309Dic43⋊C4—24no—
310Dic43⋊C4—24no—
311Dic43⋊C4C2×D414yes—
312C4×Dic43C2×D412yes—
313C4×Dic43C2412yes—
314C2×C43⋊C8—22no—
315C2×C43⋊C8—28no—
316C2×C43⋊C8C2×D414yes—
317C2×C43⋊C8C2412yes—
318C2×C43⋊C8C2412yes—
319Dic172—44no—
320#10621873—28no—
321C8×D43—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—24no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
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—28no—
366C22⋊D43—48no—
367C22⋊D43—48no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—48no—
374C2×Dic43—42no—
375C2×Dic43—42no—
376C2×Dic43—42no—
377C2×Dic43—48no—
378C2×Dic43#13514yescomplemented
379C2×Dic43C22×D412yes—
380C2×Dic43C22×D412yes—
381C2×Dic43C22×D412yes—
382D172—24no—
383D172—22no—
384D172—48no—
385D172C22×D414yes—
386C4×D43—24no—
387C4×D43—22no—
388C4×D43—22no—
389C4×D43—48no—
390C4×D43—48no—
391C4×D43—48no—
392Dic86—22no—
393Dic86—22no—
394Dic86—22no—
395Dic86—22no—
396Dic86—42no—
397Dic86—42no—
398C8×C43—22no—
399C8×C43—22no—
400C43⋊C8—22no—
401C43⋊C8C22×D414yes—
402C2×#3283—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×C43C2×#13512yes—
413C22×C43#57812yes—
414C22×C43C23×D411yescharacteristic
415C2×D43—24no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—22no—
419C2×D43—44no—
420C2×D43—48no—
421C2×D43—42no—
422C2×D43—42no—
423C4×C43—22no—
424C4×C43—42no—
425C4×C43—42no—
426C4×C43—42no—
427C4×C43D4212yes—
428C4×C43C23×D411yescharacteristic
429C4×C43C2×H(5,𝔽2)11yescharacteristic
430Dic43—22no—
431Dic43—22no—
432Dic43—42no—
433Dic43—42no—
434Dic43—42no—
435Dic43C2×#13514yescomplemented
436C22×#135—431no—
437C22×#135—431no—
438C2×#547—431no—
439C2×#547—431no—
440#3283—4316no—
441C2×#494—431no—
442C2×#467—431no—
443C2×#467—431no—
444C2×#461—431no—
445C2×#461—431no—
446C2×#452—431no—
447C2×#452—431no—
448C2×#452—431no—
449C2×#452D4311yescharacteristic, complemented
450C2×C4×D8—431no—
451C2×C8×D4—431no—
452C2×C43—42no—
453C2×C43—44no—
454C2×C43#328314yescomplemented
455C2×C43C2×D4211yescharacteristic
456C2×C43C22×#13511yescharacteristic
457C2×C43C2×#57811yescharacteristic
458D43—42no—
459D43—44no—
460C22×#41—431no—
461C22×#41—431no—
462C22×#41—431no—
463C22×#41C2×D4311yescharacteristic
464C2×#135—438no—
465C2×#135—438no—
466C2×#135—868no—
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—
477C23×C8—431no—
478C23×C8—431no—
479#547—438no—
480#547—438no—
481#547—864no—
482#547—864no—
483C2×C4⋊Q8—431no—
484C2×C4⋊Q8—431no—
485C2×#123—861no—
486C2×#123—861no—
487C2×#123—861no—
488C2×#123—861no—
489C2×C22⋊Q8—431no—
490C2×C22⋊Q8—431no—
491C2×C22⋊Q8—431no—
492C2×C22⋊Q8C2×D4311yescharacteristic
493C2×#121—861no—
494C2×#121—861no—
495C2×C4×D4—431no—
496C2×C4×D4—431no—
497C2×C4×D4—431no—
498C22×C4⋊C4—861no—
499C22×C4⋊C4—861no—
500#494—438no—
501#467—438no—
502#467—438no—
503#461—438no—
504#461—438no—
505#452—438no—
506#452—438no—
507#452—438no—
508#452C2×D4318yescomplemented
509C4×D8—438no—
510C8×D4—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×C4×C8—431no—
522C43C2×#328311yescharacteristic, complemented, Sylow
523C2×#41—22no—
524C2×#41—24no—
525C2×#41—42no—
526C2×#41—434no—
527C2×#41—434no—
528C2×#41—434no—
529C2×#41—864no—
530C2×#41—862no—
531C2×#41—862no—
532C2×#41—862no—
533C2×#41—864no—
534C2×#41—864no—
535C2×#41—1722no—
536C2×#41—1722no—
537C2×#41—1722no—
538C2×#41C22×D4314yes—
539C22×Q8—431no—
540C22×Q8—431no—
541C22×Q8C22×D4311yescharacteristic
542C22×Q8C22×D4311yescharacteristic
543C22×D4—21no—
544C22×D4—431no—
545C22×D4—431no—
546C22×D4—861no—
547C22×D4—861no—
548C22×D4—861no—
549C22×D4C22×D4311yescharacteristic
550C23×C4—21no—
551C23×C4—431no—
552C23×C4—861no—
553C23×C4—861no—
554C23×C4—861no—
555C23×C4—861no—
556C23×C4—861no—
557C23×C4C22×D4311yescharacteristic
558#135—8632no—
559#135—8632no—
560C2×Q16—42no—
561C2×Q16—434no—
562C2×Q16—434no—
563C2×Q16—434no—
564C2×Q16—864no—
565C2×Q16—864no—
566C2×Q16—1722no—
567C2×Q16C22×D4314yes—
568C2×SD16—24no—
569C2×SD16—434no—
570C2×SD16—434no—
571C2×SD16—434no—
572C2×SD16—864no—
573C2×SD16—864no—
574C2×SD16—864no—
575C2×SD16C22×D4314yes—
576C2×D8—438no—
577C2×D8—434no—
578C22×C8—431no—
579C22×C8—431no—
580C22×C8—434no—
581C22×C8—434no—
582C22×C8—864no—
583C22×C8—864no—
584C22×C8C22×D4311yescharacteristic
585C22×C8C22×D4311yescharacteristic
586C4⋊Q8—434no—
587C4⋊Q8—434no—
588C4⋊Q8—862no—
589C4⋊Q8—862no—
590#123—868no—
591#123—868no—
592#123—868no—
593#123—868no—
594C22⋊Q8—22no—
595C22⋊Q8—434no—
596C22⋊Q8—434no—
597C22⋊Q8—434no—
598C22⋊Q8—862no—
599C22⋊Q8—862no—
600C22⋊Q8—862no—
601C22⋊Q8C22×D4314yes—
602#121—868no—
603#121—868no—
604C4×D4—434no—
605C4×D4—434no—
606C4×D4—434no—
607C4×D4—434no—
608C4×D4—862no—
609C4×D4—862no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—868no—
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⋊C4—861no—
621C2×C4⋊C4—861no—
622C2×C4⋊C4C22×D4311yescharacteristic
623C2×C22⋊C4—21no—
624C2×C22⋊C4—431no—
625C2×C22⋊C4—431no—
626C2×C22⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C22⋊C4—861no—
629C2×C22⋊C4—861no—
630C2×C22⋊C4—861no—
631C2×C42—431no—
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—
642C4×C8—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—868no—
653#41—1724no—
654#41—1728no—
655#41—1724no—
656#41—1728no—
657#41—1724no—
658#41—1728no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—432no—
666C2×Q8—432no—
667C2×Q8—861no—
668C2×Q8—861no—
669C2×Q8—862no—
670C2×Q8—862no—
671C2×Q8—862no—
672C2×Q8—862no—
673C2×Q8C23×D4312yes—
674C2×Q8C23×D4312yes—
675C2×D4—24no—
676C2×D4—21no—
677C2×D4—22no—
678C2×D4—44no—
679C2×D4—434no—
680C2×D4—434no—
681C2×D4—432no—
682C2×D4—864no—
683C2×D4—864no—
684C2×D4—864no—
685C2×D4—864no—
686C2×D4—861no—
687C2×D4—862no—
688C2×D4—1724no—
689C2×D4—1724no—
690C2×D4—1724no—
691C2×D4D4×D4314yes—
692C2×D4C23×D4312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—44no—
700C22×C4—431no—
701C22×C4—431no—
702C22×C4—431no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4—864no—
706C22×C4—864no—
707C22×C4—864no—
708C22×C4—864no—
709C22×C4—862no—
710C22×C4—862no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—864no—
715C22×C4—1724no—
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—1724no—
728SD16—28no—
729SD16—868no—
730SD16—868no—
731SD16—868no—
732D8—4316no—
733C2×C8—22no—
734C2×C8—22no—
735C2×C8—434no—
736C2×C8—432no—
737C2×C8—432no—
738C2×C8—868no—
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—864no—
752C4⋊C4—864no—
753C4⋊C4—861no—
754C4⋊C4—864no—
755C4⋊C4C23×D4312yes—
756C22⋊C4—24no—
757C22⋊C4—434no—
758C22⋊C4—434no—
759C22⋊C4—864no—
760C22⋊C4—864no—
761C22⋊C4—864no—
762C22⋊C4—864no—
763C22⋊C4—864no—
764C42—432no—
765C42—432no—
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—864no—
779C23—1722no—
780C23—1722no—
781C23C2×D4×D4312yes—
782C23C2×D4×D4311yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—42no—
788Q8—42no—
789Q8—862no—
790Q8—862no—
791Q8—862no—
792Q8—862no—
793Q8—1722no—
794Q8—1722no—
795D4—22no—
796D4—24no—
797D4—48no—
798D4—434no—
799D4—868no—
800D4—862no—
801D4—864no—
802D4—1728no—
803D4—1728no—
804D4—1728no—
805D4C2×D4×D4314yes—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—48no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—434no—
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—862no—
829C2×C4—1728no—
830C2×C4—1728no—
831C2×C4—1728no—
832C2×C4—1728no—
833C2×C4—1728no—
834C2×C4—1722no—
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—864no—
858C22—1722no—
859C22—1722no—
860C22—1724no—
861C22—1728no—
862C22#1458353112yes—
863C22#135×D4312yes—
864C22#1458371512yes—
865C22C22×D4×D4311yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—434no—
871C4—862no—
872C4—862no—
873C4—1722no—
874C4—1722no—
875C4—1722no—
876C4#1458353112yes—
877C4C22×D4×D4311yescharacteristic
878C4C2×#1306337011yescharacteristic
879C2—42no—
880C2—44no—
881C2—1722no—
882C2—1724no—
883C2#1914631014yesdirect product factor
884C2C2×#1458353111yescharacteristic
885C2C2×#135×D4311yescharacteristic
886C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
hypercenterC2×#452D43
hypocenterC43C2×#3283
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×#13063346C2semidirect
2. C22×#13063345C2semidirect
3. C2×#14583551C2semidirect
4. C2×#14583548C2semidirect
5. #19146310C2direct (N × H)
6. C2×#14583277C2semidirect
7. C2×#14583139C2semidirect
8. C2×#14583138C2semidirect
9. C2×#14583103C2semidirect
10. C2×#14583102C2semidirect
11. C2×#14583063C2semidirect
12. C2×#14583062C2semidirect
13. C2×#14583060C2semidirect
14. C2×#14582979C2semidirect
15. C2×(C22⋊D43)⋊C8C2semidirect
16. C2×C43×#452C2semidirect
21. C2×#13063346C22semidirect
23. C2×#13063345C22semidirect
34. #14583551C22semidirect
36. #14583548C22semidirect
53. #14583277C22semidirect
54. #14583139C22semidirect
55. #14583138C22semidirect
56. #14583103C22semidirect
57. #14583102C22semidirect
58. #14583063C22semidirect
59. #14583062C22semidirect
60. #14583060C22semidirect
61. #14582979C22semidirect
62. (C22⋊D43)⋊C8C22semidirect
75. C43×#452C22semidirect
118. C2×#10621882D4semidirect
297. #10621882C2×D4semidirect
378. C2×Dic43#135semidirect
435. Dic43C2×#135semidirect
449. C2×#452D43semidirect
454. C2×C43#3283semidirect
508. #452C2×D43semidirect
522. C43C2×#3283semidirect
883. C2#19146310direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633462
C22×#130633452
C2×#145835512
C2×#145835482
#191463102
C2×#145832772
C2×#145831392
C2×#145831382
C2×#145831032
C2×#145831022
C2×#145830632
C2×#145830622
C2×#145830602
C2×#145829792
C2×(C22⋊D43)⋊C82
C2×C43×#4522
C2×#328343