Finite Group Databasebeta

← C2×#19146323 #25971848

Subgroups — C2×#19146323 #25971848

Order 11008.

2858 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063345C211yesmaximal, characteristic, complemented
2C22×#13063344C211yesmaximal, characteristic, complemented
3C2×#14583567C211yesmaximal, characteristic, complemented
4C2×#14583548C211yesmaximal, characteristic, complemented
5#19146323C2116yesmaximal, direct product factor
6C2×#14583270C211yesmaximal, characteristic, complemented
7C2×#14583131C211yesmaximal, characteristic, complemented
8C2×#14583126C211yesmaximal, characteristic, complemented
9C2×#14583108C211yesmaximal, characteristic, complemented
10C2×#14583092C211yesmaximal, characteristic, complemented
11C2×#14583063C211yesmaximal, characteristic, complemented
12C2×#14583058C211yesmaximal, characteristic, complemented
13C2×#14583045C211yesmaximal, characteristic, complemented
14C2×#14582990C211yesmaximal, characteristic, complemented
15C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
16C2×C43×#449C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×#10621900C2211yescharacteristic
20C2×#13063345—28no—
21C2×#13063345C2218yescomplemented
22C2×#13063344—28no—
23C2×#13063344C2218yescomplemented
24C22×Dic172C2211yescharacteristic
25C22×#10621885C2211yescharacteristic
26C22×#10621873C2211yescharacteristic
27C22×#10621883C2211yescharacteristic
28C22×#10621883C2211yescharacteristic
29C22×#10621884C2211yescharacteristic
30C22×#10621882C2211yescharacteristic
31C23×C43⋊C8C2211yescharacteristic
32C22×C8×D43C2211yescharacteristic
33#14583567—24no—
34#14583567C2218yescomplemented
35#14583548—24no—
36#14583548C2218yescomplemented
37C2×#13063323C2211yescharacteristic
38C2×#13063321—21no—
39C2×#13063321C2211yescharacteristic
40C2×#13063308—21no—
41C2×#13063306—21no—
42C2×#13063304C2211yescharacteristic
43C2×#13063301C2211yescharacteristic
44C2×#13063300C2211yescharacteristic
45C2×#13063298—21no—
46C2×#13063297—21no—
47C2×#13063297—21no—
48C2×#13063290C2211yescharacteristic
49C2×D4×Dic43C2211yescharacteristic
50C2×C4×C22⋊D43C2211yescharacteristic
51C2×(C22⋊D43)⋊C4—21no—
52C22×Dic43⋊C4—21no—
53#14583270C2218yescomplemented
54#14583131C2218yescomplemented
55#14583126C2218yescomplemented
56#14583108C2218yescomplemented
57#14583092C2218yescomplemented
58#14583063C2218yescomplemented
59#14583058C2218yescomplemented
60#14583045C2218yescomplemented
61#14582990C2218yescomplemented
62(C22⋊D43)⋊C8C2218yescomplemented
63C2×#13063256C2211yescharacteristic
64C2×Dic43⋊C8C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063248C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063246C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×C8×Dic43C2211yescharacteristic
71C22×#41×C43C2211yescharacteristic
72C22×SD16×C43C2211yescharacteristic
73C22×D8×C43C2211yescharacteristic
74C2×#121×C43C2211yescharacteristic
75C43×#449C2218yescomplemented
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—22no—
86C2×#10621900—24no—
87C2×#10621900—42no—
88C2×#10621900—42no—
89C2×#10621900C2314yes—
90C2×#10621900C2314yes—
91C22×Dic86C2311yescharacteristic
92C22×Dic86C2311yescharacteristic
93C22×D172—21no—
94C22×D172C2311yescharacteristic
95C22×C22⋊D43—21no—
96C22×C22⋊D43—21no—
97C22×C22⋊D43—21no—
98C22×C22⋊D43—21no—
99C22×C22⋊D43—21no—
100C22×C22⋊D43D411yescharacteristic
101C23×Dic43—21no—
102C23×Dic43—21no—
103C23×Dic43—21no—
104C22×C4×D43—21no—
105C22×C4×D43C2311yescharacteristic
106#13063345—232no—
107#13063344—232no—
108C2×Dic172—24no—
109C2×Dic172C2314yes—
110C2×#10621885—24no—
111C2×#10621885C2314yes—
112C2×#10621873—42no—
113C2×#10621873C2314yes—
114C2×#10621883—24no—
115C2×#10621883D418yescomplemented
116C2×#10621883C2314yes—
117C2×#10621883C2314yes—
118C2×#10621884—24no—
119C2×#10621884C2314yes—
120C2×#10621882—24no—
121C2×#10621882C2314yes—
122C22×C43⋊C8—24no—
123C22×C43⋊C8C2311yescharacteristic
124C22×C43⋊C8C2314yes—
125C22×C43⋊C8C2311yescharacteristic
126C2×C8×D43—24no—
127C2×C8×D43C2314yes—
128#13063323—22no—
129#13063323C2314yes—
130#13063321—28no—
131#13063321—22no—
132#13063321C2314yes—
133#13063308—28no—
134#13063306—28no—
135#13063304—22no—
136#13063304C2314yes—
137#13063301—22no—
138#13063301C2314yes—
139#13063300—22no—
140#13063300C2314yes—
141#13063298—28no—
142#13063297—28no—
143#13063297—28no—
144#13063290—22no—
145#13063290C2314yes—
146D4×Dic43—22no—
147D4×Dic43C2314yes—
148C4×C22⋊D43D414yes—
149C4×C22⋊D43C2314yes—
150(C22⋊D43)⋊C4—28no—
151C2×C4⋊Dic43C2311yescharacteristic
152C2×Dic43⋊C4—21no—
153C2×Dic43⋊C4—21no—
154C2×Dic43⋊C4—21no—
155C2×Dic43⋊C4—21no—
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4—28no—
158C2×Dic43⋊C4D411yescharacteristic
159C2×C22⋊Dic43—21no—
160C2×C22⋊Dic43—21no—
161C2×C22⋊Dic43D411yescharacteristic
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4D411yescharacteristic
165C2×C4×Dic43—21no—
166C2×C4×Dic43C2311yescharacteristic
167#13063256C2314yes—
168Dic43⋊C8C2314yes—
169#13063250C2314yes—
170#13063248C2314yes—
171#13063247C2314yes—
172#13063246C2314yes—
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×D4×C43—21no—
181C22×D4×C43—21no—
182C22×D4×C43C2311yescharacteristic
183C22×D4×C43C2311yescharacteristic
184C23×C4×C43—21no—
185C23×C4×C43C2311yescharacteristic
186C2×SD16×C43—42no—
187C2×SD16×C43C2314yes—
188C2×D8×C43—24no—
189C2×D8×C43C2314yes—
190C22×C8×C43C2311yescharacteristic
191C22×C8×C43C2311yescharacteristic
192#121×C43—22no—
193#121×C43C2314yes—
194C2×C4⋊C4×C43C2311yescharacteristic
195C2×C22⋊C4×C43—21no—
196#103×C43C2314yes—
197#102×C43C2314yes—
198C22⋊C8×C43C2314yes—
199C24×C43—21no—
200C24×C43—21no—
201C24×C43C2×D411yescharacteristic
202C23×D43—21no—
203C23×D43C2×D411yescharacteristic
204#41×C43—28no—
205#41×C43—44no—
206#41×C43—48no—
207C2×Q8×C43—21no—
208C2×Q8×C43—22no—
209C2×Q8×C43—22no—
210C2×Q8×C43C2412yes—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—22no—
214C2×D4×C43—24no—
215C2×D4×C43—24no—
216C2×D4×C43—22no—
217C2×D4×C43—22no—
218C2×D4×C43—44no—
219C2×D4×C43—82no—
220C2×D4×C43C2×D414yes—
221C2×D4×C43C2412yes—
222C2×D4×C43C2412yes—
223C22×C4×C43—22no—
224C22×C4×C43—22no—
225C22×C4×C43—24no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—44no—
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D412yes—
231C22×C4×C43C2412yes—
232C22×C4×C43C2411yescharacteristic
233C2×C22⋊D43—24no—
234C2×C22⋊D43—24no—
235C2×C22⋊D43—24no—
236C2×C22⋊D43—24no—
237C2×C22⋊D43—24no—
238C2×C22⋊D43—24no—
239C2×C22⋊D43—44no—
240C2×C22⋊D43—44no—
241C2×C22⋊D43—44no—
242C2×C22⋊D43—44no—
243C2×C22⋊D43—82no—
244C2×C22⋊D43C2×D414yes—
245C22×Dic43—24no—
246C22×Dic43—24no—
247C22×Dic43—24no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—44no—
252C22×Dic43—44no—
253C22×Dic43—44no—
254C22×Dic43C2×D411yescharacteristic
255C22×Dic43C2×D411yescharacteristic
256C22×Dic43C2×D411yescharacteristic
257#10621900—28no—
258#10621900—28no—
259#10621900—44no—
260#10621900—44no—
261#10621900—48no—
262#10621900—48no—
263#10621898—28no—
264#10621898—44no—
265#10621898—48no—
266C2×D172—21no—
267C2×D172—24no—
268C2×D172—22no—
269C2×D172—22no—
270C2×D172—82no—
271C2×D172C2412yes—
272C2×C4×D43—22no—
273C2×C4×D43—22no—
274C2×C4×D43—24no—
275C2×C4×D43—44no—
276C2×C4×D43C2×D412yes—
277C2×C4×D43C2412yes—
278C2×Dic86—21no—
279C2×Dic86—22no—
280C2×Dic86—22no—
281C2×Dic86—22no—
282C2×Dic86—21no—
283C2×Dic86C2×D414yes—
284C2×Dic86C2412yes—
285C2×Dic86C2412yes—
286SD16×C43—44no—
287D8×C43—28no—
288C2×C8×C43—22no—
289C2×C8×C43—22no—
290C2×C8×C43C2412yes—
291C2×C8×C43C2412yes—
292C4⋊C4×C43—21no—
293C4⋊C4×C43C2412yes—
294C22⋊C4×C43—24no—
295C22⋊Dic43—24no—
296C22⋊Dic43—24no—
297C22⋊Dic43C2×D414yes—
298#10621885—28no—
299#10621884—28no—
300#10621883—28no—
301#10621883C2×D4116yescomplemented
302#10621882—28no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4C2×D414yes—
306C4⋊Dic43—21no—
307C4⋊Dic43C2412yes—
308Dic43⋊C4—24no—
309Dic43⋊C4—24no—
310Dic43⋊C4—24no—
311Dic43⋊C4—24no—
312Dic43⋊C4—24no—
313Dic43⋊C4C2×D414yes—
314C4×Dic43—24no—
315C4×Dic43C2×D412yes—
316C4×Dic43C2412yes—
317C2×C43⋊C8—22no—
318C2×C43⋊C8—28no—
319C2×C43⋊C8C2×D414yes—
320C2×C43⋊C8C2412yes—
321C2×C43⋊C8C2412yes—
322Dic172—28no—
323#10621873—44no—
324C8×D43—28no—
325C23×C43—24no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—42no—
332C23×C43—42no—
333C23×C43—42no—
334C23×C43—42no—
335C23×C43—42no—
336C23×C43C22×D412yes—
337C23×C43C22×D411yescharacteristic
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—42no—
345C22×D43C22×D412yes—
346Q8×C43—22no—
347Q8×C43—22no—
348Q8×C43—42no—
349D4×C43—24no—
350D4×C43—22no—
351D4×C43—22no—
352D4×C43—22no—
353D4×C43—48no—
354D4×C43—42no—
355D4×C43—84no—
356D4×C43C22×D414yes—
357C2×C4×C43—22no—
358C2×C4×C43—24no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—48no—
364C2×C4×C43—42no—
365C2×C4×C43—42no—
366C2×C4×C43C22×D412yes—
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C22×D412yes—
369C2×C4×C43H(5,𝔽2)12yes—
370C2×C4×C43C2511yescharacteristic
371C22⋊D43—28no—
372C22⋊D43—48no—
373C22⋊D43—48no—
374C22⋊D43—48no—
375C22⋊D43—48no—
376C22⋊D43—84no—
377C2×Dic43—24no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—48no—
384C2×Dic43—48no—
385C2×Dic43—42no—
386C2×Dic43—42no—
387C2×Dic43—48no—
388C2×Dic43#13514yescomplemented
389C2×Dic43C22×D412yes—
390C2×Dic43C22×D412yes—
391C2×Dic43C22×D412yes—
392D172—22no—
393D172—22no—
394D172—42no—
395D172—84no—
396C4×D43—24no—
397C4×D43—22no—
398C4×D43—22no—
399C4×D43—48no—
400Dic86—24no—
401Dic86—22no—
402Dic86—22no—
403Dic86—22no—
404Dic86—42no—
405Dic86C22×D414yes—
406C8×C43—22no—
407C8×C43—22no—
408C43⋊C8—22no—
409C43⋊C8C22×D414yes—
410C2×#3284—431nomaximal, Sylow
411C22×C43—24no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—44no—
416C22×C43—48no—
417C22×C43—42no—
418C22×C43—42no—
419C22×C43—42no—
420C22×C43—42no—
421C22×C43—42no—
422C22×C43—84no—
423C22×C43D4212yes—
424C22×C43C2×#13512yes—
425C22×C43#57712yes—
426C22×C43C23×D411yescharacteristic
427C2×D43—22no—
428C2×D43—22no—
429C2×D43—22no—
430C2×D43—44no—
431C2×D43—42no—
432C2×D43—42no—
433C2×D43—42no—
434C2×D43—84no—
435C4×C43—22no—
436C4×C43—42no—
437C4×C43—42no—
438C4×C43D4212yes—
439C4×C43C23×D411yescharacteristic
440C4×C43C2×H(5,𝔽2)11yescharacteristic
441Dic43—24no—
442Dic43—22no—
443Dic43—22no—
444Dic43—42no—
445Dic43—42no—
446Dic43C2×#13514yescomplemented
447C22×#135—431no—
448C22×#135—431no—
449C2×#550—431no—
450C2×#547—431no—
451#3284—4316no—
452C2×#492—431no—
453C2×#465—431no—
454C2×#465—431no—
455C2×#462—431no—
456C2×#459—431no—
457C2×#452—431no—
458C2×#452—431no—
459C2×#449—431no—
460C2×#449D4311yescharacteristic, complemented
461C2×C4×SD16—431no—
462C2×C8×D4—431no—
463C2×C43—42no—
464C2×C43—44no—
465C2×C43—82no—
466C2×C43#328414yescomplemented
467C2×C43C2×D4211yescharacteristic
468C2×C43C22×#13511yescharacteristic
469C2×C43C2×#57711yescharacteristic
470D43—42no—
471D43—82no—
472C22×#41—431no—
473C22×#41—431no—
474C22×#41—431no—
475C22×#41C2×D4311yescharacteristic
476C2×#135—438no—
477C2×#135—438no—
478C2×#135—868no—
479C2×#135—868no—
480C22×Q16—431no—
481C22×Q16—431no—
482C22×SD16—431no—
483C22×SD16—431no—
484C22×SD16—431no—
485C22×SD16—431no—
486C22×SD16C2×D4311yescharacteristic
487C22×D8—431no—
488C22×D8C2×D4311yescharacteristic
489C23×C8—431no—
490C23×C8—431no—
491#550—438no—
492#550—864no—
493#547—438no—
494#547—864no—
495C2×C4⋊Q8—431no—
496C2×#127—431no—
497C2×#127—861no—
498C2×#123—861no—
499C2×#123—861no—
500C2×C22⋊Q8—431no—
501C2×C22⋊Q8—431no—
502C2×#121—431no—
503C2×#121—861no—
504C2×#121—861no—
505C2×#121—861no—
506C2×#121C2×D4311yescharacteristic
507C2×C4×Q8—431no—
508C2×C4×D4—431no—
509C2×C4×D4—431no—
510C2×C4×D4—861no—
511C22×C4⋊C4—861no—
512#492—438no—
513#465—438no—
514#465—438no—
515#462—438no—
516#459—438no—
517#452—438no—
518#452—438no—
519#449—438no—
520#449C2×D4318yescomplemented
521C4×SD16—438no—
522C8×D4—438no—
523C2×#106—431no—
524C2×C4⋊C8—431no—
525C2×#103—431no—
526C2×#103—431no—
527C2×#103C2×D4311yescharacteristic
528C2×#102—431no—
529C2×#102—431no—
530C2×#102C2×D4311yescharacteristic
531C2×C22⋊C8—431no—
532C2×C22⋊C8C2×D4311yescharacteristic
533C2×C4×C8—431no—
534C43C2×#328411yescharacteristic, complemented, Sylow
535C2×#41—22no—
536C2×#41—24no—
537C2×#41—42no—
538C2×#41—434no—
539C2×#41—434no—
540C2×#41—434no—
541C2×#41—864no—
542C2×#41—862no—
543C2×#41—862no—
544C2×#41—862no—
545C2×#41—864no—
546C2×#41—864no—
547C2×#41—1722no—
548C2×#41—1722no—
549C2×#41—1722no—
550C2×#41C22×D4314yes—
551C22×Q8—431no—
552C22×Q8—431no—
553C22×Q8C22×D4311yescharacteristic
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—431no—
557C22×D4—431no—
558C22×D4—861no—
559C22×D4—861no—
560C22×D4—861no—
561C22×D4—861no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4C22×D4311yescharacteristic
565C22×D4C22×D4311yescharacteristic
566C23×C4—21no—
567C23×C4—431no—
568C23×C4—861no—
569C23×C4—861no—
570C23×C4—861no—
571C23×C4—861no—
572C23×C4C22×D4311yescharacteristic
573#135—8632no—
574#135—8632no—
575C2×Q16—434no—
576C2×Q16—434no—
577C2×Q16—864no—
578C2×Q16—864no—
579C2×SD16—42no—
580C2×SD16—438no—
581C2×SD16—434no—
582C2×SD16—434no—
583C2×SD16—434no—
584C2×SD16—434no—
585C2×SD16—864no—
586C2×SD16—864no—
587C2×SD16—1722no—
588C2×SD16C22×D4314yes—
589C2×D8—24no—
590C2×D8—434no—
591C2×D8—864no—
592C2×D8C22×D4314yes—
593C22×C8—431no—
594C22×C8—431no—
595C22×C8—434no—
596C22×C8—434no—
597C22×C8—864no—
598C22×C8—864no—
599C22×C8C22×D4311yescharacteristic
600C22×C8C22×D4311yescharacteristic
601C4⋊Q8—434no—
602C4⋊Q8—862no—
603#127—434no—
604#127—862no—
605#127—868no—
606#123—868no—
607#123—868no—
608C22⋊Q8—434no—
609C22⋊Q8—434no—
610C22⋊Q8—862no—
611C22⋊Q8—862no—
612#121—22no—
613#121—434no—
614#121—868no—
615#121—868no—
616#121—862no—
617#121—868no—
618#121C22×D4314yes—
619C4×Q8—434no—
620C4×Q8—862no—
621C4×D4—434no—
622C4×D4—434no—
623C4×D4—434no—
624C4×D4—862no—
625C4×D4—868no—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—868no—
629C2×C4⋊C4—861no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4—861no—
633C2×C4⋊C4—861no—
634C2×C4⋊C4C22×D4311yescharacteristic
635C2×C22⋊C4—21no—
636C2×C22⋊C4—431no—
637C2×C22⋊C4—431no—
638C2×C22⋊C4—861no—
639C2×C22⋊C4—861no—
640C2×C22⋊C4—861no—
641C2×C22⋊C4—861no—
642C2×C42—431no—
643C2×C42—861no—
644#106—434no—
645C4⋊C8—434no—
646#103—434no—
647#103—434no—
648#103C22×D4314yes—
649#102—434no—
650#102—434no—
651#102C22×D4314yes—
652C22⋊C8—434no—
653C22⋊C8C22×D4314yes—
654C4×C8—434no—
655C24—21no—
656C24—21no—
657C24—431no—
658C24—861no—
659C24D4×D4311yescharacteristic
660#41—28no—
661#41—44no—
662#41—48no—
663#41—868no—
664#41—868no—
665#41—868no—
666#41—1724no—
667#41—1728no—
668#41—1724no—
669#41—1724no—
670#41—1728no—
671#41—1728no—
672C2×Q8—21no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—434no—
676C2×Q8—432no—
677C2×Q8—432no—
678C2×Q8—861no—
679C2×Q8—861no—
680C2×Q8—862no—
681C2×Q8—862no—
682C2×Q8—862no—
683C2×Q8C23×D4312yes—
684C2×D4—24no—
685C2×D4—24no—
686C2×D4—21no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—44no—
692C2×D4—82no—
693C2×D4—434no—
694C2×D4—432no—
695C2×D4—864no—
696C2×D4—864no—
697C2×D4—864no—
698C2×D4—864no—
699C2×D4—864no—
700C2×D4—864no—
701C2×D4—864no—
702C2×D4—862no—
703C2×D4—861no—
704C2×D4—862no—
705C2×D4—3442no—
706C2×D4—3442no—
707C2×D4—1724no—
708C2×D4—1724no—
709C2×D4—1724no—
710C2×D4—1724no—
711C2×D4D4×D4314yes—
712C2×D4C23×D4312yes—
713C2×D4C23×D4312yes—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—44no—
720C22×C4—431no—
721C22×C4—431no—
722C22×C4—431no—
723C22×C4—432no—
724C22×C4—432no—
725C22×C4—864no—
726C22×C4—864no—
727C22×C4—864no—
728C22×C4—861no—
729C22×C4—862no—
730C22×C4—862no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—864no—
734C22×C4—1724no—
735C22×C4—1724no—
736C22×C4—1724no—
737C22×C4—1724no—
738C22×C4D4×D4312yes—
739C22×C4D4×D4311yescharacteristic
740C22×C4C23×D4312yes—
741C22×C4C23×D4311yescharacteristic
742Q16—868no—
743Q16—868no—
744SD16—44no—
745SD16—4316no—
746SD16—868no—
747SD16—868no—
748SD16—1724no—
749D8—28no—
750D8—868no—
751C2×C8—22no—
752C2×C8—22no—
753C2×C8—434no—
754C2×C8—432no—
755C2×C8—432no—
756C2×C8—868no—
757C2×C8—868no—
758C2×C8—862no—
759C2×C8C23×D4312yes—
760C2×C8C23×D4312yes—
761C4⋊C4—21no—
762C4⋊C4—434no—
763C4⋊C4—432no—
764C4⋊C4—864no—
765C4⋊C4—864no—
766C4⋊C4—864no—
767C4⋊C4—864no—
768C4⋊C4—861no—
769C4⋊C4—864no—
770C4⋊C4C23×D4312yes—
771C22⋊C4—24no—
772C22⋊C4—434no—
773C22⋊C4—434no—
774C22⋊C4—864no—
775C22⋊C4—864no—
776C22⋊C4—864no—
777C22⋊C4—864no—
778C42—432no—
779C42—432no—
780C42—864no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—24no—
786C23—22no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—432no—
793C23—862no—
794C23—862no—
795C23—862no—
796C23—862no—
797C23—1722no—
798C23—1722no—
799C23—1722no—
800C23C2×D4×D4312yes—
801C23C2×D4×D4311yescharacteristic
802Q8—22no—
803Q8—22no—
804Q8—42no—
805Q8—434no—
806Q8—862no—
807Q8—864no—
808Q8—862no—
809Q8—862no—
810Q8—1722no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—24no—
815D4—48no—
816D4—42no—
817D4—84no—
818D4—868no—
819D4—862no—
820D4—862no—
821D4—3444no—
822D4—3444no—
823D4—1728no—
824D4—1728no—
825D4—1728no—
826D4—1728no—
827D4—1722no—
828D4C2×D4×D4314yes—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—48no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—434no—
839C2×C4—432no—
840C2×C4—432no—
841C2×C4—432no—
842C2×C4—862no—
843C2×C4—862no—
844C2×C4—862no—
845C2×C4—864no—
846C2×C4—862no—
847C2×C4—862no—
848C2×C4—864no—
849C2×C4—862no—
850C2×C4—862no—
851C2×C4—1728no—
852C2×C4—1728no—
853C2×C4—1728no—
854C2×C4—1728no—
855C2×C4—1722no—
856C2×C4—1722no—
857C2×C4C2×D4×D4312yes—
858C2×C4C2×D4×D4312yes—
859C2×C4C2×D4×D4311yescharacteristic
860C2×C4#1306337012yes—
861C2×C4C24×D4311yescharacteristic
862C8—22no—
863C8—22no—
864C8—434no—
865C8—862no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—24no—
870C22—42no—
871C22—42no—
872C22—44no—
873C22—48no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—84no—
878C22—862no—
879C22—862no—
880C22—862no—
881C22—3444no—
882C22—1722no—
883C22—1722no—
884C22—1722no—
885C22—1724no—
886C22#1458353112yes—
887C22#135×D4312yes—
888C22#1458370912yes—
889C22C22×D4×D4311yescharacteristic
890C4—22no—
891C4—42no—
892C4—42no—
893C4—434no—
894C4—862no—
895C4—862no—
896C4—864no—
897C4—1722no—
898C4—1722no—
899C4#1458353112yes—
900C4C22×D4×D4311yescharacteristic
901C4C2×#1306337011yescharacteristic
902C2—42no—
903C2—44no—
904C2—82no—
905C2—3442no—
906C2—1722no—
907C2#1914632314yesdirect product factor
908C2C2×#1458353111yescharacteristic
909C2C2×#135×D4311yescharacteristic
910C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#449C2
socleC23×C43C22×D4
hypercenterC2×#449D43
hypocenterC43C2×#3284
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C22×#13063345C2semidirect
2. C22×#13063344C2semidirect
3. C2×#14583567C2semidirect
4. C2×#14583548C2semidirect
5. #19146323C2direct (N × H)
6. C2×#14583270C2semidirect
7. C2×#14583131C2semidirect
8. C2×#14583126C2semidirect
9. C2×#14583108C2semidirect
10. C2×#14583092C2semidirect
11. C2×#14583063C2semidirect
12. C2×#14583058C2semidirect
13. C2×#14583045C2semidirect
14. C2×#14582990C2semidirect
15. C2×(C22⋊D43)⋊C8C2semidirect
16. C2×C43×#449C2semidirect
21. C2×#13063345C22semidirect
23. C2×#13063344C22semidirect
34. #14583567C22semidirect
36. #14583548C22semidirect
53. #14583270C22semidirect
54. #14583131C22semidirect
55. #14583126C22semidirect
56. #14583108C22semidirect
57. #14583092C22semidirect
58. #14583063C22semidirect
59. #14583058C22semidirect
60. #14583045C22semidirect
61. #14582990C22semidirect
62. (C22⋊D43)⋊C8C22semidirect
75. C43×#449C22semidirect
115. C2×#10621883D4semidirect
301. #10621883C2×D4semidirect
388. C2×Dic43#135semidirect
446. Dic43C2×#135semidirect
460. C2×#449D43semidirect
466. C2×C43#3284semidirect
520. #449C2×D43semidirect
534. C43C2×#3284semidirect
907. C2#19146323direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633452
C22×#130633442
C2×#145835672
C2×#145835482
#191463232
C2×#145832702
C2×#145831312
C2×#145831262
C2×#145831082
C2×#145830922
C2×#145830632
C2×#145830582
C2×#145830452
C2×#145829902
C2×(C22⋊D43)⋊C82
C2×C43×#4492
C2×#328443