Finite Group Databasebeta

← C2×#19146185 #25971663

Subgroups — C2×#19146185 #25971663

Order 11008.

2826 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×#13063358C211yesmaximal, characteristic, complemented
2C22×#13063347C211yesmaximal, characteristic, complemented
3C2×#14583570C211yesmaximal, characteristic, complemented
4C2×#14583558C211yesmaximal, characteristic, complemented
5#19146185C2116yesmaximal, direct product factor
6C2×#14583288C211yesmaximal, characteristic, complemented
7C2×#14583152C211yesmaximal, characteristic, complemented
8C2×#14583128C211yesmaximal, characteristic, complemented
9C2×#14583122C211yesmaximal, characteristic, complemented
10C2×#14583100C211yesmaximal, characteristic, complemented
11C2×#14583063C211yesmaximal, characteristic, complemented
12C2×#14583046C211yesmaximal, characteristic, complemented
13C2×#14583046C211yesmaximal, characteristic, complemented
14C2×#14583040C211yesmaximal, characteristic, complemented
15C2×#14583007C211yesmaximal, 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×#10621873C2211yescharacteristic
28C22×#10621873C2211yescharacteristic
29C22×#10621873C2211yescharacteristic
30C22×#10621873C2211yescharacteristic
31C22×#10621873C2211yescharacteristic
32C22×D344C2211yescharacteristic
33C22×D344C2211yescharacteristic
34#14583570—24no—
35#14583570C2218yescomplemented
36#14583558—24no—
37#14583558C2218yescomplemented
38C2×#13063322C2211yescharacteristic
39C2×#13063321—21no—
40C2×#13063313C2211yescharacteristic
41C2×#13063311—21no—
42C2×#13063304C2211yescharacteristic
43C2×#13063303—21no—
44C2×#13063299C2211yescharacteristic
45C2×#13063299C2211yescharacteristic
46C2×#13063299C2211yescharacteristic
47C2×#13063298—21no—
48C2×#13063298—21no—
49C2×#13063297—21no—
50C2×C4×Dic86C2211yescharacteristic
51C2×C4×Dic86C2211yescharacteristic
52C2×#13063287—21no—
53C2×(C22⋊D43)⋊C4—21no—
54#14583288C2218yescomplemented
55#14583152C2218yescomplemented
56#14583128C2218yescomplemented
57#14583122C2218yescomplemented
58#14583100C2218yescomplemented
59#14583063C2218yescomplemented
60#14583046C2218yescomplemented
61#14583046C2218yescomplemented
62#14583040C2218yescomplemented
63#14583007C2218yescomplemented
64C2×#13063257C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063250C2211yescharacteristic
67C2×#13063250C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
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×Dic86C2314yes—
97C22×Dic86C2311yescharacteristic
98C22×Dic86C2311yescharacteristic
99C22×D172—21no—
100C22×D172—21no—
101C22×D172C2311yescharacteristic
102C22×D172C2311yescharacteristic
103C22×D172C2311yescharacteristic
104C22×C22⋊D43—21no—
105C22×C22⋊D43—21no—
106C22×C22⋊D43—21no—
107C22×C22⋊D43—21no—
108C22×C22⋊D43—21no—
109C22×C22⋊D43—21no—
110C23×Dic43—21no—
111C22×C4×D43—21no—
112C22×C4×D43—21no—
113C22×C4×D43—21no—
114#13063358—232no—
115#13063347—232no—
116C2×Dic172—24no—
117C2×Dic172D418yescomplemented
118C2×Dic172C2314yes—
119C2×Dic172C2314yes—
120C2×#10621873—24no—
121C2×#10621873—24no—
122C2×#10621873—24no—
123C2×#10621873—24no—
124C2×#10621873—42no—
125C2×#10621873C2314yes—
126C2×#10621873C2314yes—
127C2×#10621873C2314yes—
128C2×#10621873C2314yes—
129C2×#10621873C2314yes—
130C2×D344—24no—
131C2×D344—42no—
132C2×D344C2314yes—
133C2×D344C2314yes—
134#13063322—22no—
135#13063322C2314yes—
136#13063321—28no—
137#13063313—22no—
138#13063313C2314yes—
139#13063311—28no—
140#13063304—22no—
141#13063304C2314yes—
142#13063303—28no—
143#13063299—22no—
144#13063299—22no—
145#13063299—22no—
146#13063299C2314yes—
147#13063299C2314yes—
148#13063299C2314yes—
149#13063298—28no—
150#13063298—28no—
151#13063297—28no—
152C4×Dic86—22no—
153C4×Dic86—22no—
154C4×Dic86C2314yes—
155C4×Dic86C2314yes—
156#13063287—28no—
157(C22⋊D43)⋊C4—28no—
158C2×C4⋊Dic43C2311yescharacteristic
159C2×C4⋊Dic43C2311yescharacteristic
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4—21no—
162C2×Dic43⋊C4—21no—
163C2×C22⋊Dic43—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4—21no—
169C2×C4×Dic43—21no—
170C2×C4×Dic43—21no—
171#13063257C2314yes—
172#13063250C2314yes—
173#13063250C2314yes—
174#13063250C2314yes—
175#13063247C2314yes—
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—
203C23×D43—21no—
204C2×D4×C43—42no—
205C2×D4×C43C2×D414yes—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2412yes—
217C22×C4×C43C2412yes—
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—24no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—24no—
224C2×C22⋊D43—24no—
225C2×C22⋊D43—44no—
226C2×C22⋊D43—44no—
227C2×C22⋊D43—44no—
228C2×C22⋊D43—44no—
229C2×C22⋊D43—82no—
230C2×C22⋊D43—82no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—24no—
237C22×Dic43—44no—
238#10621898—28no—
239#10621898—28no—
240#10621898—28no—
241#10621898—44no—
242#10621898—44no—
243#10621898—44no—
244#10621898—48no—
245#10621898—48no—
246#10621898—48no—
247C2×D172—24no—
248C2×D172—21no—
249C2×D172—21no—
250C2×D172—21no—
251C2×D172—24no—
252C2×D172—22no—
253C2×D172—22no—
254C2×D172—22no—
255C2×D172—22no—
256C2×D172—22no—
257C2×D172—22no—
258C2×D172—44no—
259C2×D172—82no—
260C2×D172C2412yes—
261C2×D172C2412yes—
262C2×D172C2412yes—
263C2×C4×D43—24no—
264C2×C4×D43—24no—
265C2×C4×D43—24no—
266C2×C4×D43—44no—
267C2×C4×D43—44no—
268C2×C4×D43—44no—
269C2×Dic86—21no—
270C2×Dic86—21no—
271C2×Dic86—22no—
272C2×Dic86—22no—
273C2×Dic86—22no—
274C2×Dic86—22no—
275C2×Dic86—28no—
276C2×Dic86—24no—
277C2×Dic86—21no—
278C2×Dic86—44no—
279C2×Dic86—48no—
280C2×Dic86—44no—
281C2×Dic86C2×D414yes—
282C2×Dic86C2×D414yes—
283C2×Dic86C2412yes—
284C2×Dic86C2412yes—
285C2×Dic86C2412yes—
286M16×C43—28no—
287C2×C8×C43—22no—
288C2×C8×C43—22no—
289C2×C8×C43—22no—
290C2×C8×C43—28no—
291C2×C8×C43C2×D414yes—
292C2×C8×C43C2412yes—
293C2×C8×C43C2412yes—
294C2×C8×C43C2412yes—
295C2×C8×C43C2412yes—
296C4⋊C4×C43C2×D414yes—
297C22⋊C4×C43C2×D414yes—
298C22⋊C4×C43C2×D414yes—
299C42×C43C2×D412yes—
300C42×C43C2412yes—
301C22⋊Dic43—24no—
302(C2×D43)⋊C4—24no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4—24no—
306(C2×D43)⋊C4—24no—
307C4⋊Dic43—21no—
308C4⋊Dic43—21no—
309C4⋊Dic43C2412yes—
310C4⋊Dic43C2412yes—
311Dic43⋊C4—24no—
312Dic43⋊C4—24no—
313Dic43⋊C4—24no—
314C4×Dic43—24no—
315C4×Dic43—24no—
316Dic172—28no—
317Dic172C2×D4116yescomplemented
318D344—28no—
319D344—44no—
320#10621873—28no—
321#10621873—28no—
322#10621873—28no—
323#10621873—28no—
324#10621873—44no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43C22×D412yes—
332C23×C43C22×D412yes—
333C23×C43C22×D411yescharacteristic
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—42no—
338C22×D43—42no—
339C22×D43—42no—
340C22×D43—42no—
341C22×D43—42no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—42no—
345C22×D43—42no—
346D4×C43—44no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—24no—
352C2×C4×C43—24no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43C22×D412yes—
358C2×C4×C43C22×D412yes—
359C2×C4×C43C22×D412yes—
360C2×C4×C43C22×D412yes—
361C2×C4×C43C22×D412yes—
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43H(5,𝔽2)12yes—
364C2×C4×C43C2511yescharacteristic
365C22⋊D43—48no—
366C22⋊D43—48no—
367C22⋊D43—48no—
368C22⋊D43—48no—
369C22⋊D43—84no—
370C22⋊D43—84no—
371C2×Dic43—24no—
372C2×Dic43—24no—
373C2×Dic43—22no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—48no—
379C2×Dic43—42no—
380C2×Dic43—42no—
381C2×Dic43—42no—
382D172—22no—
383D172—22no—
384D172—22no—
385D172—22no—
386D172—22no—
387D172—22no—
388D172—48no—
389D172—42no—
390D172—42no—
391D172—42no—
392D172—84no—
393C4×D43—48no—
394C4×D43—48no—
395C4×D43—48no—
396Dic86—24no—
397Dic86—24no—
398Dic86—22no—
399Dic86—22no—
400Dic86—22no—
401Dic86—22no—
402Dic86—48no—
403Dic86—42no—
404Dic86C22×D414yes—
405Dic86C22×D414yes—
406C8×C43—22no—
407C8×C43—22no—
408C8×C43—22no—
409C8×C43C22×D414yes—
410C2×#3271—431nomaximal, Sylow
411C22×C43—22no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—22no—
416C22×C43—22no—
417C22×C43—44no—
418C22×C43—44no—
419C22×C43D4212yes—
420C22×C43#57512yes—
421C22×C43#57712yes—
422C22×C43C23×D411yescharacteristic
423C2×D43—42no—
424C2×D43—42no—
425C2×D43—42no—
426C2×D43—42no—
427C2×D43—42no—
428C2×D43—42no—
429C2×D43—42no—
430C2×D43—42no—
431C2×D43—42no—
432C2×D43—84no—
433C2×D43—84no—
434C2×D43—84no—
435C4×C43—22no—
436C4×C43—22no—
437C4×C43—22no—
438C4×C43—22no—
439C4×C43D4212yes—
440C4×C43C23×D411yescharacteristic
441C4×C43C2×H(5,𝔽2)11yescharacteristic
442Dic43—24no—
443Dic43—24no—
444Dic43—42no—
445Dic43—42no—
446Dic43—42no—
447C22×#137—431no—
448C22×#135—431no—
449C2×#550—431no—
450C2×#548—431no—
451#3271—4316no—
452C2×#496—431no—
453C2×#469—431no—
454C2×#465—431no—
455C2×#464—431no—
456C2×#460—431no—
457C2×#452—431no—
458C2×#449—431no—
459C2×#449—431no—
460C2×#448—431no—
461C2×#441—431no—
462C2×#435D4311yescharacteristic, complemented
463C2×C43—42no—
464C2×C43—42no—
465C2×C43#327114yescomplemented
466C2×C43C2×D4211yescharacteristic
467C2×C43C2×#57511yescharacteristic
468C2×C43C2×#57711yescharacteristic
469D43—82no—
470D43—82no—
471D43—82no—
472C22×#41—431no—
473C22×#41—431no—
474C22×#41—431no—
475C23×Q8—431no—
476C2×#137—438no—
477C2×#137—868no—
478C2×#135—438no—
479C2×#135—868no—
480C22×Q16—431no—
481C22×Q16—431no—
482C22×SD16—431no—
483C22×SD16—431no—
484C22×SD16—431no—
485C22×SD16—431no—
486C22×SD16—431no—
487C22×D8—431no—
488C22×D8—431no—
489C22×M16C2×D4311yescharacteristic
490C23×C8C2×D4311yescharacteristic
491#550—438no—
492#550—864no—
493#548—438no—
494#548—864no—
495C2×#127—431no—
496C2×#127—861no—
497C2×#124—431no—
498C2×#124—861no—
499C2×C22⋊Q8—431no—
500C2×C22⋊Q8—861no—
501C2×#121—431no—
502C2×#121—431no—
503C2×#121—431no—
504C2×#121—861no—
505C2×#121—861no—
506C2×#121—861no—
507C2×C4×Q8—431no—
508C2×C4×Q8—431no—
509C2×C4×D4—861no—
510C2×C4×D4—861no—
511C2×C4×D4C2×D4311yescharacteristic
512#496—438no—
513#469—438no—
514#465—438no—
515#464—438no—
516#460—438no—
517#452—438no—
518#449—438no—
519#449—438no—
520#448—438no—
521#441—438no—
522#435C2×D4318yescomplemented
523C2×#106—431no—
524C2×C4⋊C8C2×D4311yescharacteristic
525C2×#103—431no—
526C2×#103—431no—
527C2×#103—431no—
528C2×#102—431no—
529C2×#102—431no—
530C2×#102—431no—
531C2×C22⋊C8C2×D4311yescharacteristic
532C2×C22⋊C8C2×D4311yescharacteristic
533C2×#97C2×D4311yescharacteristic
534C43C2×#327111yescharacteristic, complemented, Sylow
535C2×#41—434no—
536C2×#41—434no—
537C2×#41—434no—
538C2×#41—864no—
539C2×#41—864no—
540C2×#41—864no—
541C2×#41—862no—
542C2×#41—862no—
543C2×#41—862no—
544C2×#41—1722no—
545C2×#41—1722no—
546C2×#41—1722no—
547C22×Q8—431no—
548C22×Q8—431no—
549C22×Q8—431no—
550C22×Q8—434no—
551C22×Q8—864no—
552C22×Q8—861no—
553C22×Q8—862no—
554C22×Q8—1722no—
555C22×D4—431no—
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×D4—861no—
565C22×D4—861no—
566C22×D4D17211yescharacteristic
567C23×C4—861no—
568C23×C4—861no—
569C23×C4—861no—
570C23×C4—861no—
571C23×C4C22×D4311yescharacteristic
572C23×C4C22×D4311yescharacteristic
573#137—8632no—
574#135—8632no—
575C2×Q16—438no—
576C2×Q16—434no—
577C2×Q16—434no—
578C2×Q16—864no—
579C2×SD16—434no—
580C2×SD16—434no—
581C2×SD16—434no—
582C2×SD16—434no—
583C2×SD16—434no—
584C2×SD16—864no—
585C2×SD16—864no—
586C2×SD16—864no—
587C2×SD16—864no—
588C2×SD16—1722no—
589C2×D8—434no—
590C2×D8—434no—
591C2×D8—864no—
592C2×D8—1722no—
593C2×M16—24no—
594C2×M16C22×D4314yes—
595C22×C8—24no—
596C22×C8C22×D4311yescharacteristic
597C22×C8C22×D4314yes—
598C22×C8C22×D4311yescharacteristic
599C22×C8C22×D4311yescharacteristic
600C22×C8C22×D4311yescharacteristic
601#127—434no—
602#127—868no—
603#127—862no—
604#124—434no—
605#124—868no—
606#124—862no—
607C22⋊Q8—434no—
608C22⋊Q8—862no—
609C22⋊Q8—868no—
610#121—434no—
611#121—434no—
612#121—434no—
613#121—868no—
614#121—862no—
615#121—862no—
616#121—862no—
617#121—868no—
618#121—868no—
619C4×Q8—434no—
620C4×Q8—434no—
621C4×Q8—862no—
622C4×Q8—862no—
623C4×D4—868no—
624C4×D4—868no—
625C4×D4D17214yes—
626C4×D4C22×D4314yes—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—861no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4D17211yescharacteristic
633C2×C22⋊C4—861no—
634C2×C22⋊C4—861no—
635C2×C22⋊C4—861no—
636C2×C22⋊C4—861no—
637C2×C22⋊C4—861no—
638C2×C22⋊C4—861no—
639C2×C22⋊C4D17211yescharacteristic
640C2×C22⋊C4D17211yescharacteristic
641C2×C42—861no—
642C2×C42—861no—
643C2×C42C22×D4311yescharacteristic
644#106—434no—
645C4⋊C8C22×D4314yes—
646#103—434no—
647#103—434no—
648#103—434no—
649#102—434no—
650#102—434no—
651#102—434no—
652C22⋊C8C22×D4314yes—
653C22⋊C8C22×D4314yes—
654#97C22×D4314yes—
655C24—861no—
656C24—861no—
657C24—861no—
658C24C2×D17211yescharacteristic
659C24C2×D17211yescharacteristic
660#41—868no—
661#41—868no—
662#41—868no—
663#41—1724no—
664#41—1724no—
665#41—1724no—
666#41—1728no—
667#41—1728no—
668#41—1728no—
669C2×Q8—434no—
670C2×Q8—434no—
671C2×Q8—432no—
672C2×Q8—432no—
673C2×Q8—432no—
674C2×Q8—868no—
675C2×Q8—861no—
676C2×Q8—861no—
677C2×Q8—864no—
678C2×Q8—861no—
679C2×Q8—862no—
680C2×Q8—862no—
681C2×Q8—862no—
682C2×Q8—862no—
683C2×Q8—1724no—
684C2×Q8—1724no—
685C2×Q8—1728no—
686C2×D4—42no—
687C2×D4—432no—
688C2×D4—432no—
689C2×D4—432no—
690C2×D4—864no—
691C2×D4—864no—
692C2×D4—864no—
693C2×D4—864no—
694C2×D4—864no—
695C2×D4—864no—
696C2×D4—862no—
697C2×D4—862no—
698C2×D4—862no—
699C2×D4—864no—
700C2×D4—864no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—862no—
705C2×D4—862no—
706C2×D4—862no—
707C2×D4—3442no—
708C2×D4—3442no—
709C2×D4—3442no—
710C2×D4—1724no—
711C2×D4—1724no—
712C2×D4—1724no—
713C2×D4—1724no—
714C2×D4—1724no—
715C2×D4C2×D17214yes—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—864no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—864no—
727C22×C4—864no—
728C22×C4—864no—
729C22×C4—1724no—
730C22×C4—1724no—
731C22×C4—1724no—
732C22×C4—1724no—
733C22×C4C2×D17212yes—
734C22×C4C2×D17212yes—
735C22×C4C2×D17211yescharacteristic
736C22×C4C2×D17211yescharacteristic
737C22×C4C2×D17211yescharacteristic
738C22×C4C2×D17211yescharacteristic
739C22×C4C23×D4312yes—
740C22×C4C23×D4312yes—
741C22×C4C23×D4311yescharacteristic
742Q16—4316no—
743Q16—868no—
744SD16—868no—
745SD16—868no—
746SD16—868no—
747SD16—868no—
748SD16—1724no—
749D8—868no—
750D8—1724no—
751M16—28no—
752C2×C8—22no—
753C2×C8—22no—
754C2×C8—22no—
755C2×C8—28no—
756C2×C8D4×D4314yes—
757C2×C8C23×D4312yes—
758C2×C8C23×D4312yes—
759C2×C8C23×D4312yes—
760C2×C8C23×D4312yes—
761C4⋊C4—432no—
762C4⋊C4—432no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4—864no—
766C4⋊C4—864no—
767C4⋊C4—864no—
768C4⋊C4C2×D17214yes—
769C22⋊C4—864no—
770C22⋊C4—864no—
771C22⋊C4—864no—
772C22⋊C4—864no—
773C22⋊C4—864no—
774C22⋊C4—864no—
775C22⋊C4C2×D17214yes—
776C22⋊C4C2×D17214yes—
777C42—864no—
778C42—864no—
779C42C2×D17212yes—
780C42C23×D4312yes—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—862no—
788C23—862no—
789C23—862no—
790C23—1722no—
791C23—1722no—
792C23—1722no—
793C23—1722no—
794C23—1722no—
795C23—1722no—
796C23—1722no—
797C23—1722no—
798C23—1722no—
799C23C22×D17212yes—
800C23C22×D17212yes—
801C23C22×D17211yescharacteristic
802Q8—434no—
803Q8—434no—
804Q8—862no—
805Q8—862no—
806Q8—864no—
807Q8—864no—
808Q8—862no—
809Q8—862no—
810Q8—1728no—
811Q8—1722no—
812D4—44no—
813D4—862no—
814D4—862no—
815D4—862no—
816D4—862no—
817D4—862no—
818D4—862no—
819D4—3444no—
820D4—3444no—
821D4—3444no—
822D4—1728no—
823D4—1728no—
824D4—1728no—
825D4—1728no—
826D4—1728no—
827D4—1722no—
828D4—1722no—
829D4—1722no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—862no—
841C2×C4—862no—
842C2×C4—864no—
843C2×C4—864no—
844C2×C4—862no—
845C2×C4—862no—
846C2×C4—862no—
847C2×C4—1728no—
848C2×C4—1728no—
849C2×C4—1728no—
850C2×C4—1728no—
851C2×C4—1722no—
852C2×C4—1722no—
853C2×C4—1722no—
854C2×C4C2×D4×D4312yes—
855C2×C4C22×D17212yes—
856C2×C4C22×D17212yes—
857C2×C4C22×D17212yes—
858C2×C4C22×D17212yes—
859C2×C4C22×D17211yescharacteristic
860C2×C4#1306337112yes—
861C2×C4C24×D4311yescharacteristic
862C8—22no—
863C8—22no—
864C8—22no—
865C8C2×D4×D4314yes—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—44no—
874C22—3444no—
875C22—3444no—
876C22—3444no—
877C22—1722no—
878C22—1722no—
879C22—1722no—
880C22—1722no—
881C22—1722no—
882C22—1722no—
883C22—1722no—
884C22—1722no—
885C22—1722no—
886C22D4×D17212yes—
887C22#1458369912yes—
888C22#1458371112yes—
889C22C23×D17211yescharacteristic
890C4—22no—
891C4—22no—
892C4—22no—
893C4—22no—
894C4—864no—
895C4—864no—
896C4—1722no—
897C4—1722no—
898C4—1722no—
899C4D4×D17212yes—
900C4C22×D4×D4311yescharacteristic
901C4C2×#1306337111yescharacteristic
902C2—42no—
903C2—42no—
904C2—3442no—
905C2—3442no—
906C2—3442no—
907C2#1914618514yesdirect product factor
908C2C2×D4×D17211yescharacteristic
909C2C2×#1458369911yescharacteristic
910C2C2×#1458371111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
hypercenterC2×#435D43
hypocenterC43C2×#3271
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×#14583570C2semidirect
4. C2×#14583558C2semidirect
5. #19146185C2direct (N × H)
6. C2×#14583288C2semidirect
7. C2×#14583152C2semidirect
8. C2×#14583128C2semidirect
9. C2×#14583122C2semidirect
10. C2×#14583100C2semidirect
11. C2×#14583063C2semidirect
12. C2×#14583046C2semidirect
13. C2×#14583046C2semidirect
14. C2×#14583040C2semidirect
15. C2×#14583007C2semidirect
16. C2×C43×#435C2semidirect
22. C2×#13063358C22semidirect
24. C2×#13063347C22semidirect
35. #14583570C22semidirect
37. #14583558C22semidirect
54. #14583288C22semidirect
55. #14583152C22semidirect
56. #14583128C22semidirect
57. #14583122C22semidirect
58. #14583100C22semidirect
59. #14583063C22semidirect
60. #14583046C22semidirect
61. #14583046C22semidirect
62. #14583040C22semidirect
63. #14583007C22semidirect
74. C43×#435C22semidirect
117. C2×Dic172D4semidirect
317. Dic172C2×D4semidirect
462. C2×#435D43semidirect
465. C2×C43#3271semidirect
522. #435C2×D43semidirect
534. C43C2×#3271semidirect
907. C2#19146185direct (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×#145835702
C2×#145835582
#191461852
C2×#145832882
C2×#145831522
C2×#145831282
C2×#145831222
C2×#145831002
C2×#145830632
C2×#145830462
C2×#145830402
C2×#145830072
C2×C43×#4352
C2×#327143