Finite Group Databasebeta

← C2×#19143814 #25962935

Subgroups — C2×#19143814 #25962935

Order 11008.

5130 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10621900C211yesmaximal, characteristic, complemented
2C22×#13063346C212yesmaximal, complemented
3C2×#14583412C211yesmaximal, characteristic, complemented
4#19143814C2116yesmaximal, direct product factor
5C2×#14583058C212yesmaximal, complemented
6C2×#14583045C212yesmaximal, complemented
7C2×#14583054C211yesmaximal, characteristic, complemented
8C2×#14583040C211yesmaximal, characteristic, complemented
9C2×#14583033C211yesmaximal, characteristic, complemented
10C2×#14582892C212yesmaximal, complemented
11C2×C22⋊C8×D43C211yesmaximal, characteristic, complemented
12C2×C43×#450C211yesmaximal, characteristic, complemented
13C22×#10621902C2211yescharacteristic, complemented
14C22×#10621900—216no—
15C22×#10621900—21no—
16C22×#10621900—21no—
17C22×#10621900—24no—
18C22×#10621900C2212yes—
19C22×#10621900C2212yes—
20C22×#10621900C2218yescomplemented
21C23×Dic86C2211yescharacteristic
22C23×C22⋊D43—21no—
23C24×Dic43—21no—
24C23×C4×D43C2211yescharacteristic
25C2×#13063346—216no—
26C2×#13063346C22116yescomplemented
27C22×#10621885C2212yescomplemented
28C22×#10621873C2212yescomplemented
29C22×#10621882C2212yescomplemented
30C22×C8×D43C2212yescomplemented
31#14583412—24no—
32#14583412C2218yescomplemented
33C2×#13063310—21no—
34C2×#13063301C2211yescharacteristic, complemented
35C2×#13063300C2211yescharacteristic, complemented
36C2×#13063299C2211yescharacteristic
37C2×#13063295—21no—
38C2×#13063287—21no—
39C2×(C22⋊D43)⋊C4—21no—
40C2×#13063283C2211yescharacteristic, complemented
41#14583058C22116yescomplemented
42#14583054C2218yescomplemented
43#14583045C22116yescomplemented
44#14583040C2218yescomplemented
45#14583033C2218yescomplemented
46#14582892C22116yescomplemented
47C2×#13063250C2212yescomplemented
48C2×#13063248C2212yescomplemented
49C2×#13063246C2212yescomplemented
50C2×C22⋊(C43⋊C8)C2211yescharacteristic
51C2×(C2×D43)⋊C8C2212yescomplemented
52C22⋊C8×D43C2218yescomplemented
53C23×D4×C43C2211yescharacteristic
54C22×SD16×C43C2212yescomplemented
55C2×C22⋊Q8×C43C2211yescharacteristic
56C43×#450C2218yescomplemented
57C2×#102×C43C2212yescomplemented
58C2×C22⋊C8×C43C2211yescharacteristic
59C24×D43D411yescharacteristic
60C2×#10621902—22no—
61C2×#10621902—28no—
62C2×#10621902C2314yescomplemented
63C2×#10621900—216no—
64C2×#10621900—264no—
65C2×#10621900—216no—
66C2×#10621900—28no—
67C2×#10621900—264no—
68C2×#10621900—28no—
69C2×#10621900—24no—
70C2×#10621900—24no—
71C2×#10621900—28no—
72C2×#10621900—28no—
73C2×#10621900—28no—
74C2×#10621900D4116yescomplemented
75C2×#10621900C2318yes—
76C2×#10621900C2318yes—
77C22×Dic86—21no—
78C22×Dic86—22no—
79C22×Dic86—28no—
80C22×Dic86C2314yes—
81C22×Dic86C2312yes—
82C22×D172—21no—
83C22×D172—21no—
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—216no—
86C22×C22⋊D43—22no—
87C22×C22⋊D43—22no—
88C22×C22⋊D43—28no—
89C22×C22⋊D43—21no—
90C23×Dic43—216no—
91C23×Dic43—21no—
92C23×Dic43—22no—
93C23×Dic43—22no—
94C23×Dic43—28no—
95C23×Dic43D411yescharacteristic
96C22×C4×D43—28no—
97C22×C4×D43—21no—
98C22×C4×D43D411yescharacteristic
99C22×C4×D43D411yescharacteristic
100C22×C4×D43D414yes—
101C22×C4×D43C2314yes—
102C22×C4×D43C2311yescharacteristic
103C22×C4×D43C2311yescharacteristic
104#13063346—264no—
105C2×#10621885—28no—
106C2×#10621885C2318yescomplemented
107C2×#10621873—28no—
108C2×#10621873C2318yescomplemented
109C2×#10621882—28no—
110C2×#10621882C2318yescomplemented
111C22×C43⋊C8C2312yes—
112C2×C8×D43—28no—
113C2×C8×D43C2318yescomplemented
114#13063310—28no—
115#13063301—22no—
116#13063301C2314yescomplemented
117#13063300—22no—
118#13063300C2314yescomplemented
119#13063299—22no—
120#13063299C2314yes—
121#13063295—28no—
122#13063287—28no—
123(C22⋊D43)⋊C4—28no—
124#13063283—22no—
125#13063283C2314yescomplemented
126C2×C4⋊Dic43C2311yescharacteristic
127C2×Dic43⋊C4—21no—
128C2×(C2×D43)⋊C4—21no—
129C2×(C2×D43)⋊C4—21no—
130C2×(C2×D43)⋊C4—21no—
131C2×(C2×D43)⋊C4—21no—
132C2×C4×Dic43—21no—
133#13063250C2318yescomplemented
134#13063248C2318yescomplemented
135#13063246C2318yescomplemented
136C22⋊(C43⋊C8)C2314yes—
137(C2×D43)⋊C8C2318yescomplemented
138C25×C43—21no—
139C22×Q8×C43C2311yescharacteristic
140C22×D4×C43—28no—
141C22×D4×C43—21no—
142C22×D4×C43—22no—
143C22×D4×C43C2314yes—
144C22×D4×C43C2312yes—
145C23×C4×C43C2311yescharacteristic
146C2×SD16×C43—28no—
147C2×SD16×C43C2318yescomplemented
148C22×C8×C43C2312yes—
149C22⋊Q8×C43—22no—
150C22⋊Q8×C43C2314yes—
151C2×C4⋊C4×C43—21no—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154#102×C43C2318yescomplemented
155C22⋊C8×C43C2314yes—
156C24×C43—28no—
157C24×C43—24no—
158C24×C43—22no—
159C24×C43—44no—
160C24×C43—44no—
161C24×C43C2×D411yescharacteristic
162C23×D43—24no—
163C23×D43—24no—
164C23×D43—21no—
165C23×D43—42no—
166C23×D43C2×D411yescharacteristic
167C23×D43C2×D414yes—
168C23×D43C2×D411yescharacteristic
169C2×Q8×C43—21no—
170C2×Q8×C43—24no—
171C2×Q8×C43C2412yes—
172C2×D4×C43—216no—
173C2×D4×C43—28no—
174C2×D4×C43—216no—
175C2×D4×C43—24no—
176C2×D4×C43—24no—
177C2×D4×C43—22no—
178C2×D4×C43C2×D418yes—
179C2×D4×C43C2414yes—
180C22×C4×C43—24no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D412yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2411yescharacteristic
187C2×C22⋊D43—216no—
188C2×C22⋊D43—264no—
189C2×C22⋊D43—24no—
190C2×C22⋊D43—216no—
191C2×C22⋊D43—28no—
192C2×C22⋊D43—28no—
193C2×C22⋊D43—44no—
194C22×Dic43—28no—
195C22×Dic43—264no—
196C22×Dic43—216no—
197C22×Dic43—24no—
198C22×Dic43—216no—
199C22×Dic43—28no—
200C22×Dic43—28no—
201C22×Dic43—24no—
202C22×Dic43—22no—
203C22×Dic43—21no—
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D414yes—
206C22×Dic43C2×D411yescharacteristic
207#10621902—216no—
208#10621902—48no—
209#10621900—264no—
210#10621900—264no—
211#10621900—232no—
212#10621900—216no—
213#10621900—232no—
214#10621900—216no—
215#10621900—216no—
216#10621900C2×D4132yescomplemented
217C2×D172—21no—
218C2×D172—24no—
219C2×D172—24no—
220C2×D172—24no—
221C2×D172—44no—
222C2×D172—44no—
223C2×D172C2412yes—
224C2×C4×D43—24no—
225C2×C4×D43—24no—
226C2×C4×D43—216no—
227C2×C4×D43—216no—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—44no—
231C2×C4×D43C2×D418yes—
232C2×C4×D43C2×D414yes—
233C2×C4×D43C2×D412yes—
234C2×C4×D43C2×D414yes—
235C2×C4×D43C2×D412yes—
236C2×C4×D43C2412yes—
237C2×C4×D43C2412yes—
238C2×Dic86—28no—
239C2×Dic86—216no—
240C2×Dic86—24no—
241C2×Dic86—22no—
242C2×Dic86—24no—
243C2×Dic86—216no—
244C2×Dic86C2×D418yes—
245C2×Dic86C2414yes—
246SD16×C43—216no—
247C2×C8×C43—24no—
248C2×C8×C43C2414yes—
249C4⋊C4×C43—24no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43C2412yes—
252C22⋊C4×C43—24no—
253#10621885—216no—
254#10621882—216no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259C4⋊Dic43—21no—
260C4⋊Dic43C2412yes—
261Dic43⋊C4—24no—
262C4×Dic43—24no—
263C2×C43⋊C8—24no—
264C2×C43⋊C8C2414yes—
265#10621873—216no—
266C8×D43—216no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—216no—
270C23×C43—28no—
271C23×C43—24no—
272C23×C43—432no—
273C23×C43—48no—
274C23×C43—44no—
275C23×C43—48no—
276C23×C43—44no—
277C23×C43#13514yescomplemented
278C23×C43C22×D412yes—
279C23×C43C22×D411yescharacteristic
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—28no—
285C22×D43—22no—
286C22×D43—28no—
287C22×D43—22no—
288C22×D43—44no—
289C22×D43—416no—
290C22×D43—42no—
291C22×D43—42no—
292C22×D43—42no—
293C22×D43#12014yes—
294C22×D43C22×D412yes—
295C22×D43C22×D412yes—
296Q8×C43—24no—
297Q8×C43—42no—
298D4×C43—216no—
299D4×C43—28no—
300D4×C43—24no—
301D4×C43C22×D418yes—
302C2×C4×C43—22no—
303C2×C4×C43—24no—
304C2×C4×C43—24no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C22×D414yes—
312C2×C4×C43C2511yescharacteristic
313C22⋊D43—232no—
314C22⋊D43—232no—
315C22⋊D43—48no—
316C2×Dic43—216no—
317C2×Dic43—232no—
318C2×Dic43—28no—
319C2×Dic43—22no—
320C2×Dic43—24no—
321C2×Dic43—28no—
322C2×Dic43—232no—
323C2×Dic43—22no—
324C2×Dic43—42no—
325C2×Dic43#12014yes—
326C2×Dic43C22×D412yes—
327C2×Dic43C22×D412yes—
328D172—24no—
329D172—48no—
330D172—48no—
331D172—42no—
332C4×D43—28no—
333C4×D43—24no—
334C4×D43—24no—
335C4×D43—28no—
336C4×D43—48no—
337C4×D43#12018yes—
338C4×D43C22×D418yes—
339Dic86—216no—
340Dic86—28no—
341Dic86—24no—
342Dic86C22×D418yes—
343C8×C43—24no—
344C43⋊C8—24no—
345C2×#3002—431nomaximal, Sylow
346C22×C43—22no—
347C22×C43—28no—
348C22×C43—22no—
349C22×C43—28no—
350C22×C43—432no—
351C22×C43—416no—
352C22×C43—44no—
353C22×C43—44no—
354C22×C43C2×#12012yes—
355C22×C43C2×#13512yes—
356C22×C43C2×#13514yescomplemented
357C22×C43#57512yes—
358C22×C43C23×D411yescharacteristic
359C2×D43—28no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—416no—
366C2×D43—44no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—84no—
371C2×D43C2×#12014yes—
372C4×C43—22no—
373C4×C43—42no—
374C4×C43—42no—
375C4×C43C2×#12012yes—
376C4×C43C23×D412yes—
377Dic43—28no—
378Dic43—22no—
379Dic43—42no—
380Dic43C2×#12014yes—
381C23×#41—431no—
382C22×#135—432no—
383C2×#525—431no—
384#3002—4316no—
385C2×#452—432no—
386C2×#449—432no—
387C2×#451—431no—
388C2×#448—431no—
389C2×#450D4311yescharacteristic, complemented
390C2×#447—431no—
391C2×#416—432no—
392C22×C22⋊C8—431no—
393C2×C43—24no—
394C2×C43—48no—
395C2×C43#300214yescomplemented
396C2×C43C22×#12011yescharacteristic
397C2×C43C22×#13511yescharacteristic
398C2×C43C2×#57511yescharacteristic
399D43—24no—
400D43—42no—
401D43—82no—
402C22×#41—431no—
403C22×#41—432no—
404C22×#41—432no—
405C22×#41—438no—
406C22×#41—861no—
407C22×#41—861no—
408C22×#41—864no—
409C22×#41—8616no—
410C23×Q8—431no—
411C23×D4—861no—
412C23×D4C2×D4311yescharacteristic
413C24×C4—431no—
414C24×C4—861no—
415C2×#135—4316no—
416C2×#135—8616no—
417C22×Q16—432no—
418C22×SD16—432no—
419C22×SD16C2×D4312yescomplemented
420C22×D8—432no—
421C23×C8—432no—
422#525—438no—
423#525—864no—
424C2×#123—861no—
425C2×C22⋊Q8—431no—
426C2×C22⋊Q8C2×D4311yescharacteristic
427C2×#121—431no—
428C2×#121—431no—
429C2×#120—861no—
430C2×C4×D4—861no—
431C2×C4×D4—861no—
432C2×#117—431no—
433#452—4316no—
434#451—438no—
435#450C2×D4318yescomplemented
436#449—4316no—
437#448—438no—
438#447—438no—
439#416—4316no—
440C2×#103—432no—
441C2×#103—432no—
442C2×#102—432no—
443C2×#102C2×D4312yescomplemented
444C2×C22⋊C8—431no—
445C2×C22⋊C8—432no—
446C2×C22⋊C8—438no—
447C2×C22⋊C8C2×D4311yescharacteristic
448C43C2×#300211yescharacteristic, complemented, Sylow
449C25—21no—
450C25—431no—
451C2×#41—434no—
452C2×#41—4316no—
453C2×#41—438no—
454C2×#41—438no—
455C2×#41—864no—
456C2×#41—868no—
457C2×#41—868no—
458C2×#41—864no—
459C2×#41—868no—
460C2×#41—862no—
461C2×#41—868no—
462C2×#41—868no—
463C2×#41—8664no—
464C2×#41—8616no—
465C2×#41—8664no—
466C2×#41—8616no—
467C2×#41—868no—
468C22×Q8—432no—
469C22×Q8—434no—
470C22×Q8—868no—
471C22×Q8—862no—
472C22×Q8—861no—
473C22×Q8C22×D4311yescharacteristic
474C22×D4—28no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—431no—
478C22×D4—861no—
479C22×D4—861no—
480C22×D4—868no—
481C22×D4—862no—
482C22×D4—862no—
483C22×D4—8616no—
484C22×D4—861no—
485C22×D4C22×D4314yes—
486C22×D4C22×D4312yes—
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—431no—
491C23×C4—434no—
492C23×C4—431no—
493C23×C4—434no—
494C23×C4—868no—
495C23×C4—861no—
496C23×C4—862no—
497C23×C4—868no—
498C23×C4—862no—
499C23×C4—8616no—
500C23×C4—861no—
501C23×C4C22×D4311yescharacteristic
502#135—8664no—
503C2×Q16—438no—
504C2×Q16—868no—
505C2×SD16—28no—
506C2×SD16—438no—
507C2×SD16—868no—
508C2×SD16C22×D4318yescomplemented
509C2×D8—438no—
510C2×D8—868no—
511C22×C8—432no—
512C22×C8—438no—
513C22×C8—868no—
514C22×C8C22×D4312yes—
515#123—868no—
516C22⋊Q8—22no—
517C22⋊Q8—434no—
518C22⋊Q8—862no—
519C22⋊Q8C22×D4314yes—
520#121—434no—
521#121—434no—
522#121—862no—
523#121—862no—
524#120—868no—
525C4×D4—868no—
526C4×D4—868no—
527#117—434no—
528#117—862no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—431no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4C22×D4311yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C42—861no—
539#103—438no—
540#103—438no—
541#102—438no—
542#102C22×D4318yescomplemented
543C22⋊C8—434no—
544C22⋊C8—438no—
545C22⋊C8C22×D4314yes—
546C24—28no—
547C24—24no—
548C24—22no—
549C24—44no—
550C24—44no—
551C24—431no—
552C24—431no—
553C24—434no—
554C24—864no—
555C24—864no—
556C24—861no—
557C24—1722no—
558C24D4×D4311yescharacteristic
559#41—4332no—
560#41—8632no—
561#41—8616no—
562#41—8616no—
563#41—8616no—
564#41—8664no—
565#41—8664no—
566#41—8632no—
567#41—8616no—
568#41—1728no—
569C2×Q8—21no—
570C2×Q8—24no—
571C2×Q8—438no—
572C2×Q8—434no—
573C2×Q8—8616no—
574C2×Q8—868no—
575C2×Q8—8616no—
576C2×Q8—864no—
577C2×Q8—864no—
578C2×Q8—862no—
579C2×Q8C23×D4312yes—
580C2×D4—28no—
581C2×D4—216no—
582C2×D4—216no—
583C2×D4—24no—
584C2×D4—22no—
585C2×D4—24no—
586C2×D4—432no—
587C2×D4—864no—
588C2×D4—864no—
589C2×D4—8616no—
590C2×D4—868no—
591C2×D4—868no—
592C2×D4—8664no—
593C2×D4—8616no—
594C2×D4—864no—
595C2×D4—864no—
596C2×D4—861no—
597C2×D4—1724no—
598C2×D4—1724no—
599C2×D4—1724no—
600C2×D4D4×D4318yes—
601C2×D4C23×D4314yes—
602C22×C4—24no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—431no—
606C22×C4—432no—
607C22×C4—438no—
608C22×C4—432no—
609C22×C4—434no—
610C22×C4—431no—
611C22×C4—434no—
612C22×C4—432no—
613C22×C4—434no—
614C22×C4—432no—
615C22×C4—864no—
616C22×C4—8616no—
617C22×C4—8616no—
618C22×C4—864no—
619C22×C4—864no—
620C22×C4—864no—
621C22×C4—8616no—
622C22×C4—868no—
623C22×C4—868no—
624C22×C4—868no—
625C22×C4—8664no—
626C22×C4—8616no—
627C22×C4—864no—
628C22×C4—862no—
629C22×C4—864no—
630C22×C4—861no—
631C22×C4—1724no—
632C22×C4D4×D4312yes—
633C22×C4D4×D4311yescharacteristic
634C22×C4C23×D4312yes—
635C22×C4C23×D4311yescharacteristic
636Q16—8616no—
637SD16—216no—
638SD16—8616no—
639D8—8616no—
640C2×C8—24no—
641C2×C8—434no—
642C2×C8—8616no—
643C2×C8—864no—
644C2×C8C23×D4314yes—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—432no—
648C4⋊C4—864no—
649C4⋊C4—861no—
650C4⋊C4C23×D4312yes—
651C22⋊C4—24no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C22⋊C4—864no—
656C42—864no—
657C23—22no—
658C23—22no—
659C23—216no—
660C23—28no—
661C23—24no—
662C23—48no—
663C23—432no—
664C23—44no—
665C23—48no—
666C23—44no—
667C23—434no—
668C23—432no—
669C23—432no—
670C23—868no—
671C23—862no—
672C23—862no—
673C23—862no—
674C23—862no—
675C23—868no—
676C23—862no—
677C23—862no—
678C23—1724no—
679C23—17216no—
680C23—1722no—
681C23—1722no—
682C23—1722no—
683C23#1306334614yescomplemented
684C23C2×D4×D4312yes—
685C23C2×D4×D4311yescharacteristic
686Q8—24no—
687Q8—42no—
688Q8—438no—
689Q8—8616no—
690Q8—868no—
691Q8—864no—
692D4—216no—
693D4—28no—
694D4—24no—
695D4—8632no—
696D4—8632no—
697D4—864no—
698D4—1728no—
699D4—1728no—
700D4—1728no—
701D4—1722no—
702D4C2×D4×D4318yes—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—434no—
711C2×C4—432no—
712C2×C4—438no—
713C2×C4—438no—
714C2×C4—432no—
715C2×C4—868no—
716C2×C4—868no—
717C2×C4—868no—
718C2×C4—8632no—
719C2×C4—8616no—
720C2×C4—8632no—
721C2×C4—862no—
722C2×C4—868no—
723C2×C4—864no—
724C2×C4—864no—
725C2×C4—864no—
726C2×C4—862no—
727C2×C4—1728no—
728C2×C4—1722no—
729C2×C4C2×D4×D4312yes—
730C2×C4C2×D4×D4311yescharacteristic
731C2×C4C2×D4×D4314yes—
732C2×C4C24×D4311yescharacteristic
733C8—24no—
734C8—864no—
735C22—22no—
736C22—22no—
737C22—28no—
738C22—28no—
739C22—432no—
740C22—44no—
741C22—44no—
742C22—416no—
743C22—434no—
744C22—862no—
745C22—862no—
746C22—868no—
747C22—862no—
748C22—862no—
749C22—862no—
750C22—3444no—
751C22—17216no—
752C22—1722no—
753C22—1722no—
754C22—1722no—
755C22—1724no—
756C22#120×D4312yes—
757C22C2×#1306334612yes—
758C22C2×#1306334614yescomplemented
759C22#1458369512yes—
760C22C22×D4×D4311yescharacteristic
761C4—22no—
762C4—42no—
763C4—42no—
764C4—434no—
765C4—862no—
766C4—868no—
767C4—1722no—
768C4#120×D4312yes—
769C4C22×D4×D4312yes—
770C2—24no—
771C2—48no—
772C2—864no—
773C2—3442no—
774C2—1722no—
775C2#1914381414yesdirect product factor
776C2C2×#120×D4311yescharacteristic
777C2C22×#1306334611yescharacteristic
778C2C2×#1458369511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#450C2
socleC23×C43C22×D4
hypercenterC2×#450D43
hypocenterC43C2×#3002
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C23×#10621900C2semidirect
2. C22×#13063346C2semidirect
3. C2×#14583412C2semidirect
4. #19143814C2direct (N × H)
5. C2×#14583058C2semidirect
6. C2×#14583045C2semidirect
7. C2×#14583054C2semidirect
8. C2×#14583040C2semidirect
9. C2×#14583033C2semidirect
10. C2×#14582892C2semidirect
11. C2×C22⋊C8×D43C2semidirect
12. C2×C43×#450C2semidirect
13. C22×#10621902C22semidirect
20. C22×#10621900C22semidirect
26. C2×#13063346C22semidirect
27. C22×#10621885C22semidirect
28. C22×#10621873C22semidirect
29. C22×#10621882C22semidirect
30. C22×C8×D43C22semidirect
32. #14583412C22semidirect
34. C2×#13063301C22semidirect
35. C2×#13063300C22semidirect
40. C2×#13063283C22semidirect
41. #14583058C22semidirect
42. #14583054C22semidirect
43. #14583045C22semidirect
44. #14583040C22semidirect
45. #14583033C22semidirect
46. #14582892C22semidirect
47. C2×#13063250C22semidirect
48. C2×#13063248C22semidirect
49. C2×#13063246C22semidirect
51. C2×(C2×D43)⋊C8C22semidirect
52. C22⋊C8×D43C22semidirect
54. C22×SD16×C43C22semidirect
56. C43×#450C22semidirect
57. C2×#102×C43C22semidirect
62. C2×#10621902C23semidirect
74. C2×#10621900D4semidirect
106. C2×#10621885C23semidirect
108. C2×#10621873C23semidirect
110. C2×#10621882C23semidirect
113. C2×C8×D43C23semidirect
116. #13063301C23semidirect
118. #13063300C23semidirect
125. #13063283C23semidirect
133. #13063250C23semidirect
134. #13063248C23semidirect
135. #13063246C23semidirect
137. (C2×D43)⋊C8C23semidirect
147. C2×SD16×C43C23semidirect
154. #102×C43C23semidirect
216. #10621900C2×D4semidirect
277. C23×C43#135semidirect
356. C22×C43C2×#135semidirect
389. C2×#450D43semidirect
395. C2×C43#3002semidirect
419. C22×SD16C2×D43semidirect
435. #450C2×D43semidirect
443. C2×#102C2×D43semidirect
448. C43C2×#3002semidirect
508. C2×SD16C22×D43semidirect
542. #102C22×D43semidirect
683. C23#13063346semidirect
758. C22C2×#13063346semidirect
775. C2#19143814direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106219002
C22×#130633462
C2×#145834122
#191438142
C2×#145830582
C2×#145830452
C2×#145830542
C2×#145830402
C2×#145830332
C2×#145828922
C2×C22⋊C8×D432
C2×C43×#4502
C2×#300243