Finite Group Databasebeta

← C2×#19143808 #25962929

Subgroups — C2×#19143808 #25962929

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×#13063344C212yesmaximal, complemented
3C2×#14583409C211yesmaximal, characteristic, complemented
4#19143808C2116yesmaximal, direct product factor
5C2×#14583062C212yesmaximal, complemented
6C2×#14583041C212yesmaximal, complemented
7C2×#14583057C211yesmaximal, characteristic, complemented
8C2×#14583037C211yesmaximal, characteristic, complemented
9C2×#14583050C211yesmaximal, characteristic, complemented
10C2×#14582892C212yesmaximal, complemented
11C2×C22⋊C8×D43C211yesmaximal, characteristic, complemented
12C2×C43×#447C211yesmaximal, characteristic, complemented
13C22×#10621900—216no—
14C22×#10621900—21no—
15C22×#10621900—21no—
16C22×#10621900—24no—
17C22×#10621900C2212yes—
18C22×#10621900C2212yes—
19C22×#10621900C2218yescomplemented
20C22×#10621900C2211yescharacteristic, complemented
21C23×Dic86C2211yescharacteristic
22C23×C22⋊D43—21no—
23C24×Dic43—21no—
24C23×C4×D43C2211yescharacteristic
25C2×#13063344—216no—
26C2×#13063344C22116yescomplemented
27C22×Dic172C2212yescomplemented
28C22×#10621883C2212yescomplemented
29C22×#10621883C2212yescomplemented
30C22×C8×D43C2212yescomplemented
31#14583409—24no—
32#14583409C2218yescomplemented
33C2×#13063307—21no—
34C2×#13063305C2211yescharacteristic, complemented
35C2×#13063304C2211yescharacteristic
36C2×#13063296C2211yescharacteristic, complemented
37C2×#13063293—21no—
38C2×D4×Dic43—21no—
39C2×(C22⋊D43)⋊C4—21no—
40C2×#13063283C2211yescharacteristic, complemented
41#14583062C22116yescomplemented
42#14583057C2218yescomplemented
43#14583050C2218yescomplemented
44#14583041C22116yescomplemented
45#14583037C2218yescomplemented
46#14582892C22116yescomplemented
47C2×#13063250C2212yescomplemented
48C2×#13063248C2212yescomplemented
49C2×#13063246C2212yescomplemented
50C2×C22⋊(C43⋊C8)C2211yescharacteristic
51C2×(C2×D43)⋊C8C2212yescomplemented
52C22⋊C8×D43C2218yescomplemented
53C23×D4×C43C2211yescharacteristic
54C22×D8×C43C2212yescomplemented
55C2×#121×C43C2211yescharacteristic
56C43×#447C2218yescomplemented
57C2×#102×C43C2212yescomplemented
58C2×C22⋊C8×C43C2211yescharacteristic
59C24×D43D411yescharacteristic
60C2×#10621900—216no—
61C2×#10621900—264no—
62C2×#10621900—216no—
63C2×#10621900—28no—
64C2×#10621900—264no—
65C2×#10621900—28no—
66C2×#10621900—24no—
67C2×#10621900—24no—
68C2×#10621900—28no—
69C2×#10621900—28no—
70C2×#10621900—28no—
71C2×#10621900—22no—
72C2×#10621900—28no—
73C2×#10621900D4116yescomplemented
74C2×#10621900C2318yes—
75C2×#10621900C2318yes—
76C2×#10621900C2314yescomplemented
77C22×Dic86—21no—
78C22×Dic86—22no—
79C22×Dic86—28no—
80C22×Dic86C2314yes—
81C22×Dic86C2311yescharacteristic
82C22×Dic86C2312yes—
83C22×C22⋊D43—216no—
84C22×C22⋊D43—22no—
85C22×C22⋊D43—22no—
86C22×C22⋊D43—28no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C23×Dic43—216no—
90C23×Dic43—21no—
91C23×Dic43—22no—
92C23×Dic43—22no—
93C23×Dic43—28no—
94C23×Dic43—21no—
95C23×Dic43D411yescharacteristic
96C22×C4×D43—28no—
97C22×C4×D43D411yescharacteristic
98C22×C4×D43D411yescharacteristic
99C22×C4×D43D414yes—
100C22×C4×D43C2314yes—
101C22×C4×D43C2311yescharacteristic
102C22×C4×D43C2311yescharacteristic
103#13063344—264no—
104C2×Dic172—28no—
105C2×Dic172C2318yescomplemented
106C2×#10621883—28no—
107C2×#10621883—28no—
108C2×#10621883C2318yescomplemented
109C2×#10621883C2318yescomplemented
110C22×C43⋊C8C2312yes—
111C2×C8×D43—28no—
112C2×C8×D43C2318yescomplemented
113#13063307—28no—
114#13063305—22no—
115#13063305C2314yescomplemented
116#13063304—22no—
117#13063304C2314yes—
118#13063296—22no—
119#13063296C2314yescomplemented
120#13063293—28no—
121D4×Dic43—28no—
122(C22⋊D43)⋊C4—28no—
123#13063283—22no—
124#13063283C2314yescomplemented
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×Dic43⋊C4—21no—
128C2×C22⋊Dic43—21no—
129C2×C22⋊Dic43—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×D4×C43—28no—
140C22×D4×C43—21no—
141C22×D4×C43—21no—
142C22×D4×C43—22no—
143C22×D4×C43C2314yes—
144C22×D4×C43C2311yescharacteristic
145C22×D4×C43C2312yes—
146C23×C4×C43C2311yescharacteristic
147C2×D8×C43—28no—
148C2×D8×C43C2318yescomplemented
149C22×C8×C43C2312yes—
150#121×C43—22no—
151#121×C43C2314yes—
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—21no—
160C24×C43—44no—
161C24×C43—44no—
162C24×C43C2×D411yescharacteristic
163C23×D43—24no—
164C23×D43—24no—
165C23×D43—42no—
166C23×D43C2×D411yescharacteristic
167C23×D43C2×D414yes—
168C23×D43C2×D411yescharacteristic
169C2×D4×C43—216no—
170C2×D4×C43—28no—
171C2×D4×C43—216no—
172C2×D4×C43—24no—
173C2×D4×C43—24no—
174C2×D4×C43—22no—
175C2×D4×C43—21no—
176C2×D4×C43—24no—
177C2×D4×C43—24no—
178C2×D4×C43—44no—
179C2×D4×C43C2×D418yes—
180C2×D4×C43C2412yes—
181C2×D4×C43C2414yes—
182C22×C4×C43—24no—
183C22×C4×C43—21no—
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2411yescharacteristic
188C2×C22⋊D43—216no—
189C2×C22⋊D43—264no—
190C2×C22⋊D43—216no—
191C2×C22⋊D43—28no—
192C2×C22⋊D43—28no—
193C2×C22⋊D43—24no—
194C2×C22⋊D43—24no—
195C2×C22⋊D43—44no—
196C2×C22⋊D43—44no—
197C22×Dic43—28no—
198C22×Dic43—264no—
199C22×Dic43—216no—
200C22×Dic43—24no—
201C22×Dic43—216no—
202C22×Dic43—28no—
203C22×Dic43—28no—
204C22×Dic43—24no—
205C22×Dic43—24no—
206C22×Dic43—22no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—44no—
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D414yes—
212C22×Dic43C2×D411yescharacteristic
213#10621900—264no—
214#10621900—264no—
215#10621900—232no—
216#10621900—216no—
217#10621900—232no—
218#10621900—216no—
219#10621900—216no—
220#10621900—216no—
221#10621900—48no—
222#10621900C2×D4132yescomplemented
223C2×C4×D43—24no—
224C2×C4×D43—24no—
225C2×C4×D43—216no—
226C2×C4×D43—216no—
227C2×C4×D43—24no—
228C2×C4×D43C2×D418yes—
229C2×C4×D43C2×D414yes—
230C2×C4×D43C2×D412yes—
231C2×C4×D43C2×D414yes—
232C2×C4×D43C2×D412yes—
233C2×C4×D43C2412yes—
234C2×C4×D43C2412yes—
235C2×Dic86—28no—
236C2×Dic86—216no—
237C2×Dic86—24no—
238C2×Dic86—22no—
239C2×Dic86—24no—
240C2×Dic86—216no—
241C2×Dic86—24no—
242C2×Dic86—21no—
243C2×Dic86C2×D418yes—
244C2×Dic86C2412yes—
245C2×Dic86C2414yes—
246D8×C43—216no—
247C2×C8×C43—24no—
248C2×C8×C43C2414yes—
249C4⋊C4×C43—21no—
250C4⋊C4×C43C2412yes—
251C22⋊C4×C43—24no—
252C22⋊Dic43—24no—
253C22⋊Dic43—24no—
254#10621883—216no—
255#10621883—216no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258C4⋊Dic43—21no—
259C4⋊Dic43—24no—
260C4⋊Dic43C2412yes—
261Dic43⋊C4—24no—
262C4×Dic43—24no—
263C2×C43⋊C8—24no—
264C2×C43⋊C8C2414yes—
265Dic172—216no—
266C8×D43—216no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—216no—
270C23×C43—28no—
271C23×C43—24no—
272C23×C43—22no—
273C23×C43—432no—
274C23×C43—48no—
275C23×C43—44no—
276C23×C43—48no—
277C23×C43—44no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43#13514yescomplemented
282C23×C43C22×D412yes—
283C23×C43C22×D411yescharacteristic
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—28no—
289C22×D43—22no—
290C22×D43—28no—
291C22×D43—44no—
292C22×D43—416no—
293C22×D43#12014yes—
294C22×D43C22×D412yes—
295C22×D43C22×D412yes—
296D4×C43—216no—
297D4×C43—28no—
298D4×C43—24no—
299D4×C43—24no—
300D4×C43—48no—
301D4×C43—42no—
302D4×C43C22×D418yes—
303C2×C4×C43—22no—
304C2×C4×C43—24no—
305C2×C4×C43—24no—
306C2×C4×C43—22no—
307C2×C4×C43—42no—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C22×D414yes—
311C2×C4×C43C2511yescharacteristic
312C22⋊D43—232no—
313C22⋊D43—232no—
314C22⋊D43—48no—
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—22no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—48no—
328C2×Dic43#12014yes—
329C2×Dic43C22×D412yes—
330C2×Dic43C22×D412yes—
331C4×D43—28no—
332C4×D43—24no—
333C4×D43—24no—
334C4×D43—28no—
335C4×D43#12018yes—
336C4×D43C22×D418yes—
337Dic86—216no—
338Dic86—28no—
339Dic86—24no—
340Dic86—24no—
341Dic86—42no—
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×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—84no—
358C22×C43C2×#12012yes—
359C22×C43C2×#13512yes—
360C22×C43C2×#13514yescomplemented
361C22×C43#57512yes—
362C22×C43C23×D411yescharacteristic
363C2×D43—28no—
364C2×D43—22no—
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—416no—
370C2×D43—44no—
371C2×D43C2×#12014yes—
372C4×C43—22no—
373C4×C43—42no—
374C4×C43C2×#12012yes—
375C4×C43C23×D412yes—
376Dic43—28no—
377Dic43—22no—
378Dic43—42no—
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×#450—431no—
390C2×#447D4311yescharacteristic, complemented
391C2×#416—432no—
392C22×C22⋊C8—431no—
393C2×C43—24no—
394C2×C43—48no—
395C2×C43—82no—
396C2×C43#300214yescomplemented
397C2×C43C22×#12011yescharacteristic
398C2×C43C22×#13511yescharacteristic
399C2×C43C2×#57511yescharacteristic
400D43—24no—
401D43—42no—
402C22×#41—432no—
403C22×#41—432no—
404C22×#41—438no—
405C22×#41—431no—
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×SD16—432no—
420C22×D8C2×D4312yescomplemented
421C23×C8—432no—
422#525—438no—
423#525—864no—
424C2×#123—861no—
425C2×C22⋊Q8—431no—
426C2×C22⋊Q8—431no—
427C2×#121—431no—
428C2×#121C2×D4311yescharacteristic
429C2×#120—861no—
430C2×C4×D4—861no—
431C2×C4×D4—861no—
432C2×#117—431no—
433#452—4316no—
434#451—438no—
435#450—438no—
436#449—4316no—
437#448—438no—
438#447C2×D4318yescomplemented
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—4316no—
452C2×#41—438no—
453C2×#41—434no—
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—431no—
470C22×Q8—434no—
471C22×Q8—868no—
472C22×Q8—862no—
473C22×Q8—861no—
474C22×D4—28no—
475C22×D4—21no—
476C22×D4—22no—
477C22×D4—21no—
478C22×D4—868no—
479C22×D4—862no—
480C22×D4—862no—
481C22×D4—8616no—
482C22×D4—861no—
483C22×D4—861no—
484C22×D4C22×D4311yescharacteristic
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—862no—
496C23×C4—868no—
497C23×C4—862no—
498C23×C4—861no—
499C23×C4—8616no—
500C23×C4—861no—
501C23×C4C22×D4311yescharacteristic
502#135—8664no—
503C2×Q16—438no—
504C2×Q16—868no—
505C2×SD16—438no—
506C2×SD16—438no—
507C2×SD16—868no—
508C2×SD16—868no—
509C2×D8—28no—
510C2×D8C22×D4318yescomplemented
511C22×C8—432no—
512C22×C8—438no—
513C22×C8—868no—
514C22×C8C22×D4312yes—
515#123—868no—
516C22⋊Q8—434no—
517C22⋊Q8—434no—
518C22⋊Q8—862no—
519C22⋊Q8—862no—
520#121—22no—
521#121—434no—
522#121—862no—
523#121C22×D4314yes—
524#120—868no—
525C4×D4—868no—
526C4×D4—868no—
527#117—434no—
528#117—862no—
529C2×C4⋊C4—431no—
530C2×C4⋊C4—861no—
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—21no—
550C24—44no—
551C24—44no—
552C24—431no—
553C24—431no—
554C24—434no—
555C24—864no—
556C24—864no—
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—438no—
570C2×Q8—434no—
571C2×Q8—432no—
572C2×Q8—8616no—
573C2×Q8—868no—
574C2×Q8—8616no—
575C2×Q8—864no—
576C2×Q8—864no—
577C2×Q8—862no—
578C2×Q8—861no—
579C2×Q8—864no—
580C2×D4—28no—
581C2×D4—216no—
582C2×D4—216no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—22no—
586C2×D4—24no—
587C2×D4—24no—
588C2×D4—21no—
589C2×D4—44no—
590C2×D4—8616no—
591C2×D4—868no—
592C2×D4—868no—
593C2×D4—8664no—
594C2×D4—8616no—
595C2×D4—864no—
596C2×D4—864no—
597C2×D4—1724no—
598C2×D4—1724no—
599C2×D4D4×D4318yes—
600C2×D4C23×D4312yes—
601C2×D4C23×D4314yes—
602C22×C4—24no—
603C22×C4—21no—
604C22×C4—431no—
605C22×C4—432no—
606C22×C4—438no—
607C22×C4—432no—
608C22×C4—434no—
609C22×C4—431no—
610C22×C4—434no—
611C22×C4—432no—
612C22×C4—434no—
613C22×C4—432no—
614C22×C4—864no—
615C22×C4—8616no—
616C22×C4—8616no—
617C22×C4—864no—
618C22×C4—864no—
619C22×C4—8616no—
620C22×C4—868no—
621C22×C4—868no—
622C22×C4—864no—
623C22×C4—868no—
624C22×C4—8664no—
625C22×C4—8616no—
626C22×C4—864no—
627C22×C4—862no—
628C22×C4—864no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—1724no—
632C22×C4D4×D4312yes—
633C22×C4D4×D4311yescharacteristic
634C22×C4C23×D4312yes—
635C22×C4C23×D4311yescharacteristic
636Q16—8616no—
637SD16—8616no—
638SD16—8616no—
639D8—216no—
640C2×C8—24no—
641C2×C8—434no—
642C2×C8—8616no—
643C2×C8—864no—
644C2×C8C23×D4314yes—
645C4⋊C4—21no—
646C4⋊C4—432no—
647C4⋊C4—864no—
648C4⋊C4—861no—
649C4⋊C4—864no—
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—22no—
663C23—48no—
664C23—432no—
665C23—44no—
666C23—48no—
667C23—44no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—434no—
672C23—432no—
673C23—432no—
674C23—868no—
675C23—862no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23—868no—
680C23—862no—
681C23—1724no—
682C23—17216no—
683C23#1306334414yescomplemented
684C23C2×D4×D4312yes—
685C23C2×D4×D4311yescharacteristic
686Q8—438no—
687Q8—8616no—
688Q8—868no—
689Q8—864no—
690Q8—864no—
691Q8—1722no—
692D4—216no—
693D4—28no—
694D4—24no—
695D4—24no—
696D4—48no—
697D4—42no—
698D4—8632no—
699D4—8632no—
700D4—1728no—
701D4—1728no—
702D4C2×D4×D4318yes—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—42no—
708C2×C4—434no—
709C2×C4—432no—
710C2×C4—438no—
711C2×C4—438no—
712C2×C4—432no—
713C2×C4—868no—
714C2×C4—868no—
715C2×C4—868no—
716C2×C4—8632no—
717C2×C4—8616no—
718C2×C4—8632no—
719C2×C4—862no—
720C2×C4—868no—
721C2×C4—864no—
722C2×C4—864no—
723C2×C4—864no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—1728no—
727C2×C4—1722no—
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—42no—
744C22—42no—
745C22—42no—
746C22—84no—
747C22—434no—
748C22—862no—
749C22—862no—
750C22—868no—
751C22—862no—
752C22—862no—
753C22—862no—
754C22—17216no—
755C22—1724no—
756C22#120×D4312yes—
757C22C2×#1306334412yes—
758C22C2×#1306334414yescomplemented
759C22#1458369512yes—
760C22C22×D4×D4311yescharacteristic
761C4—22no—
762C4—42no—
763C4—434no—
764C4—862no—
765C4—868no—
766C4—1722no—
767C4—1722no—
768C4#120×D4312yes—
769C4C22×D4×D4312yes—
770C2—24no—
771C2—48no—
772C2—82no—
773C2—864no—
774C2—1722no—
775C2#1914380814yesdirect product factor
776C2C2×#120×D4311yescharacteristic
777C2C22×#1306334411yescharacteristic
778C2C2×#1458369511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#447C2
socleC23×C43C22×D4
hypercenterC2×#447D43
hypocenterC43C2×#3002
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C23×#10621900C2semidirect
2. C22×#13063344C2semidirect
3. C2×#14583409C2semidirect
4. #19143808C2direct (N × H)
5. C2×#14583062C2semidirect
6. C2×#14583041C2semidirect
7. C2×#14583057C2semidirect
8. C2×#14583037C2semidirect
9. C2×#14583050C2semidirect
10. C2×#14582892C2semidirect
11. C2×C22⋊C8×D43C2semidirect
12. C2×C43×#447C2semidirect
19. C22×#10621900C22semidirect
20. C22×#10621900C22semidirect
26. C2×#13063344C22semidirect
27. C22×Dic172C22semidirect
28. C22×#10621883C22semidirect
29. C22×#10621883C22semidirect
30. C22×C8×D43C22semidirect
32. #14583409C22semidirect
34. C2×#13063305C22semidirect
36. C2×#13063296C22semidirect
40. C2×#13063283C22semidirect
41. #14583062C22semidirect
42. #14583057C22semidirect
43. #14583050C22semidirect
44. #14583041C22semidirect
45. #14583037C22semidirect
46. #14582892C22semidirect
47. C2×#13063250C22semidirect
48. C2×#13063248C22semidirect
49. C2×#13063246C22semidirect
51. C2×(C2×D43)⋊C8C22semidirect
52. C22⋊C8×D43C22semidirect
54. C22×D8×C43C22semidirect
56. C43×#447C22semidirect
57. C2×#102×C43C22semidirect
73. C2×#10621900D4semidirect
76. C2×#10621900C23semidirect
105. C2×Dic172C23semidirect
108. C2×#10621883C23semidirect
109. C2×#10621883C23semidirect
112. C2×C8×D43C23semidirect
115. #13063305C23semidirect
119. #13063296C23semidirect
124. #13063283C23semidirect
133. #13063250C23semidirect
134. #13063248C23semidirect
135. #13063246C23semidirect
137. (C2×D43)⋊C8C23semidirect
148. C2×D8×C43C23semidirect
154. #102×C43C23semidirect
222. #10621900C2×D4semidirect
281. C23×C43#135semidirect
360. C22×C43C2×#135semidirect
390. C2×#447D43semidirect
396. C2×C43#3002semidirect
420. C22×D8C2×D43semidirect
438. #447C2×D43semidirect
443. C2×#102C2×D43semidirect
448. C43C2×#3002semidirect
510. C2×D8C22×D43semidirect
542. #102C22×D43semidirect
683. C23#13063344semidirect
758. C22C2×#13063344semidirect
775. C2#19143808direct (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×#130633442
C2×#145834092
#191438082
C2×#145830622
C2×#145830412
C2×#145830572
C2×#145830372
C2×#145830502
C2×#145828922
C2×C22⋊C8×D432
C2×C43×#4472
C2×#300243