Finite Group Databasebeta

← C2×#19145450 #25967253

Subgroups — C2×#19145450 #25967253

Order 11008.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583479C211yesmaximal, characteristic, complemented
2C2×#14583465C211yesmaximal, characteristic, complemented
3#19145450C2116yesmaximal, direct product factor
4C2×#14583219C211yesmaximal, characteristic, complemented
5C2×#14583239C211yesmaximal, characteristic, complemented
6C2×#14583225C211yesmaximal, characteristic, complemented
7C2×#14583211C211yesmaximal, characteristic, complemented
8C2×#14583150C211yesmaximal, characteristic, complemented
9C2×#14583147C211yesmaximal, characteristic, complemented
10C2×#14583135C211yesmaximal, characteristic, complemented
11C2×#14583047C211yesmaximal, characteristic, complemented
12C2×#14583043C211yesmaximal, characteristic, complemented
13C2×#14583048C211yesmaximal, characteristic, complemented
14C2×#14583034C211yesmaximal, characteristic, complemented
15C2×#14582865C211yesmaximal, characteristic, complemented
16C2×C43×#465C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic, complemented
18C22×#10621898C2211yescharacteristic
19C22×D4×D43C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×D344C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621877C2211yescharacteristic, complemented
24#14583479—24no—
25#14583479C2218yescomplemented
26#14583465—24no—
27#14583465C2218yescomplemented
28C2×#13063321—21no—
29C2×#13063311—21no—
30C2×#13063303—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063300—21no—
33C2×#13063300C2211yescharacteristic
34C2×#13063300C2211yescharacteristic
35C2×#13063299C2211yescharacteristic
36C2×#13063299C2211yescharacteristic, complemented
37C2×#13063298—21no—
38C2×#13063298—21no—
39C2×#13063296C2211yescharacteristic
40C2×#13063295—21no—
41C2×#13063293—21no—
42C2×#13063283C2211yescharacteristic
43C2×C4⋊C4×D43C2211yescharacteristic, complemented
44#14583239C2218yescomplemented
45#14583225C2218yescomplemented
46#14583219C2218yescomplemented
47#14583211C2218yescomplemented
48#14583150C2218yescomplemented
49#14583147C2218yescomplemented
50#14583135C2218yescomplemented
51#14583048C2218yescomplemented
52#14583047C2218yescomplemented
53#14583043C2218yescomplemented
54#14583034C2218yescomplemented
55C2×#13063259C2211yescharacteristic, complemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063256C2211yescharacteristic, complemented
58C2×#13063249C2211yescharacteristic, complemented
59C2×#13063247C2211yescharacteristic
60C2×#13063247C2211yescharacteristic, complemented
61C2×#13063246C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic, complemented
64#14582865C2218yescomplemented
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic, complemented
71C2×C22⋊Q8×C43C2211yescharacteristic, complemented
72C2×#121×C43C2211yescharacteristic
73C43×#465C2218yescomplemented
74C2×#106×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×#102×C43C2211yescharacteristic
77C24×D43—21no—
78C2×#10621902—22no—
79C2×#10621902—42no—
80C2×#10621902—42no—
81C2×#10621902C2314yescomplemented
82C2×#10621898—42no—
83C2×#10621898—42no—
84C2×#10621898D414yes—
85C2×#10621898C2314yes—
86C22×Dic86D411yescharacteristic
87C22×D172—21no—
88C22×D172—21no—
89C22×D172—21no—
90C22×D172D411yescharacteristic
91C22×D172C2311yescharacteristic
92C22×D172C2311yescharacteristic
93C22×C22⋊D43—21no—
94C22×C22⋊D43—21no—
95C22×C22⋊D43—21no—
96C22×C22⋊D43—21no—
97C22×C22⋊D43D411yescharacteristic
98C22×C22⋊D43D411yescharacteristic
99C2×D4×D43—22no—
100C2×D4×D43—42no—
101C2×D4×D43—42no—
102C2×D4×D43C2314yes—
103C22×C4×D43—21no—
104C22×C4×D43—21no—
105C22×C4×D43C2311yescharacteristic
106C22×C4×D43C2311yescharacteristic
107C2×#10621884—42no—
108C2×#10621884C2314yes—
109C2×D344—42no—
110C2×D344C2314yes—
111C2×#10621882—42no—
112C2×#10621882C2314yes—
113C2×#10621877—42no—
114C2×#10621877C2314yescomplemented
115C22×C43⋊C8C2311yescharacteristic
116C22×C43⋊C8C2311yescharacteristic
117#13063321—28no—
118#13063311—28no—
119#13063303—28no—
120#13063301—22no—
121#13063301C2314yes—
122#13063300—28no—
123#13063300—22no—
124#13063300—22no—
125#13063300C2314yes—
126#13063300C2314yes—
127#13063299—22no—
128#13063299—22no—
129#13063299C2314yes—
130#13063299C2314yescomplemented
131#13063298—28no—
132#13063298—28no—
133#13063296—22no—
134#13063296C2314yes—
135#13063295—28no—
136#13063293—28no—
137#13063283—22no—
138#13063283C2314yes—
139C2×C4⋊Dic43C2311yescharacteristic
140C2×C4⋊Dic43C2311yescharacteristic
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4—21no—
143C4⋊C4×D43—22no—
144C4⋊C4×D43C2314yescomplemented
145C2×C22⋊Dic43—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—21no—
152C2×C4×Dic43—21no—
153#13063259C2314yescomplemented
154#13063258C2314yescomplemented
155#13063256C2314yescomplemented
156#13063249C2314yescomplemented
157#13063247C2314yes—
158#13063247C2314yescomplemented
159#13063246C2314yes—
160#13063245C2314yes—
161#13063245C2314yescomplemented
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164(C2×D43)⋊C8C2314yescomplemented
165(C2×D43)⋊C8C2314yescomplemented
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43—21no—
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43C2311yescharacteristic
170C2×SD16×C43—42no—
171C2×SD16×C43C2314yes—
172C22×C8×C43—42no—
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2314yescomplemented
176C22⋊Q8×C43—22no—
177C22⋊Q8×C43C2314yescomplemented
178#121×C43—22no—
179#121×C43C2314yes—
180C2×C4⋊C4×C43—21no—
181C2×C4⋊C4×C43C2311yescharacteristic
182C2×C4⋊C4×C43C2311yescharacteristic
183C2×C22⋊C4×C43—21no—
184C2×C22⋊C4×C43—21no—
185#106×C43C2314yescomplemented
186#103×C43C2314yescomplemented
187#102×C43C2314yes—
188C24×C43—21no—
189C24×C43C2×D411yescharacteristic
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—24no—
193C23×D43—44no—
194C23×D43—82no—
195C23×D43—82no—
196C23×D43C2×D411yescharacteristic
197C23×D43C2×D411yescharacteristic
198C2×Q8×C43—21no—
199C2×Q8×C43—22no—
200C2×Q8×C43—22no—
201C2×Q8×C43C2412yes—
202C2×D4×C43—21no—
203C2×D4×C43—24no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43—82no—
207C2×D4×C43C2412yes—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—42no—
222C2×C22⋊D43—42no—
223C2×C22⋊D43—44no—
224C2×C22⋊D43—82no—
225C2×C22⋊D43—82no—
226C2×C22⋊D43—82no—
227C2×C22⋊D43C2×D414yes—
228C2×C22⋊D43C2×D414yes—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43C2×D411yescharacteristic
232C22×Dic43C2×D411yescharacteristic
233#10621902—44no—
234#10621902—44no—
235#10621902—48no—
236D4×D43—44no—
237D4×D43—44no—
238D4×D43—48no—
239#10621898—48no—
240#10621898—44no—
241#10621898—44no—
242C2×D172—21no—
243C2×D172—21no—
244C2×D172—24no—
245C2×D172—24no—
246C2×D172—24no—
247C2×D172—22no—
248C2×D172—22no—
249C2×D172—22no—
250C2×D172—22no—
251C2×D172—42no—
252C2×D172—44no—
253C2×D172—82no—
254C2×D172—82no—
255C2×D172C2×D414yes—
256C2×D172C2412yes—
257C2×D172C2412yes—
258C2×C4×D43—22no—
259C2×C4×D43—22no—
260C2×C4×D43—22no—
261C2×C4×D43—22no—
262C2×C4×D43—24no—
263C2×C4×D43—24no—
264C2×C4×D43—44no—
265C2×C4×D43—82no—
266C2×C4×D43C2×D412yes—
267C2×C4×D43C2×D412yes—
268C2×C4×D43C2412yes—
269C2×C4×D43C2412yes—
270C2×Dic86—42no—
271C2×Dic86C2×D414yes—
272SD16×C43—44no—
273C2×C8×C43—22no—
274C2×C8×C43—22no—
275C2×C8×C43—44no—
276C2×C8×C43C2412yes—
277C2×C8×C43C2412yes—
278C4⋊C4×C43—24no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43C2412yes—
282C4⋊C4×C43C2412yes—
283C22⋊C4×C43—24no—
284C22⋊C4×C43—24no—
285C22⋊Dic43—24no—
286#10621884—44no—
287#10621882—44no—
288(C2×D43)⋊C4—24no—
289(C2×D43)⋊C4—24no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—24no—
292(C2×D43)⋊C4—24no—
293(C2×D43)⋊C4—24no—
294C4⋊Dic43—21no—
295C4⋊Dic43—21no—
296C4⋊Dic43C2412yes—
297C4⋊Dic43C2412yes—
298Dic43⋊C4—24no—
299Dic43⋊C4—24no—
300C4×Dic43—24no—
301#10621877—44no—
302C2×C43⋊C8—22no—
303C2×C43⋊C8—22no—
304C2×C43⋊C8C2412yes—
305C2×C43⋊C8C2412yes—
306D344—44no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—42no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43C22×D412yes—
315C23×C43C22×D411yescharacteristic
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—48no—
325C22×D43—42no—
326C22×D43—42no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43—42no—
331C22×D43—84no—
332C22×D43—84no—
333C22×D43—816no—
334C22×D43C22×D412yes—
335C22×D43C22×D412yes—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—42no—
339D4×C43—22no—
340D4×C43—22no—
341D4×C43—42no—
342D4×C43—84no—
343C2×C4×C43—22no—
344C2×C4×C43—24no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—42no—
351C2×C4×C43—42no—
352C2×C4×C43—42no—
353C2×C4×C43C22×D412yes—
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43H(5,𝔽2)12yes—
356C2×C4×C43H(5,𝔽2)12yes—
357C2×C4×C43C2511yescharacteristic
358C22⋊D43—44no—
359C22⋊D43—44no—
360C22⋊D43—48no—
361C22⋊D43—84no—
362C22⋊D43—84no—
363C22⋊D43—84no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—42no—
369C2×Dic43—42no—
370C2×Dic43C22×D412yes—
371C2×Dic43C22×D412yes—
372D172—22no—
373D172—22no—
374D172—22no—
375D172—22no—
376D172—44no—
377D172—48no—
378D172—42no—
379D172—42no—
380D172—84no—
381D172—84no—
382C4×D43—24no—
383C4×D43—24no—
384C4×D43—22no—
385C4×D43—22no—
386C4×D43—22no—
387C4×D43—22no—
388C4×D43—48no—
389C4×D43—84no—
390Dic86—44no—
391C8×C43—22no—
392C8×C43—22no—
393C43⋊C8—22no—
394C43⋊C8—22no—
395C2×#3198—431nomaximal, Sylow
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—44no—
400C22×C43—42no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—84no—
404C22×C43#53412yes—
405C22×C43#57612yes—
406C22×C43#57712yes—
407C22×C43C23×D411yescharacteristic
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—22no—
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—44no—
415C2×D43—44no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—42no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—816no—
423C2×D43—84no—
424C2×D43—84no—
425C4×C43—22no—
426C4×C43—42no—
427C4×C43—42no—
428C4×C43—42no—
429C4×C43#53412yes—
430C4×C43C2×H(5,𝔽2)11yescharacteristic
431C4×C43C2×H(5,𝔽2)11yescharacteristic
432Dic43—22no—
433Dic43—22no—
434Dic43—42no—
435Dic43—42no—
436C2×#537—431no—
437C2×#535—431no—
438#3198—4316no—
439C2×#481—431no—
440C2×#485—431no—
441C2×#482—431no—
442C2×#480—431no—
443C2×#469—431no—
444C2×#468—431no—
445C2×#466—431no—
446C2×#465D4311yescharacteristic, complemented
447C2×#449—431no—
448C2×#449—431no—
449C2×#450—431no—
450C2×#447—431no—
451C2×#408—431no—
452C2×C43—42no—
453C2×C43—82no—
454C2×C43#319814yescomplemented
455C2×C43C2×#53411yescharacteristic
456C2×C43C2×#57611yescharacteristic
457C2×C43C2×#57711yescharacteristic
458D43—42no—
459D43—42no—
460D43—82no—
461D43—82no—
462C22×#41—431no—
463C22×#41—431no—
464C23×D4—431no—
465C22×SD16—431no—
466C22×SD16C2×D4311yescharacteristic
467C22×D8—431no—
468C22×D8—431no—
469C22×M16—431no—
470C23×C8C2×D4311yescharacteristic, complemented
471#537—438no—
472#537—864no—
473#535—438no—
474#535—864no—
475C2×#127—861no—
476C2×#124—861no—
477C2×C22⋊Q8—431no—
478C2×C22⋊Q8—861no—
479C2×C22⋊Q8C2×D4311yescharacteristic, complemented
480C2×#121—431no—
481C2×#121—431no—
482C2×#121—431no—
483C2×#121—431no—
484C2×#121—431no—
485C2×#121—861no—
486C2×#121—861no—
487C2×#121—861no—
488C2×#121C2×D4311yescharacteristic
489C2×#120—861no—
490C2×#120—861no—
491C2×#117—431no—
492C22×C4⋊C4—431no—
493#485—438no—
494#482—438no—
495#481—438no—
496#480—438no—
497#469—438no—
498#468—438no—
499#466—438no—
500#465C2×D4318yescomplemented
501#450—438no—
502#449—438no—
503#449—438no—
504#447—438no—
505C2×#107—431no—
506C2×#107—431no—
507C2×#106—431no—
508C2×#106C2×D4311yescharacteristic, complemented
509C2×#103—431no—
510C2×#103C2×D4311yescharacteristic, complemented
511C2×#102—431no—
512C2×#102—431no—
513C2×#102—431no—
514C2×#102—431no—
515C2×#102—431no—
516C2×#102C2×D4311yescharacteristic
517#408—438no—
518C2×C22⋊C8—431no—
519C2×C22⋊C8—431no—
520C2×C22⋊C8—431no—
521C2×C22⋊C8—431no—
522C43C2×#319811yescharacteristic, complemented, Sylow
523C25—861no—
524C2×#41—434no—
525C2×#41—434no—
526C2×#41—434no—
527C2×#41—862no—
528C2×#41—1722no—
529C2×#41—1722no—
530C2×#41—1722no—
531C2×#41—1722no—
532C22×Q8—431no—
533C22×Q8C22×D4311yescharacteristic
534C22×D4—21no—
535C22×D4—431no—
536C22×D4—431no—
537C22×D4—434no—
538C22×D4—431no—
539C22×D4—431no—
540C22×D4—431no—
541C22×D4—861no—
542C22×D4—861no—
543C22×D4—861no—
544C22×D4—862no—
545C22×D4—861no—
546C22×D4—861no—
547C22×D4—861no—
548C22×D4—861no—
549C22×D4—1722no—
550C22×D4—1722no—
551C22×D4C22×D4311yescharacteristic
552C23×C4—431no—
553C23×C4—431no—
554C23×C4—861no—
555C23×C4—861no—
556C23×C4C22×D4311yescharacteristic
557C2×SD16—42no—
558C2×SD16—434no—
559C2×SD16—1722no—
560C2×SD16C22×D4314yes—
561C2×D8—434no—
562C2×D8—434no—
563C2×D8—1722no—
564C2×D8—1722no—
565C2×M16—434no—
566C2×M16—1722no—
567C22×C8—42no—
568C22×C8—431no—
569C22×C8—431no—
570C22×C8C22×D4311yescharacteristic
571C22×C8C22×D4311yescharacteristic
572C22×C8C22×D4314yescomplemented
573#127—868no—
574#124—868no—
575C22⋊Q8—22no—
576C22⋊Q8—434no—
577C22⋊Q8—868no—
578C22⋊Q8—862no—
579C22⋊Q8C22×D4314yescomplemented
580#121—22no—
581#121—434no—
582#121—434no—
583#121—434no—
584#121—434no—
585#121—434no—
586#121—868no—
587#121—868no—
588#121—862no—
589#121—862no—
590#121—868no—
591#121—862no—
592#121—862no—
593#121—862no—
594#121C22×D4314yes—
595#120—868no—
596#120—868no—
597#117—434no—
598#117—862no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—434no—
603C2×C4⋊C4—862no—
604C2×C4⋊C4—861no—
605C2×C4⋊C4—861no—
606C2×C4⋊C4C22×D4311yescharacteristic
607C2×C4⋊C4C22×D4311yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4—861no—
616C2×C22⋊C4—861no—
617C2×C42—861no—
618#107—434no—
619#107—434no—
620#106—434no—
621#106C22×D4314yescomplemented
622#103—434no—
623#103C22×D4314yescomplemented
624#102—434no—
625#102—434no—
626#102—434no—
627#102—434no—
628#102—434no—
629#102C22×D4314yes—
630C22⋊C8—434no—
631C22⋊C8—434no—
632C22⋊C8—434no—
633C22⋊C8—434no—
634C24—21no—
635C24—431no—
636C24—431no—
637C24—864no—
638C24—861no—
639C24—861no—
640C24—3442no—
641C24—3442no—
642C24—1724no—
643C24D4×D4311yescharacteristic
644#41—1728no—
645#41—1724no—
646#41—1724no—
647#41—1724no—
648#41—1724no—
649#41—1728no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—434no—
654C2×Q8—1722no—
655C2×Q8C23×D4312yes—
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—82no—
661C2×D4—434no—
662C2×D4—434no—
663C2×D4—434no—
664C2×D4—432no—
665C2×D4—432no—
666C2×D4—864no—
667C2×D4—864no—
668C2×D4—864no—
669C2×D4—864no—
670C2×D4—864no—
671C2×D4—864no—
672C2×D4—864no—
673C2×D4—861no—
674C2×D4—861no—
675C2×D4—862no—
676C2×D4—862no—
677C2×D4—862no—
678C2×D4—862no—
679C2×D4—3442no—
680C2×D4—3442no—
681C2×D4—3442no—
682C2×D4—3442no—
683C2×D4—3442no—
684C2×D4—1722no—
685C2×D4—1724no—
686C2×D4—1724no—
687C2×D4—1724no—
688C2×D4—1728no—
689C2×D4—1722no—
690C2×D4—1722no—
691C2×D4—1724no—
692C2×D4C23×D4312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—431no—
699C22×C4—431no—
700C22×C4—432no—
701C22×C4—432no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—864no—
705C22×C4—864no—
706C22×C4—862no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—862no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—3442no—
713C22×C4—1724no—
714C22×C4D4×D4312yes—
715C22×C4D4×D4311yescharacteristic
716C22×C4C23×D4312yes—
717C22×C4C23×D4311yescharacteristic
718SD16—44no—
719SD16—1724no—
720D8—1724no—
721D8—1724no—
722M16—1724no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—44no—
726C2×C8—432no—
727C2×C8—432no—
728C2×C8—862no—
729C2×C8—862no—
730C2×C8C23×D4312yes—
731C2×C8C23×D4312yes—
732C4⋊C4—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—432no—
736C4⋊C4—432no—
737C4⋊C4—864no—
738C4⋊C4—864no—
739C4⋊C4—861no—
740C4⋊C4—861no—
741C4⋊C4C23×D4312yes—
742C4⋊C4C23×D4312yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—864no—
746C22⋊C4—864no—
747C22⋊C4—864no—
748C22⋊C4—864no—
749C22⋊C4—864no—
750C22⋊C4—864no—
751C22⋊C4—864no—
752C42—864no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—432no—
761C23—432no—
762C23—862no—
763C23—862no—
764C23—862no—
765C23—862no—
766C23—862no—
767C23—862no—
768C23—862no—
769C23—862no—
770C23—3444no—
771C23—3444no—
772C23—34416no—
773C23—1728no—
774C23—1722no—
775C23—1722no—
776C23—1722no—
777C23—1722no—
778C23—1722no—
779C23—1722no—
780C23C2×D4×D4312yes—
781C23C2×D4×D4311yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—1724no—
786D4—22no—
787D4—22no—
788D4—42no—
789D4—84no—
790D4—862no—
791D4—862no—
792D4—862no—
793D4—862no—
794D4—3444no—
795D4—3444no—
796D4—3444no—
797D4—3444no—
798D4—3444no—
799D4—1724no—
800D4—1728no—
801D4—1724no—
802D4—1724no—
803D4—1728no—
804D4—1722no—
805D4—1722no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—432no—
817C2×C4—432no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—864no—
821C2×C4—864no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—3444no—
829C2×C4—1728no—
830C2×C4—1722no—
831C2×C4—1722no—
832C2×C4C2×D4×D4312yes—
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4#1306337012yes—
835C2×C4#1306337112yes—
836C2×C4C24×D4311yescharacteristic
837C8—22no—
838C8—22no—
839C8—862no—
840C8—862no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—84no—
849C22—862no—
850C22—862no—
851C22—862no—
852C22—862no—
853C22—862no—
854C22—862no—
855C22—34416no—
856C22—3444no—
857C22—3444no—
858C22—1722no—
859C22—1722no—
860C22—1722no—
861C22—1722no—
862C22—1722no—
863C22—1722no—
864C22—1724no—
865C22—1724no—
866C22#1458345712yes—
867C22#1458370112yes—
868C22#1458370512yes—
869C22C22×D4×D4311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—862no—
875C4—862no—
876C4—1722no—
877C4—1722no—
878C4#1458345712yes—
879C4C2×#1306337011yescharacteristic
880C4C2×#1306337111yescharacteristic
881C2—42no—
882C2—82no—
883C2—3442no—
884C2—3442no—
885C2—1722no—
886C2—1722no—
887C2#1914545014yesdirect product factor
888C2C2×#1458345711yescharacteristic
889C2C2×#1458370111yescharacteristic
890C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#465C2
socleC23×C43C22×D4
hypercenterC2×#465D43
hypocenterC43C2×#3198
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#14583479C2semidirect
2. C2×#14583465C2semidirect
3. #19145450C2direct (N × H)
4. C2×#14583219C2semidirect
5. C2×#14583239C2semidirect
6. C2×#14583225C2semidirect
7. C2×#14583211C2semidirect
8. C2×#14583150C2semidirect
9. C2×#14583147C2semidirect
10. C2×#14583135C2semidirect
11. C2×#14583047C2semidirect
12. C2×#14583043C2semidirect
13. C2×#14583048C2semidirect
14. C2×#14583034C2semidirect
15. C2×#14582865C2semidirect
16. C2×C43×#465C2semidirect
17. C22×#10621902C22semidirect
23. C22×#10621877C22semidirect
25. #14583479C22semidirect
27. #14583465C22semidirect
36. C2×#13063299C22semidirect
43. C2×C4⋊C4×D43C22semidirect
44. #14583239C22semidirect
45. #14583225C22semidirect
46. #14583219C22semidirect
47. #14583211C22semidirect
48. #14583150C22semidirect
49. #14583147C22semidirect
50. #14583135C22semidirect
51. #14583048C22semidirect
52. #14583047C22semidirect
53. #14583043C22semidirect
54. #14583034C22semidirect
55. C2×#13063259C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063256C22semidirect
58. C2×#13063249C22semidirect
60. C2×#13063247C22semidirect
63. C2×#13063245C22semidirect
64. #14582865C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
70. C23×C8×C43C22semidirect
71. C2×C22⋊Q8×C43C22semidirect
73. C43×#465C22semidirect
74. C2×#106×C43C22semidirect
75. C2×#103×C43C22semidirect
81. C2×#10621902C23semidirect
114. C2×#10621877C23semidirect
130. #13063299C23semidirect
144. C4⋊C4×D43C23semidirect
153. #13063259C23semidirect
154. #13063258C23semidirect
155. #13063256C23semidirect
156. #13063249C23semidirect
158. #13063247C23semidirect
161. #13063245C23semidirect
164. (C2×D43)⋊C8C23semidirect
165. (C2×D43)⋊C8C23semidirect
175. C22×C8×C43C23semidirect
177. C22⋊Q8×C43C23semidirect
185. #106×C43C23semidirect
186. #103×C43C23semidirect
446. C2×#465D43semidirect
454. C2×C43#3198semidirect
470. C23×C8C2×D43semidirect
479. C2×C22⋊Q8C2×D43semidirect
500. #465C2×D43semidirect
508. C2×#106C2×D43semidirect
510. C2×#103C2×D43semidirect
522. C43C2×#3198semidirect
572. C22×C8C22×D43semidirect
579. C22⋊Q8C22×D43semidirect
621. #106C22×D43semidirect
623. #103C22×D43semidirect
887. C2#19145450direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834792
C2×#145834652
#191454502
C2×#145832192
C2×#145832392
C2×#145832252
C2×#145832112
C2×#145831502
C2×#145831472
C2×#145831352
C2×#145830472
C2×#145830432
C2×#145830482
C2×#145830342
C2×#145828652
C2×C43×#4652
C2×#319843