Finite Group Databasebeta

← C2×#19145454 #25967257

Subgroups — C2×#19145454 #25967257

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×#14583480C211yesmaximal, characteristic, complemented
2C2×#14583465C211yesmaximal, characteristic, complemented
3#19145454C2116yesmaximal, direct product factor
4C2×#14583217C211yesmaximal, characteristic, complemented
5C2×#14583242C211yesmaximal, characteristic, complemented
6C2×#14583226C211yesmaximal, characteristic, complemented
7C2×#14583151C211yesmaximal, characteristic, complemented
8C2×#14583146C211yesmaximal, characteristic, complemented
9C2×#14583136C211yesmaximal, characteristic, complemented
10C2×#14583127C211yesmaximal, characteristic, complemented
11C2×#14583046C211yesmaximal, characteristic, complemented
12C2×#14583042C211yesmaximal, characteristic, complemented
13C2×#14583051C211yesmaximal, characteristic, complemented
14C2×#14583034C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#480C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621898C2211yescharacteristic, complemented
19C22×D4×D43C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×D344C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621872C2211yescharacteristic, complemented
25C22×C8×D43C2211yescharacteristic, complemented
26#14583480—24no—
27#14583480C2218yescomplemented
28#14583465—24no—
29#14583465C2218yescomplemented
30C2×#13063321—21no—
31C2×#13063311—21no—
32C2×#13063305—21no—
33C2×#13063305C2211yescharacteristic
34C2×#13063305C2211yescharacteristic, complemented
35C2×#13063300—21no—
36C2×#13063300C2211yescharacteristic
37C2×#13063300C2211yescharacteristic
38C2×#13063300C2211yescharacteristic, complemented
39C2×#13063299—21no—
40C2×#13063299—21no—
41C2×#13063299C2211yescharacteristic
42C2×#13063296C2211yescharacteristic
43C2×#13063295—21no—
44C2×#13063293—21no—
45C2×#13063283C2211yescharacteristic
46#14583242C2218yescomplemented
47#14583226C2218yescomplemented
48#14583217C2218yescomplemented
49#14583151C2218yescomplemented
50#14583146C2218yescomplemented
51#14583136C2218yescomplemented
52#14583127C2218yescomplemented
53#14583051C2218yescomplemented
54#14583046C2218yescomplemented
55#14583042C2218yescomplemented
56#14583034C2218yescomplemented
57C2×#13063256C2211yescharacteristic, complemented
58C2×#13063256C2211yescharacteristic, complemented
59C2×#13063250C2211yescharacteristic, complemented
60C2×#13063248C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic, complemented
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic, complemented
65#14582864C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×#121×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2211yescharacteristic, complemented
71C43×#480C2218yescomplemented
72C2×#107×C43C2211yescharacteristic, complemented
73C2×#107×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621898—22no—
79C2×#10621898—42no—
80C2×#10621898—42no—
81C2×#10621898—42no—
82C2×#10621898—42no—
83C2×#10621898D414yes—
84C2×#10621898C2314yes—
85C2×#10621898C2314yescomplemented
86C22×Dic86D411yescharacteristic
87C22×Dic86C2311yescharacteristic
88C22×D172—21no—
89C22×D172—21no—
90C22×D172—21no—
91C22×D172D411yescharacteristic
92C22×D172C2311yescharacteristic
93C22×D172C2311yescharacteristic
94C22×C22⋊D43—21no—
95C22×C22⋊D43—21no—
96C22×C22⋊D43—21no—
97C22×C22⋊D43—21no—
98C22×C22⋊D43D411yescharacteristic
99C22×C22⋊D43D411yescharacteristic
100C2×D4×D43—22no—
101C2×D4×D43—42no—
102C2×D4×D43—42no—
103C2×D4×D43C2314yes—
104C22×C4×D43—21no—
105C22×C4×D43C2311yescharacteristic
106C22×C4×D43C2311yescharacteristic
107C2×#10621873—42no—
108C2×#10621873C2314yes—
109C2×#10621883—42no—
110C2×#10621883C2314yes—
111C2×D344—42no—
112C2×D344C2314yes—
113C2×#10621882—42no—
114C2×#10621882C2314yes—
115C2×#10621872—42no—
116C2×#10621872C2314yescomplemented
117C22×C43⋊C8C2311yescharacteristic
118C22×C43⋊C8C2311yescharacteristic
119C2×C8×D43—42no—
120C2×C8×D43C2314yescomplemented
121#13063321—28no—
122#13063311—28no—
123#13063305—22no—
124#13063305—22no—
125#13063305—28no—
126#13063305C2314yes—
127#13063305C2314yescomplemented
128#13063300—28no—
129#13063300—22no—
130#13063300—22no—
131#13063300—22no—
132#13063300C2314yes—
133#13063300C2314yes—
134#13063300C2314yescomplemented
135#13063299—22no—
136#13063299—28no—
137#13063299—28no—
138#13063299C2314yes—
139#13063296—22no—
140#13063296C2314yes—
141#13063295—28no—
142#13063293—28no—
143#13063283—22no—
144#13063283C2314yes—
145C2×C4⋊Dic43—21no—
146C2×C4⋊Dic43—21no—
147C2×C4⋊Dic43C2311yescharacteristic
148C2×C22⋊Dic43—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4—21no—
155C2×(C2×D43)⋊C4—21no—
156C2×C4×Dic43—21no—
157#13063256C2314yescomplemented
158#13063256C2314yescomplemented
159#13063250C2314yescomplemented
160#13063248C2314yescomplemented
161#13063247C2314yescomplemented
162#13063245C2314yes—
163#13063245C2314yes—
164#13063245C2314yescomplemented
165C22⋊(C43⋊C8)C2314yescomplemented
166(C2×D43)⋊C8C2314yes—
167(C2×D43)⋊C8C2314yes—
168C22×D4×C43—21no—
169C22×D4×C43C2311yescharacteristic
170C23×C4×C43—21no—
171C23×C4×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174#121×C43—22no—
175#121×C43C2314yes—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43—22no—
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C4⋊C4×C43C2314yescomplemented
182C2×C22⋊C4×C43—21no—
183#107×C43C2314yescomplemented
184#107×C43C2314yescomplemented
185#102×C43C2314yes—
186#102×C43C2314yes—
187C22⋊C8×C43C2314yescomplemented
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×D4×C43—21no—
199C2×D4×C43—24no—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43—82no—
203C2×D4×C43C2412yes—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—24no—
210C22×C4×C43—82no—
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D412yes—
213C22×C4×C43C2412yes—
214C22×C4×C43C2411yescharacteristic
215C2×C22⋊D43—24no—
216C2×C22⋊D43—24no—
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—42no—
220C2×C22⋊D43—42no—
221C2×C22⋊D43—44no—
222C2×C22⋊D43—44no—
223C2×C22⋊D43—82no—
224C2×C22⋊D43—82no—
225C2×C22⋊D43C2×D414yes—
226C2×C22⋊D43C2×D414yes—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231D4×D43—44no—
232D4×D43—44no—
233D4×D43—48no—
234#10621898—44no—
235#10621898—44no—
236#10621898—48no—
237#10621898—44no—
238#10621898—44no—
239#10621898—48no—
240C2×D172—21no—
241C2×D172—21no—
242C2×D172—24no—
243C2×D172—24no—
244C2×D172—24no—
245C2×D172—22no—
246C2×D172—22no—
247C2×D172—22no—
248C2×D172—22no—
249C2×D172—42no—
250C2×D172—82no—
251C2×D172—82no—
252C2×D172—82no—
253C2×D172C2×D414yes—
254C2×D172C2412yes—
255C2×D172C2412yes—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—22no—
259C2×C4×D43—22no—
260C2×C4×D43—24no—
261C2×C4×D43—44no—
262C2×C4×D43C2×D412yes—
263C2×C4×D43C2×D412yes—
264C2×C4×D43C2412yes—
265C2×C4×D43C2412yes—
266C2×Dic86—22no—
267C2×Dic86—22no—
268C2×Dic86—21no—
269C2×Dic86—42no—
270C2×Dic86C2×D414yes—
271C2×Dic86C2412yes—
272C2×C8×C43—22no—
273C2×C8×C43—22no—
274C2×C8×C43C2412yes—
275C2×C8×C43C2412yes—
276C4⋊C4×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—24no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43C2412yes—
281C4⋊C4×C43C2412yes—
282C4⋊C4×C43C2412yes—
283C22⋊C4×C43—24no—
284C22⋊Dic43—24no—
285#10621883—44no—
286#10621882—44no—
287(C2×D43)⋊C4—24no—
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—24no—
296C4⋊Dic43—24no—
297C4⋊Dic43C2412yes—
298C4×Dic43—24no—
299C2×C43⋊C8—22no—
300C2×C43⋊C8—22no—
301C2×C43⋊C8C2412yes—
302C2×C43⋊C8C2412yes—
303D344—44no—
304#10621873—44no—
305#10621872—44no—
306C8×D43—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—
336D4×C43—22no—
337D4×C43—22no—
338D4×C43—42no—
339D4×C43—84no—
340C2×C4×C43—22no—
341C2×C4×C43—24no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—42no—
348C2×C4×C43—42no—
349C2×C4×C43—42no—
350C2×C4×C43—84no—
351C2×C4×C43C22×D412yes—
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43H(5,𝔽2)12yes—
354C2×C4×C43H(5,𝔽2)12yes—
355C2×C4×C43C2511yescharacteristic
356C22⋊D43—44no—
357C22⋊D43—44no—
358C22⋊D43—48no—
359C22⋊D43—48no—
360C22⋊D43—84no—
361C22⋊D43—84no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—42no—
367C2×Dic43—42no—
368C2×Dic43C22×D412yes—
369C2×Dic43C22×D412yes—
370D172—22no—
371D172—22no—
372D172—22no—
373D172—22no—
374D172—44no—
375D172—42no—
376D172—42no—
377D172—84no—
378D172—84no—
379D172—84no—
380C4×D43—24no—
381C4×D43—24no—
382C4×D43—22no—
383C4×D43—22no—
384C4×D43—22no—
385C4×D43—22no—
386C4×D43—48no—
387Dic86—22no—
388Dic86—22no—
389Dic86—44no—
390Dic86—42no—
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×#480D4311yescharacteristic, complemented
443C2×#469—431no—
444C2×#468—431no—
445C2×#466—431no—
446C2×#465—431no—
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×SD16—431no—
467C22×D8—431no—
468C22×D8—431no—
469C22×M16—431no—
470C23×C8—431no—
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—431no—
479C2×C22⋊Q8—861no—
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⋊C4C2×D4311yescharacteristic, complemented
493#485—438no—
494#482—438no—
495#481—438no—
496#480C2×D4318yescomplemented
497#469—438no—
498#468—438no—
499#466—438no—
500#465—438no—
501#450—438no—
502#449—438no—
503#449—438no—
504#447—438no—
505C2×#107C2×D4311yescharacteristic, complemented
506C2×#107C2×D4311yescharacteristic, complemented
507C2×#106—431no—
508C2×#106—431no—
509C2×#103—431no—
510C2×#103—431no—
511C2×#102—431no—
512C2×#102—431no—
513C2×#102—431no—
514C2×#102—431no—
515C2×#102C2×D4311yescharacteristic
516C2×#102C2×D4311yescharacteristic
517#408—438no—
518C2×C22⋊C8—431no—
519C2×C22⋊C8—431no—
520C2×C22⋊C8—431no—
521C2×C22⋊C8C2×D4311yescharacteristic, complemented
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×Q8—431no—
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—21no—
553C23×C4—431no—
554C23×C4—431no—
555C23×C4—861no—
556C23×C4C22×D4311yescharacteristic
557C2×SD16—434no—
558C2×SD16—434no—
559C2×SD16—1722no—
560C2×SD16—1722no—
561C2×D8—434no—
562C2×D8—434no—
563C2×D8—1722no—
564C2×D8—1722no—
565C2×M16—434no—
566C2×M16—1722no—
567C22×C8—431no—
568C22×C8—431no—
569C22×C8—434no—
570C22×C8—1722no—
571C22×C8C22×D4311yescharacteristic
572C22×C8C22×D4311yescharacteristic
573#127—868no—
574#124—868no—
575C22⋊Q8—434no—
576C22⋊Q8—434no—
577C22⋊Q8—862no—
578C22⋊Q8—862no—
579C22⋊Q8—868no—
580#121—22no—
581#121—434no—
582#121—434no—
583#121—434no—
584#121—434no—
585#121—434no—
586#121—862no—
587#121—862no—
588#121—862no—
589#121—868no—
590#121—868no—
591#121—868no—
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—22no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4C22×D4311yescharacteristic
605C2×C4⋊C4C22×D4311yescharacteristic
606C2×C4⋊C4C22×D4311yescharacteristic
607C2×C4⋊C4C22×D4314yescomplemented
608C2×C22⋊C4—21no—
609C2×C22⋊C4—861no—
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#107C22×D4314yescomplemented
619#107C22×D4314yescomplemented
620#106—434no—
621#106—434no—
622#103—434no—
623#103—434no—
624#102—434no—
625#102—434no—
626#102—434no—
627#102—434no—
628#102C22×D4314yes—
629#102C22×D4314yes—
630C22⋊C8—434no—
631C22⋊C8—434no—
632C22⋊C8—434no—
633C22⋊C8C22×D4314yescomplemented
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—434no—
651C2×Q8—432no—
652C2×Q8—861no—
653C2×Q8—862no—
654C2×Q8—862no—
655C2×Q8—1722no—
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—1728no—
688C2×D4—1722no—
689C2×D4—1722no—
690C2×D4—1724no—
691C2×D4—1724no—
692C2×D4C23×D4312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—82no—
700C22×C4—431no—
701C22×C4—431no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4—432no—
706C22×C4—862no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—862no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—864no—
713C22×C4—1724no—
714C22×C4D4×D4312yes—
715C22×C4D4×D4311yescharacteristic
716C22×C4C23×D4312yes—
717C22×C4C23×D4311yescharacteristic
718SD16—1724no—
719SD16—1724no—
720D8—1724no—
721D8—1724no—
722M16—1724no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—432no—
726C2×C8—432no—
727C2×C8—862no—
728C2×C8—862no—
729C2×C8—1724no—
730C2×C8C23×D4312yes—
731C2×C8C23×D4312yes—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—432no—
737C4⋊C4—864no—
738C4⋊C4—864no—
739C4⋊C4—861no—
740C4⋊C4C23×D4312yes—
741C4⋊C4C23×D4312yes—
742C4⋊C4C23×D4312yes—
743C22⋊C4—24no—
744C22⋊C4—864no—
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—862no—
783Q8—862no—
784Q8—1724no—
785Q8—1722no—
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—1724no—
801D4—1724no—
802D4—1728no—
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—84no—
817C2×C4—432no—
818C2×C4—432no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—864no—
822C2×C4—864no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—862no—
829C2×C4—1728no—
830C2×C4—1722no—
831C2×C4—1722no—
832C2×C4C2×D4×D4312yes—
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4#1306337112yes—
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#1458346012yes—
867C22#1458370012yes—
868C22#1458370812yes—
869C22C22×D4×D4311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—862no—
875C4—862no—
876C4—1722no—
877C4—1722no—
878C4#1458346012yes—
879C4C2×#1306337111yescharacteristic
880C4C2×#1306337111yescharacteristic
881C2—42no—
882C2—82no—
883C2—3442no—
884C2—3442no—
885C2—1722no—
886C2—1722no—
887C2#1914545414yesdirect product factor
888C2C2×#1458346011yescharacteristic
889C2C2×#1458370011yescharacteristic
890C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#480C2
socleC23×C43C22×D4
hypercenterC2×#480D43
hypocenterC43C2×#3198
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#14583480C2semidirect
2. C2×#14583465C2semidirect
3. #19145454C2direct (N × H)
4. C2×#14583217C2semidirect
5. C2×#14583242C2semidirect
6. C2×#14583226C2semidirect
7. C2×#14583151C2semidirect
8. C2×#14583146C2semidirect
9. C2×#14583136C2semidirect
10. C2×#14583127C2semidirect
11. C2×#14583046C2semidirect
12. C2×#14583042C2semidirect
13. C2×#14583051C2semidirect
14. C2×#14583034C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#480C2semidirect
18. C22×#10621898C22semidirect
24. C22×#10621872C22semidirect
25. C22×C8×D43C22semidirect
27. #14583480C22semidirect
29. #14583465C22semidirect
34. C2×#13063305C22semidirect
38. C2×#13063300C22semidirect
46. #14583242C22semidirect
47. #14583226C22semidirect
48. #14583217C22semidirect
49. #14583151C22semidirect
50. #14583146C22semidirect
51. #14583136C22semidirect
52. #14583127C22semidirect
53. #14583051C22semidirect
54. #14583046C22semidirect
55. #14583042C22semidirect
56. #14583034C22semidirect
57. C2×#13063256C22semidirect
58. C2×#13063256C22semidirect
59. C2×#13063250C22semidirect
60. C2×#13063248C22semidirect
61. C2×#13063247C22semidirect
64. C2×#13063245C22semidirect
65. #14582864C22semidirect
66. C2×C22⋊(C43⋊C8)C22semidirect
70. C22×C4⋊C4×C43C22semidirect
71. C43×#480C22semidirect
72. C2×#107×C43C22semidirect
73. C2×#107×C43C22semidirect
76. C2×C22⋊C8×C43C22semidirect
85. C2×#10621898C23semidirect
116. C2×#10621872C23semidirect
120. C2×C8×D43C23semidirect
127. #13063305C23semidirect
134. #13063300C23semidirect
157. #13063256C23semidirect
158. #13063256C23semidirect
159. #13063250C23semidirect
160. #13063248C23semidirect
161. #13063247C23semidirect
164. #13063245C23semidirect
165. C22⋊(C43⋊C8)C23semidirect
181. C2×C4⋊C4×C43C23semidirect
183. #107×C43C23semidirect
184. #107×C43C23semidirect
187. C22⋊C8×C43C23semidirect
442. C2×#480D43semidirect
454. C2×C43#3198semidirect
492. C22×C4⋊C4C2×D43semidirect
496. #480C2×D43semidirect
505. C2×#107C2×D43semidirect
506. C2×#107C2×D43semidirect
521. C2×C22⋊C8C2×D43semidirect
522. C43C2×#3198semidirect
607. C2×C4⋊C4C22×D43semidirect
618. #107C22×D43semidirect
619. #107C22×D43semidirect
633. C22⋊C8C22×D43semidirect
887. C2#19145454direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834802
C2×#145834652
#191454542
C2×#145832172
C2×#145832422
C2×#145832262
C2×#145831512
C2×#145831462
C2×#145831362
C2×#145831272
C2×#145830462
C2×#145830422
C2×#145830512
C2×#145830342
C2×#145828642
C2×C43×#4802
C2×#319843