Finite Group Databasebeta

← C2×#19145441 #25967244

Subgroups — C2×#19145441 #25967244

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×#14583463C211yesmaximal, characteristic, complemented
2#19145441C2116yesmaximal, direct product factor
3C2×#14583217C211yesmaximal, characteristic, complemented
4C2×#14583237C211yesmaximal, characteristic, complemented
5C2×#14583220C211yesmaximal, characteristic, complemented
6C2×#14583212C211yesmaximal, characteristic, complemented
7C2×#14583150C211yesmaximal, characteristic, complemented
8C2×#14583147C211yesmaximal, characteristic, complemented
9C2×#14583133C211yesmaximal, characteristic, complemented
10C2×#14583130C211yesmaximal, characteristic, complemented
11C2×#14583044C211yesmaximal, characteristic, complemented
12C2×#14583044C211yesmaximal, characteristic, complemented
13C2×#14583049C211yesmaximal, characteristic, complemented
14C2×#14583032C211yesmaximal, characteristic, complemented
15C2×#14582866C211yesmaximal, characteristic, complemented
16C2×C43×#537C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C22×#10621877C2211yescharacteristic, complemented
23C23×C43⋊C8C2211yescharacteristic, complemented
24#14583463—24no—
25#14583463C2218yescomplemented
26C2×#13063321—21no—
27C2×#13063314—21no—
28C2×#13063299C2211yescharacteristic
29C2×#13063299C2211yescharacteristic
30C2×#13063299C2211yescharacteristic
31C2×#13063299C2211yescharacteristic
32C2×#13063293—21no—
33C2×#13063293—21no—
34C2×#13063284C2211yescharacteristic
35#14583237C2218yescomplemented
36#14583220C2218yescomplemented
37#14583217C2218yescomplemented
38#14583212C2218yescomplemented
39#14583150C2218yescomplemented
40#14583147C2218yescomplemented
41#14583133C2218yescomplemented
42#14583130C2218yescomplemented
43#14583049C2218yescomplemented
44#14583044C2218yescomplemented
45#14583044C2218yescomplemented
46#14583032C2218yescomplemented
47C2×#13063258C2211yescharacteristic, complemented
48C2×#13063258C2211yescharacteristic, complemented
49C2×#13063256C2211yescharacteristic, complemented
50C2×#13063256C2211yescharacteristic, complemented
51C2×#13063249C2211yescharacteristic, complemented
52C2×#13063249C2211yescharacteristic, complemented
53C2×#13063246C2211yescharacteristic, complemented
54C2×#13063246C2211yescharacteristic, complemented
55C2×#13063245C2211yescharacteristic
56C2×#13063245C2211yescharacteristic
57C2×#13063245C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59#14582866C2218yescomplemented
60C2×C22⋊(C43⋊C8)C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
63C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
64C22×#41×C43C2211yescharacteristic
65C22×#41×C43C2211yescharacteristic, complemented
66C43×#537—24no—
67C43×#537C2218yescomplemented
68C2×C22⋊Q8×C43—21no—
69C2×C22⋊Q8×C43C2211yescharacteristic
70C2×C22⋊Q8×C43C2211yescharacteristic, complemented
71C2×#121×C43—21no—
72C2×#121×C43—21no—
73C2×#121×C43—21no—
74C2×#121×C43C2211yescharacteristic
75C2×#121×C43C2211yescharacteristic, complemented
76C22×C4⋊C4×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C22×D172—21no—
79C22×D172—22no—
80C22×D172—42no—
81C22×D172—42no—
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×D172C2314yes—
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C2×#10621884—42no—
90C2×#10621884—42no—
91C2×#10621884C2314yes—
92C2×#10621884C2314yes—
93C2×#10621882—42no—
94C2×#10621882—42no—
95C2×#10621882C2314yes—
96C2×#10621882C2314yes—
97C2×#10621877—42no—
98C2×#10621877C2314yescomplemented
99C22×C43⋊C8—42no—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2314yescomplemented
105#13063321—28no—
106#13063314—28no—
107#13063299—22no—
108#13063299—22no—
109#13063299—22no—
110#13063299—22no—
111#13063299C2314yes—
112#13063299C2314yes—
113#13063299C2314yes—
114#13063299C2314yes—
115#13063293—28no—
116#13063293—28no—
117#13063284—22no—
118#13063284C2314yes—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C22⋊Dic43—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125C2×(C2×D43)⋊C4—21no—
126C2×C4×Dic43—21no—
127#13063258C2314yescomplemented
128#13063258C2314yescomplemented
129#13063256C2314yescomplemented
130#13063256C2314yescomplemented
131#13063249C2314yescomplemented
132#13063249C2314yescomplemented
133#13063246C2314yescomplemented
134#13063246C2314yescomplemented
135#13063245C2314yes—
136#13063245C2314yes—
137#13063245C2314yes—
138#13063245C2314yes—
139C22⋊(C43⋊C8)C2314yes—
140C22⋊(C43⋊C8)C2314yes—
141C22⋊(C43⋊C8)C2314yescomplemented
142C22⋊(C43⋊C8)C2314yescomplemented
143C2×#41×C43—22no—
144C2×#41×C43—42no—
145C2×#41×C43—42no—
146C2×#41×C43—42no—
147C2×#41×C43—42no—
148C2×#41×C43D414yes—
149C2×#41×C43C2314yes—
150C2×#41×C43C2314yescomplemented
151C22×Q8×C43D411yescharacteristic
152C22×Q8×C43C2311yescharacteristic
153C22×D4×C43—21no—
154C22×D4×C43—21no—
155C22×D4×C43—21no—
156C22×D4×C43D411yescharacteristic
157C22×D4×C43D411yescharacteristic
158C22×D4×C43D411yescharacteristic
159C22×D4×C43C2311yescharacteristic
160C23×C4×C43—21no—
161C23×C4×C43—21no—
162C23×C4×C43C2311yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C23×C4×C43C2311yescharacteristic
165C22⋊Q8×C43—28no—
166C22⋊Q8×C43—22no—
167C22⋊Q8×C43—22no—
168C22⋊Q8×C43C2314yes—
169C22⋊Q8×C43C2314yescomplemented
170#121×C43—28no—
171#121×C43—28no—
172#121×C43—28no—
173#121×C43—22no—
174#121×C43—22no—
175#121×C43C2314yes—
176#121×C43C2314yescomplemented
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43—22no—
179C2×C4⋊C4×C43—21no—
180C2×C4⋊C4×C43—21no—
181C2×C4⋊C4×C43C2311yescharacteristic
182C2×C4⋊C4×C43C2311yescharacteristic
183C2×C4⋊C4×C43C2314yescomplemented
184C2×C22⋊C4×C43—21no—
185C2×C22⋊C4×C43—21no—
186C2×C22⋊C4×C43—21no—
187C2×C22⋊C4×C43—21no—
188C24×C43—21no—
189C24×C43C2×D411yescharacteristic
190C24×C43C2×D411yescharacteristic
191C24×C43C2×D411yescharacteristic
192C23×D43—21no—
193C23×D43—21no—
194C23×D43—24no—
195C23×D43—44no—
196C23×D43—82no—
197C23×D43—82no—
198#41×C43—48no—
199#41×C43—44no—
200#41×C43—44no—
201#41×C43—44no—
202#41×C43—44no—
203#41×C43—48no—
204C2×Q8×C43—21no—
205C2×Q8×C43—22no—
206C2×Q8×C43—22no—
207C2×Q8×C43—42no—
208C2×Q8×C43C2×D414yes—
209C2×Q8×C43C2412yes—
210C2×D4×C43—21no—
211C2×D4×C43—24no—
212C2×D4×C43—24no—
213C2×D4×C43—24no—
214C2×D4×C43—22no—
215C2×D4×C43—22no—
216C2×D4×C43—42no—
217C2×D4×C43—42no—
218C2×D4×C43—42no—
219C2×D4×C43—44no—
220C2×D4×C43—82no—
221C2×D4×C43—82no—
222C2×D4×C43C2×D414yes—
223C2×D4×C43C2×D414yes—
224C2×D4×C43C2×D414yes—
225C2×D4×C43C2412yes—
226C22×C4×C43—22no—
227C22×C4×C43—22no—
228C22×C4×C43—22no—
229C22×C4×C43—22no—
230C22×C4×C43—22no—
231C22×C4×C43—22no—
232C22×C4×C43—24no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—24no—
237C22×C4×C43—44no—
238C22×C4×C43—82no—
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2×D411yescharacteristic
242C22×C4×C43C2×D412yes—
243C22×C4×C43C2×D412yes—
244C22×C4×C43C2×D412yes—
245C22×C4×C43C2412yes—
246C22×C4×C43C2412yes—
247C22×C4×C43C2412yes—
248C22×C4×C43C2411yescharacteristic
249C2×C22⋊D43—24no—
250C2×C22⋊D43—24no—
251C2×C22⋊D43—24no—
252C2×C22⋊D43—24no—
253C2×C22⋊D43—82no—
254C2×C22⋊D43—82no—
255C2×C22⋊D43—82no—
256C2×C22⋊D43—82no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C2×D172—21no—
260C2×D172—21no—
261C2×D172—24no—
262C2×D172—22no—
263C2×D172—22no—
264C2×D172—22no—
265C2×D172—22no—
266C2×D172—44no—
267C2×D172—44no—
268C2×D172—48no—
269C2×D172—44no—
270C2×D172C2412yes—
271C2×D172C2412yes—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—24no—
275C4⋊C4×C43—24no—
276C4⋊C4×C43—24no—
277C4⋊C4×C43C2412yes—
278C4⋊C4×C43C2412yes—
279C22⋊C4×C43—24no—
280C22⋊C4×C43—24no—
281C22⋊C4×C43—24no—
282C22⋊C4×C43—24no—
283C22⋊Dic43—24no—
284#10621884—44no—
285#10621884—44no—
286#10621882—44no—
287#10621882—44no—
288(C2×D43)⋊C4—24no—
289(C2×D43)⋊C4—24no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—24no—
292C4⋊Dic43—21no—
293C4⋊Dic43—21no—
294C4⋊Dic43C2412yes—
295C4⋊Dic43C2412yes—
296C4×Dic43—24no—
297#10621877—44no—
298C2×C43⋊C8—22no—
299C2×C43⋊C8—22no—
300C2×C43⋊C8—22no—
301C2×C43⋊C8—22no—
302C2×C43⋊C8—44no—
303C2×C43⋊C8C2412yes—
304C2×C43⋊C8C2412yes—
305C2×C43⋊C8C2412yes—
306C2×C43⋊C8C2412yes—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43—22no—
315C23×C43—22no—
316C23×C43—22no—
317C23×C43—42no—
318C23×C43—42no—
319C23×C43—42no—
320C23×C43C22×D412yes—
321C23×C43C22×D412yes—
322C23×C43C22×D412yes—
323C23×C43C22×D411yescharacteristic
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—48no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43—42no—
331C22×D43—42no—
332C22×D43—42no—
333C22×D43—84no—
334C22×D43—84no—
335C22×D43—816no—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—44no—
339Q8×C43—42no—
340D4×C43—22no—
341D4×C43—22no—
342D4×C43—44no—
343D4×C43—44no—
344D4×C43—44no—
345D4×C43—48no—
346D4×C43—42no—
347D4×C43—84no—
348D4×C43—84no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—24no—
353C2×C4×C43—24no—
354C2×C4×C43—24no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—48no—
365C2×C4×C43—42no—
366C2×C4×C43—42no—
367C2×C4×C43—42no—
368C2×C4×C43—84no—
369C2×C4×C43C22×D412yes—
370C2×C4×C43C22×D412yes—
371C2×C4×C43C22×D412yes—
372C2×C4×C43C22×D411yescharacteristic
373C2×C4×C43H(5,𝔽2)12yes—
374C2×C4×C43H(5,𝔽2)12yes—
375C2×C4×C43C2511yescharacteristic
376C22⋊D43—84no—
377C22⋊D43—84no—
378C22⋊D43—84no—
379C22⋊D43—84no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—42no—
383C2×Dic43—42no—
384D172—22no—
385D172—22no—
386D172—22no—
387D172—22no—
388D172—48no—
389D172—42no—
390D172—42no—
391C43⋊C8—22no—
392C43⋊C8—22no—
393C43⋊C8—22no—
394C43⋊C8—22no—
395C2×#3198—431nomaximal, Sylow
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—22no—
400C22×C43—22no—
401C22×C43—22no—
402C22×C43—22no—
403C22×C43—22no—
404C22×C43—22no—
405C22×C43—44no—
406C22×C43—44no—
407C22×C43—44no—
408C22×C43—42no—
409C22×C43—42no—
410C22×C43—42no—
411C22×C43—84no—
412C22×C43#53412yes—
413C22×C43#57612yes—
414C22×C43#57712yes—
415C22×C43C23×D411yescharacteristic
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—22no—
427C4×C43—22no—
428C4×C43—42no—
429C4×C43—42no—
430C4×C43—42no—
431C4×C43#53412yes—
432C4×C43C2×H(5,𝔽2)11yescharacteristic
433C4×C43C2×H(5,𝔽2)11yescharacteristic
434Dic43—42no—
435Dic43—42no—
436C2×#537D4311yescharacteristic, complemented
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×#465—431no—
447C2×#449—431no—
448C2×#449—431no—
449C2×#450—431no—
450C2×#447—431no—
451C2×#408—431no—
452C2×C43—42no—
453C2×C43—42no—
454C2×C43—42no—
455C2×C43—82no—
456C2×C43#319814yescomplemented
457C2×C43C2×#53411yescharacteristic
458C2×C43C2×#57611yescharacteristic
459C2×C43C2×#57711yescharacteristic
460D43—82no—
461D43—82no—
462C22×#41C2×D4311yescharacteristic
463C22×#41C2×D4311yescharacteristic, complemented
464C23×D4—431no—
465C22×SD16—431no—
466C22×SD16—431no—
467C22×D8—431no—
468C22×D8—431no—
469C22×M16—431no—
470C23×C8—431no—
471#537—24no—
472#537C2×D4318yescomplemented
473#535—438no—
474#535—864no—
475C2×#127—861no—
476C2×#124—861no—
477C2×C22⋊Q8—21no—
478C2×C22⋊Q8C2×D4311yescharacteristic
479C2×C22⋊Q8C2×D4311yescharacteristic, complemented
480C2×#121—21no—
481C2×#121—21no—
482C2×#121—21no—
483C2×#121—431no—
484C2×#121—431no—
485C2×#121—431no—
486C2×#121—431no—
487C2×#121C2×D4311yescharacteristic
488C2×#121C2×D4311yescharacteristic, complemented
489C2×#120—861no—
490C2×#120—861no—
491C2×#117—431no—
492C22×C4⋊C4C2×D4311yescharacteristic, complemented
493#485—438no—
494#482—438no—
495#481—438no—
496#480—438no—
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×#107—431no—
506C2×#107—431no—
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×#102—431no—
516C2×#102—431no—
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—22no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—42no—
528C2×#41—42no—
529C2×#41C22⋊D4314yes—
530C2×#41C22×D4314yes—
531C2×#41C22×D4314yescomplemented
532C22×Q8C22⋊D4311yescharacteristic
533C22×Q8C22×D4311yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—431no—
538C22×D4—431no—
539C22×D4—434no—
540C22×D4—861no—
541C22×D4—861no—
542C22×D4—861no—
543C22×D4—861no—
544C22×D4—861no—
545C22×D4—862no—
546C22×D4—1722no—
547C22×D4—1722no—
548C22×D4C22⋊D4311yescharacteristic
549C22×D4C22⋊D4311yescharacteristic
550C22×D4C22⋊D4311yescharacteristic
551C22×D4C22×D4311yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
554C23×C4C22×D4311yescharacteristic
555C23×C4C22×D4311yescharacteristic
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—431no—
570C22×C8—431no—
571C22×C8—434no—
572C22×C8—1722no—
573#127—868no—
574#124—868no—
575C22⋊Q8—28no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8C22×D4314yes—
579C22⋊Q8C22×D4314yescomplemented
580#121—28no—
581#121—28no—
582#121—28no—
583#121—22no—
584#121—22no—
585#121—434no—
586#121—434no—
587#121—434no—
588#121—434no—
589#121—862no—
590#121—862no—
591#121—862no—
592#121—862no—
593#121C22×D4314yes—
594#121C22×D4314yescomplemented
595#120—868no—
596#120—868no—
597#117—434no—
598#117—862no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—431no—
605C2×C4⋊C4C22×D4311yescharacteristic
606C2×C4⋊C4C22×D4311yescharacteristic
607C2×C4⋊C4C22×D4314yescomplemented
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
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#106—434no—
622#103—434no—
623#103—434no—
624#102—434no—
625#102—434no—
626#102—434no—
627#102—434no—
628#102—434no—
629#102—434no—
630C22⋊C8—434no—
631C22⋊C8—434no—
632C22⋊C8—434no—
633C22⋊C8—434no—
634C24—21no—
635C24—864no—
636C24—861no—
637C24—861no—
638C24—3442no—
639C24—3442no—
640C24—1724no—
641C24C2×C22⋊D4311yescharacteristic
642C24C2×C22⋊D4311yescharacteristic
643C24C2×C22⋊D4311yescharacteristic
644#41—44no—
645#41—44no—
646#41—48no—
647#41—44no—
648#41—44no—
649#41—48no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—42no—
654C2×Q8C2×C22⋊D4314yes—
655C2×Q8C23×D4312yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—82no—
667C2×D4—82no—
668C2×D4—432no—
669C2×D4—432no—
670C2×D4—864no—
671C2×D4—864no—
672C2×D4—864no—
673C2×D4—864no—
674C2×D4—861no—
675C2×D4—861no—
676C2×D4—864no—
677C2×D4—862no—
678C2×D4—862no—
679C2×D4—862no—
680C2×D4—862no—
681C2×D4—3442no—
682C2×D4—3442no—
683C2×D4—3442no—
684C2×D4—3442no—
685C2×D4—1724no—
686C2×D4—1724no—
687C2×D4—1724no—
688C2×D4—1728no—
689C2×D4C2×C22⋊D4314yes—
690C2×D4C2×C22⋊D4314yes—
691C2×D4C2×C22⋊D4314yes—
692C2×D4C23×D4312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—44no—
705C22×C4—82no—
706C22×C4—861no—
707C22×C4—861no—
708C22×C4C2×C22⋊D4312yes—
709C22×C4C2×C22⋊D4312yes—
710C22×C4C2×C22⋊D4312yes—
711C22×C4C2×C22⋊D4311yescharacteristic
712C22×C4C2×C22⋊D4311yescharacteristic
713C22×C4C2×C22⋊D4311yescharacteristic
714C22×C4C23×D4312yes—
715C22×C4C23×D4312yes—
716C22×C4C23×D4312yes—
717C22×C4C23×D4311yescharacteristic
718SD16—1724no—
719SD16—1724no—
720D8—1724no—
721D8—1724no—
722M16—1724no—
723C2×C8—432no—
724C2×C8—432no—
725C2×C8—432no—
726C2×C8—432no—
727C2×C8—862no—
728C2×C8—862no—
729C2×C8—862no—
730C2×C8—862no—
731C2×C8—1724no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—432no—
738C4⋊C4—432no—
739C4⋊C4—861no—
740C4⋊C4—861no—
741C4⋊C4C23×D4312yes—
742C4⋊C4C23×D4312yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
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—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—862no—
767C23—862no—
768C23—3444no—
769C23—3444no—
770C23—34416no—
771C23—1728no—
772C23—1722no—
773C23—1722no—
774C23—1722no—
775C23—1722no—
776C23—1722no—
777C23—1722no—
778C23C22×C22⋊D4312yes—
779C23C22×C22⋊D4312yes—
780C23C22×C22⋊D4312yes—
781C23C22×C22⋊D4311yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—42no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—44no—
790D4—44no—
791D4—48no—
792D4—42no—
793D4—84no—
794D4—84no—
795D4—862no—
796D4—862no—
797D4—862no—
798D4—862no—
799D4—3444no—
800D4—3444no—
801D4—3444no—
802D4—3444no—
803D4—1728no—
804D4—1722no—
805D4—1722no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—48no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—84no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—1722no—
829C2×C4—1722no—
830C2×C4C22×C22⋊D4312yes—
831C2×C4C22×C22⋊D4312yes—
832C2×C4C22×C22⋊D4312yes—
833C2×C4C22×C22⋊D4311yescharacteristic
834C2×C4#1306337012yes—
835C2×C4#1306337012yes—
836C2×C4C24×D4311yescharacteristic
837C8—862no—
838C8—862no—
839C8—862no—
840C8—862no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—84no—
857C22—34416no—
858C22—3444no—
859C22—3444no—
860C22—1722no—
861C22—1722no—
862C22—1722no—
863C22—1722no—
864C22—1722no—
865C22—1722no—
866C22#1458345812yes—
867C22#1458370212yes—
868C22#1458370712yes—
869C22C23×C22⋊D4311yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—1722no—
877C4—1722no—
878C4#1458345812yes—
879C4C2×#1306337011yescharacteristic
880C4C2×#1306337011yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—3442no—
886C2—3442no—
887C2#1914544114yesdirect product factor
888C2C2×#1458345811yescharacteristic
889C2C2×#1458370211yescharacteristic
890C2C2×#1458370711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#537C2
socleC23×C43C22×D4
hypercenterC2×#537D43
hypocenterC43C2×#3198
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#14583463C2semidirect
2. #19145441C2direct (N × H)
3. C2×#14583217C2semidirect
4. C2×#14583237C2semidirect
5. C2×#14583220C2semidirect
6. C2×#14583212C2semidirect
7. C2×#14583150C2semidirect
8. C2×#14583147C2semidirect
9. C2×#14583133C2semidirect
10. C2×#14583130C2semidirect
11. C2×#14583044C2semidirect
12. C2×#14583044C2semidirect
13. C2×#14583049C2semidirect
14. C2×#14583032C2semidirect
15. C2×#14582866C2semidirect
16. C2×C43×#537C2semidirect
22. C22×#10621877C22semidirect
23. C23×C43⋊C8C22semidirect
25. #14583463C22semidirect
35. #14583237C22semidirect
36. #14583220C22semidirect
37. #14583217C22semidirect
38. #14583212C22semidirect
39. #14583150C22semidirect
40. #14583147C22semidirect
41. #14583133C22semidirect
42. #14583130C22semidirect
43. #14583049C22semidirect
44. #14583044C22semidirect
45. #14583044C22semidirect
46. #14583032C22semidirect
47. C2×#13063258C22semidirect
48. C2×#13063258C22semidirect
49. C2×#13063256C22semidirect
50. C2×#13063256C22semidirect
51. C2×#13063249C22semidirect
52. C2×#13063249C22semidirect
53. C2×#13063246C22semidirect
54. C2×#13063246C22semidirect
59. #14582866C22semidirect
62. C2×C22⋊(C43⋊C8)C22semidirect
63. C2×C22⋊(C43⋊C8)C22semidirect
65. C22×#41×C43C22semidirect
67. C43×#537C22semidirect
70. C2×C22⋊Q8×C43C22semidirect
75. C2×#121×C43C22semidirect
76. C22×C4⋊C4×C43C22semidirect
98. C2×#10621877C23semidirect
104. C22×C43⋊C8C23semidirect
127. #13063258C23semidirect
128. #13063258C23semidirect
129. #13063256C23semidirect
130. #13063256C23semidirect
131. #13063249C23semidirect
132. #13063249C23semidirect
133. #13063246C23semidirect
134. #13063246C23semidirect
141. C22⋊(C43⋊C8)C23semidirect
142. C22⋊(C43⋊C8)C23semidirect
150. C2×#41×C43C23semidirect
169. C22⋊Q8×C43C23semidirect
176. #121×C43C23semidirect
183. C2×C4⋊C4×C43C23semidirect
436. C2×#537D43semidirect
456. C2×C43#3198semidirect
463. C22×#41C2×D43semidirect
472. #537C2×D43semidirect
479. C2×C22⋊Q8C2×D43semidirect
488. C2×#121C2×D43semidirect
492. C22×C4⋊C4C2×D43semidirect
522. C43C2×#3198semidirect
531. C2×#41C22×D43semidirect
579. C22⋊Q8C22×D43semidirect
594. #121C22×D43semidirect
607. C2×C4⋊C4C22×D43semidirect
887. C2#19145441direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834632
#191454412
C2×#145832172
C2×#145832372
C2×#145832202
C2×#145832122
C2×#145831502
C2×#145831472
C2×#145831332
C2×#145831302
C2×#145830442
C2×#145830492
C2×#145830322
C2×#145828662
C2×C43×#5372
C2×#319843