Finite Group Databasebeta

← C2×#19146491 #25973014

Subgroups — C2×#19146491 #25973014

Order 11008.

2210 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583558C211yesmaximal, characteristic, complemented
2#19146491C2116yesmaximal, direct product factor
3C2×#14583256C211yesmaximal, characteristic, complemented
4C2×#14583217C211yesmaximal, characteristic, complemented
5C2×#14583240C211yesmaximal, characteristic, complemented
6C2×#14583203C211yesmaximal, characteristic, complemented
7C2×#14583133C211yesmaximal, characteristic, complemented
8C2×#14583126C211yesmaximal, characteristic, complemented
9C2×#14583114C211yesmaximal, characteristic, complemented
10C2×#14583042C211yesmaximal, characteristic, complemented
11C2×#14583037C211yesmaximal, characteristic, complemented
12C2×C4×#10621883C211yesmaximal, characteristic, complemented
13C2×D4×C43⋊C8C211yesmaximal, characteristic, complemented
14C2×#14582893C211yesmaximal, characteristic, complemented
15C22×#13063248C211yesmaximal, characteristic, complemented
16C2×C43×#553C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C23×C43⋊C8C2211yescharacteristic
23C23×C43⋊C8C2211yescharacteristic
24#14583558—24no—
25#14583558C2218yescomplemented
26C2×#13063313C2211yescharacteristic
27C2×#13063311—21no—
28C2×#13063304C2211yescharacteristic
29C2×#13063303—21no—
30C2×#13063299C2211yescharacteristic
31C2×#13063297—21no—
32C2×C4×Dic86C2211yescharacteristic
33C2×(C22⋊D43)⋊C4—21no—
34#14583256C2218yescomplemented
35#14583240C2218yescomplemented
36#14583217C2218yescomplemented
37#14583203C2218yescomplemented
38#14583133C2218yescomplemented
39#14583126C2218yescomplemented
40#14583114C2218yescomplemented
41#14583042C2218yescomplemented
42#14583037C2218yescomplemented
43C4×#10621883C2218yescomplemented
44D4×C43⋊C8C2218yescomplemented
45C2×#13063258C2211yescharacteristic
46C2×#13063256C2211yescharacteristic
47C2×#13063256C2211yescharacteristic
48C2×C4⋊(C43⋊C8)C2211yescharacteristic
49#14582893C2218yescomplemented
50C2×#13063248C2211yescharacteristic
51C2×#13063248C2211yescharacteristic
52C2×#13063248C2211yescharacteristic
53C2×#13063248C2211yescharacteristic
54C2×#13063248C2211yescharacteristic
55C2×#13063248C2211yescharacteristic
56C2×#13063248C2218yescomplemented
57C2×#13063246C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59C2×#13063245C2211yescharacteristic
60C2×#13063245C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C22⋊(C43⋊C8)C2211yescharacteristic
63C2×C4×C43⋊C8C2211yescharacteristic
64C43×#553—24no—
65C43×#553C2218yescomplemented
66C2×#126×C43—21no—
67C2×#125×C43C2211yescharacteristic
68C2×#123×C43—21no—
69C2×#121×C43—21no—
70C2×#121×C43C2211yescharacteristic
71C2×#121×C43C2211yescharacteristic
72C2×C4×D4×C43—21no—
73C2×C4×D4×C43C2211yescharacteristic
74C2×C4×D4×C43C2211yescharacteristic
75C2×#117×C43C2211yescharacteristic
76C22×C4⋊C4×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—24no—
79C2×#10621898—42no—
80C2×#10621898C2314yes—
81C22×Dic86—24no—
82C22×Dic86—22no—
83C22×Dic86—21no—
84C22×Dic86—42no—
85C22×Dic86C2311yescharacteristic
86C22×Dic86C2314yes—
87C22×Dic86C2311yescharacteristic
88C22×D172C2311yescharacteristic
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C2×#10621883—24no—
94C2×#10621883—42no—
95C2×#10621883C2314yes—
96C2×#10621883C2314yes—
97C2×#10621882—42no—
98C2×#10621882C2314yes—
99C22×C43⋊C8—42no—
100C22×C43⋊C8—42no—
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2314yes—
106C22×C43⋊C8C2314yes—
107#13063313—22no—
108#13063313C2314yes—
109#13063311—28no—
110#13063304—22no—
111#13063304C2314yes—
112#13063303—28no—
113#13063299—22no—
114#13063299C2314yes—
115#13063297—28no—
116C4×Dic86—22no—
117C4×Dic86C2314yes—
118(C22⋊D43)⋊C4—28no—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×Dic43⋊C4—21no—
121C2×Dic43⋊C4—21no—
122C2×C22⋊Dic43—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125C2×(C2×D43)⋊C4—21no—
126C2×C4×Dic43—21no—
127#13063258C2314yes—
128#13063256C2314yes—
129#13063256C2314yes—
130C4⋊(C43⋊C8)C2314yes—
131#13063248C2314yes—
132#13063248C2314yes—
133#13063248C2314yes—
134#13063248C2314yes—
135#13063248C2314yes—
136#13063248C2314yes—
137#13063246C2314yes—
138#13063245C2314yes—
139#13063245C2314yes—
140#13063245C2314yes—
141C22⋊(C43⋊C8)C2314yes—
142C22⋊(C43⋊C8)C2314yes—
143C4×C43⋊C8C2314yes—
144C22×D4×C43—21no—
145C22×D4×C43—21no—
146C22×D4×C43D411yescharacteristic
147C22×D4×C43C2311yescharacteristic
148C23×C4×C43—21no—
149C23×C4×C43—21no—
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152#126×C43—28no—
153#125×C43—22no—
154#125×C43C2314yes—
155#123×C43—28no—
156#121×C43—28no—
157#121×C43—22no—
158#121×C43—22no—
159#121×C43C2314yes—
160#121×C43C2314yes—
161C4×D4×C43—28no—
162C4×D4×C43—22no—
163C4×D4×C43D414yes—
164C4×D4×C43C2314yes—
165C4×D4×C43C2314yes—
166#117×C43—22no—
167#117×C43C2314yes—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—22no—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43D411yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2314yes—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43D411yescharacteristic
182C2×C22⋊C4×C43D411yescharacteristic
183C2×C42×C43—21no—
184C2×C42×C43C2311yescharacteristic
185C24×C43—21no—
186C24×C43C2×D411yescharacteristic
187C24×C43C2×D411yescharacteristic
188C23×D43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—24no—
191C2×D4×C43—24no—
192C2×D4×C43—24no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—44no—
196C2×D4×C43—82no—
197C2×D4×C43C2×D414yes—
198C2×D4×C43C2412yes—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43—24no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—24no—
208C22×C4×C43—82no—
209C22×C4×C43—82no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2412yes—
217C22×C4×C43C2412yes—
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—44no—
222C2×C22⋊D43—44no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—24no—
227C22×Dic43—44no—
228#10621898—28no—
229#10621898—44no—
230#10621898—48no—
231C2×D172—21no—
232C2×D172—22no—
233C2×D172—22no—
234C2×D172C2412yes—
235C2×C4×D43—24no—
236C2×C4×D43—44no—
237C2×Dic86—21no—
238C2×Dic86—22no—
239C2×Dic86—22no—
240C2×Dic86—22no—
241C2×Dic86—28no—
242C2×Dic86—24no—
243C2×Dic86—21no—
244C2×Dic86—44no—
245C2×Dic86—48no—
246C2×Dic86—44no—
247C2×Dic86#4114yes—
248C2×Dic86C2412yes—
249C2×Dic86C2412yes—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—24no—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C2×D414yes—
257C4⋊C4×C43C2412yes—
258C4⋊C4×C43C2412yes—
259C4⋊C4×C43C2412yes—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—24no—
263C22⋊C4×C43—24no—
264C22⋊C4×C43C2×D414yes—
265C22⋊C4×C43C2×D414yes—
266C42×C43—24no—
267C42×C43C2×D412yes—
268C42×C43C2412yes—
269C22⋊Dic43—24no—
270#10621883—28no—
271#10621883—44no—
272#10621882—44no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276C4⋊Dic43—21no—
277C4⋊Dic43C2412yes—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280C4×Dic43—24no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8—22no—
285C2×C43⋊C8—44no—
286C2×C43⋊C8—44no—
287C2×C43⋊C8C2412yes—
288C2×C43⋊C8C2412yes—
289C2×C43⋊C8C2412yes—
290C2×C43⋊C8C2412yes—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43#13514yes—
301C23×C43C22×D412yes—
302C23×C43C22×D412yes—
303C23×C43C22×D411yescharacteristic
304C22×D43—22no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43—42no—
308D4×C43—28no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—48no—
312D4×C43—42no—
313D4×C43—84no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—24no—
319C2×C4×C43—24no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43—84no—
331C2×C4×C43—84no—
332C2×C4×C43C22×D412yes—
333C2×C4×C43C22×D412yes—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D412yes—
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C2×#4112yes—
338C2×C4×C43H(5,𝔽2)12yes—
339C2×C4×C43C2511yescharacteristic
340C22⋊D43—48no—
341C22⋊D43—48no—
342C2×Dic43—24no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—48no—
347C2×Dic43—42no—
348C2×Dic43—42no—
349D172—22no—
350D172—22no—
351D172—42no—
352C4×D43—48no—
353Dic86—24no—
354Dic86—22no—
355Dic86—22no—
356Dic86—22no—
357Dic86—48no—
358Dic86—42no—
359Dic86C2×#4114yes—
360C43⋊C8—22no—
361C43⋊C8—22no—
362C43⋊C8—22no—
363C43⋊C8—22no—
364C2×#3301—431nomaximal, Sylow
365C22×C43—22no—
366C22×C43—28no—
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—44no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—84no—
376C22×C43#54612yes—
377C22×C43C2×#13514yes—
378C22×C43C2×#13512yes—
379C22×C43#57712yes—
380C22×C43C23×D411yescharacteristic
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—84no—
385C4×C43—22no—
386C4×C43—22no—
387C4×C43—22no—
388C4×C43—22no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43#54612yes—
393C4×C43C22×#4111yescharacteristic
394C4×C43C2×H(5,𝔽2)11yescharacteristic
395Dic43—24no—
396Dic43—42no—
397Dic43—42no—
398C2×#553D4311yescharacteristic, complemented
399C2×#548—431no—
400#3301—4316no—
401C2×#488—431no—
402C2×#481—431no—
403C2×#485—431no—
404C2×#479—431no—
405C2×#466—431no—
406C2×#465—431no—
407C2×#463—431no—
408C2×#449—431no—
409C2×#448—431no—
410C2×C4×SD16—431no—
411C2×C8×D4—431no—
412C2×#416—431no—
413C22×#103—431no—
414C2×C43—24no—
415C2×C43—42no—
416C2×C43—82no—
417C2×C43#330114yescomplemented
418C2×C43C2×#54611yescharacteristic
419C2×C43C22×#13511yescharacteristic
420C2×C43C2×#57711yescharacteristic
421D43—82no—
422C22×#41—431no—
423C23×Q8—431no—
424C22×SD16—431no—
425C22×SD16—431no—
426C22×D8—431no—
427C23×C8—431no—
428C23×C8—431no—
429#553—24no—
430#553C2×D4318yescomplemented
431#548—438no—
432#548—864no—
433C2×#126—21no—
434C2×#125C2×D4311yescharacteristic
435C2×#124—431no—
436C2×#124—861no—
437C2×#123—21no—
438C2×C22⋊Q8—431no—
439C2×C22⋊Q8—861no—
440C2×#121—21no—
441C2×#121—431no—
442C2×#121—861no—
443C2×#121C2×D4311yescharacteristic
444C2×#121C2×D4311yescharacteristic
445C2×C4×Q8—431no—
446C2×C4×D4—21no—
447C2×C4×D4—861no—
448C2×C4×D4C2×D4311yescharacteristic
449C2×C4×D4C2×D4311yescharacteristic
450C2×#117C2×D4311yescharacteristic
451C22×C4⋊C4C2×D4311yescharacteristic
452#488—438no—
453#485—438no—
454#481—438no—
455#479—438no—
456#466—438no—
457#465—438no—
458#463—438no—
459#449—438no—
460#448—438no—
461C4×SD16—438no—
462C8×D4—438no—
463C2×#107—431no—
464C2×#106—431no—
465C2×#106—431no—
466C2×C4⋊C8—431no—
467#416—438no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103—438no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×C22⋊C8—431no—
480C2×C22⋊C8—431no—
481C2×C4×C8—431no—
482C43C2×#330111yescharacteristic, complemented, Sylow
483C2×#41—434no—
484C2×#41—864no—
485C2×#41—862no—
486C2×#41—1722no—
487C22×Q8—431no—
488C22×Q8—431no—
489C22×Q8—434no—
490C22×Q8—864no—
491C22×Q8—861no—
492C22×Q8—862no—
493C22×Q8—1722no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—431no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4C22⋊D4311yescharacteristic
500C22×D4C22×D4311yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—861no—
504C23×C4—861no—
505C23×C4C22×D4311yescharacteristic
506C23×C4C22×D4311yescharacteristic
507C2×SD16—434no—
508C2×SD16—434no—
509C2×SD16—864no—
510C2×SD16—1722no—
511C2×D8—434no—
512C2×D8—1722no—
513C22×C8—431no—
514C22×C8—431no—
515C22×C8—431no—
516C22×C8—431no—
517C22×C8—434no—
518C22×C8—434no—
519C22×C8—1722no—
520C22×C8—1722no—
521#126—28no—
522#125—22no—
523#125C22×D4314yes—
524#124—434no—
525#124—868no—
526#124—862no—
527#123—28no—
528C22⋊Q8—434no—
529C22⋊Q8—862no—
530C22⋊Q8—868no—
531#121—28no—
532#121—22no—
533#121—22no—
534#121—434no—
535#121—868no—
536#121—862no—
537#121C22×D4314yes—
538#121C22×D4314yes—
539C4×Q8—434no—
540C4×Q8—862no—
541C4×D4—28no—
542C4×D4—22no—
543C4×D4—868no—
544C4×D4C22⋊D4314yes—
545C4×D4C22×D4314yes—
546C4×D4C22×D4314yes—
547#117—22no—
548#117C22×D4314yes—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4C22⋊D4311yescharacteristic
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C4⋊C4C22×D4311yescharacteristic
559C2×C4⋊C4C22×D4314yes—
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4C22⋊D4311yescharacteristic
570C2×C22⋊C4C22⋊D4311yescharacteristic
571C2×C42—21no—
572C2×C42—861no—
573C2×C42C22×D4311yescharacteristic
574#107—434no—
575#106—434no—
576#106—434no—
577C4⋊C8—434no—
578#103—434no—
579#103—434no—
580#103—434no—
581#103—434no—
582#103—434no—
583#103—434no—
584#102—434no—
585#102—434no—
586#102—434no—
587#102—434no—
588C22⋊C8—434no—
589C22⋊C8—434no—
590C4×C8—434no—
591C24—21no—
592C24—861no—
593C24C2×C22⋊D4311yescharacteristic
594C24C2×C22⋊D4311yescharacteristic
595#41—868no—
596#41—1724no—
597#41—1728no—
598C2×Q8—434no—
599C2×Q8—432no—
600C2×Q8—432no—
601C2×Q8—868no—
602C2×Q8—861no—
603C2×Q8—864no—
604C2×Q8—861no—
605C2×Q8—862no—
606C2×Q8—862no—
607C2×Q8—862no—
608C2×Q8—1724no—
609C2×Q8—1724no—
610C2×Q8—1728no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—24no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—82no—
619C2×D4—432no—
620C2×D4—864no—
621C2×D4—864no—
622C2×D4—861no—
623C2×D4—862no—
624C2×D4—862no—
625C2×D4—1724no—
626C2×D4—1724no—
627C2×D4C2×C22⋊D4314yes—
628C2×D4C23×D4312yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—82no—
639C22×C4—82no—
640C22×C4—861no—
641C22×C4—864no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—864no—
645C22×C4—1724no—
646C22×C4—1724no—
647C22×C4C2×C22⋊D4312yes—
648C22×C4C2×C22⋊D4312yes—
649C22×C4C2×C22⋊D4311yescharacteristic
650C22×C4C2×C22⋊D4311yescharacteristic
651C22×C4C2×C22⋊D4311yescharacteristic
652C22×C4C2×C22⋊D4311yescharacteristic
653C22×C4C23×D4312yes—
654C22×C4C23×D4312yes—
655C22×C4C23×D4311yescharacteristic
656SD16—868no—
657SD16—1724no—
658D8—1724no—
659C2×C8—432no—
660C2×C8—432no—
661C2×C8—432no—
662C2×C8—432no—
663C2×C8—862no—
664C2×C8—862no—
665C2×C8—862no—
666C2×C8—862no—
667C2×C8—1724no—
668C2×C8—1724no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—21no—
675C4⋊C4—432no—
676C4⋊C4—861no—
677C4⋊C4—864no—
678C4⋊C4—864no—
679C4⋊C4C2×C22⋊D4314yes—
680C4⋊C4C23×D4312yes—
681C4⋊C4C23×D4312yes—
682C4⋊C4C23×D4312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4C2×C22⋊D4314yes—
692C22⋊C4C2×C22⋊D4314yes—
693C42—24no—
694C42—864no—
695C42C2×C22⋊D4312yes—
696C42C23×D4312yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—862no—
707C23—1722no—
708C23—1722no—
709C23—1722no—
710C23#1306334514yes—
711C23C22×C22⋊D4312yes—
712C23C22×C22⋊D4312yes—
713C23C22×C22⋊D4311yescharacteristic
714Q8—434no—
715Q8—862no—
716Q8—864no—
717Q8—862no—
718Q8—862no—
719Q8—1728no—
720Q8—1722no—
721D4—28no—
722D4—22no—
723D4—22no—
724D4—48no—
725D4—42no—
726D4—84no—
727D4—862no—
728D4—862no—
729D4—1728no—
730D4—1728no—
731D4—1722no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4—862no—
751C2×C4—864no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—1728no—
755C2×C4—1728no—
756C2×C4—1722no—
757C2×C4—1722no—
758C2×C4C22×C22⋊D4312yes—
759C2×C4C22×C22⋊D4312yes—
760C2×C4C22×C22⋊D4312yes—
761C2×C4C22×C22⋊D4312yes—
762C2×C4C22×C22⋊D4311yescharacteristic
763C2×C4#41×D4312yes—
764C2×C4#1306337112yes—
765C2×C4C24×D4311yescharacteristic
766C8—862no—
767C8—862no—
768C8—862no—
769C8—862no—
770C22—22no—
771C22—22no—
772C22—28no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—3444no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22#1458353712yes—
786C22C2×#1306334514yes—
787C22C2×#1306334512yes—
788C22#1458371012yes—
789C22C23×C22⋊D4311yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—864no—
798C4—1722no—
799C4—1722no—
800C4#1458353712yes—
801C4C2×#41×D4311yescharacteristic
802C4C2×#1306337111yescharacteristic
803C2—24no—
804C2—42no—
805C2—82no—
806C2—3442no—
807C2#1914649114yesdirect product factor
808C2C2×#1458353711yescharacteristic
809C2C22×#1306334511yescharacteristic
810C2C2×#1458371011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#553C2
socleC23×C43C22×D4
hypercenterC2×#553D43
hypocenterC43C2×#3301
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#14583558C2semidirect
2. #19146491C2direct (N × H)
3. C2×#14583256C2semidirect
4. C2×#14583217C2semidirect
5. C2×#14583240C2semidirect
6. C2×#14583203C2semidirect
7. C2×#14583133C2semidirect
8. C2×#14583126C2semidirect
9. C2×#14583114C2semidirect
10. C2×#14583042C2semidirect
11. C2×#14583037C2semidirect
12. C2×C4×#10621883C2semidirect
13. C2×D4×C43⋊C8C2semidirect
14. C2×#14582893C2semidirect
15. C22×#13063248C2semidirect
16. C2×C43×#553C2semidirect
25. #14583558C22semidirect
34. #14583256C22semidirect
35. #14583240C22semidirect
36. #14583217C22semidirect
37. #14583203C22semidirect
38. #14583133C22semidirect
39. #14583126C22semidirect
40. #14583114C22semidirect
41. #14583042C22semidirect
42. #14583037C22semidirect
43. C4×#10621883C22semidirect
44. D4×C43⋊C8C22semidirect
49. #14582893C22semidirect
56. C2×#13063248C22semidirect
65. C43×#553C22semidirect
398. C2×#553D43semidirect
417. C2×C43#3301semidirect
430. #553C2×D43semidirect
482. C43C2×#3301semidirect
807. C2#19146491direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835582
#191464912
C2×#145832562
C2×#145832172
C2×#145832402
C2×#145832032
C2×#145831332
C2×#145831262
C2×#145831142
C2×#145830422
C2×#145830372
C2×C4×#106218832
C2×D4×C43⋊C82
C2×#145828932
C22×#130632482
C2×C43×#5532
C2×#330143