Finite Group Databasebeta

← C2×#19146656 #25973326

Subgroups — C2×#19146656 #25973326

Order 11008.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583620C211yesmaximal, characteristic, complemented
2C2×#14583555C211yesmaximal, characteristic
3#19146656C2116yesmaximal, direct product factor
4C2×#14583257C211yesmaximal, characteristic, complemented
5C2×#14583242C211yesmaximal, characteristic, complemented
6C2×#14583220C211yesmaximal, characteristic, complemented
7C2×#14583193C211yesmaximal, characteristic, complemented
8C2×#14583139C211yesmaximal, characteristic, complemented
9C2×#14583119C211yesmaximal, characteristic, complemented
10C2×#14583058C211yesmaximal, characteristic, complemented
11C2×#14583054C211yesmaximal, characteristic, complemented
12C2×#14583003C211yesmaximal, characteristic, complemented
13C2×#14582968C211yesmaximal, characteristic, complemented
14C2×#14582909C211yesmaximal, characteristic, complemented
15C2×#14582892C211yesmaximal, characteristic, complemented
16C2×C43×#468C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22#14583620—24no—
23#14583620C2218yescomplemented
24#14583555—24no—
25#14583555C2218yes—
26C2×#13063324C2211yescharacteristic
27C2×#13063320—21no—
28C2×#13063318—21no—
29C2×#13063312C2211yescharacteristic
30C2×#13063311—21no—
31C2×#13063311—21no—
32C2×#13063305C2211yescharacteristic
33C2×#13063302—21no—
34C2×#13063301C2211yescharacteristic
35C2×#13063297—21no—
36C2×Q8×Dic43C2211yescharacteristic
37C2×#13063290—21no—
38C2×#13063290C2211yescharacteristic
39C2×D4×Dic43—21no—
40C2×C4×C22⋊D43C2211yescharacteristic
41C2×#13063284C2211yescharacteristic
42C2×#13063283C2211yescharacteristic
43#14583257C2218yescomplemented
44#14583242C2218yescomplemented
45#14583220C2218yescomplemented
46#14583193C2218yescomplemented
47#14583139C2218yescomplemented
48#14583119C2218yescomplemented
49#14583058C2218yescomplemented
50#14583054C2218yescomplemented
51#14583003C2218yescomplemented
52#14582968C2218yescomplemented
53C2×#13063258C2211yescharacteristic
54C2×#13063256C2211yescharacteristic
55C2×Dic43⋊C8C2211yescharacteristic
56#14582909C2218yescomplemented
57#14582892C2218yescomplemented
58C2×#13063250C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#468C2218yescomplemented
74C2×#107×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621900—22no—
78C2×#10621900—24no—
79C2×#10621900—42no—
80C2×#10621900C2314yes—
81C22×Dic86—24no—
82C22×Dic86—22no—
83C22×Dic86—21no—
84C22×Dic86—21no—
85C22×Dic86—42no—
86C22×Dic86C2311yescharacteristic
87C22×Dic86C2314yes—
88C22×Dic86C2311yescharacteristic
89C22×C22⋊D43—21no—
90C22×C22⋊D43D411yescharacteristic
91C23×Dic43—21no—
92C23×Dic43—21no—
93C22×C4×D43C2311yescharacteristic
94C2×#10621885—24no—
95C2×#10621885—42no—
96C2×#10621885C2314yes—
97C2×#10621885C2314yes—
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100C2×C8×D43—42no—
101C2×C8×D43C2314yes—
102#13063324—22no—
103#13063324C2314yes—
104#13063320—28no—
105#13063318—28no—
106#13063312—22no—
107#13063312C2314yes—
108#13063311—28no—
109#13063311—28no—
110#13063305—22no—
111#13063305C2314yes—
112#13063302—28no—
113#13063301—22no—
114#13063301C2314yes—
115#13063297—28no—
116Q8×Dic43—22no—
117Q8×Dic43C2314yes—
118#13063290—28no—
119#13063290—22no—
120#13063290C2314yes—
121D4×Dic43—28no—
122C4×C22⋊D43D414yes—
123C4×C22⋊D43C2314yes—
124#13063284—22no—
125#13063284C2314yes—
126#13063283—22no—
127#13063283C2314yes—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4D411yescharacteristic
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43D411yescharacteristic
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4D411yescharacteristic
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yes—
150#13063256C2314yes—
151Dic43⋊C8C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063248C2314yes—
157#13063248C2314yes—
158#13063246C2314yes—
159#13063246C2314yes—
160C22⋊(C43⋊C8)C2314yes—
161(C2×D43)⋊C8C2314yes—
162#13063235C2314yes—
163C22×Q8×C43C2311yescharacteristic
164C22×D4×C43—21no—
165C22×D4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C2×SD16×C43—42no—
168C2×SD16×C43C2314yes—
169C2×M16×C43—42no—
170C2×M16×C43C2314yes—
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C22⋊Q8×C43—22no—
174C22⋊Q8×C43C2314yes—
175#121×C43—22no—
176#121×C43C2314yes—
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182#107×C43C2314yes—
183#103×C43C2314yes—
184#102×C43C2314yes—
185C24×C43—21no—
186C24×C43C2×D411yescharacteristic
187C23×D43C2×D411yescharacteristic
188C2×Q8×C43—21no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43C2412yes—
192C2×D4×C43—21no—
193C2×D4×C43—24no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—44no—
197C2×D4×C43C2412yes—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D412yes—
205C22×C4×C43C2412yes—
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—24no—
208C2×C22⋊D43—42no—
209C2×C22⋊D43—44no—
210C2×C22⋊D43C2×D414yes—
211C22×Dic43—24no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—24no—
217C22×Dic43—44no—
218C22×Dic43—44no—
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222#10621900—28no—
223#10621900—44no—
224#10621900—48no—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×C4×D43C2×D412yes—
228C2×C4×D43C2412yes—
229C2×Dic86—21no—
230C2×Dic86—22no—
231C2×Dic86—22no—
232C2×Dic86—22no—
233C2×Dic86—28no—
234C2×Dic86—24no—
235C2×Dic86—21no—
236C2×Dic86—24no—
237C2×Dic86—44no—
238C2×Dic86—48no—
239C2×Dic86—44no—
240C2×Dic86—44no—
241C2×Dic86#4114yes—
242C2×Dic86C2412yes—
243C2×Dic86C2412yes—
244SD16×C43—44no—
245M16×C43—44no—
246C2×C8×C43—22no—
247C2×C8×C43—22no—
248C2×C8×C43C2412yes—
249C2×C8×C43C2412yes—
250C4⋊C4×C43—24no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43C2412yes—
254C4⋊C4×C43C2412yes—
255C22⋊C4×C43—24no—
256C22⋊C4×C43—24no—
257C22⋊Dic43—24no—
258C22⋊Dic43—24no—
259C22⋊Dic43—24no—
260C22⋊Dic43C2×D414yes—
261#10621885—28no—
262#10621885—44no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4C2×D414yes—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—24no—
270C4⋊Dic43—24no—
271C4⋊Dic43C2412yes—
272C4⋊Dic43C2412yes—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276Dic43⋊C4C2×D414yes—
277C4×Dic43—24no—
278C4×Dic43—24no—
279C4×Dic43—24no—
280C4×Dic43—24no—
281C4×Dic43C2×D412yes—
282C4×Dic43C2412yes—
283C2×C43⋊C8—22no—
284C2×C43⋊C8—22no—
285C2×C43⋊C8C2412yes—
286C2×C43⋊C8C2412yes—
287C8×D43—44no—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43C22×D412yes—
296C23×C43C22×D411yescharacteristic
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43C22×D412yes—
301Q8×C43—22no—
302Q8×C43—22no—
303Q8×C43—42no—
304D4×C43—22no—
305D4×C43—22no—
306D4×C43—48no—
307D4×C43—42no—
308C2×C4×C43—22no—
309C2×C4×C43—24no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43C22×D412yes—
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C2×#4112yes—
321C2×C4×C43H(5,𝔽2)12yes—
322C2×C4×C43C2511yescharacteristic
323C22⋊D43—44no—
324C22⋊D43—48no—
325C2×Dic43—24no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—48no—
334C2×Dic43—48no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43C22×D412yes—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341C4×D43—24no—
342C4×D43—22no—
343C4×D43—22no—
344Dic86—24no—
345Dic86—22no—
346Dic86—22no—
347Dic86—22no—
348Dic86—48no—
349Dic86—48no—
350Dic86—42no—
351Dic86C2×#4114yes—
352C8×C43—22no—
353C8×C43—22no—
354C43⋊C8—22no—
355C43⋊C8—22no—
356C2×#3313—431nomaximal, Sylow
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—44no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—84no—
365C22×C43#54612yes—
366C22×C43#57512yes—
367C22×C43#57812yes—
368C22×C43C23×D411yescharacteristic
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—44no—
373C4×C43—22no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43#54612yes—
378C4×C43C22×#4111yescharacteristic
379C4×C43C2×H(5,𝔽2)11yescharacteristic
380Dic43—24no—
381Dic43—22no—
382Dic43—22no—
383Dic43—22no—
384Dic43—42no—
385Dic43—42no—
386Dic43—42no—
387C2×#556—431no—
388C2×#548—431no—
389#3313—4316no—
390C2×#489—431no—
391C2×#485—431no—
392C2×#482—431no—
393C2×#477—431no—
394C2×#468D4311yescharacteristic, complemented
395C2×#467—431no—
396C2×#464—431no—
397C2×#452—431no—
398C2×#451—431no—
399C2×#441—431no—
400C2×#435—431no—
401C2×#419—431no—
402C2×#416—431no—
403C2×C43—42no—
404C2×C43—82no—
405C2×C43#331314yescomplemented
406C2×C43C2×#54611yescharacteristic
407C2×C43C2×#57511yescharacteristic
408C2×C43C2×#57811yescharacteristic
409D43—42no—
410C22×#41—431no—
411C23×Q8—431no—
412C22×Q16—431no—
413C22×Q16—431no—
414C22×SD16C2×D4311yescharacteristic
415C22×M16C2×D4311yescharacteristic
416C23×C8—431no—
417#556—438no—
418#556—864no—
419#548—438no—
420#548—864no—
421C2×C4⋊Q8—431no—
422C2×#126—861no—
423C2×#126—861no—
424C2×#124—431no—
425C2×#124—861no—
426C2×#124—861no—
427C2×C22⋊Q8—431no—
428C2×C22⋊Q8—431no—
429C2×C22⋊Q8—861no—
430C2×C22⋊Q8C2×D4311yescharacteristic
431C2×#121—861no—
432C2×#121C2×D4311yescharacteristic
433C2×C4×Q8—431no—
434C2×C4×Q8—431no—
435C2×C4×Q8—861no—
436C2×C4×D4—431no—
437C2×C4×D4—861no—
438C2×#117—431no—
439C2×#117—431no—
440#489—438no—
441#485—438no—
442#482—438no—
443#477—438no—
444#468C2×D4318yescomplemented
445#467—438no—
446#464—438no—
447#452—438no—
448#451—438no—
449#441—438no—
450#435—438no—
451C2×#107—431no—
452C2×#107C2×D4311yescharacteristic
453C2×#106—431no—
454C2×C4⋊C8—431no—
455#419—438no—
456#416—438no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103C2×D4311yescharacteristic
464C2×#102—431no—
465C2×#102—431no—
466C2×#102C2×D4311yescharacteristic
467C2×C22⋊C8—431no—
468C2×C22⋊C8—431no—
469C2×#97—431no—
470C43C2×#331311yescharacteristic, complemented, Sylow
471C2×#41—434no—
472C2×#41—862no—
473C2×#41—864no—
474C2×#41—1722no—
475C22×Q8—431no—
476C22×Q8—431no—
477C22×Q8—434no—
478C22×Q8—861no—
479C22×Q8—864no—
480C22×Q8—861no—
481C22×Q8—862no—
482C22×Q8—1722no—
483C22×Q8C22×D4311yescharacteristic
484C22×D4—21no—
485C22×D4—431no—
486C22×D4—861no—
487C22×D4C22×D4311yescharacteristic
488C23×C4—431no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4C22×D4311yescharacteristic
492C2×Q16—434no—
493C2×Q16—434no—
494C2×Q16—864no—
495C2×Q16—1722no—
496C2×SD16—42no—
497C2×SD16C22×D4314yes—
498C2×M16—42no—
499C2×M16C22×D4314yes—
500C22×C8—431no—
501C22×C8—431no—
502C22×C8—434no—
503C22×C8—1722no—
504C22×C8C22×D4311yescharacteristic
505C22×C8C22×D4311yescharacteristic
506C4⋊Q8—434no—
507C4⋊Q8—862no—
508#126—868no—
509#126—868no—
510#124—434no—
511#124—862no—
512#124—868no—
513#124—868no—
514C22⋊Q8—22no—
515C22⋊Q8—434no—
516C22⋊Q8—434no—
517C22⋊Q8—868no—
518C22⋊Q8—862no—
519C22⋊Q8—862no—
520C22⋊Q8C22×D4314yes—
521#121—22no—
522#121—868no—
523#121C22×D4314yes—
524C4×Q8—434no—
525C4×Q8—434no—
526C4×Q8—862no—
527C4×Q8—862no—
528C4×Q8—868no—
529C4×D4—434no—
530C4×D4—434no—
531C4×D4—868no—
532#117—434no—
533#117—434no—
534#117—862no—
535#117—862no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4C22×D4311yescharacteristic
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—431no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C42—431no—
558C2×C42—861no—
559C2×C42—861no—
560C2×C42—861no—
561C2×C42—861no—
562#107—434no—
563#107C22×D4314yes—
564#106—434no—
565C4⋊C8—434no—
566#103—434no—
567#103—434no—
568#103—434no—
569#103—434no—
570#103—434no—
571#103—434no—
572#103C22×D4314yes—
573#102—434no—
574#102—434no—
575#102C22×D4314yes—
576C22⋊C8—434no—
577C22⋊C8—434no—
578#97—434no—
579C24—21no—
580C24—431no—
581C24D4×D4311yescharacteristic
582#41—868no—
583#41—1724no—
584#41—1728no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—434no—
589C2×Q8—432no—
590C2×Q8—432no—
591C2×Q8—864no—
592C2×Q8—868no—
593C2×Q8—861no—
594C2×Q8—864no—
595C2×Q8—861no—
596C2×Q8—862no—
597C2×Q8—862no—
598C2×Q8—862no—
599C2×Q8—1724no—
600C2×Q8—1724no—
601C2×Q8—1728no—
602C2×Q8—1724no—
603C2×Q8C23×D4312yes—
604C2×D4—24no—
605C2×D4—21no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—44no—
609C2×D4—434no—
610C2×D4—864no—
611C2×D4—1722no—
612C2×D4—1724no—
613C2×D4C23×D4312yes—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—864no—
625C22×C4—861no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—864no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—1724no—
633C22×C4—1724no—
634C22×C4D4×D4312yes—
635C22×C4D4×D4311yescharacteristic
636C22×C4C23×D4312yes—
637C22×C4C23×D4311yescharacteristic
638Q16—868no—
639Q16—1724no—
640SD16—44no—
641M16—44no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—432no—
645C2×C8—432no—
646C2×C8—862no—
647C2×C8—862no—
648C2×C8—1724no—
649C2×C8C23×D4312yes—
650C2×C8C23×D4312yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—434no—
655C4⋊C4—432no—
656C4⋊C4—432no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—864no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4C23×D4312yes—
665C4⋊C4C23×D4312yes—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—434no—
669C22⋊C4—434no—
670C22⋊C4—864no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C22⋊C4—864no—
675C22⋊C4—864no—
676C42—432no—
677C42—432no—
678C42—864no—
679C42—864no—
680C42—864no—
681C42—864no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—432no—
690C23—862no—
691C23—862no—
692C23—862no—
693C23C2×D4×D4312yes—
694C23C2×D4×D4311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—434no—
699Q8—862no—
700Q8—864no—
701Q8—862no—
702Q8—862no—
703Q8—1728no—
704Q8—1728no—
705Q8—1722no—
706D4—22no—
707D4—22no—
708D4—48no—
709D4—42no—
710D4—1724no—
711D4—1728no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—432no—
723C2×C4—432no—
724C2×C4—432no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—864no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—864no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—1728no—
737C2×C4—1728no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4—1722no—
741C2×C4C2×D4×D4312yes—
742C2×C4C2×D4×D4311yescharacteristic
743C2×C4#41×D4312yes—
744C2×C4#1306337012yes—
745C2×C4C24×D4311yescharacteristic
746C8—22no—
747C8—22no—
748C8—862no—
749C8—862no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—862no—
759C22—862no—
760C22—862no—
761C22—1724no—
762C22#1458353812yes—
763C22#1458369512yes—
764C22#1458371512yes—
765C22C22×D4×D4311yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—862no—
771C4—864no—
772C4—862no—
773C4—862no—
774C4—1722no—
775C4—1722no—
776C4—1722no—
777C4#1458353812yes—
778C4C2×#41×D4311yescharacteristic
779C4C2×#1306337011yescharacteristic
780C2—42no—
781C2—82no—
782C2—1722no—
783C2#1914665614yesdirect product factor
784C2C2×#1458353811yescharacteristic
785C2C2×#1458369511yescharacteristic
786C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#468C2
socleC23×C43C22×D4
prime radicalC2×#14583555C2
hypercenterC2×#468D43
hypocenterC43C2×#3313
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#14583620C2semidirect
3. #19146656C2direct (N × H)
4. C2×#14583257C2semidirect
5. C2×#14583242C2semidirect
6. C2×#14583220C2semidirect
7. C2×#14583193C2semidirect
8. C2×#14583139C2semidirect
9. C2×#14583119C2semidirect
10. C2×#14583058C2semidirect
11. C2×#14583054C2semidirect
12. C2×#14583003C2semidirect
13. C2×#14582968C2semidirect
14. C2×#14582909C2semidirect
15. C2×#14582892C2semidirect
16. C2×C43×#468C2semidirect
23. #14583620C22semidirect
43. #14583257C22semidirect
44. #14583242C22semidirect
45. #14583220C22semidirect
46. #14583193C22semidirect
47. #14583139C22semidirect
48. #14583119C22semidirect
49. #14583058C22semidirect
50. #14583054C22semidirect
51. #14583003C22semidirect
52. #14582968C22semidirect
56. #14582909C22semidirect
57. #14582892C22semidirect
73. C43×#468C22semidirect
394. C2×#468D43semidirect
405. C2×C43#3313semidirect
444. #468C2×D43semidirect
470. C43C2×#3313semidirect
783. C2#19146656direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836202
C2×#145835552
#191466562
C2×#145832572
C2×#145832422
C2×#145832202
C2×#145831932
C2×#145831392
C2×#145831192
C2×#145830582
C2×#145830542
C2×#145830032
C2×#145829682
C2×#145829092
C2×#145828922
C2×C43×#4682
C2×#331343