Finite Group Databasebeta

← C2×#19146663 #25973333

Subgroups — C2×#19146663 #25973333

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×#14583619C211yesmaximal, characteristic, complemented
2C2×#14583558C211yesmaximal, characteristic
3#19146663C2116yesmaximal, direct product factor
4C2×#14583259C211yesmaximal, characteristic, complemented
5C2×#14583241C211yesmaximal, characteristic, complemented
6C2×#14583224C211yesmaximal, characteristic, complemented
7C2×#14583195C211yesmaximal, characteristic, complemented
8C2×#14583145C211yesmaximal, characteristic, complemented
9C2×#14583140C211yesmaximal, characteristic, complemented
10C2×#14583122C211yesmaximal, characteristic, complemented
11C2×#14583063C211yesmaximal, characteristic, complemented
12C2×#14583057C211yesmaximal, characteristic, complemented
13C2×#14583007C211yesmaximal, characteristic, complemented
14C2×#14582909C211yesmaximal, characteristic, complemented
15C2×#14582896C211yesmaximal, characteristic, complemented
16C2×C43×#435C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C22×Dic172C2211yescharacteristic
20C22×Dic172C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22#14583619—24no—
23#14583619C2218yescomplemented
24#14583558—24no—
25#14583558C2218yes—
26C2×#13063325C2211yescharacteristic
27C2×#13063318—21no—
28C2×#13063318—21no—
29C2×#13063313C2211yescharacteristic
30C2×#13063312—21no—
31C2×#13063311—21no—
32C2×#13063304C2211yescharacteristic
33C2×#13063304C2211yescharacteristic
34C2×#13063304C2211yescharacteristic
35C2×#13063303—21no—
36C2×#13063299C2211yescharacteristic
37C2×#13063297—21no—
38C2×C4×Dic86C2211yescharacteristic
39C2×C4×Dic86C2211yescharacteristic
40C2×#13063290—21no—
41C2×(C22⋊D43)⋊C4—21no—
42C2×#13063284C2211yescharacteristic
43C2×#13063284C2211yescharacteristic
44#14583259C2218yescomplemented
45#14583241C2218yescomplemented
46#14583224C2218yescomplemented
47#14583195C2218yescomplemented
48#14583145C2218yescomplemented
49#14583140C2218yescomplemented
50#14583122C2218yescomplemented
51#14583063C2218yescomplemented
52#14583057C2218yescomplemented
53#14583007C2218yescomplemented
54C2×#13063259C2211yescharacteristic
55C2×#13063259C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57#14582909C2218yescomplemented
58#14582896C2218yescomplemented
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#435C2218yescomplemented
73C2×C4⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×C22⋊C8×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—24no—
79C2×#10621898—42no—
80C2×#10621898C2314yes—
81C22×Dic86—24no—
82C22×Dic86—22no—
83C22×Dic86—21no—
84C22×Dic86—21no—
85C22×Dic86—42no—
86C22×Dic86C2311yescharacteristic
87C22×Dic86C2311yescharacteristic
88C22×Dic86C2314yes—
89C22×Dic86C2311yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C23×Dic43—21no—
94C22×C4×D43—21no—
95C2×Dic172—24no—
96C2×Dic172—42no—
97C2×Dic172C2314yes—
98C2×Dic172C2314yes—
99C2×#10621873—42no—
100C2×#10621873C2314yes—
101#13063325—22no—
102#13063325C2314yes—
103#13063318—28no—
104#13063318—28no—
105#13063313—22no—
106#13063313C2314yes—
107#13063312—28no—
108#13063311—28no—
109#13063304—22no—
110#13063304—22no—
111#13063304—22no—
112#13063304C2314yes—
113#13063304C2314yes—
114#13063304C2314yes—
115#13063303—28no—
116#13063299—22no—
117#13063299C2314yes—
118#13063297—28no—
119C4×Dic86—22no—
120C4×Dic86—22no—
121C4×Dic86C2314yes—
122C4×Dic86C2314yes—
123#13063290—28no—
124(C22⋊D43)⋊C4—28no—
125#13063284—22no—
126#13063284—22no—
127#13063284C2314yes—
128#13063284C2314yes—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43—21no—
143C2×C22⋊Dic43—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151#13063259C2314yes—
152#13063259C2314yes—
153#13063257C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063250C2314yes—
158#13063250C2314yes—
159#13063250C2314yes—
160#13063250C2314yes—
161#13063247C2314yes—
162#13063247C2314yes—
163#13063247C2314yes—
164C22×D4×C43D411yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C2×M16×C43—42no—
168C2×M16×C43C2314yes—
169C22×C8×C43—42no—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2314yes—
175C4×D4×C43D414yes—
176C4×D4×C43C2314yes—
177C2×C4⋊C4×C43D411yescharacteristic
178C2×C22⋊C4×C43D411yescharacteristic
179C2×C22⋊C4×C43D411yescharacteristic
180C2×C42×C43C2311yescharacteristic
181C4⋊C8×C43C2314yes—
182C22⋊C8×C43C2314yes—
183C22⋊C8×C43C2314yes—
184#97×C43C2314yes—
185C24×C43C2×D411yescharacteristic
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C2×D4×C43—42no—
189C2×D4×C43C2×D414yes—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2412yes—
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—44no—
206C2×C22⋊D43—44no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—24no—
215C22×Dic43—44no—
216#10621898—28no—
217#10621898—44no—
218#10621898—48no—
219C2×D172—21no—
220C2×D172—22no—
221C2×D172—22no—
222C2×D172C2412yes—
223C2×C4×D43—24no—
224C2×C4×D43—44no—
225C2×Dic86—21no—
226C2×Dic86—22no—
227C2×Dic86—22no—
228C2×Dic86—22no—
229C2×Dic86—22no—
230C2×Dic86—22no—
231C2×Dic86—28no—
232C2×Dic86—24no—
233C2×Dic86—21no—
234C2×Dic86—24no—
235C2×Dic86—21no—
236C2×Dic86—44no—
237C2×Dic86—48no—
238C2×Dic86—44no—
239C2×Dic86—44no—
240C2×Dic86#4114yes—
241C2×Dic86C2412yes—
242C2×Dic86C2412yes—
243C2×Dic86C2412yes—
244M16×C43—44no—
245C2×C8×C43—22no—
246C2×C8×C43—22no—
247C2×C8×C43—22no—
248C2×C8×C43—22no—
249C2×C8×C43—44no—
250C2×C8×C43C2412yes—
251C2×C8×C43C2412yes—
252C2×C8×C43C2412yes—
253C2×C8×C43C2412yes—
254C4⋊C4×C43C2×D414yes—
255C22⋊C4×C43C2×D414yes—
256C22⋊C4×C43C2×D414yes—
257C42×C43C2×D412yes—
258C42×C43C2412yes—
259C22⋊Dic43—24no—
260C22⋊Dic43—24no—
261C22⋊Dic43—24no—
262C22⋊Dic43—24no—
263C22⋊Dic43—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267C4⋊Dic43—24no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43C2412yes—
273C4⋊Dic43C2412yes—
274C4⋊Dic43C2412yes—
275C4⋊Dic43C2412yes—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281C4×Dic43—24no—
282C4×Dic43—24no—
283C4×Dic43—24no—
284C4×Dic43—24no—
285Dic172—28no—
286Dic172—44no—
287#10621873—44no—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43C22×D412yes—
295C23×C43C22×D412yes—
296C23×C43C22×D411yescharacteristic
297C22×D43—22no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—42no—
301D4×C43—44no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—24no—
307C2×C4×C43—24no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43C22×D412yes—
313C2×C4×C43C22×D412yes—
314C2×C4×C43C22×D412yes—
315C2×C4×C43C22×D412yes—
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C2×#4112yes—
318C2×C4×C43H(5,𝔽2)12yes—
319C2×C4×C43C2511yescharacteristic
320C22⋊D43—48no—
321C22⋊D43—48no—
322C2×Dic43—24no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—48no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337D172—22no—
338D172—22no—
339D172—42no—
340C4×D43—48no—
341Dic86—24no—
342Dic86—22no—
343Dic86—22no—
344Dic86—22no—
345Dic86—22no—
346Dic86—22no—
347Dic86—48no—
348Dic86—48no—
349Dic86—42no—
350Dic86—42no—
351Dic86C2×#4114yes—
352C8×C43—22no—
353C8×C43—22no—
354C8×C43—22no—
355C8×C43—22no—
356C2×#3313—431nomaximal, Sylow
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—44no—
364C22×C43—44no—
365C22×C43#54612yes—
366C22×C43#57512yes—
367C22×C43#57812yes—
368C22×C43C23×D411yescharacteristic
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—84no—
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—22no—
376C4×C43—22no—
377C4×C43#54612yes—
378C4×C43C22×#4111yescharacteristic
379C4×C43C2×H(5,𝔽2)11yescharacteristic
380Dic43—24no—
381Dic43—42no—
382Dic43—42no—
383Dic43—42no—
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×#468—431no—
395C2×#467—431no—
396C2×#464—431no—
397C2×#452—431no—
398C2×#451—431no—
399C2×#441—431no—
400C2×#435D4311yescharacteristic, complemented
401C2×#419—431no—
402C2×#416—431no—
403C2×C43—42no—
404C2×C43—42no—
405C2×C43#331314yescomplemented
406C2×C43C2×#54611yescharacteristic
407C2×C43C2×#57511yescharacteristic
408C2×C43C2×#57811yescharacteristic
409D43—82no—
410C22×#41—431no—
411C23×Q8—431no—
412C22×Q16—431no—
413C22×Q16—431no—
414C22×SD16—431no—
415C22×M16C2×D4311yescharacteristic
416C23×C8C2×D4311yescharacteristic
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—431no—
430C2×C22⋊Q8—861no—
431C2×#121—431no—
432C2×#121—861no—
433C2×C4×Q8—431no—
434C2×C4×Q8—431no—
435C2×C4×Q8—861no—
436C2×C4×D4—861no—
437C2×C4×D4C2×D4311yescharacteristic
438C2×#117—431no—
439C2×#117—431no—
440#489—438no—
441#485—438no—
442#482—438no—
443#477—438no—
444#468—438no—
445#467—438no—
446#464—438no—
447#452—438no—
448#451—438no—
449#441—438no—
450#435C2×D4318yescomplemented
451C2×#107—431no—
452C2×#107—431no—
453C2×#106—431no—
454C2×C4⋊C8C2×D4311yescharacteristic
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×#103—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×C22⋊C8C2×D4311yescharacteristic
468C2×C22⋊C8C2×D4311yescharacteristic
469C2×#97C2×D4311yescharacteristic
470C43C2×#331311yescharacteristic, complemented, Sylow
471C2×#41—434no—
472C2×#41—864no—
473C2×#41—862no—
474C2×#41—1722no—
475C22×Q8—431no—
476C22×Q8—431no—
477C22×Q8—431no—
478C22×Q8—434no—
479C22×Q8—864no—
480C22×Q8—861no—
481C22×Q8—861no—
482C22×Q8—862no—
483C22×Q8—1722no—
484C22×D4—431no—
485C22×D4—861no—
486C22×D4—861no—
487C22×D4D17211yescharacteristic
488C23×C4—861no—
489C23×C4—861no—
490C23×C4C22×D4311yescharacteristic
491C23×C4C22×D4311yescharacteristic
492C2×Q16—434no—
493C2×Q16—434no—
494C2×Q16—864no—
495C2×Q16—1722no—
496C2×SD16—434no—
497C2×SD16—1722no—
498C2×M16—42no—
499C2×M16C22×D4314yes—
500C22×C8—42no—
501C22×C8C22×D4311yescharacteristic
502C22×C8C22×D4311yescharacteristic
503C22×C8C22×D4311yescharacteristic
504C22×C8C22×D4311yescharacteristic
505C22×C8C22×D4314yes—
506C4⋊Q8—434no—
507C4⋊Q8—862no—
508#126—868no—
509#126—868no—
510#124—434no—
511#124—868no—
512#124—868no—
513#124—862no—
514C22⋊Q8—434no—
515C22⋊Q8—434no—
516C22⋊Q8—434no—
517C22⋊Q8—862no—
518C22⋊Q8—862no—
519C22⋊Q8—862no—
520C22⋊Q8—868no—
521#121—434no—
522#121—868no—
523#121—862no—
524C4×Q8—434no—
525C4×Q8—434no—
526C4×Q8—868no—
527C4×Q8—862no—
528C4×Q8—862no—
529C4×D4—868no—
530C4×D4D17214yes—
531C4×D4C22×D4314yes—
532#117—434no—
533#117—434no—
534#117—862no—
535#117—862no—
536C2×C4⋊C4—431no—
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⋊C4—861no—
546C2×C4⋊C4D17211yescharacteristic
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4D17211yescharacteristic
556C2×C22⋊C4D17211yescharacteristic
557C2×C42—861no—
558C2×C42—861no—
559C2×C42—861no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562#107—434no—
563#107—434no—
564#106—434no—
565C4⋊C8C22×D4314yes—
566#103—434no—
567#103—434no—
568#103—434no—
569#103—434no—
570#103—434no—
571#103—434no—
572#103—434no—
573#102—434no—
574#102—434no—
575#102—434no—
576C22⋊C8C22×D4314yes—
577C22⋊C8C22×D4314yes—
578#97C22×D4314yes—
579C24—861no—
580C24C2×D17211yescharacteristic
581C24C2×D17211yescharacteristic
582#41—868no—
583#41—1724no—
584#41—1728no—
585C2×Q8—434no—
586C2×Q8—432no—
587C2×Q8—432no—
588C2×Q8—432no—
589C2×Q8—868no—
590C2×Q8—861no—
591C2×Q8—861no—
592C2×Q8—864no—
593C2×Q8—864no—
594C2×Q8—861no—
595C2×Q8—862no—
596C2×Q8—862no—
597C2×Q8—862no—
598C2×Q8—862no—
599C2×Q8—862no—
600C2×Q8—1724no—
601C2×Q8—1724no—
602C2×Q8—1728no—
603C2×Q8—1724no—
604C2×D4—42no—
605C2×D4—432no—
606C2×D4—864no—
607C2×D4—864no—
608C2×D4—861no—
609C2×D4—862no—
610C2×D4—862no—
611C2×D4—1724no—
612C2×D4—1724no—
613C2×D4C2×D17214yes—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—861no—
619C22×C4—864no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—864no—
627C22×C4—1724no—
628C22×C4—1724no—
629C22×C4C2×D17212yes—
630C22×C4C2×D17212yes—
631C22×C4C2×D17211yescharacteristic
632C22×C4C2×D17211yescharacteristic
633C22×C4C2×D17211yescharacteristic
634C22×C4C2×D17211yescharacteristic
635C22×C4C23×D4312yes—
636C22×C4C23×D4312yes—
637C22×C4C23×D4311yescharacteristic
638Q16—868no—
639Q16—1724no—
640SD16—1724no—
641M16—44no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—44no—
647C2×C8C23×D4312yes—
648C2×C8C23×D4312yes—
649C2×C8C23×D4312yes—
650C2×C8C23×D4312yes—
651C4⋊C4—432no—
652C4⋊C4—432no—
653C4⋊C4—432no—
654C4⋊C4—432no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—864no—
662C4⋊C4—864no—
663C4⋊C4—864no—
664C4⋊C4—864no—
665C4⋊C4C2×D17214yes—
666C22⋊C4—864no—
667C22⋊C4—864no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C22⋊C4—864no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C22⋊C4C2×D17214yes—
675C22⋊C4C2×D17214yes—
676C42—864no—
677C42—864no—
678C42—864no—
679C42—864no—
680C42C2×D17212yes—
681C42C23×D4312yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—862no—
689C23—1722no—
690C23—1722no—
691C23—1722no—
692C23C22×D17212yes—
693C23C22×D17212yes—
694C23C22×D17211yescharacteristic
695Q8—434no—
696Q8—862no—
697Q8—864no—
698Q8—862no—
699Q8—862no—
700Q8—862no—
701Q8—862no—
702Q8—1728no—
703Q8—1728no—
704Q8—1722no—
705Q8—1722no—
706D4—44no—
707D4—862no—
708D4—862no—
709D4—1728no—
710D4—1728no—
711D4—1722no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—862no—
723C2×C4—864no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—1728no—
731C2×C4—1728no—
732C2×C4—1722no—
733C2×C4—1722no—
734C2×C4—1722no—
735C2×C4—1722no—
736C2×C4—1722no—
737C2×C4—1722no—
738C2×C4C22×D17212yes—
739C2×C4C22×D17212yes—
740C2×C4C22×D17212yes—
741C2×C4C22×D17212yes—
742C2×C4C22×D17211yescharacteristic
743C2×C4#41×D4312yes—
744C2×C4#1306337012yes—
745C2×C4C24×D4311yescharacteristic
746C8—22no—
747C8—22no—
748C8—22no—
749C8—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—3444no—
759C22—1722no—
760C22—1722no—
761C22—1722no—
762C22#1458354412yes—
763C22#1458369912yes—
764C22#1458371612yes—
765C22C23×D17211yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—864no—
771C4—1722no—
772C4—1722no—
773C4—1722no—
774C4—1722no—
775C4—1722no—
776C4—1722no—
777C4#1458354412yes—
778C4C2×#41×D4311yescharacteristic
779C4C2×#1306337011yescharacteristic
780C2—42no—
781C2—42no—
782C2—3442no—
783C2#1914666314yesdirect product factor
784C2C2×#1458354411yescharacteristic
785C2C2×#1458369911yescharacteristic
786C2C2×#1458371611yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×#14583558C2
hypercenterC2×#435D43
hypocenterC43C2×#3313
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#14583619C2semidirect
3. #19146663C2direct (N × H)
4. C2×#14583259C2semidirect
5. C2×#14583241C2semidirect
6. C2×#14583224C2semidirect
7. C2×#14583195C2semidirect
8. C2×#14583145C2semidirect
9. C2×#14583140C2semidirect
10. C2×#14583122C2semidirect
11. C2×#14583063C2semidirect
12. C2×#14583057C2semidirect
13. C2×#14583007C2semidirect
14. C2×#14582909C2semidirect
15. C2×#14582896C2semidirect
16. C2×C43×#435C2semidirect
23. #14583619C22semidirect
44. #14583259C22semidirect
45. #14583241C22semidirect
46. #14583224C22semidirect
47. #14583195C22semidirect
48. #14583145C22semidirect
49. #14583140C22semidirect
50. #14583122C22semidirect
51. #14583063C22semidirect
52. #14583057C22semidirect
53. #14583007C22semidirect
57. #14582909C22semidirect
58. #14582896C22semidirect
72. C43×#435C22semidirect
400. C2×#435D43semidirect
405. C2×C43#3313semidirect
450. #435C2×D43semidirect
470. C43C2×#3313semidirect
783. C2#19146663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836192
C2×#145835582
#191466632
C2×#145832592
C2×#145832412
C2×#145832242
C2×#145831952
C2×#145831452
C2×#145831402
C2×#145831222
C2×#145830632
C2×#145830572
C2×#145830072
C2×#145829092
C2×#145828962
C2×C43×#4352
C2×#331343