Finite Group Databasebeta

← C2×#19146928 #25973537

Subgroups — C2×#19146928 #25973537

Order 11008.

2210 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic, complemented
2C2×#14583567C211yesmaximal, characteristic
3#19146928C2116yesmaximal, direct product factor
4C2×#14583244C211yesmaximal, characteristic, complemented
5C2×#14583214C211yesmaximal, characteristic, complemented
6C2×#14583210C211yesmaximal, characteristic, complemented
7C2×#14583193C211yesmaximal, characteristic, complemented
8C2×#14583148C211yesmaximal, characteristic, complemented
9C2×#14583097C211yesmaximal, characteristic, complemented
10C2×#14583059C211yesmaximal, characteristic, complemented
11C2×#14583058C211yesmaximal, characteristic, complemented
12C2×#14582991C211yesmaximal, characteristic, complemented
13C2×#14582975C211yesmaximal, characteristic, complemented
14C2×#14582901C211yesmaximal, characteristic, complemented
15C2×#14582897C211yesmaximal, characteristic, complemented
16C2×C43×#468C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22#14583607—24no—
23#14583607C2218yescomplemented
24#14583567—24no—
25#14583567C2218yes—
26C2×#13063324C2211yescharacteristic
27C2×#13063321—21no—
28C2×#13063321C2211yescharacteristic
29C2×#13063315—21no—
30C2×#13063305—21no—
31C2×#13063302—21no—
32C2×#13063301C2211yescharacteristic
33C2×#13063300C2211yescharacteristic
34C2×#13063298—21no—
35C2×#13063297—21no—
36C2×Q8×Dic43C2211yescharacteristic
37C2×#13063290C2211yescharacteristic
38C2×C4×C22⋊D43C2211yescharacteristic
39C2×(C22⋊D43)⋊C4—21no—
40C2×(C22⋊D43)⋊C4—21no—
41C22×C4⋊Dic43C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583244C2218yescomplemented
44#14583214C2218yescomplemented
45#14583210C2218yescomplemented
46#14583193C2218yescomplemented
47#14583148C2218yescomplemented
48#14583097C2218yescomplemented
49#14583059C2218yescomplemented
50#14583058C2218yescomplemented
51#14582991C2218yescomplemented
52#14582975C2218yescomplemented
53C2×#13063258C2211yescharacteristic
54C2×#13063258C2211yescharacteristic
55C2×Dic43⋊C8C2211yescharacteristic
56#14582901C2218yescomplemented
57#14582897C2218yescomplemented
58C2×#13063250C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063248C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
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×#10621898—22no—
78C2×#10621898—24no—
79C2×#10621898—42no—
80C2×#10621898C2314yes—
81C2×#10621900—22no—
82C2×#10621900—24no—
83C2×#10621900—42no—
84C2×#10621900C2314yes—
85C22×Dic86—21no—
86C22×Dic86C2311yescharacteristic
87C22×D172—21no—
88C22×D172C2311yescharacteristic
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43D411yescharacteristic
94C23×Dic43—21no—
95C23×Dic43—21no—
96C22×C4×D43—21no—
97C22×C4×D43—21no—
98C22×C4×D43C2311yescharacteristic
99C2×#10621885—24no—
100C2×#10621885C2314yes—
101C2×#10621884—42no—
102C2×#10621884C2314yes—
103C2×#10621872—42no—
104C2×#10621872C2314yes—
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107#13063324—22no—
108#13063324C2314yes—
109#13063321—28no—
110#13063321—22no—
111#13063321C2314yes—
112#13063315—28no—
113#13063305—28no—
114#13063302—28no—
115#13063301—22no—
116#13063301C2314yes—
117#13063300—22no—
118#13063300C2314yes—
119#13063298—28no—
120#13063297—28no—
121Q8×Dic43—22no—
122Q8×Dic43C2314yes—
123#13063290—22no—
124#13063290C2314yes—
125C4×C22⋊D43D414yes—
126C4×C22⋊D43C2314yes—
127(C22⋊D43)⋊C4—28no—
128(C22⋊D43)⋊C4—28no—
129C2×C4⋊Dic43—22no—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2314yes—
134C2×C4⋊Dic43C2311yescharacteristic
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4D411yescharacteristic
140C4⋊C4×D43—22no—
141C4⋊C4×D43C2314yes—
142C2×C22⋊Dic43D411yescharacteristic
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4D411yescharacteristic
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yes—
150#13063258C2314yes—
151Dic43⋊C8C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063248C2314yes—
155#13063247C2314yes—
156#13063247C2314yes—
157#13063246C2314yes—
158#13063246C2314yes—
159#13063245C2314yes—
160C22⋊(C43⋊C8)C2314yes—
161(C2×D43)⋊C8C2314yes—
162C8×Dic43C2314yes—
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×D43—21no—
188C23×D43C2×D411yescharacteristic
189C2×Q8×C43—21no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43C2412yes—
193C2×D4×C43—21no—
194C2×D4×C43—24no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—82no—
198C2×D4×C43C2412yes—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D412yes—
206C22×C4×C43C2412yes—
207C22×C4×C43C2411yescharacteristic
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—44no—
214C2×C22⋊D43—44no—
215C2×C22⋊D43—44no—
216C2×C22⋊D43—82no—
217C2×C22⋊D43C2×D414yes—
218C22×Dic43—24no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—24no—
223C22×Dic43—44no—
224C22×Dic43—82no—
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228#10621900—28no—
229#10621900—44no—
230#10621900—48no—
231#10621898—28no—
232#10621898—44no—
233#10621898—48no—
234C2×D172—21no—
235C2×D172—24no—
236C2×D172—22no—
237C2×D172—22no—
238C2×D172—82no—
239C2×D172C2412yes—
240C2×C4×D43—22no—
241C2×C4×D43—22no—
242C2×C4×D43—24no—
243C2×C4×D43—24no—
244C2×C4×D43—44no—
245C2×C4×D43—82no—
246C2×C4×D43C2×D412yes—
247C2×C4×D43C2412yes—
248C2×Dic86—21no—
249C2×Dic86—22no—
250C2×Dic86—24no—
251C2×Dic86—82no—
252C2×Dic86#4114yes—
253C2×Dic86C2412yes—
254SD16×C43—44no—
255M16×C43—44no—
256C2×C8×C43—22no—
257C2×C8×C43—22no—
258C2×C8×C43C2412yes—
259C2×C8×C43C2412yes—
260C4⋊C4×C43—24no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43C2412yes—
264C4⋊C4×C43C2412yes—
265C22⋊C4×C43—24no—
266C22⋊C4×C43—24no—
267C22⋊Dic43C2×D414yes—
268#10621885—28no—
269#10621884—44no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4C2×D414yes—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—24no—
276C4⋊Dic43—24no—
277C4⋊Dic43C2412yes—
278C4⋊Dic43C2412yes—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283Dic43⋊C4C2×D414yes—
284C4×Dic43—24no—
285C4×Dic43—24no—
286C4×Dic43C2×D412yes—
287C4×Dic43C2412yes—
288C2×C43⋊C8—22no—
289C2×C43⋊C8—22no—
290C2×C43⋊C8C2412yes—
291C2×C43⋊C8C2412yes—
292#10621872—44no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43C22×D412yes—
301C23×C43C22×D411yescharacteristic
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43C22×D412yes—
310Q8×C43—22no—
311Q8×C43—22no—
312Q8×C43—42no—
313D4×C43—22no—
314D4×C43—22no—
315D4×C43—42no—
316D4×C43—84no—
317C2×C4×C43—22no—
318C2×C4×C43—24no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43C22×D412yes—
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4112yes—
330C2×C4×C43H(5,𝔽2)12yes—
331C2×C4×C43C2511yescharacteristic
332C22⋊D43—28no—
333C22⋊D43—48no—
334C22⋊D43—48no—
335C22⋊D43—48no—
336C22⋊D43—84no—
337C2×Dic43—24no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—48no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43—84no—
347C2×Dic43#13714yes—
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350C2×Dic43C22×D412yes—
351D172—22no—
352D172—22no—
353D172—42no—
354D172—84no—
355C4×D43—24no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—48no—
359C4×D43—84no—
360Dic86—24no—
361Dic86—22no—
362Dic86—84no—
363Dic86C2×#4114yes—
364C8×C43—22no—
365C8×C43—22no—
366C43⋊C8—22no—
367C43⋊C8—22no—
368C2×#3333—431nomaximal, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—44no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—84no—
377C22×C43#54612yes—
378C22×C43C2×#13712yes—
379C22×C43#57612yes—
380C22×C43C23×D411yescharacteristic
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—44no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—84no—
389C4×C43—22no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43#54612yes—
394C4×C43C22×#4111yescharacteristic
395C4×C43C2×H(5,𝔽2)11yescharacteristic
396Dic43—24no—
397Dic43—22no—
398Dic43—22no—
399Dic43—42no—
400Dic43—42no—
401Dic43C2×#13714yes—
402C2×#554—431no—
403C2×#550—431no—
404#3333—4316no—
405C2×#486—431no—
406C2×#480—431no—
407C2×#480—431no—
408C2×#477—431no—
409C2×#468—431no—
410C2×#468D4311yescharacteristic, complemented
411C2×#460—431no—
412C2×#452—431no—
413C2×#452—431no—
414C2×C4×Q16—431no—
415C2×#436—431no—
416C2×#417—431no—
417C2×#417—431no—
418C2×C43—42no—
419C2×C43—82no—
420C2×C43#333314yescomplemented
421C2×C43C2×#54611yescharacteristic
422C2×C43C22×#13711yescharacteristic
423C2×C43C2×#57611yescharacteristic
424D43—42no—
425D43—82no—
426C22×#41—431no—
427C22×#41—431no—
428C22×Q16—431no—
429C22×SD16—431no—
430C22×SD16C2×D4311yescharacteristic
431C22×M16—431no—
432C22×M16C2×D4311yescharacteristic
433#554—438no—
434#554—864no—
435#550—438no—
436#550—864no—
437C2×C4⋊Q8—431no—
438C2×#127—431no—
439C2×#127—861no—
440C2×#125—861no—
441C2×C22⋊Q8—431no—
442C2×C22⋊Q8—861no—
443C2×C22⋊Q8—861no—
444C2×C22⋊Q8C2×D4311yescharacteristic
445C2×#121—431no—
446C2×#121—861no—
447C2×#121—861no—
448C2×#121C2×D4311yescharacteristic
449C2×C4×Q8—431no—
450C2×C4×Q8—431no—
451C2×C4×D4—431no—
452C2×C4×D4—861no—
453C2×C4×D4—861no—
454C22×C4⋊C4—431no—
455C22×C4⋊C4—431no—
456#486—438no—
457#480—438no—
458#480—438no—
459#477—438no—
460#468—438no—
461#468C2×D4318yescomplemented
462#460—438no—
463#452—438no—
464#452—438no—
465C4×Q16—438no—
466#436—438no—
467C2×#107—431no—
468C2×#107—431no—
469C2×#107C2×D4311yescharacteristic
470C2×C4⋊C8—431no—
471#417—438no—
472#417—438no—
473C2×#103—431no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103C2×D4311yescharacteristic
477C2×#102—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102C2×D4311yescharacteristic
483C2×C22⋊C8—431no—
484C2×C22⋊C8—431no—
485C2×C4×C8—431no—
486C43C2×#333311yescharacteristic, complemented, Sylow
487C2×#41—434no—
488C2×#41—434no—
489C2×#41—864no—
490C2×#41—862no—
491C2×#41—862no—
492C2×#41—864no—
493C2×#41—1722no—
494C2×#41—1722no—
495C22×Q8—431no—
496C22×Q8—861no—
497C22×Q8C22×D4311yescharacteristic
498C22×D4—21no—
499C22×D4—431no—
500C22×D4—431no—
501C22×D4—861no—
502C22×D4—861no—
503C22×D4—861no—
504C22×D4—861no—
505C22×D4—861no—
506C22×D4C22×D4311yescharacteristic
507C23×C4—431no—
508C23×C4—861no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4—861no—
512C23×C4C22×D4311yescharacteristic
513C2×Q16—434no—
514C2×Q16—864no—
515C2×SD16—42no—
516C2×SD16—434no—
517C2×SD16—1722no—
518C2×SD16C22×D4314yes—
519C2×M16—42no—
520C2×M16—434no—
521C2×M16—1722no—
522C2×M16C22×D4314yes—
523C22×C8—431no—
524C22×C8—431no—
525C22×C8C22×D4311yescharacteristic
526C22×C8C22×D4311yescharacteristic
527C4⋊Q8—434no—
528C4⋊Q8—862no—
529#127—434no—
530#127—862no—
531#127—868no—
532#125—868no—
533C22⋊Q8—22no—
534C22⋊Q8—434no—
535C22⋊Q8—868no—
536C22⋊Q8—868no—
537C22⋊Q8—862no—
538C22⋊Q8C22×D4314yes—
539#121—22no—
540#121—434no—
541#121—868no—
542#121—868no—
543#121—862no—
544#121C22×D4314yes—
545C4×Q8—434no—
546C4×Q8—434no—
547C4×Q8—862no—
548C4×Q8—862no—
549C4×D4—434no—
550C4×D4—434no—
551C4×D4—868no—
552C4×D4—868no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—431no—
557C2×C4⋊C4—434no—
558C2×C4⋊C4—434no—
559C2×C4⋊C4—862no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—862no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C42—431no—
576C2×C42—861no—
577C2×C42—861no—
578#107—434no—
579#107—434no—
580#107C22×D4314yes—
581C4⋊C8—434no—
582#103—434no—
583#103—434no—
584#103—434no—
585#103C22×D4314yes—
586#102—434no—
587#102—434no—
588#102—434no—
589#102—434no—
590#102—434no—
591#102C22×D4314yes—
592C22⋊C8—434no—
593C22⋊C8—434no—
594C4×C8—434no—
595C24—21no—
596C24—431no—
597C24—861no—
598C24D4×D4311yescharacteristic
599#41—868no—
600#41—868no—
601#41—1724no—
602#41—1728no—
603#41—1724no—
604#41—1728no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—434no—
609C2×Q8—432no—
610C2×Q8—864no—
611C2×Q8—861no—
612C2×Q8—862no—
613C2×Q8—3442no—
614C2×Q8C23×D4312yes—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—82no—
620C2×D4—434no—
621C2×D4—432no—
622C2×D4—864no—
623C2×D4—864no—
624C2×D4—864no—
625C2×D4—864no—
626C2×D4—864no—
627C2×D4—864no—
628C2×D4—861no—
629C2×D4—862no—
630C2×D4—862no—
631C2×D4—3442no—
632C2×D4—3442no—
633C2×D4—1724no—
634C2×D4—1724no—
635C2×D4—1724no—
636C2×D4C23×D4312yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—431no—
643C22×C4—431no—
644C22×C4—431no—
645C22×C4—432no—
646C22×C4—432no—
647C22×C4—864no—
648C22×C4—864no—
649C22×C4—861no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—864no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—864no—
656C22×C4—3442no—
657C22×C4—3442no—
658C22×C4—1724no—
659C22×C4—1724no—
660C22×C4D4×D4312yes—
661C22×C4D4×D4311yescharacteristic
662C22×C4C23×D4312yes—
663C22×C4C23×D4311yescharacteristic
664Q16—868no—
665SD16—44no—
666SD16—1724no—
667M16—44no—
668M16—1724no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—432no—
672C2×C8—432no—
673C2×C8—862no—
674C2×C8—862no—
675C2×C8C23×D4312yes—
676C2×C8C23×D4312yes—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—434no—
681C4⋊C4—432no—
682C4⋊C4—432no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—861no—
689C4⋊C4—864no—
690C4⋊C4—861no—
691C4⋊C4C23×D4312yes—
692C4⋊C4C23×D4312yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—434no—
696C22⋊C4—434no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C42—432no—
700C42—432no—
701C42—864no—
702C42—864no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—432no—
711C23—862no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—1722no—
716C23—1722no—
717C23—1722no—
718C23C2×D4×D4312yes—
719C23C2×D4×D4311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—434no—
724Q8—862no—
725Q8—864no—
726Q8—3444no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—868no—
732D4—862no—
733D4—862no—
734D4—3444no—
735D4—3444no—
736D4—1728no—
737D4—1728no—
738D4—1728no—
739D4—1722no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—434no—
751C2×C4—432no—
752C2×C4—432no—
753C2×C4—432no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—864no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—864no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—3444no—
764C2×C4—3444no—
765C2×C4—1728no—
766C2×C4—1728no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4C2×D4×D4312yes—
770C2×C4C2×D4×D4311yescharacteristic
771C2×C4#41×D4312yes—
772C2×C4#1306337012yes—
773C2×C4C24×D4311yescharacteristic
774C8—22no—
775C8—22no—
776C8—862no—
777C8—862no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—862no—
787C22—862no—
788C22—862no—
789C22—3444no—
790C22—1722no—
791C22—1722no—
792C22—1722no—
793C22—1724no—
794C22#1458353812yes—
795C22#137×D4312yes—
796C22#1458370312yes—
797C22C22×D4×D4311yescharacteristic
798C4—22no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—434no—
803C4—862no—
804C4—864no—
805C4—862no—
806C4—1722no—
807C4—1722no—
808C4#1458353812yes—
809C4C2×#41×D4311yescharacteristic
810C4C2×#1306337011yescharacteristic
811C2—42no—
812C2—82no—
813C2—3442no—
814C2—1722no—
815C2#1914692814yesdirect product factor
816C2C2×#1458353811yescharacteristic
817C2C2×#137×D4311yescharacteristic
818C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#468C2
socleC23×C43C22×D4
prime radicalC2×#14583567C2
hypercenterC2×#468D43
hypocenterC43C2×#3333
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×#14583607C2semidirect
3. #19146928C2direct (N × H)
4. C2×#14583244C2semidirect
5. C2×#14583214C2semidirect
6. C2×#14583210C2semidirect
7. C2×#14583193C2semidirect
8. C2×#14583148C2semidirect
9. C2×#14583097C2semidirect
10. C2×#14583059C2semidirect
11. C2×#14583058C2semidirect
12. C2×#14582991C2semidirect
13. C2×#14582975C2semidirect
14. C2×#14582901C2semidirect
15. C2×#14582897C2semidirect
16. C2×C43×#468C2semidirect
23. #14583607C22semidirect
43. #14583244C22semidirect
44. #14583214C22semidirect
45. #14583210C22semidirect
46. #14583193C22semidirect
47. #14583148C22semidirect
48. #14583097C22semidirect
49. #14583059C22semidirect
50. #14583058C22semidirect
51. #14582991C22semidirect
52. #14582975C22semidirect
56. #14582901C22semidirect
57. #14582897C22semidirect
73. C43×#468C22semidirect
410. C2×#468D43semidirect
420. C2×C43#3333semidirect
461. #468C2×D43semidirect
486. C43C2×#3333semidirect
815. C2#19146928direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836072
C2×#145835672
#191469282
C2×#145832442
C2×#145832142
C2×#145832102
C2×#145831932
C2×#145831482
C2×#145830972
C2×#145830592
C2×#145830582
C2×#145829912
C2×#145829752
C2×#145829012
C2×#145828972
C2×C43×#4682
C2×#333343