Finite Group Databasebeta

← C2×#19146582 #25973167

Subgroups — C2×#19146582 #25973167

Order 11008.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583560C211yesmaximal, characteristic, complemented
2C2×#14583550C211yesmaximal, characteristic, complemented
3#19146582C2116yesmaximal, direct product factor
4C2×#14583260C211yesmaximal, characteristic, complemented
5C2×#14583233C211yesmaximal, characteristic, complemented
6C2×#14583212C211yesmaximal, characteristic, complemented
7C2×#14583192C211yesmaximal, characteristic, complemented
8C2×#14583148C211yesmaximal, characteristic, complemented
9C2×#14583135C211yesmaximal, characteristic, complemented
10C2×#14583117C211yesmaximal, characteristic, complemented
11C2×#14583047C211yesmaximal, characteristic, complemented
12C2×#14583038C211yesmaximal, characteristic, complemented
13C2×#14583002C211yesmaximal, characteristic, complemented
14C2×#14582970C211yesmaximal, characteristic, complemented
15C2×#14582899C211yesmaximal, characteristic, complemented
16C22×#103×C43C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621898—21no—
19C22×#10621884C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×D344C2211yescharacteristic
22C22×#10621872C2211yescharacteristic
23#14583560—24no—
24#14583560C2218yescomplemented
25#14583550—24no—
26#14583550C2218yescomplemented
27C2×#13063324C2211yescharacteristic
28C2×#13063314—21no—
29C2×#13063314C2211yescharacteristic
30C2×#13063310—21no—
31C2×#13063308—21no—
32C2×#13063303—21no—
33C2×#13063301—21no—
34C2×#13063301C2211yescharacteristic
35C2×#13063300C2211yescharacteristic
36C2×#13063299—21no—
37C2×#13063299C2211yescharacteristic
38C2×#13063299C2211yescharacteristic
39C2×Q8×Dic43C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×C4×C22⋊D43—21no—
42C2×C4×C22⋊D43C2211yescharacteristic
43C2×C4⋊C4×D43C2211yescharacteristic
44#14583260C2218yescomplemented
45#14583233C2218yescomplemented
46#14583212C2218yescomplemented
47#14583192C2218yescomplemented
48#14583148C2218yescomplemented
49#14583135C2218yescomplemented
50#14583117C2218yescomplemented
51#14583047C2218yescomplemented
52#14583038C2218yescomplemented
53#14583002C2218yescomplemented
54#14582970C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59#14582899C2218yescomplemented
60C2×#13063249C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C23×Q8×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C22×C4⋊C4×C43C2211yescharacteristic
72C2×#103×C43C2211yescharacteristic
73C2×#103×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2218yescomplemented
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C2×#10621898—28no—
82C2×#10621898—48no—
83C22×Dic86—21no—
84C22×D172—21no—
85C22×D172—21no—
86C22×D172C2311yescharacteristic
87C22×D172C2311yescharacteristic
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43D411yescharacteristic
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43C2311yescharacteristic
95C2×#10621884—24no—
96C2×#10621884—42no—
97C2×#10621884C2314yes—
98C2×#10621884C2314yes—
99C2×D344—42no—
100C2×D344C2314yes—
101C2×#10621872—42no—
102C2×#10621872C2314yes—
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105#13063324—22no—
106#13063324C2314yes—
107#13063314—28no—
108#13063314—22no—
109#13063314C2314yes—
110#13063310—28no—
111#13063308—28no—
112#13063303—28no—
113#13063301—22no—
114#13063301—28no—
115#13063301C2314yes—
116#13063300—22no—
117#13063300C2314yes—
118#13063299—22no—
119#13063299—22no—
120#13063299—28no—
121#13063299C2314yes—
122#13063299C2314yes—
123Q8×Dic43—22no—
124Q8×Dic43C2314yes—
125#13063287—22no—
126#13063287C2314yes—
127C4×C22⋊D43—28no—
128C4×C22⋊D43D414yes—
129C4×C22⋊D43C2314yes—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4D411yescharacteristic
137C4⋊C4×D43—22no—
138C4⋊C4×D43C2314yes—
139C2×C22⋊Dic43D411yescharacteristic
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4D411yescharacteristic
148C2×C4×Dic43—21no—
149C2×C4×Dic43C2311yescharacteristic
150#13063259C2314yes—
151#13063258C2314yes—
152#13063258C2314yes—
153Dic43⋊C8C2314yes—
154#13063249C2314yes—
155#13063249C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063245C2314yes—
159#13063245C2314yes—
160C22⋊(C43⋊C8)C2314yes—
161(C2×D43)⋊C8C2314yes—
162#13063235C2314yes—
163C22×Q8×C43—22no—
164C22×Q8×C43—21no—
165C22×Q8×C43—24no—
166C22×Q8×C43—42no—
167C22×Q8×C43C2311yescharacteristic
168C22×Q8×C43C2314yes—
169C22×Q8×C43C2311yescharacteristic
170C23×C4×C43—21no—
171C23×C4×C43—21no—
172C23×C4×C43C2311yescharacteristic
173C22×C8×C43—42no—
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2311yescharacteristic
176C22×C8×C43C2314yes—
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43—22no—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C4⋊C4×C43C2314yes—
182#103×C43C2314yes—
183#103×C43C2314yes—
184#103×C43C2314yes—
185#103×C43C2314yes—
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C23×D43—21no—
189C23×D43C2×D411yescharacteristic
190C2×Q8×C43—21no—
191C2×Q8×C43—24no—
192C2×Q8×C43—21no—
193C2×Q8×C43—22no—
194C2×Q8×C43—28no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43—44no—
198C2×Q8×C43—44no—
199C2×Q8×C43—48no—
200C2×Q8×C43#4114yescomplemented
201C2×Q8×C43C2412yes—
202C2×Q8×C43C2412yes—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—24no—
209C22×C4×C43—21no—
210C22×C4×C43—24no—
211C22×C4×C43—44no—
212C22×C4×C43—44no—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—44no—
221C2×C22⋊D43—44no—
222C2×C22⋊D43C2×D414yes—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228#10621902—28no—
229#10621902—44no—
230#10621902—48no—
231#10621898—432no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—24no—
235C2×D172—24no—
236C2×D172—22no—
237C2×D172—22no—
238C2×D172—22no—
239C2×D172—22no—
240C2×D172—44no—
241C2×D172—44no—
242C2×D172C2412yes—
243C2×D172C2412yes—
244C2×C4×D43—22no—
245C2×C4×D43—22no—
246C2×C4×D43—24no—
247C2×C4×D43—24no—
248C2×C4×D43—24no—
249C2×C4×D43—44no—
250C2×C4×D43—44no—
251C2×C4×D43—44no—
252C2×C4×D43C2×D412yes—
253C2×C4×D43C2412yes—
254C2×Dic86—24no—
255C2×Dic86—44no—
256C2×C8×C43—22no—
257C2×C8×C43—22no—
258C2×C8×C43—44no—
259C2×C8×C43C2412yes—
260C2×C8×C43C2412yes—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—24no—
264C4⋊C4×C43C2412yes—
265C4⋊C4×C43C2412yes—
266C22⋊Dic43C2×D414yes—
267#10621884—28no—
268#10621884—44no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4C2×D414yes—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—24no—
280C4⋊Dic43C2412yes—
281C4⋊Dic43C2412yes—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285Dic43⋊C4C2×D414yes—
286C4×Dic43—24no—
287C4×Dic43C2×D412yes—
288C4×Dic43C2412yes—
289C2×C43⋊C8—22no—
290C2×C43⋊C8—22no—
291C2×C43⋊C8C2412yes—
292C2×C43⋊C8C2412yes—
293D344—44no—
294#10621872—44no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43AGL(1,ℤ/8)14yes—
298C23×C43C22×D412yes—
299C23×C43C22×D411yescharacteristic
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43C22×D412yes—
312Q8×C43—24no—
313Q8×C43—22no—
314Q8×C43—22no—
315Q8×C43—22no—
316Q8×C43—48no—
317Q8×C43—42no—
318Q8×C43C2×#4114yescomplemented
319C2×C4×C43—24no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—24no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—48no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43—48no—
333C2×C4×C43C22×D412yes—
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C2×#4112yes—
336C2×C4×C43H(5,𝔽2)12yes—
337C2×C4×C43C2511yescharacteristic
338C22⋊D43—28no—
339C22⋊D43—48no—
340C22⋊D43—48no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350C2×Dic43C22×D412yes—
351D172—22no—
352D172—22no—
353D172—22no—
354D172—22no—
355D172—48no—
356D172—48no—
357D172—42no—
358D172—42no—
359C4×D43—24no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—48no—
363C4×D43—48no—
364C4×D43—48no—
365Dic86—48no—
366C8×C43—22no—
367C8×C43—22no—
368C43⋊C8—22no—
369C43⋊C8—22no—
370C2×#3308—431nomaximal, Sylow
371C22×C43—22no—
372C22×C43—28no—
373C22×C43—22no—
374C22×C43#54612yes—
375C22×C43C2×AGL(1,ℤ/8)14yes—
376C22×C43C2×AGL(1,ℤ/8)12yes—
377C22×C43#57812yes—
378C22×C43C23×D411yescharacteristic
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—44no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—84no—
390C2×D43—84no—
391C4×C43—24no—
392C4×C43—22no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43—42no—
396C4×C43#54612yes—
397C4×C43C22×#4111yescharacteristic
398C4×C43C2×H(5,𝔽2)11yescharacteristic
399Dic43—22no—
400Dic43—22no—
401Dic43—22no—
402Dic43—42no—
403Dic43—42no—
404C2×#548—431no—
405C2×#547—431no—
406#3308—4316no—
407C2×#489—431no—
408C2×#484—431no—
409C2×#480—431no—
410C2×#477—431no—
411C2×#468—431no—
412C2×#466—431no—
413C2×#463—431no—
414C2×#449—431no—
415C2×#448—431no—
416C2×#440—431no—
417C2×#435—431no—
418C2×#417—431no—
419C22×#103D4311yescharacteristic, complemented
420C2×C43—24no—
421C2×C43#330814yescomplemented
422C2×C43C2×#54611yescharacteristic
423C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
424C2×C43C2×#57811yescharacteristic
425D43—42no—
426D43—82no—
427D43—82no—
428C22×#41—431no—
429C22×#41—861no—
430C23×Q8C2×D4311yescharacteristic
431C22×SD16—431no—
432C22×SD16—431no—
433C22×D8—431no—
434C22×M16—431no—
435C23×C8C2×D4311yescharacteristic
436#548—438no—
437#548—864no—
438#547—438no—
439#547—864no—
440C2×C4⋊Q8—431no—
441C2×#124—431no—
442C2×#124—861no—
443C2×#123—861no—
444C2×#123—861no—
445C2×C22⋊Q8—431no—
446C2×C22⋊Q8—861no—
447C2×C22⋊Q8—861no—
448C2×#121—431no—
449C2×#121—431no—
450C2×#121—431no—
451C2×#121—861no—
452C2×C4×Q8—431no—
453C2×C4×D4—431no—
454C2×C4×D4—431no—
455C2×C4×D4—861no—
456C22×C4⋊C4—431no—
457C22×C4⋊C4C2×D4311yescharacteristic
458#489—438no—
459#484—438no—
460#480—438no—
461#477—438no—
462#468—438no—
463#466—438no—
464#463—438no—
465#449—438no—
466#448—438no—
467#440—438no—
468#435—438no—
469C2×#107—431no—
470C2×#107—431no—
471C2×#107—431no—
472C2×C4⋊C8—431no—
473#417—438no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103C2×D4311yescharacteristic
477C2×#103C2×D4311yescharacteristic
478C2×#103C2×D4311yescharacteristic
479C2×#103C2×D4311yescharacteristic
480C2×#103C2×D4318yescomplemented
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×#102—431no—
485C2×C22⋊C8—431no—
486C2×C22⋊C8—431no—
487C2×#97—431no—
488C43C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—434no—
490C2×#41—868no—
491C2×#41—862no—
492C2×#41—864no—
493C2×#41—1728no—
494C2×#41—1722no—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—24no—
498C22×Q8—42no—
499C22×Q8—861no—
500C22×Q8C22×D4311yescharacteristic
501C22×Q8C22×D4314yes—
502C22×Q8C22×D4311yescharacteristic
503C22×D4—431no—
504C22×D4—431no—
505C22×D4—431no—
506C22×D4—861no—
507C22×D4—861no—
508C22×D4—861no—
509C22×D4—861no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—431no—
513C23×C4—861no—
514C23×C4—861no—
515C23×C4—861no—
516C23×C4C22×D4311yescharacteristic
517C2×SD16—434no—
518C2×SD16—434no—
519C2×SD16—864no—
520C2×SD16—1722no—
521C2×D8—434no—
522C2×D8—1722no—
523C2×M16—434no—
524C2×M16—1722no—
525C22×C8—42no—
526C22×C8—431no—
527C22×C8—431no—
528C22×C8C22×D4311yescharacteristic
529C22×C8C22×D4311yescharacteristic
530C22×C8C22×D4314yes—
531C4⋊Q8—434no—
532C4⋊Q8—862no—
533#124—434no—
534#124—862no—
535#124—868no—
536#123—868no—
537#123—868no—
538C22⋊Q8—434no—
539C22⋊Q8—868no—
540C22⋊Q8—868no—
541C22⋊Q8—862no—
542#121—434no—
543#121—434no—
544#121—434no—
545#121—862no—
546#121—868no—
547#121—862no—
548#121—862no—
549C4×Q8—434no—
550C4×Q8—862no—
551C4×D4—434no—
552C4×D4—434no—
553C4×D4—434no—
554C4×D4—862no—
555C4×D4—868no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—434no—
562C2×C4⋊C4—862no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C4⋊C4C22×D4314yes—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C42—431no—
580C2×C42—861no—
581#107—434no—
582#107—434no—
583#107—434no—
584C4⋊C8—434no—
585#103—434no—
586#103—434no—
587#103C22×D4314yes—
588#103C22×D4314yes—
589#103C22×D4314yes—
590#103C22×D4314yes—
591#102—434no—
592#102—434no—
593#102—434no—
594#102—434no—
595C22⋊C8—434no—
596C22⋊C8—434no—
597#97—434no—
598C24—431no—
599C24—861no—
600C24—861no—
601C24D4×D4311yescharacteristic
602#41—868no—
603#41—17232no—
604#41—1724no—
605#41—1728no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—28no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—48no—
616C2×Q8—864no—
617C2×Q8—1724no—
618C2×Q8#1062189814yescomplemented
619C2×Q8C23×D4312yes—
620C2×Q8C23×D4312yes—
621C2×D4—434no—
622C2×D4—432no—
623C2×D4—432no—
624C2×D4—864no—
625C2×D4—864no—
626C2×D4—864no—
627C2×D4—864no—
628C2×D4—864no—
629C2×D4—861no—
630C2×D4—861no—
631C2×D4—862no—
632C2×D4—862no—
633C2×D4—862no—
634C2×D4—862no—
635C2×D4—1724no—
636C2×D4—1724no—
637C2×D4—1724no—
638C2×D4—1724no—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—431no—
650C22×C4—431no—
651C22×C4—431no—
652C22×C4—432no—
653C22×C4—432no—
654C22×C4—864no—
655C22×C4—864no—
656C22×C4—864no—
657C22×C4—862no—
658C22×C4—862no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—1724no—
662C22×C4—1724no—
663C22×C4—1724no—
664C22×C4D4×D4312yes—
665C22×C4D4×D4311yescharacteristic
666C22×C4C23×D4312yes—
667C22×C4C23×D4311yescharacteristic
668SD16—868no—
669SD16—1724no—
670D8—1724no—
671M16—1724no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—44no—
675C2×C8—432no—
676C2×C8—432no—
677C2×C8—862no—
678C2×C8—862no—
679C2×C8C23×D4312yes—
680C2×C8C23×D4312yes—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—24no—
684C4⋊C4—434no—
685C4⋊C4—432no—
686C4⋊C4—432no—
687C4⋊C4—864no—
688C4⋊C4—864no—
689C4⋊C4—864no—
690C4⋊C4—864no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4C23×D4312yes—
694C4⋊C4C23×D4312yes—
695C22⋊C4—434no—
696C22⋊C4—434no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C42—432no—
705C42—432no—
706C42—864no—
707C23—22no—
708C23—22no—
709C23—432no—
710C23—862no—
711C23—862no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—1722no—
716C23—1722no—
717C23—1722no—
718C23—1722no—
719C23—1722no—
720C23—1722no—
721C23#1306335214yes—
722C23C2×D4×D4312yes—
723C23C2×D4×D4311yescharacteristic
724Q8—22no—
725Q8—24no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—42no—
730Q8—1728no—
731Q8C2×#1062189814yescomplemented
732D4—868no—
733D4—862no—
734D4—862no—
735D4—862no—
736D4—862no—
737D4—1728no—
738D4—1728no—
739D4—1728no—
740D4—1728no—
741D4—1722no—
742D4—1722no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—48no—
756C2×C4—42no—
757C2×C4—432no—
758C2×C4—432no—
759C2×C4—432no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—864no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—1728no—
769C2×C4—1728no—
770C2×C4—1728no—
771C2×C4—1722no—
772C2×C4—1722no—
773C2×C4C2×D4×D4312yes—
774C2×C4C2×D4×D4311yescharacteristic
775C2×C4C2×#1062189812yes—
776C2×C4#1306337012yes—
777C2×C4C24×D4311yescharacteristic
778C8—22no—
779C8—22no—
780C8—862no—
781C8—862no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—862no—
786C22—862no—
787C22—862no—
788C22—3444no—
789C22—3444no—
790C22—1722no—
791C22—1722no—
792C22—1722no—
793C22—1722no—
794C22—1722no—
795C22—1722no—
796C22—1724no—
797C22#1458353912yes—
798C22C2×#1306335214yes—
799C22C2×#1306335212yes—
800C22#1458371212yes—
801C22C22×D4×D4311yescharacteristic
802C4—22no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—862no—
808C4—862no—
809C4—862no—
810C4—1722no—
811C4—1722no—
812C4#1458353912yes—
813C4C22×#1062189811yescharacteristic
814C4C2×#1306337011yescharacteristic
815C2—24no—
816C2—3442no—
817C2—3442no—
818C2—1722no—
819C2#1914658214yesdirect product factor
820C2C2×#1458353911yescharacteristic
821C2C22×#1306335211yescharacteristic
822C2C2×#1458371211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#103×C43C2
socleC23×C43C22×D4
hypercenterC22×#103D43
hypocenterC43C2×#3308
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×#14583560C2semidirect
2. C2×#14583550C2semidirect
3. #19146582C2direct (N × H)
4. C2×#14583260C2semidirect
5. C2×#14583233C2semidirect
6. C2×#14583212C2semidirect
7. C2×#14583192C2semidirect
8. C2×#14583148C2semidirect
9. C2×#14583135C2semidirect
10. C2×#14583117C2semidirect
11. C2×#14583047C2semidirect
12. C2×#14583038C2semidirect
13. C2×#14583002C2semidirect
14. C2×#14582970C2semidirect
15. C2×#14582899C2semidirect
16. C22×#103×C43C2semidirect
24. #14583560C22semidirect
26. #14583550C22semidirect
44. #14583260C22semidirect
45. #14583233C22semidirect
46. #14583212C22semidirect
47. #14583192C22semidirect
48. #14583148C22semidirect
49. #14583135C22semidirect
50. #14583117C22semidirect
51. #14583047C22semidirect
52. #14583038C22semidirect
53. #14583002C22semidirect
54. #14582970C22semidirect
59. #14582899C22semidirect
76. C2×#103×C43C22semidirect
200. C2×Q8×C43#41semidirect
318. Q8×C43C2×#41semidirect
419. C22×#103D43semidirect
421. C2×C43#3308semidirect
480. C2×#103C2×D43semidirect
488. C43C2×#3308semidirect
618. C2×Q8#10621898semidirect
731. Q8C2×#10621898semidirect
819. C2#19146582direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835602
C2×#145835502
#191465822
C2×#145832602
C2×#145832332
C2×#145832122
C2×#145831922
C2×#145831482
C2×#145831352
C2×#145831172
C2×#145830472
C2×#145830382
C2×#145830022
C2×#145829702
C2×#145828992
C22×#103×C432
C2×#330843