Finite Group Databasebeta

← C2×#19146586 #25973171

Subgroups — C2×#19146586 #25973171

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×#14583553C211yesmaximal, characteristic, complemented
2#19146586C2116yesmaximal, direct product factor
3C2×#14583258C211yesmaximal, characteristic, complemented
4C2×#14583232C211yesmaximal, characteristic, complemented
5C2×#14583210C211yesmaximal, characteristic, complemented
6C2×#14583194C211yesmaximal, characteristic, complemented
7C2×#14583147C211yesmaximal, characteristic, complemented
8C2×#14583133C211yesmaximal, characteristic, complemented
9C2×#14583111C211yesmaximal, characteristic, complemented
10C2×#14583044C211yesmaximal, characteristic, complemented
11C2×#14583038C211yesmaximal, characteristic, complemented
12C2×#14582997C211yesmaximal, characteristic, complemented
13C2×#14582971C211yesmaximal, characteristic, complemented
14C2×#14582900C211yesmaximal, characteristic, complemented
15C22×#13063249C211yesmaximal, characteristic, complemented
16C2×C43×#548C211yesmaximal, characteristic, complemented
17C22×#10621900—21no—
18C22×#10621884C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621877C2211yescharacteristic
22C23×C43⋊C8C2211yescharacteristic
23#14583553—24no—
24#14583553C2218yescomplemented
25C2×#13063325C2211yescharacteristic
26C2×#13063309—21no—
27C2×#13063309—21no—
28C2×#13063305—21no—
29C2×#13063299C2211yescharacteristic
30C2×#13063299C2211yescharacteristic
31C2×C4×D172C2211yescharacteristic
32C22×C4⋊Dic43C2211yescharacteristic
33C22×C4⋊Dic43C2211yescharacteristic
34#14583258C2218yescomplemented
35#14583232C2218yescomplemented
36#14583210C2218yescomplemented
37#14583194C2218yescomplemented
38#14583147C2218yescomplemented
39#14583133C2218yescomplemented
40#14583111C2218yescomplemented
41#14583044C2218yescomplemented
42#14583038C2218yescomplemented
43#14582997C2218yescomplemented
44#14582971C2218yescomplemented
45C2×#13063258C2211yescharacteristic
46C2×#13063258C2211yescharacteristic
47C2×#13063258C2211yescharacteristic
48C2×C4⋊(C43⋊C8)C2211yescharacteristic
49#14582900C2218yescomplemented
50C2×#13063249C2211yescharacteristic
51C2×#13063249C2211yescharacteristic
52C2×#13063249C2211yescharacteristic
53C2×#13063249C2211yescharacteristic
54C2×#13063249C2211yescharacteristic
55C2×#13063249C2211yescharacteristic
56C2×#13063249C2218yescomplemented
57C2×#13063246C2211yescharacteristic
58C2×#13063246C2211yescharacteristic
59C2×#13063246C2211yescharacteristic
60C2×#13063245C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C22⋊(C43⋊C8)C2211yescharacteristic
63C2×#13063236C2211yescharacteristic
64C22×#41×C43C2211yescharacteristic
65C23×Q8×C43C2211yescharacteristic
66C43×#548—24no—
67C43×#548C2218yescomplemented
68C2×#124×C43—21no—
69C2×#124×C43C2211yescharacteristic
70C2×C22⋊Q8×C43—21no—
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×#121×C43—21no—
73C2×#121×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic
75C2×C4×D4×C43—21no—
76C2×C4×D4×C43C2211yescharacteristic
77C2×#10621900—28no—
78C2×#10621900—48no—
79C22×Dic86—21no—
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C23×Dic43—21no—
84C23×Dic43—21no—
85C22×C4×D43—21no—
86C2×#10621884—24no—
87C2×#10621884—42no—
88C2×#10621884C2314yes—
89C2×#10621884C2314yes—
90C2×#10621882—42no—
91C2×#10621882C2314yes—
92C2×#10621877—42no—
93C2×#10621877C2314yes—
94C22×C43⋊C8—42no—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2314yes—
100#13063325—22no—
101#13063325C2314yes—
102#13063309—28no—
103#13063309—28no—
104#13063305—28no—
105#13063299—22no—
106#13063299—22no—
107#13063299C2314yes—
108#13063299C2314yes—
109C4×D172—22no—
110C4×D172C2314yes—
111C2×C4⋊Dic43—22no—
112C2×C4⋊Dic43—22no—
113C2×C4⋊Dic43—21no—
114C2×C4⋊Dic43—21no—
115C2×C4⋊Dic43—21no—
116C2×C4⋊Dic43C2314yes—
117C2×C4⋊Dic43C2314yes—
118C2×C4⋊Dic43C2311yescharacteristic
119C2×C4⋊Dic43C2311yescharacteristic
120C2×C4⋊Dic43C2311yescharacteristic
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124#13063258C2314yes—
125#13063258C2314yes—
126#13063258C2314yes—
127C4⋊(C43⋊C8)C2314yes—
128#13063249C2314yes—
129#13063249C2314yes—
130#13063249C2314yes—
131#13063249C2314yes—
132#13063249C2314yes—
133#13063249C2314yes—
134#13063246C2314yes—
135#13063246C2314yes—
136#13063246C2314yes—
137#13063245C2314yes—
138C22⋊(C43⋊C8)C2314yes—
139C22⋊(C43⋊C8)C2314yes—
140#13063236C2314yes—
141C2×#41×C43—22no—
142C2×#41×C43—24no—
143C2×#41×C43—42no—
144C2×#41×C43C2314yes—
145C22×Q8×C43—21no—
146C22×Q8×C43—22no—
147C22×Q8×C43—24no—
148C22×Q8×C43—42no—
149C22×Q8×C43C2311yescharacteristic
150C22×Q8×C43C2314yes—
151C22×Q8×C43C2311yescharacteristic
152C22×D4×C43—21no—
153C22×D4×C43—21no—
154C22×D4×C43D411yescharacteristic
155C22×D4×C43C2311yescharacteristic
156C23×C4×C43—21no—
157C23×C4×C43—21no—
158C23×C4×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160#124×C43—28no—
161#124×C43—22no—
162#124×C43C2314yes—
163C22⋊Q8×C43—22no—
164C22⋊Q8×C43—28no—
165C22⋊Q8×C43C2314yes—
166#121×C43—28no—
167#121×C43—22no—
168#121×C43C2314yes—
169C4×Q8×C43—22no—
170C4×Q8×C43C2314yes—
171C4×D4×C43—28no—
172C4×D4×C43D414yes—
173C4×D4×C43C2314yes—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43D411yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182C2×C22⋊C4×C43D411yescharacteristic
183C2×C22⋊C4×C43D411yescharacteristic
184C2×C42×C43—21no—
185C2×C42×C43C2311yescharacteristic
186C24×C43—21no—
187C24×C43C2×D411yescharacteristic
188C24×C43C2×D411yescharacteristic
189C23×D43—21no—
190#41×C43—28no—
191#41×C43—44no—
192#41×C43—48no—
193C2×Q8×C43—21no—
194C2×Q8×C43—24no—
195C2×Q8×C43—21no—
196C2×Q8×C43—22no—
197C2×Q8×C43—28no—
198C2×Q8×C43—22no—
199C2×Q8×C43—22no—
200C2×Q8×C43—44no—
201C2×Q8×C43—44no—
202C2×Q8×C43—48no—
203C2×Q8×C43#4114yescomplemented
204C2×Q8×C43C2412yes—
205C2×Q8×C43C2412yes—
206C2×D4×C43—21no—
207C2×D4×C43—24no—
208C2×D4×C43—24no—
209C2×D4×C43—24no—
210C2×D4×C43—22no—
211C2×D4×C43—22no—
212C2×D4×C43—44no—
213C2×D4×C43—44no—
214C2×D4×C43C2×D414yes—
215C2×D4×C43C2412yes—
216C22×C4×C43—22no—
217C22×C4×C43—22no—
218C22×C4×C43—22no—
219C22×C4×C43—22no—
220C22×C4×C43—24no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—24no—
225C22×C4×C43—44no—
226C22×C4×C43—44no—
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D412yes—
232C22×C4×C43C2×D412yes—
233C22×C4×C43C2412yes—
234C22×C4×C43C2412yes—
235C22×C4×C43C2411yescharacteristic
236C2×C22⋊D43—24no—
237C2×C22⋊D43—24no—
238C2×C22⋊D43—44no—
239C2×C22⋊D43—44no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—24no—
244C22×Dic43—24no—
245C22×Dic43—44no—
246C22×Dic43—44no—
247#10621900—432no—
248C2×D172—21no—
249C2×D172—22no—
250C2×D172—22no—
251C2×D172C2412yes—
252C2×C4×D43—24no—
253C2×C4×D43—44no—
254C2×Dic86—24no—
255C2×Dic86—44no—
256C4⋊C4×C43—24no—
257C4⋊C4×C43—24no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43C2×D414yes—
260C4⋊C4×C43C2412yes—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—24no—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—24no—
265C22⋊C4×C43C2×D414yes—
266C22⋊C4×C43C2×D414yes—
267C42×C43—24no—
268C42×C43C2×D412yes—
269C42×C43C2412yes—
270#10621884—28no—
271#10621884—44no—
272#10621882—44no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—24no—
280C4⋊Dic43—24no—
281C4⋊Dic43—24no—
282C4⋊Dic43C2412yes—
283C4⋊Dic43C2412yes—
284C4⋊Dic43C2412yes—
285#10621877—44no—
286C2×C43⋊C8—22no—
287C2×C43⋊C8—22no—
288C2×C43⋊C8—22no—
289C2×C43⋊C8—22no—
290C2×C43⋊C8—44no—
291C2×C43⋊C8C2412yes—
292C2×C43⋊C8C2412yes—
293C2×C43⋊C8C2412yes—
294C2×C43⋊C8C2412yes—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—42no—
302C23×C43—42no—
303C23×C43—42no—
304C23×C43AGL(1,ℤ/8)14yes—
305C23×C43C22×D412yes—
306C23×C43C22×D412yes—
307C23×C43C22×D411yescharacteristic
308C22×D43—22no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43—42no—
312Q8×C43—24no—
313Q8×C43—22no—
314Q8×C43—22no—
315Q8×C43—22no—
316Q8×C43—48no—
317Q8×C43—42no—
318Q8×C43C2×#4114yescomplemented
319D4×C43—28no—
320D4×C43—22no—
321D4×C43—22no—
322D4×C43—48no—
323D4×C43—48no—
324D4×C43—42no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—24no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—24no—
332C2×C4×C43—24no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—48no—
340C2×C4×C43—48no—
341C2×C4×C43—42no—
342C2×C4×C43—42no—
343C2×C4×C43C22×D412yes—
344C2×C4×C43C22×D412yes—
345C2×C4×C43C22×D412yes—
346C2×C4×C43C22×D412yes—
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C2×#4112yes—
349C2×C4×C43H(5,𝔽2)12yes—
350C2×C4×C43C2511yescharacteristic
351C22⋊D43—48no—
352C22⋊D43—48no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—48no—
357C2×Dic43—42no—
358C2×Dic43—42no—
359C2×Dic43—42no—
360C2×Dic43—48no—
361D172—22no—
362D172—22no—
363D172—42no—
364C4×D43—48no—
365Dic86—48no—
366C43⋊C8—22no—
367C43⋊C8—22no—
368C43⋊C8—22no—
369C43⋊C8—22no—
370C2×#3308—431nomaximal, Sylow
371C22×C43—22no—
372C22×C43—28no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—44no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—84no—
382C22×C43#54612yes—
383C22×C43C2×AGL(1,ℤ/8)14yes—
384C22×C43C2×AGL(1,ℤ/8)12yes—
385C22×C43#57812yes—
386C22×C43C23×D411yescharacteristic
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—84no—
391C4×C43—22no—
392C4×C43—22no—
393C4×C43—24no—
394C4×C43—22no—
395C4×C43—22no—
396C4×C43—42no—
397C4×C43—42no—
398C4×C43#54612yes—
399C4×C43C22×#4111yescharacteristic
400C4×C43C2×H(5,𝔽2)11yescharacteristic
401Dic43—42no—
402Dic43—42no—
403Dic43—42no—
404C2×#548D4311yescharacteristic, complemented
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×#103—431no—
420C2×C43—24no—
421C2×C43—42no—
422C2×C43—82no—
423C2×C43#330814yescomplemented
424C2×C43C2×#54611yescharacteristic
425C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
426C2×C43C2×#57811yescharacteristic
427D43—82no—
428C22×#41—861no—
429C22×#41C2×D4311yescharacteristic
430C23×Q8C2×D4311yescharacteristic
431C22×SD16—431no—
432C22×SD16—431no—
433C22×D8—431no—
434C22×M16—431no—
435C23×C8—431no—
436#548—24no—
437#548C2×D4318yescomplemented
438#547—438no—
439#547—864no—
440C2×C4⋊Q8—431no—
441C2×#124—21no—
442C2×#124C2×D4311yescharacteristic
443C2×#123—861no—
444C2×#123—861no—
445C2×C22⋊Q8—21no—
446C2×C22⋊Q8—861no—
447C2×C22⋊Q8C2×D4311yescharacteristic
448C2×#121—21no—
449C2×#121—431no—
450C2×#121—431no—
451C2×#121C2×D4311yescharacteristic
452C2×C4×Q8C2×D4311yescharacteristic
453C2×C4×D4—21no—
454C2×C4×D4—431no—
455C2×C4×D4C2×D4311yescharacteristic
456C22×C4⋊C4—431no—
457C22×C4⋊C4—431no—
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×#103—431no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103—431no—
480C2×#103—438no—
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—22no—
490C2×#41—24no—
491C2×#41—42no—
492C2×#41—868no—
493C2×#41—1728no—
494C2×#41C22×D4314yes—
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—21no—
504C22×D4—21no—
505C22×D4—431no—
506C22×D4—861no—
507C22×D4—861no—
508C22×D4C22⋊D4311yescharacteristic
509C22×D4C22×D4311yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—861no—
513C23×C4—861no—
514C23×C4—861no—
515C23×C4C22×D4311yescharacteristic
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—431no—
526C22×C8—431no—
527C22×C8—431no—
528C22×C8—431no—
529C22×C8—434no—
530C22×C8—1722no—
531C4⋊Q8—434no—
532C4⋊Q8—862no—
533#124—28no—
534#124—22no—
535#124C22×D4314yes—
536#123—868no—
537#123—868no—
538C22⋊Q8—22no—
539C22⋊Q8—28no—
540C22⋊Q8—868no—
541C22⋊Q8C22×D4314yes—
542#121—28no—
543#121—22no—
544#121—434no—
545#121—434no—
546#121—862no—
547#121—862no—
548#121C22×D4314yes—
549C4×Q8—22no—
550C4×Q8C22×D4314yes—
551C4×D4—28no—
552C4×D4—434no—
553C4×D4—862no—
554C4×D4C22⋊D4314yes—
555C4×D4C22×D4314yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—434no—
562C2×C4⋊C4—434no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—862no—
566C2×C4⋊C4—862no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4C22⋊D4311yescharacteristic
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4C22⋊D4311yescharacteristic
578C2×C22⋊C4C22⋊D4311yescharacteristic
579C2×C42—21no—
580C2×C42C22×D4311yescharacteristic
581#107—434no—
582#107—434no—
583#107—434no—
584C4⋊C8—434no—
585#103—434no—
586#103—434no—
587#103—434no—
588#103—434no—
589#103—434no—
590#103—434no—
591#102—434no—
592#102—434no—
593#102—434no—
594#102—434no—
595C22⋊C8—434no—
596C22⋊C8—434no—
597#97—434no—
598C24—21no—
599C24—861no—
600C24C2×C22⋊D4311yescharacteristic
601C24C2×C22⋊D4311yescharacteristic
602#41—28no—
603#41—44no—
604#41—48no—
605#41—17232no—
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#1062190014yescomplemented
619C2×Q8C23×D4312yes—
620C2×Q8C23×D4312yes—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—432no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—861no—
633C2×D4—862no—
634C2×D4—862no—
635C2×D4—1724no—
636C2×D4—1724no—
637C2×D4C2×C22⋊D4314yes—
638C2×D4C23×D4312yes—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—24no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—864no—
651C22×C4—864no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—864no—
656C22×C4—1724no—
657C22×C4—1724no—
658C22×C4—1724no—
659C22×C4C2×C22⋊D4312yes—
660C22×C4C2×C22⋊D4312yes—
661C22×C4C2×C22⋊D4311yescharacteristic
662C22×C4C2×C22⋊D4311yescharacteristic
663C22×C4C2×C22⋊D4311yescharacteristic
664C22×C4C2×C22⋊D4311yescharacteristic
665C22×C4C23×D4312yes—
666C22×C4C23×D4312yes—
667C22×C4C23×D4311yescharacteristic
668SD16—868no—
669SD16—1724no—
670D8—1724no—
671M16—1724no—
672C2×C8—432no—
673C2×C8—432no—
674C2×C8—432no—
675C2×C8—432no—
676C2×C8—862no—
677C2×C8—862no—
678C2×C8—862no—
679C2×C8—862no—
680C2×C8—1724no—
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—21no—
684C4⋊C4—432no—
685C4⋊C4—432no—
686C4⋊C4—432no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—864no—
691C4⋊C4—864no—
692C4⋊C4—864no—
693C4⋊C4C2×C22⋊D4314yes—
694C4⋊C4C23×D4312yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4C2×C22⋊D4314yes—
703C22⋊C4C2×C22⋊D4314yes—
704C42—24no—
705C42C2×C22⋊D4312yes—
706C42C23×D4312yes—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—862no—
717C23—1722no—
718C23—1722no—
719C23—1722no—
720C23#1306335014yes—
721C23C22×C22⋊D4312yes—
722C23C22×C22⋊D4312yes—
723C23C22×C22⋊D4311yescharacteristic
724Q8—22no—
725Q8—24no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—42no—
730Q8—1728no—
731Q8C2×#1062190014yescomplemented
732D4—28no—
733D4—22no—
734D4—22no—
735D4—48no—
736D4—48no—
737D4—42no—
738D4—862no—
739D4—862no—
740D4—1728no—
741D4—1728no—
742D4—1722no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—48no—
758C2×C4—48no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—1728no—
765C2×C4—1728no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4—1728no—
770C2×C4C22×C22⋊D4312yes—
771C2×C4C22×C22⋊D4312yes—
772C2×C4C22×C22⋊D4312yes—
773C2×C4C22×C22⋊D4312yes—
774C2×C4C22×C22⋊D4311yescharacteristic
775C2×C4C2×#1062190012yes—
776C2×C4#1306337012yes—
777C2×C4C24×D4311yescharacteristic
778C8—862no—
779C8—862no—
780C8—862no—
781C8—862no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—84no—
793C22—3444no—
794C22—1722no—
795C22—1722no—
796C22—1722no—
797C22#1458354312yes—
798C22C2×#1306335014yes—
799C22C2×#1306335012yes—
800C22#1458371412yes—
801C22C23×C22⋊D4311yescharacteristic
802C4—22no—
803C4—22no—
804C4—24no—
805C4—22no—
806C4—22no—
807C4—42no—
808C4—42no—
809C4—1722no—
810C4—1722no—
811C4—1722no—
812C4#1458354312yes—
813C4C22×#1062190011yescharacteristic
814C4C2×#1306337011yescharacteristic
815C2—24no—
816C2—42no—
817C2—82no—
818C2—3442no—
819C2#1914658614yesdirect product factor
820C2C2×#1458354311yescharacteristic
821C2C22×#1306335011yescharacteristic
822C2C2×#1458371411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#548C2
socleC23×C43C22×D4
hypercenterC2×#548D43
hypocenterC43C2×#3308
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#14583553C2semidirect
2. #19146586C2direct (N × H)
3. C2×#14583258C2semidirect
4. C2×#14583232C2semidirect
5. C2×#14583210C2semidirect
6. C2×#14583194C2semidirect
7. C2×#14583147C2semidirect
8. C2×#14583133C2semidirect
9. C2×#14583111C2semidirect
10. C2×#14583044C2semidirect
11. C2×#14583038C2semidirect
12. C2×#14582997C2semidirect
13. C2×#14582971C2semidirect
14. C2×#14582900C2semidirect
15. C22×#13063249C2semidirect
16. C2×C43×#548C2semidirect
24. #14583553C22semidirect
34. #14583258C22semidirect
35. #14583232C22semidirect
36. #14583210C22semidirect
37. #14583194C22semidirect
38. #14583147C22semidirect
39. #14583133C22semidirect
40. #14583111C22semidirect
41. #14583044C22semidirect
42. #14583038C22semidirect
43. #14582997C22semidirect
44. #14582971C22semidirect
49. #14582900C22semidirect
56. C2×#13063249C22semidirect
67. C43×#548C22semidirect
203. C2×Q8×C43#41semidirect
318. Q8×C43C2×#41semidirect
404. C2×#548D43semidirect
423. C2×C43#3308semidirect
437. #548C2×D43semidirect
488. C43C2×#3308semidirect
618. C2×Q8#10621900semidirect
731. Q8C2×#10621900semidirect
819. C2#19146586direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835532
#191465862
C2×#145832582
C2×#145832322
C2×#145832102
C2×#145831942
C2×#145831472
C2×#145831332
C2×#145831112
C2×#145830442
C2×#145830382
C2×#145829972
C2×#145829712
C2×#145829002
C22×#130632492
C2×C43×#5482
C2×#330843