Finite Group Databasebeta

← C2×#19146135 #25971610

Subgroups — C2×#19146135 #25971610

Order 11008.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063352C211yesmaximal, characteristic, complemented
2C2×#14583568C211yesmaximal, characteristic, complemented
3C2×#14583537C211yesmaximal, characteristic, complemented
4#19146135C2116yesmaximal, direct product factor
5C2×#14583285C211yesmaximal, characteristic, complemented
6C2×#14583142C211yesmaximal, characteristic, complemented
7C2×#14583135C211yesmaximal, characteristic, complemented
8C2×#14583123C211yesmaximal, characteristic, complemented
9C2×#14583092C211yesmaximal, characteristic, complemented
10C2×#14583060C211yesmaximal, characteristic, complemented
11C2×#14583044C211yesmaximal, characteristic, complemented
12C2×#14583044C211yesmaximal, characteristic, complemented
13C2×#14583031C211yesmaximal, characteristic, complemented
14C2×#14583000C211yesmaximal, characteristic, complemented
15C2×#14582970C211yesmaximal, characteristic, complemented
16C22×#135×C43C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C2×#13063352—28no—
20C2×#13063352C2218yescomplemented
21C22×#10621884C2211yescharacteristic
22C22×#10621884C2211yescharacteristic, complemented
23C22×D344C2211yescharacteristic
24C22×#10621882C2211yescharacteristic
25C22×#10621882C2211yescharacteristic
26C22×#10621872C2211yescharacteristic
27#14583568—24no—
28#14583568C2218yescomplemented
29#14583537—24no—
30#14583537C2218yescomplemented
31C2×#13063321—21no—
32C2×#13063321C2211yescharacteristic, complemented
33C2×#13063314C2211yescharacteristic
34C2×#13063308—21no—
35C2×#13063301C2211yescharacteristic
36C2×#13063299—21no—
37C2×#13063299C2211yescharacteristic
38C2×#13063299C2211yescharacteristic, complemented
39C2×#13063297—21no—
40C2×#13063296—21no—
41C2×#13063296C2211yescharacteristic
42C2×#13063293—21no—
43C2×Q8×Dic43C2211yescharacteristic, complemented
44C2×D4×Dic43C2211yescharacteristic
45C2×C4×C22⋊D43—21no—
46C2×C4×C22⋊D43C2211yescharacteristic
47C22×(C2×D43)⋊C4—21no—
48#14583285C2218yescomplemented
49#14583142C2218yescomplemented
50#14583135C2218yescomplemented
51#14583123C2218yescomplemented
52#14583092C2218yescomplemented
53#14583060C2218yescomplemented
54#14583044C2218yescomplemented
55#14583044C2218yescomplemented
56#14583031C2218yescomplemented
57#14583000C2218yescomplemented
58#14582970C2218yescomplemented
59C2×#13063259C2211yescharacteristic, complemented
60C2×Dic43⋊C8C2211yescharacteristic, complemented
61C2×#13063249C2211yescharacteristic, complemented
62C2×#13063249C2211yescharacteristic, complemented
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic, complemented
65C2×#13063246C2211yescharacteristic
66C2×#13063246C2211yescharacteristic, complemented
67C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×#13063235C2211yescharacteristic, complemented
70C22×#41×C43C2211yescharacteristic
71C22×#41×C43C2211yescharacteristic, complemented
72C2×#135×C43—28no—
73C2×#135×C43C2218yescomplemented
74C22×Q16×C43C2211yescharacteristic, complemented
75C22×SD16×C43C2211yescharacteristic
76C22×SD16×C43C2211yescharacteristic, complemented
77C22×D8×C43C2211yescharacteristic
78C23×C8×C43C2211yescharacteristic, complemented
79C24×D43—21no—
80C2×#10621902—22no—
81C2×#10621902—24no—
82C2×#10621902—42no—
83C2×#10621902C2314yes—
84C22×D172—21no—
85C22×D172C2311yescharacteristic
86C22×D172C2311yescharacteristic
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43D411yescharacteristic
94C2×D4×D43—24no—
95C2×D4×D43—22no—
96C2×D4×D43—42no—
97C2×D4×D43C2314yes—
98C23×Dic43—21no—
99C22×C4×D43—21no—
100C22×C4×D43C2311yescharacteristic
101#13063352—232no—
102C2×#10621884—24no—
103C2×#10621884—42no—
104C2×#10621884C2314yes—
105C2×#10621884C2314yescomplemented
106C2×D344—24no—
107C2×D344C2314yes—
108C2×#10621882—24no—
109C2×#10621882—42no—
110C2×#10621882C2314yes—
111C2×#10621882C2314yes—
112C2×#10621872—24no—
113C2×#10621872C2314yes—
114C22×C43⋊C8C2311yescharacteristic
115C22×C43⋊C8C2311yescharacteristic
116#13063321—28no—
117#13063321—22no—
118#13063321C2314yescomplemented
119#13063314—22no—
120#13063314C2314yes—
121#13063308—28no—
122#13063301—22no—
123#13063301C2314yes—
124#13063299—22no—
125#13063299—22no—
126#13063299—28no—
127#13063299C2314yes—
128#13063299C2314yescomplemented
129#13063297—28no—
130#13063296—22no—
131#13063296—28no—
132#13063296C2314yes—
133#13063293—28no—
134Q8×Dic43—22no—
135Q8×Dic43C2314yescomplemented
136D4×Dic43—22no—
137D4×Dic43C2314yes—
138C4×C22⋊D43—28no—
139C4×C22⋊D43D414yes—
140C4×C22⋊D43C2314yes—
141C2×C4⋊Dic43—21no—
142C2×C4⋊Dic43C2311yescharacteristic
143C2×C4⋊Dic43C2311yescharacteristic
144C2×Dic43⋊C4—21no—
145C2×Dic43⋊C4D411yescharacteristic
146C2×C22⋊Dic43—21no—
147C2×C22⋊Dic43—21no—
148C2×C22⋊Dic43D411yescharacteristic
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4—28no—
155C2×(C2×D43)⋊C4D411yescharacteristic
156C2×C4×Dic43—21no—
157C2×C4×Dic43C2311yescharacteristic
158#13063259C2314yescomplemented
159Dic43⋊C8C2314yescomplemented
160#13063249C2314yescomplemented
161#13063249C2314yescomplemented
162#13063247C2314yes—
163#13063247C2314yescomplemented
164#13063246C2314yes—
165#13063246C2314yescomplemented
166C22⋊(C43⋊C8)C2314yescomplemented
167(C2×D43)⋊C8C2314yes—
168#13063235C2314yescomplemented
169C2×#41×C43—22no—
170C2×#41×C43—22no—
171C2×#41×C43—24no—
172C2×#41×C43—24no—
173C2×#41×C43—42no—
174C2×#41×C43—42no—
175C2×#41×C43C2314yes—
176C2×#41×C43C2314yescomplemented
177C22×Q8×C43C2311yescharacteristic
178C22×Q8×C43C2311yescharacteristic
179C22×D4×C43—21no—
180C22×D4×C43—21no—
181C22×D4×C43C2311yescharacteristic
182C22×D4×C43C2311yescharacteristic
183C23×C4×C43—21no—
184C23×C4×C43—21no—
185C23×C4×C43C2311yescharacteristic
186#135×C43—232no—
187C2×Q16×C43—24no—
188C2×Q16×C43C2314yescomplemented
189C2×SD16×C43—24no—
190C2×SD16×C43D418yescomplemented
191C2×SD16×C43C2314yes—
192C2×SD16×C43C2314yescomplemented
193C2×D8×C43—24no—
194C2×D8×C43C2314yes—
195C22×C8×C43—24no—
196C22×C8×C43C2311yescharacteristic
197C22×C8×C43C2311yescharacteristic
198C22×C8×C43C2314yescomplemented
199C24×C43—21no—
200C24×C43—21no—
201C24×C43C2×D411yescharacteristic
202C23×D43—21no—
203C23×D43—21no—
204C23×D43—24no—
205C23×D43—44no—
206C23×D43—44no—
207C23×D43—82no—
208C23×D43C2×D411yescharacteristic
209#41×C43—28no—
210#41×C43—28no—
211#41×C43—44no—
212#41×C43—44no—
213#41×C43—48no—
214#41×C43—48no—
215C2×Q8×C43—21no—
216C2×Q8×C43—21no—
217C2×Q8×C43—22no—
218C2×Q8×C43—22no—
219C2×Q8×C43—22no—
220C2×Q8×C43C2×D414yes—
221C2×Q8×C43C2412yes—
222C2×Q8×C43C2412yes—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—22no—
226C2×D4×C43—24no—
227C2×D4×C43—24no—
228C2×D4×C43—22no—
229C2×D4×C43—22no—
230C2×D4×C43—44no—
231C2×D4×C43—44no—
232C2×D4×C43C2×D414yes—
233C2×D4×C43C2412yes—
234C2×D4×C43C2412yes—
235C22×C4×C43—22no—
236C22×C4×C43—22no—
237C22×C4×C43—24no—
238C22×C4×C43—24no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—44no—
242C22×C4×C43—44no—
243C22×C4×C43C2×D411yescharacteristic
244C22×C4×C43C2×D412yes—
245C22×C4×C43C2412yes—
246C22×C4×C43C2411yescharacteristic
247C2×C22⋊D43—24no—
248C2×C22⋊D43—24no—
249C2×C22⋊D43—24no—
250C2×C22⋊D43—24no—
251C2×C22⋊D43—24no—
252C2×C22⋊D43—24no—
253C2×C22⋊D43—42no—
254C2×C22⋊D43—44no—
255C2×C22⋊D43—44no—
256C2×C22⋊D43—82no—
257C2×C22⋊D43—82no—
258C2×C22⋊D43—82no—
259C2×C22⋊D43—82no—
260C2×C22⋊D43C2×D414yes—
261C22×Dic43—24no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—82no—
265C22×Dic43C2×D411yescharacteristic
266C22×Dic43C2×D411yescharacteristic
267C22×Dic43C2×D411yescharacteristic
268#10621902—28no—
269#10621902—44no—
270#10621902—48no—
271D4×D43—28no—
272D4×D43—44no—
273D4×D43—48no—
274C2×D172—21no—
275C2×D172—21no—
276C2×D172—24no—
277C2×D172—22no—
278C2×D172—22no—
279C2×D172—22no—
280C2×D172—22no—
281C2×D172—44no—
282C2×D172C2412yes—
283C2×D172C2412yes—
284C2×C4×D43—22no—
285C2×C4×D43—22no—
286C2×C4×D43—24no—
287C2×C4×D43—44no—
288C2×C4×D43C2×D412yes—
289C2×C4×D43C2412yes—
290Q16×C43—28no—
291SD16×C43—28no—
292SD16×C43C2×D4116yescomplemented
293D8×C43—28no—
294C2×C8×C43—22no—
295C2×C8×C43—28no—
296C2×C8×C43C2×D414yes—
297C2×C8×C43C2412yes—
298C2×C8×C43C2412yes—
299C22⋊Dic43—24no—
300C22⋊Dic43—24no—
301C22⋊Dic43C2×D414yes—
302#10621884—28no—
303#10621884—44no—
304#10621882—28no—
305#10621882—44no—
306(C2×D43)⋊C4—24no—
307(C2×D43)⋊C4—24no—
308(C2×D43)⋊C4—24no—
309(C2×D43)⋊C4—24no—
310(C2×D43)⋊C4—24no—
311(C2×D43)⋊C4C2×D414yes—
312C4⋊Dic43—21no—
313C4⋊Dic43—21no—
314C4⋊Dic43—24no—
315C4⋊Dic43C2412yes—
316C4⋊Dic43C2412yes—
317Dic43⋊C4—24no—
318Dic43⋊C4C2×D414yes—
319C4×Dic43—24no—
320C4×Dic43C2×D412yes—
321C4×Dic43C2412yes—
322C2×C43⋊C8—22no—
323C2×C43⋊C8—22no—
324C2×C43⋊C8C2412yes—
325C2×C43⋊C8C2412yes—
326D344—28no—
327#10621872—28no—
328C23×C43—24no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—22no—
332C23×C43—22no—
333C23×C43—22no—
334C23×C43—42no—
335C23×C43—42no—
336C23×C43—42no—
337C23×C43—42no—
338C23×C43—42no—
339C23×C43C22×D412yes—
340C23×C43C22×D411yescharacteristic
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—48no—
347C22×D43—48no—
348C22×D43—42no—
349C22×D43—42no—
350C22×D43—42no—
351C22×D43—42no—
352C22×D43—42no—
353C22×D43—42no—
354C22×D43—84no—
355C22×D43—816no—
356C22×D43C22×D412yes—
357Q8×C43—24no—
358Q8×C43—22no—
359Q8×C43—22no—
360Q8×C43—22no—
361Q8×C43—42no—
362Q8×C43C22×D414yes—
363D4×C43—24no—
364D4×C43—22no—
365D4×C43—22no—
366D4×C43—22no—
367D4×C43—48no—
368D4×C43—48no—
369D4×C43—42no—
370D4×C43C22×D414yes—
371C2×C4×C43—24no—
372C2×C4×C43—22no—
373C2×C4×C43—22no—
374C2×C4×C43—24no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—48no—
379C2×C4×C43—48no—
380C2×C4×C43—42no—
381C2×C4×C43C22×D412yes—
382C2×C4×C43C22×D411yescharacteristic
383C2×C4×C43C22×D412yes—
384C2×C4×C43H(5,𝔽2)12yes—
385C2×C4×C43C2511yescharacteristic
386C22⋊D43—44no—
387C22⋊D43—48no—
388C22⋊D43—48no—
389C22⋊D43—84no—
390C22⋊D43—84no—
391C22⋊D43—84no—
392C22⋊D43—84no—
393C2×Dic43—22no—
394C2×Dic43—22no—
395C2×Dic43—22no—
396C2×Dic43—22no—
397C2×Dic43—22no—
398C2×Dic43—42no—
399C2×Dic43—42no—
400C2×Dic43—84no—
401C2×Dic43C22×D412yes—
402C2×Dic43C22×D412yes—
403C2×Dic43C22×D412yes—
404D172—22no—
405D172—22no—
406D172—22no—
407D172—22no—
408D172—48no—
409D172—42no—
410D172—42no—
411C4×D43—24no—
412C4×D43—22no—
413C4×D43—22no—
414C4×D43—48no—
415C8×C43—22no—
416C8×C43C22×D414yes—
417C43⋊C8—22no—
418C43⋊C8—22no—
419C2×#3268—431nomaximal, Sylow
420C22×C43—24no—
421C22×C43—22no—
422C22×C43—22no—
423C22×C43—22no—
424C22×C43—48no—
425C22×C43—44no—
426C22×C43—42no—
427C22×C43—42no—
428C22×C43—42no—
429C22×C43—42no—
430C22×C43—42no—
431C22×C43—84no—
432C22×C43D4212yes—
433C22×C43#57512yes—
434C22×C43#57612yes—
435C22×C43C23×D411yescharacteristic
436C2×D43—22no—
437C2×D43—22no—
438C2×D43—22no—
439C2×D43—44no—
440C2×D43—42no—
441C2×D43—42no—
442C2×D43—42no—
443C2×D43—42no—
444C2×D43—42no—
445C2×D43—42no—
446C2×D43—816no—
447C2×D43—84no—
448C2×D43—84no—
449C4×C43—24no—
450C4×C43—22no—
451C4×C43—42no—
452C4×C43D4212yes—
453C4×C43C23×D411yescharacteristic
454C4×C43C2×H(5,𝔽2)11yescharacteristic
455Dic43—22no—
456Dic43—22no—
457Dic43—22no—
458Dic43—42no—
459Dic43—42no—
460C22×AGL(1,ℤ/8)—431no—
461C22×#135D4311yescharacteristic, complemented
462C2×#550—431no—
463C2×#546—431no—
464#3268—4316no—
465C2×#496—431no—
466C2×#468—431no—
467C2×#466—431no—
468C2×#464—431no—
469C2×#459—431no—
470C2×#452—431no—
471C2×#449—431no—
472C2×#449—431no—
473C2×#447—431no—
474C2×#440—431no—
475C2×#435—431no—
476C2×C43—44no—
477C2×C43—42no—
478C2×C43—82no—
479C2×C43#326814yescomplemented
480C2×C43C2×D4211yescharacteristic
481C2×C43C2×#57511yescharacteristic
482C2×C43C2×#57611yescharacteristic
483D43—42no—
484D43—82no—
485D43—82no—
486C22×#41—431no—
487C22×#41C2×D4311yescharacteristic
488C22×#41C2×D4311yescharacteristic, complemented
489C23×D4—431no—
490C2×AGL(1,ℤ/8)—438no—
491C2×AGL(1,ℤ/8)—868no—
492C2×#135—28no—
493C2×#135C2×D4318yescomplemented
494C22×Q16C2×D4311yescharacteristic, complemented
495C22×SD16—431no—
496C22×SD16—431no—
497C22×SD16C2×D4311yescharacteristic
498C22×SD16C2×D4311yescharacteristic, complemented
499C22×D8—431no—
500C22×D8—431no—
501C22×D8—431no—
502C22×D8C2×D4311yescharacteristic
503C22×M16—431no—
504C23×C8C2×D4311yescharacteristic, complemented
505#550—438no—
506#550—864no—
507#546—438no—
508#546—864no—
509C2×#127—431no—
510C2×#127—861no—
511C2×#124—431no—
512C2×#123—861no—
513C2×C22⋊Q8—431no—
514C2×#121—431no—
515C2×#121—431no—
516C2×#121—431no—
517C2×#121—861no—
518C2×#121—861no—
519C2×#121—861no—
520C2×#120—861no—
521C2×C4×Q8—431no—
522C2×C4×D4—431no—
523C2×C4×D4—431no—
524C2×C4×D4—861no—
525C22×C22⋊C4—861no—
526#496—438no—
527#468—438no—
528#466—438no—
529#464—438no—
530#459—438no—
531#452—438no—
532#449—438no—
533#449—438no—
534#447—438no—
535#440—438no—
536#435—438no—
537C2×#107—431no—
538C2×C4⋊C8—431no—
539C2×#103—431no—
540C2×#103—431no—
541C2×#102—431no—
542C2×#102—431no—
543C2×#102—431no—
544C2×#102—431no—
545C2×C22⋊C8—431no—
546C2×C22⋊C8—431no—
547C2×#97—431no—
548C43C2×#326811yescharacteristic, complemented, Sylow
549C25—861no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—24no—
553C2×#41—24no—
554C2×#41—42no—
555C2×#41—42no—
556C2×#41—434no—
557C2×#41—862no—
558C2×#41—864no—
559C2×#41—1722no—
560C2×#41C22×D4314yes—
561C2×#41C22×D4314yescomplemented
562C22×Q8C22×D4311yescharacteristic
563C22×Q8C22×D4311yescharacteristic
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—431no—
567C22×D4—434no—
568C22×D4—431no—
569C22×D4—431no—
570C22×D4—861no—
571C22×D4—862no—
572C22×D4—861no—
573C22×D4—861no—
574C22×D4—861no—
575C22×D4—864no—
576C22×D4—861no—
577C22×D4—861no—
578C22×D4—861no—
579C22×D4—1722no—
580C22×D4C22×D4311yescharacteristic
581C22×D4C22×D4311yescharacteristic
582C23×C4—21no—
583C23×C4—21no—
584C23×C4—431no—
585C23×C4—861no—
586C23×C4—861no—
587C23×C4C22×D4311yescharacteristic
588AGL(1,ℤ/8)—8632no—
589#135—232no—
590C2×Q16—24no—
591C2×Q16C22×D4314yescomplemented
592C2×SD16—24no—
593C2×SD16—434no—
594C2×SD16—434no—
595C2×SD16—864no—
596C2×SD16—1722no—
597C2×SD16C22⋊D4318yescomplemented
598C2×SD16C22×D4314yes—
599C2×SD16C22×D4314yescomplemented
600C2×D8—24no—
601C2×D8—434no—
602C2×D8—434no—
603C2×D8—434no—
604C2×D8—864no—
605C2×D8—864no—
606C2×D8—1722no—
607C2×D8C22×D4314yes—
608C2×M16—434no—
609C2×M16—864no—
610C22×C8—24no—
611C22×C8—431no—
612C22×C8—431no—
613C22×C8C22×D4311yescharacteristic
614C22×C8C22×D4311yescharacteristic
615C22×C8C22×D4314yescomplemented
616#127—434no—
617#127—862no—
618#127—868no—
619#124—434no—
620#124—862no—
621#123—868no—
622C22⋊Q8—434no—
623C22⋊Q8—862no—
624#121—434no—
625#121—434no—
626#121—434no—
627#121—868no—
628#121—868no—
629#121—868no—
630#121—862no—
631#121—862no—
632#121—862no—
633#120—868no—
634C4×Q8—434no—
635C4×Q8—862no—
636C4×D4—434no—
637C4×D4—434no—
638C4×D4—434no—
639C4×D4—862no—
640C4×D4—868no—
641C2×C4⋊C4—431no—
642C2×C4⋊C4—431no—
643C2×C4⋊C4—431no—
644C2×C4⋊C4—861no—
645C2×C4⋊C4—861no—
646C2×C22⋊C4—431no—
647C2×C22⋊C4—431no—
648C2×C22⋊C4—868no—
649C2×C22⋊C4—861no—
650C2×C22⋊C4—861no—
651C2×C22⋊C4—861no—
652C2×C22⋊C4—861no—
653C2×C22⋊C4—861no—
654C2×C22⋊C4—861no—
655C2×C22⋊C4—861no—
656C2×C42—431no—
657C2×C42—861no—
658#107—434no—
659C4⋊C8—434no—
660#103—434no—
661#103—434no—
662#102—434no—
663#102—434no—
664#102—434no—
665#102—434no—
666C22⋊C8—434no—
667C22⋊C8—434no—
668#97—434no—
669C24—21no—
670C24—21no—
671C24—431no—
672C24—864no—
673C24—861no—
674C24—861no—
675C24—3442no—
676C24—1724no—
677C24—1724no—
678C24D4×D4311yescharacteristic
679#41—28no—
680#41—28no—
681#41—44no—
682#41—44no—
683#41—48no—
684#41—48no—
685#41—868no—
686#41—1724no—
687#41—1728no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—22no—
691C2×Q8—22no—
692C2×Q8—22no—
693C2×Q8C2×C22⋊D4314yes—
694C2×Q8C23×D4312yes—
695C2×Q8C23×D4312yes—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—434no—
706C2×D4—432no—
707C2×D4—432no—
708C2×D4—864no—
709C2×D4—864no—
710C2×D4—864no—
711C2×D4—864no—
712C2×D4—868no—
713C2×D4—864no—
714C2×D4—864no—
715C2×D4—864no—
716C2×D4—861no—
717C2×D4—861no—
718C2×D4—862no—
719C2×D4—862no—
720C2×D4—862no—
721C2×D4—862no—
722C2×D4—3442no—
723C2×D4—3442no—
724C2×D4—3442no—
725C2×D4—3442no—
726C2×D4—1724no—
727C2×D4—1724no—
728C2×D4—1728no—
729C2×D4—1722no—
730C2×D4—1724no—
731C2×D4—1724no—
732C2×D4C2×C22⋊D4314yes—
733C2×D4C23×D4312yes—
734C2×D4C23×D4312yes—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—431no—
744C22×C4—431no—
745C22×C4—431no—
746C22×C4—432no—
747C22×C4—432no—
748C22×C4—864no—
749C22×C4—864no—
750C22×C4—862no—
751C22×C4—862no—
752C22×C4—861no—
753C22×C4—861no—
754C22×C4—3442no—
755C22×C4—1724no—
756C22×C4D4×D4312yes—
757C22×C4D4×D4311yescharacteristic
758C22×C4C23×D4312yes—
759C22×C4C23×D4311yescharacteristic
760Q16—28no—
761SD16—28no—
762SD16—868no—
763SD16—1724no—
764SD16C2×C22⋊D43116yescomplemented
765D8—28no—
766D8—868no—
767D8—868no—
768D8—1724no—
769M16—868no—
770C2×C8—22no—
771C2×C8—28no—
772C2×C8—432no—
773C2×C8—432no—
774C2×C8—862no—
775C2×C8—862no—
776C2×C8C2×C22⋊D4314yes—
777C2×C8C23×D4312yes—
778C2×C8C23×D4312yes—
779C4⋊C4—434no—
780C4⋊C4—432no—
781C4⋊C4—432no—
782C4⋊C4—864no—
783C4⋊C4—864no—
784C4⋊C4—861no—
785C4⋊C4—861no—
786C22⋊C4—434no—
787C22⋊C4—434no—
788C22⋊C4—864no—
789C22⋊C4—864no—
790C22⋊C4—864no—
791C22⋊C4—864no—
792C22⋊C4—864no—
793C22⋊C4—864no—
794C22⋊C4—864no—
795C42—432no—
796C42—432no—
797C42—864no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—24no—
803C23—22no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—432no—
810C23—862no—
811C23—862no—
812C23—862no—
813C23—862no—
814C23—862no—
815C23—3444no—
816C23—34416no—
817C23—1728no—
818C23—1728no—
819C23—1722no—
820C23—1722no—
821C23—1722no—
822C23—1722no—
823C23—1722no—
824C23—1722no—
825C23C2×D4×D4312yes—
826C23C2×D4×D4311yescharacteristic
827Q8—22no—
828Q8—24no—
829Q8—22no—
830Q8—22no—
831Q8—42no—
832Q8C22×C22⋊D4314yes—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—24no—
837D4—48no—
838D4—48no—
839D4—42no—
840D4—862no—
841D4—862no—
842D4—862no—
843D4—862no—
844D4—3444no—
845D4—3444no—
846D4—3444no—
847D4—3444no—
848D4—1728no—
849D4—1724no—
850D4—1728no—
851D4—1728no—
852D4—1722no—
853D4—1722no—
854D4C22×C22⋊D4314yes—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—24no—
861C2×C4—22no—
862C2×C4—48no—
863C2×C4—48no—
864C2×C4—42no—
865C2×C4—432no—
866C2×C4—432no—
867C2×C4—432no—
868C2×C4—862no—
869C2×C4—862no—
870C2×C4—862no—
871C2×C4—862no—
872C2×C4—862no—
873C2×C4—864no—
874C2×C4—862no—
875C2×C4—862no—
876C2×C4—3444no—
877C2×C4—1728no—
878C2×C4—1722no—
879C2×C4—1722no—
880C2×C4C2×D4×D4312yes—
881C2×C4C2×D4×D4311yescharacteristic
882C2×C4C22×C22⋊D4312yes—
883C2×C4#1306337012yes—
884C2×C4C24×D4311yescharacteristic
885C8—22no—
886C8—862no—
887C8—862no—
888C8C22×C22⋊D4314yes—
889C22—22no—
890C22—24no—
891C22—22no—
892C22—22no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—48no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—84no—
901C22—862no—
902C22—862no—
903C22—862no—
904C22—34416no—
905C22—3444no—
906C22—3444no—
907C22—1722no—
908C22—1722no—
909C22—1722no—
910C22—1722no—
911C22—1722no—
912C22—1722no—
913C22—1724no—
914C22D4×C22⋊D4312yes—
915C22#1458369612yes—
916C22#1458370112yes—
917C22C22×D4×D4311yescharacteristic
918C4—22no—
919C4—24no—
920C4—42no—
921C4—862no—
922C4—862no—
923C4—862no—
924C4—1722no—
925C4—1722no—
926C4D4×C22⋊D4312yes—
927C4C23×C22⋊D4311yescharacteristic
928C4C2×#1306337011yescharacteristic
929C2—42no—
930C2—44no—
931C2—82no—
932C2—3442no—
933C2—3442no—
934C2—1722no—
935C2#1914613514yesdirect product factor
936C2C2×D4×C22⋊D4311yescharacteristic
937C2C2×#1458369611yescharacteristic
938C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#135×C43C2
socleC23×C43C22×D4
hypercenterC22×#135D43
hypocenterC43C2×#3268
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C22×#13063352C2semidirect
2. C2×#14583568C2semidirect
3. C2×#14583537C2semidirect
4. #19146135C2direct (N × H)
5. C2×#14583285C2semidirect
6. C2×#14583142C2semidirect
7. C2×#14583135C2semidirect
8. C2×#14583123C2semidirect
9. C2×#14583092C2semidirect
10. C2×#14583060C2semidirect
11. C2×#14583044C2semidirect
12. C2×#14583044C2semidirect
13. C2×#14583031C2semidirect
14. C2×#14583000C2semidirect
15. C2×#14582970C2semidirect
16. C22×#135×C43C2semidirect
20. C2×#13063352C22semidirect
22. C22×#10621884C22semidirect
28. #14583568C22semidirect
30. #14583537C22semidirect
32. C2×#13063321C22semidirect
38. C2×#13063299C22semidirect
43. C2×Q8×Dic43C22semidirect
48. #14583285C22semidirect
49. #14583142C22semidirect
50. #14583135C22semidirect
51. #14583123C22semidirect
52. #14583092C22semidirect
53. #14583060C22semidirect
54. #14583044C22semidirect
55. #14583044C22semidirect
56. #14583031C22semidirect
57. #14583000C22semidirect
58. #14582970C22semidirect
59. C2×#13063259C22semidirect
60. C2×Dic43⋊C8C22semidirect
61. C2×#13063249C22semidirect
62. C2×#13063249C22semidirect
64. C2×#13063247C22semidirect
66. C2×#13063246C22semidirect
67. C2×C22⋊(C43⋊C8)C22semidirect
69. C2×#13063235C22semidirect
71. C22×#41×C43C22semidirect
73. C2×#135×C43C22semidirect
74. C22×Q16×C43C22semidirect
76. C22×SD16×C43C22semidirect
78. C23×C8×C43C22semidirect
105. C2×#10621884C23semidirect
118. #13063321C23semidirect
128. #13063299C23semidirect
135. Q8×Dic43C23semidirect
158. #13063259C23semidirect
159. Dic43⋊C8C23semidirect
160. #13063249C23semidirect
161. #13063249C23semidirect
163. #13063247C23semidirect
165. #13063246C23semidirect
166. C22⋊(C43⋊C8)C23semidirect
168. #13063235C23semidirect
176. C2×#41×C43C23semidirect
188. C2×Q16×C43C23semidirect
190. C2×SD16×C43D4semidirect
192. C2×SD16×C43C23semidirect
198. C22×C8×C43C23semidirect
292. SD16×C43C2×D4semidirect
461. C22×#135D43semidirect
479. C2×C43#3268semidirect
488. C22×#41C2×D43semidirect
493. C2×#135C2×D43semidirect
494. C22×Q16C2×D43semidirect
498. C22×SD16C2×D43semidirect
504. C23×C8C2×D43semidirect
548. C43C2×#3268semidirect
561. C2×#41C22×D43semidirect
591. C2×Q16C22×D43semidirect
597. C2×SD16C22⋊D43semidirect
599. C2×SD16C22×D43semidirect
615. C22×C8C22×D43semidirect
764. SD16C2×C22⋊D43semidirect
935. C2#19146135direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633522
C2×#145835682
C2×#145835372
#191461352
C2×#145832852
C2×#145831422
C2×#145831352
C2×#145831232
C2×#145830922
C2×#145830602
C2×#145830442
C2×#145830312
C2×#145830002
C2×#145829702
C22×#135×C432
C2×#326843