Finite Group Databasebeta

← C2×#19145655 #25967967

Subgroups — C2×#19145655 #25967967

Order 11008.

2150 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583500C211yesmaximal, characteristic, complemented
2C2×#14583474C211yesmaximal, characteristic, complemented
3#19145655C2116yesmaximal, direct product factor
4C2×#14583285C211yesmaximal, characteristic, complemented
5C2×#14583270C211yesmaximal, characteristic, complemented
6C2×#14583266C211yesmaximal, characteristic, complemented
7C2×#14583255C211yesmaximal, characteristic, complemented
8C2×#14583115C211yesmaximal, characteristic, complemented
9C2×#14583114C211yesmaximal, characteristic, complemented
10C2×#14583101C211yesmaximal, characteristic, complemented
11C2×#14583047C211yesmaximal, characteristic, complemented
12C2×#14583043C211yesmaximal, characteristic, complemented
13C2×#14583039C211yesmaximal, characteristic, complemented
14C2×#14583036C211yesmaximal, characteristic, complemented
15C2×#14582959C211yesmaximal, characteristic, complemented
16C2×C43×#461C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×#10621884C2211yescharacteristic
23C22×D344C2211yescharacteristic
24C22×#10621882C2211yescharacteristic
25#14583500—24no—
26#14583500C2218yescomplemented
27#14583474—24no—
28#14583474C2218yescomplemented
29C2×#13063323C2211yescharacteristic
30C2×#13063321C2211yescharacteristic
31C2×#13063316C2211yescharacteristic
32C2×#13063314C2211yescharacteristic
33C2×#13063313C2211yescharacteristic
34C2×#13063310—21no—
35C2×#13063310—21no—
36C2×#13063308—21no—
37C2×#13063307—21no—
38C2×#13063303—21no—
39C2×#13063303—21no—
40C2×#13063300C2211yescharacteristic
41C2×#13063299—21no—
42C2×#13063298—21no—
43C2×#13063296C2211yescharacteristic
44C2×C4×D172C2211yescharacteristic
45C2×#13063282C2211yescharacteristic
46#14583285C2218yescomplemented
47#14583270C2218yescomplemented
48#14583266C2218yescomplemented
49#14583255C2218yescomplemented
50#14583115C2218yescomplemented
51#14583114C2218yescomplemented
52#14583101C2218yescomplemented
53#14583047C2218yescomplemented
54#14583043C2218yescomplemented
55#14583039C2218yescomplemented
56#14583036C2218yescomplemented
57#14582959C2218yescomplemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×C4⋊Q8×C43C2211yescharacteristic
72C2×C4×D4×C43C2211yescharacteristic
73C43×#461C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—42no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C2×Q8×D43—22no—
84C2×Q8×D43—42no—
85C2×Q8×D43—42no—
86C2×Q8×D43C2314yes—
87C22×D172—21no—
88C22×D172—21no—
89C22×D172C2311yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98C2×#10621873—42no—
99C2×#10621873C2314yes—
100C2×#10621883—42no—
101C2×#10621883C2314yes—
102C2×#10621884—42no—
103C2×#10621884—42no—
104C2×#10621884C2314yes—
105C2×#10621884C2314yes—
106C2×D344—42no—
107C2×D344C2314yes—
108C2×#10621882—42no—
109C2×#10621882C2314yes—
110C22×C43⋊C8C2311yescharacteristic
111C22×C43⋊C8C2311yescharacteristic
112#13063323—22no—
113#13063323C2314yes—
114#13063321—22no—
115#13063321C2314yes—
116#13063316—22no—
117#13063316C2314yes—
118#13063314—22no—
119#13063314C2314yes—
120#13063313—22no—
121#13063313C2314yes—
122#13063310—28no—
123#13063310—28no—
124#13063308—28no—
125#13063307—28no—
126#13063303—28no—
127#13063303—28no—
128#13063300—22no—
129#13063300C2314yes—
130#13063299—28no—
131#13063298—28no—
132#13063296—22no—
133#13063296C2314yes—
134C4×D172—22no—
135C4×D172C2314yes—
136#13063282D414yes—
137#13063282C2314yes—
138C2×C4⋊Dic43—21no—
139C2×C4⋊Dic43C2311yescharacteristic
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4—21no—
143C2×Dic43⋊C4D411yescharacteristic
144C2×Dic43⋊C4D411yescharacteristic
145C2×C22⋊Dic43—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—21no—
152C2×(C2×D43)⋊C4D411yescharacteristic
153C2×(C2×D43)⋊C4D411yescharacteristic
154C2×C4×Dic43C2311yescharacteristic
155C4⋊(C43⋊C8)C2314yes—
156#13063250C2314yes—
157#13063249C2314yes—
158#13063249C2314yes—
159#13063248C2314yes—
160#13063247C2314yes—
161#13063245C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164#13063235C2314yes—
165C8×Dic43C2314yes—
166C22×Q8×C43C2311yescharacteristic
167C22×Q8×C43C2311yescharacteristic
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C2×SD16×C43—42no—
171C2×SD16×C43—42no—
172C2×SD16×C43C2314yes—
173C2×SD16×C43C2314yes—
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2311yescharacteristic
176C4⋊Q8×C43—22no—
177C4⋊Q8×C43C2314yes—
178C4×D4×C43—22no—
179C4×D4×C43C2314yes—
180C2×C4⋊C4×C43—21no—
181C2×C4⋊C4×C43—21no—
182C2×C4⋊C4×C43C2311yescharacteristic
183C2×C22⋊C4×C43—21no—
184C2×C42×C43C2311yescharacteristic
185C4⋊C8×C43C2314yes—
186#103×C43C2314yes—
187#103×C43C2314yes—
188C24×C43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43C2×D411yescharacteristic
192C2×Q8×C43—21no—
193C2×Q8×C43—21no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43—22no—
198C2×Q8×C43C2412yes—
199C2×Q8×C43C2412yes—
200C2×D4×C43—21no—
201C2×D4×C43—22no—
202C2×D4×C43—22no—
203C2×D4×C43C2412yes—
204C22×C4×C43—24no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—82no—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2411yescharacteristic
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—82no—
216C2×C22⋊D43—82no—
217C2×C22⋊D43—82no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223#10621902—44no—
224#10621902—44no—
225#10621902—48no—
226Q8×D43—44no—
227Q8×D43—44no—
228Q8×D43—48no—
229C2×D172—21no—
230C2×D172—21no—
231C2×D172—24no—
232C2×D172—24no—
233C2×D172—22no—
234C2×D172—22no—
235C2×D172—22no—
236C2×D172—22no—
237C2×D172—44no—
238C2×D172—82no—
239C2×D172C2412yes—
240C2×D172C2412yes—
241C2×C4×D43—22no—
242C2×C4×D43—22no—
243C2×C4×D43—24no—
244C2×C4×D43—24no—
245C2×C4×D43—24no—
246C2×C4×D43—44no—
247C2×C4×D43—44no—
248C2×C4×D43—82no—
249C2×C4×D43C2×D412yes—
250C2×C4×D43C2412yes—
251C2×Dic86—22no—
252C2×Dic86—22no—
253C2×Dic86—21no—
254C2×Dic86—24no—
255C2×Dic86—44no—
256C2×Dic86C2412yes—
257SD16×C43—44no—
258SD16×C43—44no—
259C2×C8×C43—22no—
260C2×C8×C43—22no—
261C2×C8×C43C2412yes—
262C2×C8×C43C2412yes—
263C4⋊C4×C43—24no—
264C4⋊C4×C43—24no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43C2412yes—
267C22⋊C4×C43—24no—
268C42×C43C2×D412yes—
269C42×C43C2412yes—
270C22⋊Dic43—24no—
271#10621884—44no—
272#10621884—44no—
273#10621883—44no—
274#10621882—44no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4—24no—
280(C2×D43)⋊C4—24no—
281(C2×D43)⋊C4C2×D414yes—
282(C2×D43)⋊C4C2×D414yes—
283C4⋊Dic43—21no—
284C4⋊Dic43—24no—
285C4⋊Dic43C2412yes—
286Dic43⋊C4—24no—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289Dic43⋊C4C2×D414yes—
290Dic43⋊C4C2×D414yes—
291C4×Dic43C2×D412yes—
292C4×Dic43C2412yes—
293C2×C43⋊C8—22no—
294C2×C43⋊C8—22no—
295C2×C43⋊C8C2412yes—
296C2×C43⋊C8C2412yes—
297D344—44no—
298#10621873—44no—
299C23×C43—22no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43—42no—
303C23×C43C22×D411yescharacteristic
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43—42no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43—42no—
315C22×D43C22×D412yes—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—22no—
320Q8×C43—42no—
321Q8×C43—42no—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—42no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43—42no—
333C2×C4×C43—84no—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D412yes—
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43H(5,𝔽2)12yes—
338C2×C4×C43H(5,𝔽2)12yes—
339C2×C4×C43C2511yescharacteristic
340C22⋊D43—84no—
341C22⋊D43—84no—
342C22⋊D43—84no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—42no—
349C2×Dic43—42no—
350C2×Dic43C22×D412yes—
351C2×Dic43C22×D412yes—
352C2×Dic43C22×D412yes—
353D172—22no—
354D172—22no—
355D172—22no—
356D172—22no—
357D172—48no—
358D172—42no—
359D172—42no—
360D172—84no—
361C4×D43—24no—
362C4×D43—22no—
363C4×D43—22no—
364C4×D43—48no—
365C4×D43—48no—
366C4×D43—84no—
367Dic86—22no—
368Dic86—22no—
369Dic86—48no—
370Dic86—42no—
371C8×C43—22no—
372C8×C43—22no—
373C43⋊C8—22no—
374C43⋊C8—22no—
375C2×#3221—431nomaximal, Sylow
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—84no—
380C22×C43#53512yes—
381C22×C43#57712yes—
382C22×C43#57712yes—
383C22×C43C23×D411yescharacteristic
384C2×D43—22no—
385C2×D43—22no—
386C2×D43—22no—
387C2×D43—44no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—84no—
395C2×D43—84no—
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—42no—
399C4×C43—42no—
400C4×C43—42no—
401C4×C43#53512yes—
402C4×C43C2×H(5,𝔽2)11yescharacteristic
403C4×C43C2×H(5,𝔽2)11yescharacteristic
404Dic43—22no—
405Dic43—22no—
406Dic43—22no—
407Dic43—42no—
408Dic43—42no—
409C2×#540—431no—
410C2×#536—431no—
411#3221—4316no—
412C2×#496—431no—
413C2×#492—431no—
414C2×#491—431no—
415C2×#488—431no—
416C2×#463—431no—
417C2×#463—431no—
418C2×#461—431no—
419C2×#461D4311yescharacteristic, complemented
420C2×#449—431no—
421C2×#449—431no—
422C2×#448—431no—
423C2×#448—431no—
424C2×#433—431no—
425C2×C43—82no—
426C2×C43#322114yescomplemented
427C2×C43C2×#53511yescharacteristic
428C2×C43C2×#57711yescharacteristic
429C2×C43C2×#57711yescharacteristic
430D43—42no—
431D43—82no—
432D43—82no—
433C22×#41—431no—
434C23×Q8—431no—
435C22×SD16—431no—
436C22×SD16—431no—
437C22×SD16—431no—
438C22×SD16—431no—
439C22×SD16C2×D4311yescharacteristic
440C22×SD16C2×D4311yescharacteristic
441C22×D8—431no—
442C22×D8—431no—
443#540—438no—
444#540—864no—
445#536—438no—
446#536—864no—
447C2×C4⋊Q8—431no—
448C2×C4⋊Q8C2×D4311yescharacteristic
449C2×#127—431no—
450C2×#125—431no—
451C2×#124—431no—
452C2×#124—431no—
453C2×#123—861no—
454C2×#123—861no—
455C2×#123—861no—
456C2×#123—861no—
457C2×C22⋊Q8—861no—
458C2×C22⋊Q8—861no—
459C2×#121—431no—
460C2×#121—431no—
461C2×#121—861no—
462C2×#121—861no—
463C2×C4×D4—431no—
464C2×C4×D4C2×D4311yescharacteristic
465C2×#117—431no—
466#496—438no—
467#492—438no—
468#491—438no—
469#488—438no—
470#463—438no—
471#463—438no—
472#461—438no—
473#461C2×D4318yescomplemented
474#449—438no—
475#449—438no—
476#448—438no—
477#448—438no—
478#433—438no—
479C2×C4⋊C8—431no—
480C2×C4⋊C8C2×D4311yescharacteristic
481C2×#103—431no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#103C2×D4311yescharacteristic
486C2×#103C2×D4311yescharacteristic
487C2×#102—431no—
488C2×#102—431no—
489C2×C22⋊C8—431no—
490C2×C22⋊C8—431no—
491C2×#97—431no—
492C2×C4×C8—431no—
493C43C2×#322111yescharacteristic, complemented, Sylow
494C2×#41—434no—
495C2×#41—862no—
496C2×#41—1722no—
497C2×#41—1722no—
498C22×Q8—434no—
499C22×Q8—431no—
500C22×Q8—861no—
501C22×Q8—862no—
502C22×Q8—1722no—
503C22×Q8—1722no—
504C22×Q8C22×D4311yescharacteristic
505C22×Q8C22×D4311yescharacteristic
506C22×D4—431no—
507C22×D4—431no—
508C22×D4—861no—
509C22×D4—861no—
510C22×D4—861no—
511C22×D4—861no—
512C22×D4—861no—
513C22×D4C22×D4311yescharacteristic
514C23×C4—21no—
515C23×C4—431no—
516C23×C4—861no—
517C23×C4—861no—
518C23×C4—861no—
519C2×SD16—42no—
520C2×SD16—42no—
521C2×SD16—434no—
522C2×SD16—434no—
523C2×SD16—434no—
524C2×SD16—434no—
525C2×SD16—1722no—
526C2×SD16—1722no—
527C2×SD16—1722no—
528C2×SD16—1722no—
529C2×SD16C22×D4314yes—
530C2×SD16C22×D4314yes—
531C2×D8—434no—
532C2×D8—434no—
533C2×D8—1722no—
534C2×D8—1722no—
535C22×C8—431no—
536C22×C8—431no—
537C22×C8C22×D4311yescharacteristic
538C22×C8C22×D4311yescharacteristic
539C4⋊Q8—22no—
540C4⋊Q8—434no—
541C4⋊Q8—862no—
542C4⋊Q8C22×D4314yes—
543#127—434no—
544#127—862no—
545#125—434no—
546#125—862no—
547#124—434no—
548#124—434no—
549#124—862no—
550#124—862no—
551#123—868no—
552#123—868no—
553#123—868no—
554#123—868no—
555C22⋊Q8—868no—
556C22⋊Q8—868no—
557#121—434no—
558#121—434no—
559#121—868no—
560#121—868no—
561#121—862no—
562#121—862no—
563C4×D4—22no—
564C4×D4—434no—
565C4×D4—862no—
566C4×D4C22×D4314yes—
567#117—434no—
568#117—434no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—431no—
572C2×C4⋊C4—431no—
573C2×C4⋊C4—431no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4—861no—
577C2×C4⋊C4—861no—
578C2×C4⋊C4C22×D4311yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—431no—
581C2×C22⋊C4—431no—
582C2×C22⋊C4—861no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C42—431no—
590C2×C42C22×D4311yescharacteristic
591C4⋊C8—434no—
592C4⋊C8C22×D4314yes—
593#103—434no—
594#103—434no—
595#103—434no—
596#103—434no—
597#103C22×D4314yes—
598#103C22×D4314yes—
599#102—434no—
600#102—434no—
601C22⋊C8—434no—
602C22⋊C8—434no—
603#97—434no—
604C4×C8—434no—
605C24—21no—
606C24—431no—
607C24—861no—
608C24—861no—
609#41—1724no—
610#41—1724no—
611#41—1728no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—22no—
615C2×Q8—22no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—432no—
619C2×Q8—864no—
620C2×Q8—861no—
621C2×Q8—862no—
622C2×Q8—862no—
623C2×Q8—1724no—
624C2×Q8—1724no—
625C2×Q8—1724no—
626C2×Q8—1728no—
627C2×Q8C23×D4312yes—
628C2×Q8C23×D4312yes—
629C2×D4—21no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—432no—
633C2×D4—432no—
634C2×D4—864no—
635C2×D4—864no—
636C2×D4—864no—
637C2×D4—864no—
638C2×D4—864no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—862no—
642C2×D4—862no—
643C2×D4—862no—
644C2×D4—862no—
645C2×D4—3442no—
646C2×D4—3442no—
647C2×D4—3442no—
648C2×D4—3442no—
649C2×D4—1724no—
650C2×D4C23×D4312yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—82no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—432no—
660C22×C4—432no—
661C22×C4—864no—
662C22×C4—864no—
663C22×C4—862no—
664C22×C4—862no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—864no—
668C22×C4—3442no—
669C22×C4—1724no—
670C22×C4—1724no—
671C22×C4D4×D4311yescharacteristic
672C22×C4D4×D4311yescharacteristic
673C22×C4C23×D4311yescharacteristic
674SD16—44no—
675SD16—44no—
676SD16—1724no—
677SD16—1724no—
678SD16—1724no—
679SD16—1724no—
680D8—1724no—
681D8—1724no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—432no—
685C2×C8—432no—
686C2×C8—862no—
687C2×C8—862no—
688C2×C8C23×D4312yes—
689C2×C8C23×D4312yes—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—21no—
693C4⋊C4—434no—
694C4⋊C4—434no—
695C4⋊C4—432no—
696C4⋊C4—864no—
697C4⋊C4—864no—
698C4⋊C4—864no—
699C4⋊C4—864no—
700C4⋊C4—861no—
701C4⋊C4C23×D4312yes—
702C22⋊C4—24no—
703C22⋊C4—434no—
704C22⋊C4—434no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C22⋊C4—864no—
710C22⋊C4—864no—
711C22⋊C4—864no—
712C42—432no—
713C42—432no—
714C42D4×D4312yes—
715C42C23×D4312yes—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—432no—
721C23—862no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—1722no—
727C23—1722no—
728C23—1722no—
729C23—1722no—
730C23—1722no—
731C23—1722no—
732C23C2×D4×D4311yescharacteristic
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8—42no—
738Q8—42no—
739Q8—862no—
740Q8—862no—
741Q8—1728no—
742Q8—1722no—
743D4—22no—
744D4—22no—
745D4—42no—
746D4—862no—
747D4—862no—
748D4—862no—
749D4—862no—
750D4—3444no—
751D4—3444no—
752D4—3444no—
753D4—3444no—
754D4—1728no—
755D4—1722no—
756D4—1722no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—84no—
766C2×C4—432no—
767C2×C4—432no—
768C2×C4—432no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—864no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—3444no—
778C2×C4—1728no—
779C2×C4—1728no—
780C2×C4—1722no—
781C2×C4—1722no—
782C2×C4C2×D4×D4312yes—
783C2×C4C2×D4×D4312yes—
784C2×C4C2×D4×D4311yescharacteristic
785C2×C4#1306337012yes—
786C2×C4#1306337112yes—
787C2×C4C24×D4311yescharacteristic
788C8—22no—
789C8—22no—
790C8—862no—
791C8—862no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—84no—
796C22—862no—
797C22—862no—
798C22—862no—
799C22—3444no—
800C22—3444no—
801C22—1722no—
802C22—1722no—
803C22—1722no—
804C22—1722no—
805C22—1722no—
806C22—1722no—
807C22—1724no—
808C22#1458346512yes—
809C22#1458370512yes—
810C22#1458370812yes—
811C22C22×D4×D4311yescharacteristic
812C4—22no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—862no—
818C4—862no—
819C4—862no—
820C4—1722no—
821C4—1722no—
822C4#1458346512yes—
823C4C2×#1306337011yescharacteristic
824C4C2×#1306337111yescharacteristic
825C2—82no—
826C2—3442no—
827C2—3442no—
828C2—1722no—
829C2#1914565514yesdirect product factor
830C2C2×#1458346511yescharacteristic
831C2C2×#1458370511yescharacteristic
832C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#461C2
socleC23×C43C22×D4
hypercenterC2×#461D43
hypocenterC43C2×#3221
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#14583500C2semidirect
2. C2×#14583474C2semidirect
3. #19145655C2direct (N × H)
4. C2×#14583285C2semidirect
5. C2×#14583270C2semidirect
6. C2×#14583266C2semidirect
7. C2×#14583255C2semidirect
8. C2×#14583115C2semidirect
9. C2×#14583114C2semidirect
10. C2×#14583101C2semidirect
11. C2×#14583047C2semidirect
12. C2×#14583043C2semidirect
13. C2×#14583039C2semidirect
14. C2×#14583036C2semidirect
15. C2×#14582959C2semidirect
16. C2×C43×#461C2semidirect
26. #14583500C22semidirect
28. #14583474C22semidirect
46. #14583285C22semidirect
47. #14583270C22semidirect
48. #14583266C22semidirect
49. #14583255C22semidirect
50. #14583115C22semidirect
51. #14583114C22semidirect
52. #14583101C22semidirect
53. #14583047C22semidirect
54. #14583043C22semidirect
55. #14583039C22semidirect
56. #14583036C22semidirect
57. #14582959C22semidirect
73. C43×#461C22semidirect
419. C2×#461D43semidirect
426. C2×C43#3221semidirect
473. #461C2×D43semidirect
493. C43C2×#3221semidirect
829. C2#19145655direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835002
C2×#145834742
#191456552
C2×#145832852
C2×#145832702
C2×#145832662
C2×#145832552
C2×#145831152
C2×#145831142
C2×#145831012
C2×#145830472
C2×#145830432
C2×#145830392
C2×#145830362
C2×#145829592
C2×C43×#4612
C2×#322143