Finite Group Databasebeta

← C2×#19145495 #25967303

Subgroups — C2×#19145495 #25967303

Order 11008.

2250 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583480C211yesmaximal, characteristic, complemented
2C2×#14583478C211yesmaximal, characteristic, complemented
3#19145495C2116yesmaximal, direct product factor
4C2×#14583236C211yesmaximal, characteristic, complemented
5C2×#14583234C211yesmaximal, characteristic, complemented
6C2×#14583214C211yesmaximal, characteristic, complemented
7C2×#14583146C211yesmaximal, characteristic, complemented
8C2×#14583144C211yesmaximal, characteristic, complemented
9C2×#14583141C211yesmaximal, characteristic, complemented
10C2×#14583134C211yesmaximal, characteristic, complemented
11C2×#14583063C211yesmaximal, characteristic, complemented
12C2×#14583062C211yesmaximal, characteristic, complemented
13C2×#14583045C211yesmaximal, characteristic, complemented
14C2×#14583042C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#480C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621898C2211yescharacteristic
19C22×#10621900C2211yescharacteristic
20C22×Dic172C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22C22×#10621883C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583480—24no—
27#14583480C2218yescomplemented
28#14583478—24no—
29#14583478C2218yescomplemented
30C2×#13063305—21no—
31C2×#13063305C2211yescharacteristic
32C2×#13063305C2211yescharacteristic
33C2×#13063305C2211yescharacteristic
34C2×#13063304C2211yescharacteristic
35C2×#13063302—21no—
36C2×#13063300—21no—
37C2×#13063300C2211yescharacteristic
38C2×#13063300C2211yescharacteristic
39C2×#13063299—21no—
40C2×#13063299—21no—
41C2×#13063298—21no—
42C2×#13063297—21no—
43C2×#13063296—21no—
44C2×#13063296C2211yescharacteristic
45C2×C4⋊C4×D43C2211yescharacteristic
46#14583236C2218yescomplemented
47#14583234C2218yescomplemented
48#14583214C2218yescomplemented
49#14583146C2218yescomplemented
50#14583144C2218yescomplemented
51#14583141C2218yescomplemented
52#14583134C2218yescomplemented
53#14583063C2218yescomplemented
54#14583062C2218yescomplemented
55#14583045C2218yescomplemented
56#14583042C2218yescomplemented
57C2×#13063258C2211yescharacteristic
58C2×#13063258C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063248C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65#14582864C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×#121×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2211yescharacteristic
71C43×#480C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#107×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—42no—
79C2×#10621898—42no—
80C2×#10621898—42no—
81C2×#10621898—42no—
82C2×#10621898D414yes—
83C2×#10621898C2314yes—
84C2×#10621898C2314yes—
85C2×#10621900—22no—
86C2×#10621900—42no—
87C2×#10621900—42no—
88C2×#10621900C2314yes—
89C22×Dic86D411yescharacteristic
90C22×Dic86C2311yescharacteristic
91C22×Dic86C2311yescharacteristic
92C22×D172—21no—
93C22×D172—21no—
94C22×D172D411yescharacteristic
95C22×D172C2311yescharacteristic
96C22×C22⋊D43—21no—
97C22×C22⋊D43—21no—
98C22×C22⋊D43—21no—
99C22×C22⋊D43D411yescharacteristic
100C22×C22⋊D43D411yescharacteristic
101C23×Dic43—21no—
102C22×C4×D43—21no—
103C22×C4×D43—21no—
104C22×C4×D43C2311yescharacteristic
105C22×C4×D43C2311yescharacteristic
106C2×Dic172—42no—
107C2×Dic172C2314yes—
108C2×#10621873—42no—
109C2×#10621873C2314yes—
110C2×#10621883—42no—
111C2×#10621883C2314yes—
112C2×#10621882—42no—
113C2×#10621882C2314yes—
114C2×#10621872—42no—
115C2×#10621872C2314yes—
116C22×C43⋊C8C2311yescharacteristic
117C22×C43⋊C8C2311yescharacteristic
118C2×C8×D43—42no—
119C2×C8×D43C2314yes—
120#13063305—22no—
121#13063305—22no—
122#13063305—22no—
123#13063305—28no—
124#13063305C2314yes—
125#13063305C2314yes—
126#13063305C2314yes—
127#13063304—22no—
128#13063304C2314yes—
129#13063302—28no—
130#13063300—28no—
131#13063300—22no—
132#13063300—22no—
133#13063300C2314yes—
134#13063300C2314yes—
135#13063299—28no—
136#13063299—28no—
137#13063298—28no—
138#13063297—28no—
139#13063296—28no—
140#13063296—22no—
141#13063296C2314yes—
142C2×C4⋊Dic43—21no—
143C2×C4⋊Dic43—21no—
144C2×C4⋊Dic43—21no—
145C2×C4⋊Dic43C2311yescharacteristic
146C2×Dic43⋊C4—21no—
147C2×Dic43⋊C4—21no—
148C4⋊C4×D43—22no—
149C4⋊C4×D43C2314yes—
150C2×C22⋊Dic43—21no—
151C2×C22⋊Dic43—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4—21no—
155C2×(C2×D43)⋊C4—21no—
156C2×(C2×D43)⋊C4—21no—
157#13063258C2314yes—
158#13063258C2314yes—
159#13063250C2314yes—
160#13063248C2314yes—
161#13063248C2314yes—
162#13063248C2314yes—
163#13063247C2314yes—
164#13063245C2314yes—
165C22⋊(C43⋊C8)C2314yes—
166(C2×D43)⋊C8C2314yes—
167(C2×D43)⋊C8C2314yes—
168C22×D4×C43—21no—
169C22×D4×C43C2311yescharacteristic
170C23×C4×C43—21no—
171C23×C4×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174#121×C43—22no—
175#121×C43C2314yes—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43—22no—
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2314yes—
181C2×C4⋊C4×C43C2311yescharacteristic
182C2×C22⋊C4×C43—21no—
183#107×C43C2314yes—
184#107×C43C2314yes—
185#102×C43C2314yes—
186#102×C43C2314yes—
187C22⋊C8×C43C2314yes—
188C24×C43—21no—
189C24×C43C2×D411yescharacteristic
190C23×D43—21no—
191C23×D43C2×D411yescharacteristic
192C23×D43C2×D411yescharacteristic
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×C43—24no—
205C22×C4×C43—82no—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D412yes—
208C22×C4×C43C2412yes—
209C22×C4×C43C2411yescharacteristic
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—42no—
214C2×C22⋊D43—42no—
215C2×C22⋊D43—44no—
216C2×C22⋊D43—44no—
217C2×C22⋊D43—82no—
218C2×C22⋊D43C2×D414yes—
219C2×C22⋊D43C2×D414yes—
220C22×Dic43—24no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—44no—
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227#10621900—44no—
228#10621900—44no—
229#10621900—48no—
230#10621898—44no—
231#10621898—44no—
232#10621898—48no—
233#10621898—44no—
234#10621898—44no—
235#10621898—48no—
236C2×D172—21no—
237C2×D172—24no—
238C2×D172—24no—
239C2×D172—22no—
240C2×D172—22no—
241C2×D172—42no—
242C2×D172—82no—
243C2×D172—82no—
244C2×D172C2×D414yes—
245C2×D172C2412yes—
246C2×C4×D43—22no—
247C2×C4×D43—22no—
248C2×C4×D43—22no—
249C2×C4×D43—22no—
250C2×C4×D43—24no—
251C2×C4×D43—24no—
252C2×C4×D43—44no—
253C2×C4×D43—82no—
254C2×C4×D43C2×D412yes—
255C2×C4×D43C2×D412yes—
256C2×C4×D43C2412yes—
257C2×C4×D43C2412yes—
258C2×Dic86—22no—
259C2×Dic86—22no—
260C2×Dic86—22no—
261C2×Dic86—22no—
262C2×Dic86—21no—
263C2×Dic86—21no—
264C2×Dic86—42no—
265C2×Dic86C2×D414yes—
266C2×Dic86C2412yes—
267C2×Dic86C2412yes—
268C2×C8×C43—22no—
269C2×C8×C43—22no—
270C2×C8×C43C2412yes—
271C2×C8×C43C2412yes—
272C4⋊C4×C43—24no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43C2412yes—
277C4⋊C4×C43C2412yes—
278C4⋊C4×C43C2412yes—
279C22⋊C4×C43—24no—
280C22⋊Dic43—24no—
281C22⋊Dic43—24no—
282#10621883—44no—
283#10621882—44no—
284(C2×D43)⋊C4—24no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—24no—
287(C2×D43)⋊C4—24no—
288(C2×D43)⋊C4—24no—
289C4⋊Dic43—21no—
290C4⋊Dic43—24no—
291C4⋊Dic43—24no—
292C4⋊Dic43—24no—
293C4⋊Dic43C2412yes—
294Dic43⋊C4—24no—
295Dic43⋊C4—24no—
296C2×C43⋊C8—22no—
297C2×C43⋊C8—22no—
298C2×C43⋊C8C2412yes—
299C2×C43⋊C8C2412yes—
300Dic172—44no—
301#10621873—44no—
302#10621872—44no—
303C8×D43—44no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—42no—
309C23×C43—42no—
310C23×C43—42no—
311C23×C43C22×D412yes—
312C23×C43C22×D411yescharacteristic
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—42no—
321C22×D43—42no—
322C22×D43—42no—
323C22×D43C22×D412yes—
324C22×D43C22×D412yes—
325D4×C43—22no—
326D4×C43—22no—
327D4×C43—42no—
328D4×C43—84no—
329C2×C4×C43—22no—
330C2×C4×C43—24no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—42no—
337C2×C4×C43—42no—
338C2×C4×C43—42no—
339C2×C4×C43—84no—
340C2×C4×C43C22×D412yes—
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43H(5,𝔽2)12yes—
343C2×C4×C43H(5,𝔽2)12yes—
344C2×C4×C43C2511yescharacteristic
345C22⋊D43—44no—
346C22⋊D43—44no—
347C22⋊D43—48no—
348C22⋊D43—48no—
349C22⋊D43—84no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—48no—
356C2×Dic43—42no—
357C2×Dic43—42no—
358C2×Dic43—42no—
359C2×Dic43C22×D412yes—
360C2×Dic43C22×D412yes—
361D172—22no—
362D172—22no—
363D172—44no—
364D172—42no—
365D172—84no—
366D172—84no—
367C4×D43—24no—
368C4×D43—24no—
369C4×D43—22no—
370C4×D43—22no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—48no—
374C4×D43—84no—
375Dic86—22no—
376Dic86—22no—
377Dic86—22no—
378Dic86—22no—
379Dic86—44no—
380Dic86—42no—
381Dic86—42no—
382C8×C43—22no—
383C8×C43—22no—
384C43⋊C8—22no—
385C43⋊C8—22no—
386C2×#3203—431nomaximal, Sylow
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—44no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—84no—
395C22×C43#53412yes—
396C22×C43#57612yes—
397C22×C43#57812yes—
398C22×C43C23×D411yescharacteristic
399C2×D43—22no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—44no—
406C2×D43—44no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—84no—
411C4×C43—22no—
412C4×C43—42no—
413C4×C43—42no—
414C4×C43—42no—
415C4×C43#53412yes—
416C4×C43C2×H(5,𝔽2)11yescharacteristic
417C4×C43C2×H(5,𝔽2)11yescharacteristic
418Dic43—22no—
419Dic43—22no—
420Dic43—42no—
421Dic43—42no—
422Dic43—42no—
423C2×#537—431no—
424C2×#537—431no—
425#3203—4316no—
426C2×#484—431no—
427C2×#484—431no—
428C2×#480—431no—
429C2×#480D4311yescharacteristic, complemented
430C2×#468—431no—
431C2×#468—431no—
432C2×#467—431no—
433C2×#466—431no—
434C2×#452—431no—
435C2×#452—431no—
436C2×#449—431no—
437C2×#449—431no—
438C2×#408—431no—
439C2×C43—42no—
440C2×C43—82no—
441C2×C43#320314yescomplemented
442C2×C43C2×#53411yescharacteristic
443C2×C43C2×#57611yescharacteristic
444C2×C43C2×#57811yescharacteristic
445D43—42no—
446D43—42no—
447D43—82no—
448C22×#41—431no—
449C22×#41—431no—
450C22×#41—431no—
451C22×Q16—431no—
452C22×SD16—431no—
453C22×SD16—431no—
454C22×D8—431no—
455C22×M16—431no—
456C23×C8—431no—
457#537—438no—
458#537—438no—
459#537—864no—
460#537—864no—
461C2×C22⋊Q8—431no—
462C2×C22⋊Q8—431no—
463C2×C22⋊Q8—431no—
464C2×C22⋊Q8—431no—
465C2×C22⋊Q8—861no—
466C2×C22⋊Q8—861no—
467C2×#121—431no—
468C2×#121—431no—
469C2×#121—431no—
470C2×#121—861no—
471C2×#121—861no—
472C2×#121—861no—
473C2×#121—861no—
474C2×#121—861no—
475C2×#121—861no—
476C2×#121C2×D4311yescharacteristic
477C22×C4⋊C4—431no—
478C22×C4⋊C4C2×D4311yescharacteristic
479#484—438no—
480#484—438no—
481#480—438no—
482#480C2×D4318yescomplemented
483#468—438no—
484#468—438no—
485#467—438no—
486#466—438no—
487#452—438no—
488#452—438no—
489#449—438no—
490#449—438no—
491C2×#107—431no—
492C2×#107—431no—
493C2×#107C2×D4311yescharacteristic
494C2×#107C2×D4311yescharacteristic
495C2×#103—431no—
496C2×#103—431no—
497C2×#103—431no—
498C2×#103—431no—
499C2×#102—431no—
500C2×#102—431no—
501C2×#102C2×D4311yescharacteristic
502C2×#102C2×D4311yescharacteristic
503#408—438no—
504C2×C22⋊C8—431no—
505C2×C22⋊C8—431no—
506C2×C22⋊C8—431no—
507C2×C22⋊C8C2×D4311yescharacteristic
508C43C2×#320311yescharacteristic, complemented, Sylow
509C2×#41—434no—
510C2×#41—434no—
511C2×#41—434no—
512C2×#41—434no—
513C2×#41—862no—
514C2×#41—862no—
515C2×#41—1722no—
516C2×#41—1722no—
517C2×#41—1722no—
518C2×#41—1722no—
519C2×#41—1722no—
520C2×#41—1722no—
521C22×Q8—431no—
522C22×Q8—431no—
523C22×Q8—431no—
524C22×D4—21no—
525C22×D4—431no—
526C22×D4—431no—
527C22×D4—431no—
528C22×D4—431no—
529C22×D4—861no—
530C22×D4—861no—
531C22×D4—861no—
532C22×D4—861no—
533C22×D4—861no—
534C22×D4C22×D4311yescharacteristic
535C23×C4—21no—
536C23×C4—431no—
537C23×C4—431no—
538C23×C4—861no—
539C23×C4—861no—
540C23×C4—861no—
541C23×C4C22×D4311yescharacteristic
542C2×Q16—434no—
543C2×Q16—1722no—
544C2×SD16—434no—
545C2×SD16—434no—
546C2×SD16—1722no—
547C2×SD16—1722no—
548C2×D8—434no—
549C2×D8—1722no—
550C2×M16—434no—
551C2×M16—1722no—
552C22×C8—431no—
553C22×C8—431no—
554C22×C8—434no—
555C22×C8—1722no—
556C22×C8C22×D4311yescharacteristic
557C22×C8C22×D4311yescharacteristic
558C22⋊Q8—434no—
559C22⋊Q8—434no—
560C22⋊Q8—434no—
561C22⋊Q8—434no—
562C22⋊Q8—868no—
563C22⋊Q8—862no—
564C22⋊Q8—862no—
565C22⋊Q8—862no—
566C22⋊Q8—868no—
567C22⋊Q8—862no—
568#121—22no—
569#121—434no—
570#121—434no—
571#121—434no—
572#121—868no—
573#121—862no—
574#121—862no—
575#121—868no—
576#121—868no—
577#121—868no—
578#121—862no—
579#121—868no—
580#121—868no—
581#121C22×D4314yes—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—431no—
585C2×C4⋊C4—434no—
586C2×C4⋊C4—862no—
587C2×C4⋊C4—861no—
588C2×C4⋊C4—861no—
589C2×C4⋊C4—861no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4C22×D4311yescharacteristic
593C2×C4⋊C4C22×D4311yescharacteristic
594C2×C4⋊C4C22×D4311yescharacteristic
595C2×C4⋊C4C22×D4314yes—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—861no—
598C2×C22⋊C4—861no—
599C2×C22⋊C4—861no—
600C2×C22⋊C4—861no—
601C2×C22⋊C4—861no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604#107—434no—
605#107—434no—
606#107C22×D4314yes—
607#107C22×D4314yes—
608#103—434no—
609#103—434no—
610#103—434no—
611#103—434no—
612#102—434no—
613#102—434no—
614#102C22×D4314yes—
615#102C22×D4314yes—
616C22⋊C8—434no—
617C22⋊C8—434no—
618C22⋊C8—434no—
619C22⋊C8C22×D4314yes—
620C24—21no—
621C24—431no—
622C24—431no—
623C24—861no—
624C24D4×D4311yescharacteristic
625#41—1728no—
626#41—1724no—
627#41—1724no—
628#41—1724no—
629#41—1724no—
630#41—1728no—
631#41—1724no—
632#41—1724no—
633#41—1728no—
634C2×Q8—434no—
635C2×Q8—432no—
636C2×Q8—432no—
637C2×Q8—861no—
638C2×Q8—861no—
639C2×Q8—862no—
640C2×Q8—862no—
641C2×Q8—862no—
642C2×Q8—862no—
643C2×Q8—1722no—
644C2×D4—24no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—82no—
649C2×D4—434no—
650C2×D4—434no—
651C2×D4—434no—
652C2×D4—432no—
653C2×D4—864no—
654C2×D4—864no—
655C2×D4—864no—
656C2×D4—864no—
657C2×D4—864no—
658C2×D4—861no—
659C2×D4—862no—
660C2×D4—862no—
661C2×D4—3442no—
662C2×D4—3442no—
663C2×D4—3442no—
664C2×D4—1722no—
665C2×D4—1722no—
666C2×D4—1722no—
667C2×D4—1724no—
668C2×D4—1724no—
669C2×D4C23×D4312yes—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—82no—
677C22×C4—431no—
678C22×C4—431no—
679C22×C4—432no—
680C22×C4—432no—
681C22×C4—432no—
682C22×C4—432no—
683C22×C4—864no—
684C22×C4—864no—
685C22×C4—862no—
686C22×C4—862no—
687C22×C4—862no—
688C22×C4—862no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—861no—
692C22×C4—864no—
693C22×C4—3442no—
694C22×C4—1724no—
695C22×C4—1724no—
696C22×C4D4×D4312yes—
697C22×C4D4×D4311yescharacteristic
698C22×C4C23×D4312yes—
699C22×C4C23×D4311yescharacteristic
700Q16—1724no—
701SD16—1724no—
702SD16—1724no—
703D8—1724no—
704M16—1724no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—432no—
708C2×C8—432no—
709C2×C8—862no—
710C2×C8—862no—
711C2×C8—1724no—
712C2×C8C23×D4312yes—
713C2×C8C23×D4312yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—432no—
719C4⋊C4—864no—
720C4⋊C4—864no—
721C4⋊C4—864no—
722C4⋊C4—864no—
723C4⋊C4—861no—
724C4⋊C4—864no—
725C4⋊C4C23×D4312yes—
726C4⋊C4C23×D4312yes—
727C4⋊C4C23×D4312yes—
728C22⋊C4—24no—
729C22⋊C4—864no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—432no—
744C23—432no—
745C23—862no—
746C23—862no—
747C23—862no—
748C23—862no—
749C23—862no—
750C23—862no—
751C23—862no—
752C23—1722no—
753C23—1722no—
754C23—1722no—
755C23C2×D4×D4312yes—
756C23C2×D4×D4311yescharacteristic
757Q8—862no—
758Q8—862no—
759Q8—862no—
760Q8—862no—
761Q8—1724no—
762Q8—1722no—
763Q8—1722no—
764D4—22no—
765D4—22no—
766D4—42no—
767D4—84no—
768D4—862no—
769D4—862no—
770D4—3444no—
771D4—3444no—
772D4—3444no—
773D4—1724no—
774D4—1724no—
775D4—1724no—
776D4—1728no—
777D4—1728no—
778D4—1722no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—84no—
790C2×C4—432no—
791C2×C4—432no—
792C2×C4—862no—
793C2×C4—862no—
794C2×C4—864no—
795C2×C4—864no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—3444no—
804C2×C4—1728no—
805C2×C4—1728no—
806C2×C4—1722no—
807C2×C4—1722no—
808C2×C4—1722no—
809C2×C4C2×D4×D4312yes—
810C2×C4C2×D4×D4311yescharacteristic
811C2×C4#1306337112yes—
812C2×C4#1306337112yes—
813C2×C4C24×D4311yescharacteristic
814C8—22no—
815C8—22no—
816C8—862no—
817C8—862no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—84no—
826C22—862no—
827C22—862no—
828C22—862no—
829C22—862no—
830C22—862no—
831C22—862no—
832C22—3444no—
833C22—1722no—
834C22—1722no—
835C22—1722no—
836C22—1724no—
837C22—1724no—
838C22#1458346012yes—
839C22#1458370012yes—
840C22#1458371512yes—
841C22C22×D4×D4311yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—862no—
847C4—862no—
848C4—1722no—
849C4—1722no—
850C4—1722no—
851C4#1458346012yes—
852C4C2×#1306337111yescharacteristic
853C4C2×#1306337111yescharacteristic
854C2—42no—
855C2—82no—
856C2—3442no—
857C2—1722no—
858C2—1722no—
859C2#1914549514yesdirect product factor
860C2C2×#1458346011yescharacteristic
861C2C2×#1458370011yescharacteristic
862C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#480C2
socleC23×C43C22×D4
hypercenterC2×#480D43
hypocenterC43C2×#3203
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#14583480C2semidirect
2. C2×#14583478C2semidirect
3. #19145495C2direct (N × H)
4. C2×#14583236C2semidirect
5. C2×#14583234C2semidirect
6. C2×#14583214C2semidirect
7. C2×#14583146C2semidirect
8. C2×#14583144C2semidirect
9. C2×#14583141C2semidirect
10. C2×#14583134C2semidirect
11. C2×#14583063C2semidirect
12. C2×#14583062C2semidirect
13. C2×#14583045C2semidirect
14. C2×#14583042C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#480C2semidirect
27. #14583480C22semidirect
29. #14583478C22semidirect
46. #14583236C22semidirect
47. #14583234C22semidirect
48. #14583214C22semidirect
49. #14583146C22semidirect
50. #14583144C22semidirect
51. #14583141C22semidirect
52. #14583134C22semidirect
53. #14583063C22semidirect
54. #14583062C22semidirect
55. #14583045C22semidirect
56. #14583042C22semidirect
65. #14582864C22semidirect
71. C43×#480C22semidirect
429. C2×#480D43semidirect
441. C2×C43#3203semidirect
482. #480C2×D43semidirect
508. C43C2×#3203semidirect
859. C2#19145495direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834802
C2×#145834782
#191454952
C2×#145832362
C2×#145832342
C2×#145832142
C2×#145831462
C2×#145831442
C2×#145831412
C2×#145831342
C2×#145830632
C2×#145830622
C2×#145830452
C2×#145830422
C2×#145828642
C2×C43×#4802
C2×#320343