Finite Group Databasebeta

← C2×#21456916 #30551371

Subgroups — C2×#21456916 #30551371

Order 15616.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840386C211yesmaximal, characteristic, complemented
2C2×#16840325C211yesmaximal, characteristic, complemented
3#21456916C2116yesmaximal, direct product factor
4C2×#16840149C211yesmaximal, characteristic, complemented
5C2×#16840146C211yesmaximal, characteristic, complemented
6C2×#16840124C211yesmaximal, characteristic, complemented
7C2×#16839983C211yesmaximal, characteristic, complemented
8C2×#16839961C211yesmaximal, characteristic, complemented
9C2×#16839976C211yesmaximal, characteristic, complemented
10C2×#16839956C211yesmaximal, characteristic, complemented
11C2×#16839925C211yesmaximal, characteristic, complemented
12C2×#16839908C211yesmaximal, characteristic, complemented
13C2×#16839914C211yesmaximal, characteristic, complemented
14C2×#16839897C211yesmaximal, characteristic, complemented
15C2×#16839821C211yesmaximal, characteristic, complemented
16C2×C61×#486C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×Dic244C2211yescharacteristic, complemented
20C22×#11758190C2211yescharacteristic
21C22×#11758190C2211yescharacteristic, complemented
22C22×#11758200C2211yescharacteristic
23C22×#11758200C2211yescharacteristic, complemented
24C22×D488C2211yescharacteristic
25C22×#11758199C2211yescharacteristic
26C22×#11758199C2211yescharacteristic, complemented
27#16840386—24no—
28#16840386C2218yescomplemented
29#16840325—24no—
30#16840325C2218yescomplemented
31C2×#14519773C2211yescharacteristic
32C2×#14519772—21no—
33C2×#14519766—21no—
34C2×#14519765C2211yescharacteristic
35C2×#14519765C2211yescharacteristic, complemented
36C2×#14519764C2211yescharacteristic
37C2×#14519762—21no—
38C2×#14519757C2211yescharacteristic
39C2×#14519753—21no—
40C2×#14519752C2211yescharacteristic
41C2×#14519749—21no—
42C2×#14519749—21no—
43C2×#14519745—21no—
44C2×#14519745—21no—
45C2×#14519742C2211yescharacteristic, complemented
46C2×#14519739C2211yescharacteristic, complemented
47C2×#14519734C2211yescharacteristic
48#16840149C2218yescomplemented
49#16840146C2218yescomplemented
50#16840124C2218yescomplemented
51#16839983C2218yescomplemented
52#16839976C2218yescomplemented
53#16839961C2218yescomplemented
54#16839956C2218yescomplemented
55#16839925C2218yescomplemented
56#16839914C2218yescomplemented
57#16839908C2218yescomplemented
58#16839897C2218yescomplemented
59#16839821C2218yescomplemented
60C2×#14519706C2211yescharacteristic, complemented
61C2×#14519706C2211yescharacteristic, complemented
62C2×#14519700C2211yescharacteristic, complemented
63C2×#14519700C2211yescharacteristic, complemented
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519688C2211yescharacteristic, complemented
69C2×C4⋊Q8×C61C2211yescharacteristic, complemented
70C2×#127×C61C2211yescharacteristic
71C61×#486C2218yescomplemented
72C2×#102×C61C2211yescharacteristic
73C2×#102×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic, complemented
76C2×C4×C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758224—22no—
79C2×#11758224—42no—
80C2×#11758224—42no—
81C2×#11758224C2314yes—
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×D244—21no—
85C22×D244C2311yescharacteristic
86C22×D244C2311yescharacteristic
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C2×D4×D61—22no—
92C2×D4×D61—42no—
93C2×D4×D61—42no—
94C2×D4×D61C2314yes—
95C23×Dic61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98C2×Dic244—42no—
99C2×Dic244C2314yescomplemented
100C2×#11758190—42no—
101C2×#11758190—42no—
102C2×#11758190C2314yes—
103C2×#11758190C2314yescomplemented
104C2×#11758200—42no—
105C2×#11758200—42no—
106C2×#11758200C2314yes—
107C2×#11758200C2314yescomplemented
108C2×D488—42no—
109C2×D488C2314yes—
110C2×#11758199—42no—
111C2×#11758199—42no—
112C2×#11758199C2314yes—
113C2×#11758199C2314yescomplemented
114C22×#92418C2311yescharacteristic
115C22×#92418C2311yescharacteristic
116#14519773—22no—
117#14519773C2314yes—
118#14519772—28no—
119#14519766—28no—
120#14519765—22no—
121#14519765—22no—
122#14519765C2314yes—
123#14519765C2314yescomplemented
124#14519764—22no—
125#14519764C2314yes—
126#14519762—28no—
127#14519757—22no—
128#14519757C2314yes—
129#14519753—28no—
130#14519752—22no—
131#14519752C2314yes—
132#14519749—28no—
133#14519749—28no—
134#14519745—28no—
135#14519745—28no—
136#14519742—22no—
137#14519742C2314yescomplemented
138#14519739—22no—
139#14519739C2314yescomplemented
140#14519734D414yes—
141#14519734C2314yes—
142C2×C4⋊Dic61—21no—
143C2×#11758196—21no—
144C2×#11758196D411yescharacteristic
145C2×#11758196D411yescharacteristic
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198D411yescharacteristic
156C2×#11758198D411yescharacteristic
157C2×C4×Dic61—21no—
158C2×C4×Dic61C2311yescharacteristic
159#14519706C2314yescomplemented
160#14519706C2314yescomplemented
161#14519700C2314yescomplemented
162#14519700C2314yescomplemented
163#14519697C2314yes—
164#14519697C2314yes—
165#14519689C2314yes—
166#14519689C2314yes—
167#14519688C2314yescomplemented
168C22×Q8×C61—21no—
169C22×D4×C61—21no—
170C22×D4×C61—21no—
171C22×D4×C61C2311yescharacteristic
172C22×D4×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175C4⋊Q8×C61—22no—
176C4⋊Q8×C61C2314yescomplemented
177#127×C61—22no—
178#127×C61C2314yes—
179C2×C4⋊C4×C61—21no—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C4⋊C4×C61C2311yescharacteristic
182C2×C42×C61C2311yescharacteristic
183#102×C61C2314yes—
184#102×C61C2314yes—
185#102×C61C2314yescomplemented
186#102×C61C2314yescomplemented
187C4×C8×C61C2314yescomplemented
188C24×C61—21no—
189C24×C61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—24no—
193C23×D61—44no—
194C23×D61—82no—
195C23×D61—82no—
196C23×D61C2×D411yescharacteristic
197C2×Q8×C61—24no—
198C2×Q8×C61—82no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—24no—
202C2×D4×C61—24no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—22no—
207C2×D4×C61—82no—
208C2×D4×C61—82no—
209C2×D4×C61C2412yes—
210C2×D4×C61C2412yes—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2411yescharacteristic
216C2×C22⋊D61—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—44no—
221C2×C22⋊D61—44no—
222C2×C22⋊D61—82no—
223C2×C22⋊D61—82no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—24no—
227C22×Dic61—44no—
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231#11758224—44no—
232#11758224—44no—
233#11758224—48no—
234D4×D61—44no—
235D4×D61—44no—
236D4×D61—48no—
237C2×D244—22no—
238C2×D244—22no—
239C2×D244—22no—
240C2×D244—22no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—24no—
244C2×D244—82no—
245C2×D244C2412yes—
246C2×D244C2412yes—
247C2×C4×D61—22no—
248C2×C4×D61—22no—
249C2×C4×D61—24no—
250C2×C4×D61—82no—
251C2×C4×D61C2×D412yes—
252C2×C4×D61C2412yes—
253C2×Dic122—22no—
254C2×Dic122—22no—
255C2×Dic122—22no—
256C2×Dic122—22no—
257C2×Dic122—21no—
258C2×Dic122—21no—
259C2×Dic122C2412yes—
260C2×Dic122C2412yes—
261C2×C8×C61—22no—
262C2×C8×C61—22no—
263C2×C8×C61C2412yes—
264C2×C8×C61C2412yes—
265C4⋊C4×C61—24no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61C2412yes—
269C4⋊C4×C61C2412yes—
270C42×C61C2×D412yes—
271C42×C61C2412yes—
272C22⋊Dic61—24no—
273C22⋊Dic61—24no—
274#11758200—44no—
275#11758200—44no—
276#11758199—44no—
277#11758199—44no—
278#11758198—24no—
279#11758198—24no—
280#11758198—24no—
281#11758198—24no—
282#11758198—24no—
283#11758198—24no—
284#11758198—24no—
285#11758198C2×D414yes—
286#11758198C2×D414yes—
287C4⋊Dic61—24no—
288#11758196—24no—
289#11758196C2×D414yes—
290#11758196C2×D414yes—
291C4×Dic61—24no—
292C4×Dic61C2×D412yes—
293C4×Dic61C2412yes—
294C2×#92418—22no—
295C2×#92418—22no—
296C2×#92418C2412yes—
297C2×#92418C2412yes—
298Dic244—44no—
299D488—44no—
300#11758190—44no—
301#11758190—44no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61C22×D411yescharacteristic
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—48no—
317C22×D61—42no—
318C22×D61—42no—
319C22×D61—42no—
320C22×D61—42no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61—84no—
324C22×D61—84no—
325C22×D61—816no—
326C22×D61C22×D412yes—
327Q8×C61—84no—
328D4×C61—22no—
329D4×C61—22no—
330D4×C61—22no—
331D4×C61—22no—
332D4×C61—42no—
333D4×C61—42no—
334D4×C61—84no—
335D4×C61—84no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—42no—
341C2×C4×C61—42no—
342C2×C4×C61C22×D412yes—
343C2×C4×C61C22×D412yes—
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61H(5,𝔽2)12yes—
346C2×C4×C61H(5,𝔽2)12yes—
347C2×C4×C61C2511yescharacteristic
348C22⋊D61—48no—
349C22⋊D61—48no—
350C22⋊D61—84no—
351C22⋊D61—84no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—48no—
358C2×Dic61—42no—
359C2×Dic61—42no—
360C2×Dic61C22×D412yes—
361C2×Dic61C22×D412yes—
362C2×Dic61C22×D412yes—
363D244—22no—
364D244—22no—
365D244—22no—
366D244—22no—
367D244—42no—
368D244—42no—
369D244—84no—
370C4×D61—24no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—84no—
374Dic122—22no—
375Dic122—22no—
376Dic122—22no—
377Dic122—22no—
378Dic122—42no—
379Dic122—42no—
380C8×C61—22no—
381C8×C61—22no—
382#92418—22no—
383#92418—22no—
384C2×#3224—611nomaximal, Sylow
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—84no—
392C22×C61—84no—
393C22×C61#53512yes—
394C22×C61#57612yes—
395C22×C61#57712yes—
396C22×C61C23×D411yescharacteristic
397C2×D61—22no—
398C2×D61—22no—
399C2×D61—22no—
400C2×D61—44no—
401C2×D61—42no—
402C2×D61—42no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—816no—
408C2×D61—84no—
409C2×D61—84no—
410C4×C61—22no—
411C4×C61—22no—
412C4×C61—42no—
413C4×C61—42no—
414C4×C61#53512yes—
415C4×C61C2×H(5,𝔽2)11yescharacteristic
416C4×C61C2×H(5,𝔽2)11yescharacteristic
417Dic61—22no—
418Dic61—22no—
419Dic61—22no—
420Dic61—42no—
421Dic61—42no—
422C2×#542—611no—
423C2×#535—611no—
424#3224—6116no—
425C2×#496—611no—
426C2×#495—611no—
427C2×#489—611no—
428C2×#486D6111yescharacteristic, complemented
429C2×#464—611no—
430C2×#460—611no—
431C2×#463—611no—
432C2×#459—611no—
433C2×#452—611no—
434C2×#449—611no—
435C2×#450—611no—
436C2×#447—611no—
437C2×#433—611no—
438C2×C61—82no—
439C2×C61—82no—
440C2×C61#322414yescomplemented
441C2×C61C2×#53511yescharacteristic
442C2×C61C2×#57611yescharacteristic
443C2×C61C2×#57711yescharacteristic
444D61—42no—
445D61—82no—
446D61—82no—
447C22×#41—611no—
448C23×D4—611no—
449C22×Q16—611no—
450C22×SD16—611no—
451C22×SD16—611no—
452C22×SD16—611no—
453C22×SD16—611no—
454C22×D8—611no—
455C22×D8—611no—
456C22×D8—611no—
457#542—618no—
458#542—1224no—
459#535—618no—
460#535—1224no—
461C2×C4⋊Q8C2×D6111yescharacteristic, complemented
462C2×#127—611no—
463C2×#127C2×D6111yescharacteristic
464C2×#126—1221no—
465C2×#124—611no—
466C2×#124—611no—
467C2×#124—611no—
468C2×#124—1221no—
469C2×#123—1221no—
470C2×C22⋊Q8—611no—
471C2×C22⋊Q8—1221no—
472C2×#121—611no—
473C2×#121—1221no—
474C2×#121—1221no—
475C2×#120—1221no—
476C2×#120—1221no—
477C2×C4×Q8—611no—
478C2×C4×D4—611no—
479C2×#117—611no—
480#496—618no—
481#495—618no—
482#489—618no—
483#486C2×D6118yescomplemented
484#464—618no—
485#463—618no—
486#460—618no—
487#459—618no—
488#452—618no—
489#450—618no—
490#449—618no—
491#447—618no—
492#433—618no—
493C2×C4⋊C8—611no—
494C2×C4⋊C8—611no—
495C2×#103—611no—
496C2×#103—611no—
497C2×#102—611no—
498C2×#102—611no—
499C2×#102C2×D6111yescharacteristic
500C2×#102C2×D6111yescharacteristic
501C2×#102C2×D6111yescharacteristic, complemented
502C2×#102C2×D6111yescharacteristic, complemented
503C2×C22⋊C8—611no—
504C2×C22⋊C8—611no—
505C2×#97—611no—
506C2×C4×C8C2×D6111yescharacteristic, complemented
507C61C2×#322411yescharacteristic, complemented, Sylow
508C25—1221no—
509C2×#41—614no—
510C2×#41—1222no—
511C2×#41—2442no—
512C2×#41—2442no—
513C22×Q8—21no—
514C22×Q8—611no—
515C22×Q8—611no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—614no—
519C22×D4—611no—
520C22×D4—611no—
521C22×D4—1221no—
522C22×D4—1222no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4—1221no—
527C22×D4—2442no—
528C22×D4—2442no—
529C22×D4C22×D6111yescharacteristic
530C22×D4C22×D6111yescharacteristic
531C23×C4—611no—
532C23×C4—1221no—
533C23×C4—1221no—
534C2×Q16—614no—
535C2×Q16—2442no—
536C2×SD16—614no—
537C2×SD16—614no—
538C2×SD16—614no—
539C2×SD16—614no—
540C2×SD16—2442no—
541C2×SD16—2442no—
542C2×SD16—2442no—
543C2×SD16—2442no—
544C2×D8—614no—
545C2×D8—614no—
546C2×D8—614no—
547C2×D8—2442no—
548C2×D8—2442no—
549C2×D8—2442no—
550C22×C8—611no—
551C22×C8—611no—
552C22×C8C22×D6111yescharacteristic
553C22×C8C22×D6111yescharacteristic
554C4⋊Q8—22no—
555C4⋊Q8C22×D6114yescomplemented
556#127—22no—
557#127—614no—
558#127—1222no—
559#127C22×D6114yes—
560#126—1228no—
561#124—614no—
562#124—614no—
563#124—614no—
564#124—1222no—
565#124—1228no—
566#124—1222no—
567#124—1222no—
568#123—1228no—
569C22⋊Q8—614no—
570C22⋊Q8—1222no—
571C22⋊Q8—1228no—
572#121—614no—
573#121—1222no—
574#121—1228no—
575#121—1228no—
576#120—1228no—
577#120—1228no—
578C4×Q8—614no—
579C4×Q8—1222no—
580C4×D4—614no—
581C4×D4—1222no—
582#117—614no—
583#117—614no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—1221no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4C22×D6111yescharacteristic
590C2×C4⋊C4C22×D6111yescharacteristic
591C2×C22⋊C4—611no—
592C2×C22⋊C4—611no—
593C2×C22⋊C4—1221no—
594C2×C22⋊C4—1221no—
595C2×C22⋊C4—1221no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C42—611no—
603C2×C42—1221no—
604C2×C42C22×D6111yescharacteristic
605C4⋊C8—614no—
606C4⋊C8—614no—
607#103—614no—
608#103—614no—
609#102—614no—
610#102—614no—
611#102C22×D6114yes—
612#102C22×D6114yes—
613#102C22×D6114yescomplemented
614#102C22×D6114yescomplemented
615C22⋊C8—614no—
616C22⋊C8—614no—
617#97—614no—
618C4×C8C22×D6114yescomplemented
619C24—21no—
620C24—21no—
621C24—611no—
622C24—1224no—
623C24—1221no—
624C24—1221no—
625C24—4882no—
626C24—4882no—
627C24—2444no—
628#41—2444no—
629#41—2444no—
630#41—2448no—
631C2×Q8—24no—
632C2×Q8—82no—
633C2×Q8—612no—
634C2×Q8—612no—
635C2×Q8—1221no—
636C2×Q8—1221no—
637C2×Q8—1222no—
638C2×Q8—1222no—
639C2×Q8—1222no—
640C2×Q8—1222no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—82no—
650C2×D4—82no—
651C2×D4—612no—
652C2×D4—612no—
653C2×D4—1224no—
654C2×D4—1224no—
655C2×D4—1224no—
656C2×D4—1224no—
657C2×D4—1224no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4—1222no—
661C2×D4—1222no—
662C2×D4—1222no—
663C2×D4—1222no—
664C2×D4—4882no—
665C2×D4—4882no—
666C2×D4—4882no—
667C2×D4—2444no—
668C2×D4—2444no—
669C2×D4—2448no—
670C2×D4—2444no—
671C2×D4—2444no—
672C2×D4C23×D6112yes—
673C2×D4C23×D6112yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—612no—
680C22×C4—612no—
681C22×C4—1224no—
682C22×C4—1224no—
683C22×C4—1222no—
684C22×C4—1222no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—4882no—
688C22×C4—2444no—
689C22×C4D4×D6111yescharacteristic
690C22×C4D4×D6111yescharacteristic
691C22×C4C23×D6111yescharacteristic
692Q16—2444no—
693SD16—2444no—
694SD16—2444no—
695SD16—2444no—
696SD16—2444no—
697D8—2444no—
698D8—2444no—
699D8—2444no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—612no—
703C2×C8—612no—
704C2×C8—1222no—
705C2×C8—1222no—
706C2×C8C23×D6112yes—
707C2×C8C23×D6112yes—
708C4⋊C4—24no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—614no—
712C4⋊C4—614no—
713C4⋊C4—1224no—
714C4⋊C4—1224no—
715C4⋊C4C23×D6112yes—
716C4⋊C4C23×D6112yes—
717C22⋊C4—614no—
718C22⋊C4—614no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—1224no—
722C22⋊C4—1224no—
723C22⋊C4—1224no—
724C22⋊C4—1224no—
725C22⋊C4—1224no—
726C22⋊C4—1224no—
727C22⋊C4—1224no—
728C42—612no—
729C42—612no—
730C42—1224no—
731C42D4×D6112yes—
732C42C23×D6112yes—
733C23—22no—
734C23—22no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—612no—
742C23—1222no—
743C23—1222no—
744C23—1222no—
745C23—1222no—
746C23—1222no—
747C23—4884no—
748C23—4884no—
749C23—48816no—
750C23—2448no—
751C23—2442no—
752C23—2442no—
753C23—2442no—
754C23—2442no—
755C23—2442no—
756C23—2442no—
757C23C2×D4×D6111yescharacteristic
758Q8—84no—
759Q8—1222no—
760Q8—1222no—
761Q8—1222no—
762Q8—1222no—
763Q8—2442no—
764Q8—2442no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—42no—
771D4—84no—
772D4—84no—
773D4—1222no—
774D4—1222no—
775D4—1222no—
776D4—1222no—
777D4—4884no—
778D4—4884no—
779D4—4884no—
780D4—2448no—
781D4—2448no—
782D4—2442no—
783D4—2442no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—612no—
791C2×C4—612no—
792C2×C4—612no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1224no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—4884no—
802C2×C4—2448no—
803C2×C4—2442no—
804C2×C4—2442no—
805C2×C4C2×D4×D6112yes—
806C2×C4C2×D4×D6112yes—
807C2×C4C2×D4×D6111yescharacteristic
808C2×C4#1451982312yes—
809C2×C4#1451982312yes—
810C2×C4C24×D6111yescharacteristic
811C8—22no—
812C8—22no—
813C8—1222no—
814C8—1222no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—84no—
822C22—84no—
823C22—1222no—
824C22—1222no—
825C22—1222no—
826C22—48816no—
827C22—4884no—
828C22—4884no—
829C22—2442no—
830C22—2442no—
831C22—2442no—
832C22—2442no—
833C22—2442no—
834C22—2442no—
835C22—2444no—
836C22#1684033012yes—
837C22#1684056312yes—
838C22#1684056812yes—
839C22C22×D4×D6111yescharacteristic
840C4—22no—
841C4—22no—
842C4—42no—
843C4—42no—
844C4—1222no—
845C4—1222no—
846C4—1222no—
847C4—2442no—
848C4—2442no—
849C4#1684033012yes—
850C4C2×#1451982311yescharacteristic
851C4C2×#1451982311yescharacteristic
852C2—82no—
853C2—82no—
854C2—4882no—
855C2—4882no—
856C2—2442no—
857C2#2145691614yesdirect product factor
858C2C2×#1684033011yescharacteristic
859C2C2×#1684056311yescharacteristic
860C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#486C2
socleC23×C61C22×D4
hypercenterC2×#486D61
hypocenterC61C2×#3224
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#16840386C2semidirect
2. C2×#16840325C2semidirect
3. #21456916C2direct (N × H)
4. C2×#16840149C2semidirect
5. C2×#16840146C2semidirect
6. C2×#16840124C2semidirect
7. C2×#16839983C2semidirect
8. C2×#16839961C2semidirect
9. C2×#16839976C2semidirect
10. C2×#16839956C2semidirect
11. C2×#16839925C2semidirect
12. C2×#16839908C2semidirect
13. C2×#16839914C2semidirect
14. C2×#16839897C2semidirect
15. C2×#16839821C2semidirect
16. C2×C61×#486C2semidirect
19. C22×Dic244C22semidirect
21. C22×#11758190C22semidirect
23. C22×#11758200C22semidirect
26. C22×#11758199C22semidirect
28. #16840386C22semidirect
30. #16840325C22semidirect
35. C2×#14519765C22semidirect
45. C2×#14519742C22semidirect
46. C2×#14519739C22semidirect
48. #16840149C22semidirect
49. #16840146C22semidirect
50. #16840124C22semidirect
51. #16839983C22semidirect
52. #16839976C22semidirect
53. #16839961C22semidirect
54. #16839956C22semidirect
55. #16839925C22semidirect
56. #16839914C22semidirect
57. #16839908C22semidirect
58. #16839897C22semidirect
59. #16839821C22semidirect
60. C2×#14519706C22semidirect
61. C2×#14519706C22semidirect
62. C2×#14519700C22semidirect
63. C2×#14519700C22semidirect
68. C2×#14519688C22semidirect
69. C2×C4⋊Q8×C61C22semidirect
71. C61×#486C22semidirect
74. C2×#102×C61C22semidirect
75. C2×#102×C61C22semidirect
76. C2×C4×C8×C61C22semidirect
99. C2×Dic244C23semidirect
103. C2×#11758190C23semidirect
107. C2×#11758200C23semidirect
113. C2×#11758199C23semidirect
123. #14519765C23semidirect
137. #14519742C23semidirect
139. #14519739C23semidirect
159. #14519706C23semidirect
160. #14519706C23semidirect
161. #14519700C23semidirect
162. #14519700C23semidirect
167. #14519688C23semidirect
176. C4⋊Q8×C61C23semidirect
185. #102×C61C23semidirect
186. #102×C61C23semidirect
187. C4×C8×C61C23semidirect
428. C2×#486D61semidirect
440. C2×C61#3224semidirect
461. C2×C4⋊Q8C2×D61semidirect
483. #486C2×D61semidirect
501. C2×#102C2×D61semidirect
502. C2×#102C2×D61semidirect
506. C2×C4×C8C2×D61semidirect
507. C61C2×#3224semidirect
555. C4⋊Q8C22×D61semidirect
613. #102C22×D61semidirect
614. #102C22×D61semidirect
618. C4×C8C22×D61semidirect
857. C2#21456916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403862
C2×#168403252
#214569162
C2×#168401492
C2×#168401462
C2×#168401242
C2×#168399832
C2×#168399612
C2×#168399762
C2×#168399562
C2×#168399252
C2×#168399082
C2×#168399142
C2×#168398972
C2×#168398212
C2×C61×#4862
C2×#322461