Finite Group Databasebeta

← SD16×#11758198 #29695840

Subgroups — SD16×#11758198 #29695840

Order 15616.

1614 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×D61C211yesmaximal, characteristic
2C2×SD16×Dic61C211yesmaximal, characteristic, complemented
3Q8×#11758198C211yesmaximal, characteristic, complemented
4D4×#11758198C211yesmaximal, characteristic
5#21446673C211yesmaximal, characteristic, complemented
6#21446671C211yesmaximal, characteristic, complemented
7#21446174C211yesmaximal, characteristic, complemented
8#21446172C211yesmaximal, characteristic, complemented
9#21446153C211yesmaximal, characteristic, complemented
10#21446151C211yesmaximal, characteristic, complemented
11#21445841C211yesmaximal, characteristic, complemented
12#21445752C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic
14C8×#11758198C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C2×SD16×D61—24no—
22C2×SD16×D61—24no—
23C2×SD16×D61C418yescomplemented
24C22×C8×D61C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic, complemented
26C2×D4×Dic61C2211yescharacteristic
27C22×#11758198—21no—
28SD16×Dic61—24no—
29C2×#14519709C2211yescharacteristic, complemented
30C2×#14519702C2211yescharacteristic, complemented
31C2×#14519701C2211yescharacteristic, complemented
32C2×#14519700C2211yescharacteristic, complemented
33C2×#14519699C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic, complemented
38#16839668—21no—
39#16839668C2211yescharacteristic, complemented
40#16839667—21no—
41#16839667C2211yescharacteristic, complemented
42#16839664C2211yescharacteristic
43#16839663C2211yescharacteristic
44#16839641—21no—
45#16839639—21no—
46#16839619—21no—
47#16839619C2211yescharacteristic
48#16839619C2211yescharacteristic
49#16839617—21no—
50C4×#11758198—21no—
51C4×#11758198C2211yescharacteristic
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839517C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56C22×SD16×C61C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic, complemented
58C2×C4×D4×C61C2211yescharacteristic
59C4×SD16×C61—24no—
60C2×#106×C61C2211yescharacteristic, complemented
61C2×#103×C61C2211yescharacteristic, complemented
62C2×#102×C61C2211yescharacteristic
63C2×C4×C8×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×Dic122—21no—
66C22×Dic122C2311yescharacteristic
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—41no—
71C2×Q8×D61—41no—
72C2×Q8×D61C2×C414yescomplemented
73C22×D244C2311yescharacteristic
74C22×C22⋊D61—21no—
75C2×D4×D61—22no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—41no—
79C2×D4×D61—41no—
80C2×D4×D61C2×C414yes—
81C23×Dic61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C2×#11758190—22no—
85C2×#11758190—22no—
86C2×#11758190C2×C414yescomplemented
87C2×#11758200—22no—
88C2×#11758200—22no—
89C2×#11758200C2×C414yes—
90C2×#11758201—22no—
91C2×#11758201—22no—
92C2×#11758201C2×C414yescomplemented
93SD16×D61—232no—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C2×C8×D61—22no—
97C2×C8×D61—22no—
98C2×C8×D61C2×C414yescomplemented
99Q8×Dic61—22no—
100Q8×Dic61—41no—
101D4×Dic61—22no—
102D4×Dic61—41no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C22⋊Dic61—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—44no—
114C2×#11758198D411yescharacteristic
115C2×#11758198D411yescharacteristic
116C2×C4×Dic61—21no—
117C2×C4×Dic61C2311yescharacteristic
118#14519709—22no—
119#14519702—41no—
120#14519701—22no—
121#14519700—41no—
122#14519699—41no—
123#14519698—22no—
124#14519697—41no—
125#14519689—22no—
126C8×Dic61—22no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131#14519684—21no—
132#14519684—21no—
133#14519684D411yescharacteristic
134#14519684D411yescharacteristic
135C22×Q8×C61C2311yescharacteristic
136C22×D4×C61C2311yescharacteristic
137C23×C4×C61—21no—
138C2×SD16×C61C2×C414yes—
139C2×SD16×C61D414yes—
140C2×SD16×C61D414yes—
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C4×Q8×C61—22no—
144C4×Q8×C61—41no—
145C4×D4×C61—22no—
146C4×D4×C61—41no—
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C22⋊C4×C61—21no—
151C2×C42×C61—21no—
152C2×C42×C61C2311yescharacteristic
153#106×C61—22no—
154#103×C61—22no—
155#102×C61—22no—
156C4×C8×C61—22no—
157C24×C61—21no—
158C23×D61—21no—
159C23×D61—24no—
160C23×D61—42no—
161C23×D61—42no—
162C23×D61—42no—
163C23×D61—42no—
164C23×D61—81no—
165C23×D61—81no—
166C23×D61C2×D411yescharacteristic
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61C22×C412yes—
171C2×Q8×C61C2×D412yes—
172C2×Q8×C61C2×D412yes—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61C22×C412yes—
177C2×D4×C61C2×D412yes—
178C2×D4×C61C2×D412yes—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61—81no—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2411yescharacteristic
188C2×C22⋊D61—24no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—42no—
195C22×Dic61—42no—
196C22×Dic61—81no—
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200Q8×D61—28no—
201Q8×D61—44no—
202Q8×D61—44no—
203Q8×D61—44no—
204D4×D61—28no—
205D4×D61—44no—
206D4×D61—44no—
207D4×D61—44no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244C22×C412yes—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—24no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61C22×C412yes—
222C2×C4×D61#4112yes—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—24no—
229C2×Dic122—42no—
230C2×Dic122—42no—
231C2×Dic122C22×C412yes—
232SD16×C61C22⋊C4116yescomplemented
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61C22×C412yes—
237C2×C8×C61C2×D412yes—
238C2×C8×C61C2×D412yes—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—42no—
244C22⋊C4×C61—42no—
245C42×C61—21no—
246C42×C61—21no—
247C42×C61—42no—
248C22⋊Dic61—42no—
249#11758201—28no—
250#11758200—28no—
251#11758198—22no—
252#11758198—42no—
253#11758198—42no—
254#11758198—42no—
255#11758198—42no—
256#11758198—81no—
257#11758198—81no—
258#11758198SD1614yesdirect product factor
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—42no—
264C4×Dic61—21no—
265C4×Dic61—21no—
266C4×Dic61—42no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418C22×C412yes—
273#11758190—28no—
274C8×D61—28no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61C22×D411yescharacteristic
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—22no—
288C22×D61—48no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—48no—
296C22×D61—84no—
297C22×D61—84no—
298C22×D61—84no—
299C22×D61—84no—
300C22×D61—84no—
301C22×D61C4×D412yes—
302C22×D61C2×SD1612yes—
303C22×D61#13512yes—
304Q8×C61—22no—
305Q8×C61—22no—
306Q8×C61—22no—
307Q8×C61C2×C22⋊C414yescomplemented
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61C2×C22⋊C414yes—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—22no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—84no—
327C2×C4×C61C2×SD1612yescomplemented
328C2×C4×C61C23×C411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C2×#4111yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C2×C4×C61H(5,𝔽2)11yescharacteristic
334C22⋊D61—48no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—22no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—84no—
352C2×Dic61C4×D412yes—
353C2×Dic61C2×SD1612yescomplemented
354D244—22no—
355D244—22no—
356D244—41no—
357D244—41no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—48no—
363Dic122—22no—
364Dic122—22no—
365Dic122—48no—
366Dic122—41no—
367Dic122—41no—
368C8×C61—41no—
369C8×C61C2×C22⋊C414yescomplemented
370#92418—22no—
371#92418—41no—
372C22⋊C4×SD16—611nomaximal, Sylow
373C22×C61—24no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61C2×C4×D411yescharacteristic
381C22×C61D4211yescharacteristic
382C22×C61D4211yescharacteristic
383C22×C61C22×SD1611yescharacteristic
384C22×C61C2×#13511yescharacteristic
385C22×C61#57711yescharacteristic
386C22×C61#57711yescharacteristic
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—816no—
397C2×D61—81no—
398C2×D61—81no—
399C2×D61—81no—
400C2×D61—81no—
401C2×D61C4×SD1614yescomplemented
402C4×C61—24no—
403C4×C61—22no—
404C4×C61—41no—
405C4×C61—81no—
406C4×C61—81no—
407C4×C61C22×C22⋊C411yescharacteristic
408C4×C61#51811yescharacteristic
409C4×C61#54611yescharacteristic
410C4×C61#54611yescharacteristic
411Dic61—22no—
412Dic61—22no—
413Dic61—42no—
414Dic61—41no—
415Dic61—81no—
416Dic61—81no—
417C23×SD16—611no—
418C2×C4×SD16—611no—
419C2×C4×SD16D6111yescharacteristic, complemented
420Q8×C22⋊C4—611no—
421D4×C22⋊C4—611no—
422#1968—611no—
423#1968—611no—
424#1880—611no—
425#1880—611no—
426#1877—611no—
427#1877—611no—
428#1807—611no—
429#1787—611no—
430#1786—611no—
431C8×C22⋊C4—611no—
432C2×C61—44no—
433C2×C61D4×C22⋊C411yescharacteristic
434C2×C61C2×C4×SD1611yescharacteristic
435C2×C61#294911yescharacteristic
436C2×C61D4×SD1611yescharacteristic
437C2×C61D4×SD1611yescharacteristic
438C2×C61#328211yescharacteristic
439C2×C61#328211yescharacteristic
440D61—24no—
441D61—82no—
442C23×Q8—611no—
443C23×D4—611no—
444C22×SD16—611no—
445C22×SD16—611no—
446C22×SD16—618no—
447C22×SD16—611no—
448C22×SD16—1224no—
449C22×SD16—1224no—
450C22×SD16C2×D6111yescharacteristic
451C23×C8—611no—
452C2×C4×Q8—611no—
453C2×C4×Q8C2×D6111yescharacteristic, complemented
454C2×C4×D4—611no—
455C2×C4×D4C2×D6111yescharacteristic
456C22×C22⋊C4—1221no—
457C4×SD16—24no—
458C4×SD16—1224no—
459C2×#106—611no—
460C2×#106C2×D6111yescharacteristic, complemented
461C2×#103—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#103C2×D6111yescharacteristic, complemented
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102C2×D6111yescharacteristic
469C2×C22⋊C8—611no—
470C2×C4×C8—611no—
471C2×C4×C8C2×D6111yescharacteristic, complemented
472#391—611no—
473#391—611no—
474#391—1221no—
475#391—1221no—
476#390—611no—
477#390—611no—
478#386—1221no—
479#386—1221no—
480#380—611no—
481#380—611no—
482#380—1221no—
483#379—1221no—
484C4×C22⋊C4—611no—
485C4×C22⋊C4—1221no—
486#340—611no—
487#340—611no—
488#336—611no—
489#336—611no—
490C61C22⋊C4×SD1611yescharacteristic, complemented, Sylow
491C25—1221no—
492C22×Q8—614no—
493C22×Q8—611no—
494C22×Q8—1221no—
495C22×Q8—1222no—
496C22×Q8—1222no—
497C22×Q8—1222no—
498C22×Q8—2441no—
499C22×Q8—2441no—
500C22×Q8C22×D6111yescharacteristic
501C22×D4—614no—
502C22×D4—611no—
503C22×D4—1222no—
504C22×D4—1221no—
505C22×D4—1222no—
506C22×D4—1222no—
507C22×D4—2441no—
508C22×D4—2441no—
509C22×D4C22×D6111yescharacteristic
510C23×C4—21no—
511C23×C4—611no—
512C23×C4—1221no—
513C23×C4—1221no—
514C2×SD16—614no—
515C2×SD16—614no—
516C2×SD16—614no—
517C2×SD16—1222no—
518C2×SD16—1222no—
519C2×SD16—1222no—
520C2×SD16—1222no—
521C2×SD16—12232no—
522C2×SD16—1222no—
523C2×SD16—1222no—
524C2×SD16C4×D6114yes—
525C2×SD16D24414yes—
526C2×SD16C22⋊D6114yes—
527C22×C8—611no—
528C22×C8—614no—
529C22×C8—611no—
530C22×C8—1222no—
531C22×C8—1222no—
532C22×C8C22×D6111yescharacteristic
533C22×C8C22×D6111yescharacteristic
534C4×Q8—22no—
535C4×Q8—41no—
536C4×Q8—1222no—
537C4×Q8—2441no—
538C4×D4—22no—
539C4×D4—41no—
540C4×D4—1222no—
541C4×D4—2441no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—2444no—
559C2×C42—21no—
560C2×C42—611no—
561C2×C42—1221no—
562C2×C42C22×D6111yescharacteristic
563#106—22no—
564#106—1222no—
565#103—22no—
566#103—1222no—
567#103—2441no—
568#103—2441no—
569#102—22no—
570#102—1222no—
571#102—2441no—
572#102—2441no—
573C22⋊C8—1222no—
574C4×C8—22no—
575C4×C8—1222no—
576#95—611no—
577#95—611no—
578#95—1221no—
579#95—1221no—
580#95—1221no—
581#95—1221no—
582#95—1221no—
583#95—1221no—
584C24—21no—
585C24—611no—
586C24—1224no—
587C24—1221no—
588C24—4881no—
589C24—4881no—
590C24—2442no—
591C24—2442no—
592C24—2442no—
593C24—2442no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—612no—
598C2×Q8—1224no—
599C2×Q8—1221no—
600C2×Q8—1228no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—2442no—
606C2×Q8—2442no—
607C2×Q8—2444no—
608C2×Q8—2444no—
609C2×Q8—2444no—
610C2×Q8C2×C4×D6112yes—
611C2×Q8C2×D24412yes—
612C2×Q8C2×C22⋊D6112yes—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—612no—
617C2×D4—1224no—
618C2×D4—1228no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—2444no—
625C2×D4—2444no—
626C2×D4—2444no—
627C2×D4—2442no—
628C2×D4—2442no—
629C2×D4C2×C4×D6112yes—
630C2×D4C2×D24412yes—
631C2×D4C2×C22⋊D6112yes—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—612no—
641C22×C4—612no—
642C22×C4—611no—
643C22×C4—1224no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—4881no—
652C22×C4—2442no—
653C22×C4—2442no—
654C22×C4—2442no—
655C22×C4—2442no—
656C22×C4D4×D6111yescharacteristic
657C22×C4D4×D6111yescharacteristic
658C22×C4C23×D6111yescharacteristic
659SD16—1228no—
660SD16—1228no—
661SD16—1228no—
662SD16#11758198116yesdirect product factor
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—612no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1228no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8C2×C4×D6112yes—
674C2×C8C2×D24412yes—
675C2×C8C2×C22⋊D6112yes—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—42no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—2442no—
686C22⋊C4—42no—
687C22⋊C4—614no—
688C22⋊C4—1222no—
689C22⋊C4—4881no—
690C22⋊C4—4881no—
691C22⋊C4—2442no—
692C22⋊C4—2442no—
693C22⋊C4—2442no—
694C22⋊C4—2442no—
695C22⋊C4—2442no—
696C42—21no—
697C42—21no—
698C42—42no—
699C42—1221no—
700C42—1221no—
701C42—2442no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—612no—
710C23—612no—
711C23—612no—
712C23—1221no—
713C23—1221no—
714C23—1221no—
715C23—1221no—
716C23—1222no—
717C23—4884no—
718C23—4884no—
719C23—4884no—
720C23—4884no—
721C23—4884no—
722C23—2448no—
723C23—2448no—
724C23—2441no—
725C23—2441no—
726C23—2441no—
727C23—2441no—
728C23—2441no—
729C23—2441no—
730C23C2×D4×D6111yescharacteristic
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—1222no—
735Q8—1222no—
736Q8—2448no—
737Q8—2441no—
738Q8—2441no—
739Q8C2×#1175819814yescomplemented
740D4—22no—
741D4—22no—
742D4—22no—
743D4—1222no—
744D4—1222no—
745D4—2448no—
746D4—2441no—
747D4—2441no—
748D4C2×#1175819814yes—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—84no—
764C2×C4—612no—
765C2×C4—612no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—4884no—
779C2×C4—2448no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4SD16×D6112yescomplemented
789C2×C4C22×C4×D6111yescharacteristic
790C2×C4C22×C22⋊D6111yescharacteristic
791C2×C4C22×D24411yescharacteristic
792C2×C4#41×D6111yescharacteristic
793C2×C4#1451982211yescharacteristic
794C2×C4#1451982311yescharacteristic
795C8—41no—
796C8—1222no—
797C8—2441no—
798C8C2×#1175819814yescomplemented
799C22—24no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—614no—
807C22—1222no—
808C22—1222no—
809C22—1222no—
810C22—1222no—
811C22—1222no—
812C22—1222no—
813C22—48816no—
814C22—4881no—
815C22—4881no—
816C22—4881no—
817C22—4881no—
818C22—2442no—
819C22—2442no—
820C22—2442no—
821C22C4×D4×D6111yescharacteristic
822C22D4×C22⋊D6111yescharacteristic
823C22D4×D24411yescharacteristic
824C22C2×SD16×D6111yescharacteristic
825C22#135×D6111yescharacteristic
826C22#1684056811yescharacteristic
827C22#1684056911yescharacteristic
828C4—22no—
829C4—24no—
830C4—41no—
831C4—81no—
832C4—81no—
833C4—1222no—
834C4—1222no—
835C4—4881no—
836C4—4881no—
837C4—2441no—
838C4—2442no—
839C4C22×#1175819811yescharacteristic
840C4#1684023411yescharacteristic
841C4#1684040011yescharacteristic
842C4#1684040711yescharacteristic
843C2—44no—
844C2—1224no—
845C2—4882no—
846C2D4×#1175819811yescharacteristic
847C2C4×SD16×D6111yescharacteristic
848C2#2145467311yescharacteristic
849C2SD16×C22⋊D6111yescharacteristic
850C2SD16×D24411yescharacteristic
851C2#2145752011yescharacteristic
852C2#2145752811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×SD16×C61C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenterC2×C4×SD16D61
hypocenterC61C22⋊C4×SD16
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×SD16×Dic61C2semidirect
3. Q8×#11758198C2semidirect
5. #21446673C2semidirect
6. #21446671C2semidirect
7. #21446174C2semidirect
8. #21446172C2semidirect
9. #21446153C2semidirect
10. #21446151C2semidirect
11. #21445841C2semidirect
12. #21445752C2semidirect
14. C8×#11758198C2semidirect
15. C2×C4×SD16×C61C2semidirect
23. C2×SD16×D61C4semidirect
25. C2×Q8×Dic61C22semidirect
29. C2×#14519709C22semidirect
30. C2×#14519702C22semidirect
31. C2×#14519701C22semidirect
32. C2×#14519700C22semidirect
37. C2×C8×Dic61C22semidirect
39. #16839668C22semidirect
41. #16839667C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839517C22semidirect
55. #16839516C22semidirect
57. C2×C4×Q8×C61C22semidirect
60. C2×#106×C61C22semidirect
61. C2×#103×C61C22semidirect
63. C2×C4×C8×C61C22semidirect
72. C2×Q8×D61C2×C4semidirect
86. C2×#11758190C2×C4semidirect
92. C2×#11758201C2×C4semidirect
98. C2×C8×D61C2×C4semidirect
232. SD16×C61C22⋊C4semidirect
258. #11758198SD16direct (N × H)
307. Q8×C61C2×C22⋊C4semidirect
327. C2×C4×C61C2×SD16semidirect
353. C2×Dic61C2×SD16semidirect
369. C8×C61C2×C22⋊C4semidirect
401. C2×D61C4×SD16semidirect
419. C2×C4×SD16D61semidirect
453. C2×C4×Q8C2×D61semidirect
460. C2×#106C2×D61semidirect
464. C2×#103C2×D61semidirect
471. C2×C4×C8C2×D61semidirect
490. C61C22⋊C4×SD16semidirect
662. SD16#11758198direct (N × H)
739. Q8C2×#11758198semidirect
788. C2×C4SD16×D61semidirect
798. C8C2×#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×SD16×D612
C2×SD16×Dic612
Q8×#117581982
D4×#117581982
#214466732
#214466712
#214461742
#214461722
#214461532
#214461512
#214458412
#214457522
#214457482
C8×#117581982
C2×C4×SD16×C612
C22⋊C4×SD1661