Finite Group Databasebeta

← SD16×#11924011 #33057417

Subgroups — SD16×#11924011 #33057417

Order 18688.

716 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#11924011C211yesmaximal, characteristic, complemented
2C4×SD16×D73C211yesmaximal, characteristic
3D4×#11924011C211yesmaximal, characteristic
4#22608823C211yesmaximal, characteristic, complemented
5#22608820C211yesmaximal, characteristic, complemented
6#22608774C211yesmaximal, characteristic, complemented
7#22608771C211yesmaximal, characteristic, complemented
8#22608767C211yesmaximal, characteristic, complemented
9#22608764C211yesmaximal, characteristic, complemented
10SD16×#10596831C211yesmaximal, characteristic, complemented
11#22608685C211yesmaximal, characteristic, complemented
12#22608358C211yesmaximal, characteristic, complemented
13#22608354C211yesmaximal, characteristic
14C8×#11924011C211yesmaximal, characteristic, complemented
15C8×SD16×C73C211yesmaximal, characteristic, complemented
16C2×SD16×D73C411yescharacteristic
17C22×#11924011—21no—
18C4×Q8×D73C2211yescharacteristic
19C4×D4×D73C2211yescharacteristic
20#17988717—21no—
21#17988717C2211yescharacteristic, complemented
22#17988714—21no—
23#17988714C2211yescharacteristic, complemented
24Q8×#10596831C2211yescharacteristic, complemented
25#17988678C411yescharacteristic
26C4×#11924017C2211yescharacteristic
27SD16×Dic73C411yescharacteristic
28C4×#11924015C2211yescharacteristic
29#17988674C411yescharacteristic
30C4×#11924016C2211yescharacteristic
31#17988672C411yescharacteristic
32#17988666C2211yescharacteristic
33#17988664C2211yescharacteristic
34#17988658—21no—
35#17988655—21no—
36D4×#10596831C2211yescharacteristic
37#17988638C2211yescharacteristic
38#106×D73C411yescharacteristic
39#17988609—21no—
40#17988609C2211yescharacteristic
41#17988609C2211yescharacteristic
42#103×D73C411yescharacteristic
43#102×D73C411yescharacteristic
44#17988549—21no—
45C4×#11924011—21no—
46C4×#11924011C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988338C2211yescharacteristic, complemented
49#17988337C2211yescharacteristic, complemented
50#17988337C2211yescharacteristic, complemented
51#17988319C2211yescharacteristic, complemented
52Q8⋊#10596831C2211yescharacteristic, complemented
53#17988317C2211yescharacteristic, complemented
54#17988316C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic, complemented
58#17988308C2211yescharacteristic, complemented
59C8×#10596831C2211yescharacteristic, complemented
60C8×Q8×C73C2211yescharacteristic, complemented
61C4×SD16×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic, complemented
64Q8⋊C8×C73C2211yescharacteristic, complemented
65D4⋊C8×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic, complemented
67C2×Q8×D73C2×C411yescharacteristic
68C2×D4×D73C2×C411yescharacteristic
69C22×C4×D73—21no—
70C2×#11924017C2×C411yescharacteristic
71C2×#11924016C2×C411yescharacteristic
72C2×#11924015C2×C411yescharacteristic
73SD16×D73—24no—
74C2×#11924011—21no—
75C2×#11924011—21no—
76C2×#11924011—21no—
77C2×#11924011—21no—
78C2×#11924011—44no—
79C2×#11924011D411yescharacteristic
80C2×#11924011D411yescharacteristic
81C22×#10596831—21no—
82C2×C8×D73C2×C411yescharacteristic
83C2×C8×D73C2×C411yescharacteristic
84Q8×Dic73C2×C411yescharacteristic
85C4×Dic146—21no—
86C4×Dic146C2311yescharacteristic
87#14556556—21no—
88#14556556C2×C411yescharacteristic
89C4×D292C2311yescharacteristic
90D4×Dic73C2×C411yescharacteristic
91#14556553C2×C411yescharacteristic
92C4×C22⋊D73—21no—
93#14556551—21no—
94C4⋊C4×D73—21no—
95C4⋊C4×D73C2×C411yescharacteristic
96C4⋊C4×D73C2×C411yescharacteristic
97C22⋊C4×D73—21no—
98C42×D73—21no—
99C42×D73C2311yescharacteristic
100#14556523C2×C411yescharacteristic
101#14556522C2×C411yescharacteristic
102#14556522C2×C411yescharacteristic
103C4⋊#10596831—21no—
104C4⋊#10596831C2311yescharacteristic
105C4⋊#10596831C2311yescharacteristic
106#14556520—21no—
107#14556520—21no—
108#14556520—21no—
109#14556520—21no—
110#14556520—21no—
111#14556516C2×C411yescharacteristic
112#14556515C2×C411yescharacteristic
113#14556514C2×C411yescharacteristic
114#14556513C2×C411yescharacteristic
115#14556512C2×C411yescharacteristic
116#14556511C2×C411yescharacteristic
117C22⋊#10596831—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503—21no—
121#14556501—21no—
122#14556501—21no—
123#14556501D411yescharacteristic
124#14556501D411yescharacteristic
125C4×#10596831—21no—
126C4×#10596831C2311yescharacteristic
127C4×#10596831C2311yescharacteristic
128C4×#10596831C2311yescharacteristic
129C8×Dic73C2×C411yescharacteristic
130C8×Dic73C2×C411yescharacteristic
131C2×SD16×C73C2×C411yescharacteristic
132C22×C8×C73—21no—
133C4×Q8×C73C2311yescharacteristic
134C4×D4×C73C2311yescharacteristic
135#106×C73C2×C411yescharacteristic
136C4⋊C8×C73—21no—
137C4⋊C8×C73C2311yescharacteristic
138C4⋊C8×C73C2311yescharacteristic
139#103×C73C2×C411yescharacteristic
140#102×C73C2×C411yescharacteristic
141C22⋊C8×C73—21no—
142C4×C8×C73—21no—
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145C4×C8×C73C2311yescharacteristic
146C23×D73—21no—
147C2×Dic146—21no—
148C2×Dic146C22×C411yescharacteristic
149Q8×D73—22no—
150Q8×D73—41no—
151C2×D292C22×C411yescharacteristic
152C2×C22⋊D73—21no—
153D4×D73—22no—
154D4×D73—41no—
155C22×Dic73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—42no—
162C2×C4×D73—42no—
163C2×C4×D73C22×C411yescharacteristic
164C2×C4×D73C2×D411yescharacteristic
165C2×C4×D73#4111yescharacteristic
166#11924017—22no—
167#11924016—22no—
168#11924015—22no—
169#11924011—22no—
170#11924011—42no—
171#11924011—42no—
172#11924011—42no—
173#11924011—42no—
174#11924011SD1614yesdirect product factor
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—42no—
179C2×#10596831C22×C411yescharacteristic
180C2×#10596831C22×C411yescharacteristic
181C2×#10596831C2×D411yescharacteristic
182C2×#10596831C2×D411yescharacteristic
183C8×D73—22no—
184C8×D73—41no—
185C4⋊Dic73—21no—
186C4⋊Dic73C22×C411yescharacteristic
187C4⋊Dic73C22×C411yescharacteristic
188#11924007—21no—
189#11924007—21no—
190#11924007—21no—
191#11924007—21no—
192C22⋊Dic73—21no—
193#11924005—21no—
194#11924005—21no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C4×Dic73C22×C411yescharacteristic
199C4×Dic73C2×D411yescharacteristic
200C4×Dic73#4111yescharacteristic
201C2×Q8×C73C22×C411yescharacteristic
202C2×D4×C73C22×C411yescharacteristic
203C22×C4×C73—21no—
204SD16×C73M1614yescomplemented
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—42no—
209C2×C8×C73C22×C411yescharacteristic
210C2×C8×C73C22×C411yescharacteristic
211C2×C8×C73C2×D411yescharacteristic
212C2×C8×C73C2×D411yescharacteristic
213C4⋊C4×C73—21no—
214C4⋊C4×C73C22×C411yescharacteristic
215C4⋊C4×C73C22×C411yescharacteristic
216C22⋊C4×C73—21no—
217C42×C73—21no—
218C42×C73C2411yescharacteristic
219C23×C73—21no—
220C22×D73—21no—
221C22×D73—42no—
222C22×D73—42no—
223C22×D73—81no—
224C22×D73C4×D411yescharacteristic
225Q8×C73—21no—
226Q8×C73C2×M1612yescomplemented
227D4×C73—21no—
228D4×C73C2×M1612yes—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73C23×C411yescharacteristic
235C2×C4×C73C22×D411yescharacteristic
236C2×C4×C73C2×#4111yescharacteristic
237C22⋊D73—42no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—42no—
242C2×Dic73C4×D411yescharacteristic
243C2×Dic73C4×D411yescharacteristic
244C2×Dic73C4×D411yescharacteristic
245D292—21no—
246D292—21no—
247C4×D73—21no—
248C4×D73—21no—
249C4×D73—41no—
250C4×D73—42no—
251C4×D73—42no—
252C4×D73—41no—
253C4×D73—41no—
254C4×D73—42no—
255C4×D73—81no—
256C4×D73C2×SD1612yes—
257C4×D73#13512yes—
258Dic146—21no—
259Dic146—21no—
260Dic146—42no—
261C8×C73—21no—
262C8×C73—21no—
263C8×C73—41no—
264C8×C73—41no—
265C8×C73—41no—
266C8×C73C2×M1612yescomplemented
267C8×C73C2×SD1612yescomplemented
268#10596831—21no—
269#10596831—21no—
270#10596831—21no—
271#10596831—41no—
272#10596831—41no—
273#10596831—41no—
274#10596831C2×SD1612yescomplemented
275C22×C73—22no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73C2×C4×D411yescharacteristic
279C2×D73—21no—
280C2×D73—21no—
281C2×D73—41no—
282C2×D73—41no—
283C2×D73—41no—
284C2×D73—84no—
285C2×D73C4×SD1612yes—
286C4×C73—22no—
287C4×C73—21no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73C22×M1611yescharacteristic
291C4×C73#56811yescharacteristic
292C4×C73C22×SD1611yescharacteristic
293C4×C73C2×#13511yescharacteristic
294Dic73—21no—
295Dic73—21no—
296Dic73—41no—
297Dic73—41no—
298Dic73—41no—
299Dic73C4×SD1612yes—
300M16×SD16—731nomaximal, Sylow
301C2×C73—42no—
302C2×C73D4×M1611yescharacteristic
303C2×C73C2×C4×SD1611yescharacteristic
304C2×C73#295711yescharacteristic
305D73—22no—
306D73—81no—
307Q8×M16—731no—
308C2×C4×SD16—731no—
309D4×M16—731no—
310#1590—731no—
311#1590—731no—
312#1583—731no—
313#1583—731no—
314#1582—731no—
315#1582—731no—
316C8×SD16—731no—
317C8×SD16D7311yescharacteristic, complemented
318#1566—731no—
319#1487—731no—
320#1486—731no—
321C8×M16—731no—
322C73M16×SD1611yescharacteristic, complemented, Sylow
323C22×SD16—731no—
324C22×M16—1461no—
325C2×C4×Q8—731no—
326C2×C4×D4—731no—
327#446—731no—
328#446—731no—
329#446—1461no—
330#446—1461no—
331C8×Q8—731no—
332C8×Q8C2×D7311yescharacteristic, complemented
333C4×SD16—731no—
334C4×SD16—731no—
335C4×SD16—731no—
336C4×SD16—731no—
337C4×SD16—731no—
338C4×SD16—731no—
339C4×SD16—731no—
340C4×SD16C2×D7311yescharacteristic
341#436—731no—
342#436—731no—
343#435—1461no—
344#435—1461no—
345C8×D4—731no—
346C8×D4C2×D7311yescharacteristic
347#431—731no—
348C2×#106—731no—
349#423—731no—
350#423—731no—
351#423—1461no—
352C2×#103—731no—
353C2×#102—731no—
354#407—1461no—
355C4×M16—731no—
356C4×M16—1461no—
357C2×C4×C8—731no—
358#334—731no—
359#334—731no—
360#334—731no—
361#334C2×D7311yescharacteristic, complemented
362Q8⋊C8—731no—
363Q8⋊C8—731no—
364Q8⋊C8—731no—
365Q8⋊C8C2×D7311yescharacteristic, complemented
366D4⋊C8—731no—
367D4⋊C8—731no—
368D4⋊C8—731no—
369D4⋊C8C2×D7311yescharacteristic
370#322—731no—
371#322—731no—
372C82—731no—
373C82C2×D7311yescharacteristic, complemented
374C22×Q8—731no—
375C22×D4—731no—
376C23×C4—1461no—
377C2×SD16—731no—
378C2×SD16—731no—
379C2×SD16—731no—
380C2×SD16—1464no—
381C2×SD16C4×D7311yescharacteristic
382C2×M16—2924no—
383C2×M16—731no—
384C2×M16—731no—
385C2×M16—1461no—
386C2×M16—1461no—
387C2×M16—1461no—
388C2×M16—1461no—
389C22×C8—21no—
390C22×C8—731no—
391C22×C8—731no—
392C22×C8—1461no—
393C4×Q8—731no—
394C4×Q8—731no—
395C4×Q8—731no—
396C4×Q8—1461no—
397C4×Q8—1461no—
398C4×Q8C22×D7311yescharacteristic
399C4×D4—731no—
400C4×D4—731no—
401C4×D4—731no—
402C4×D4—1461no—
403C4×D4—1461no—
404C4×D4C22×D7311yescharacteristic
405C2×C4⋊C4—731no—
406C2×C4⋊C4—731no—
407C2×C4⋊C4—1461no—
408C2×C22⋊C4—1461no—
409C2×C42—731no—
410C2×C42—1461no—
411#106—731no—
412#106—731no—
413#106—731no—
414#106C4×D7311yescharacteristic
415C4⋊C8—21no—
416C4⋊C8—731no—
417C4⋊C8—731no—
418C4⋊C8—1461no—
419C4⋊C8—1461no—
420C4⋊C8—1461no—
421C4⋊C8—1461no—
422C4⋊C8—1461no—
423C4⋊C8—1461no—
424C4⋊C8C22×D7311yescharacteristic
425C4⋊C8C22×D7311yescharacteristic
426#103—731no—
427#103—731no—
428#103—731no—
429#103C4×D7311yescharacteristic
430#102—731no—
431#102—731no—
432#102—731no—
433#102C4×D7311yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—1461no—
436C22⋊C8—1461no—
437C22⋊C8—1461no—
438C22⋊C8—1461no—
439#97—731no—
440#97—731no—
441#97—1461no—
442#97—1461no—
443C4×C8—21no—
444C4×C8—731no—
445C4×C8—731no—
446C4×C8—731no—
447C4×C8—731no—
448C4×C8—731no—
449C4×C8—1461no—
450C4×C8C22×D7311yescharacteristic
451C4×C8C22×D7311yescharacteristic
452C4×C8C22×D7311yescharacteristic
453C24—1461no—
454C2×Q8—2921no—
455C2×Q8—731no—
456C2×Q8—1461no—
457C2×Q8—1462no—
458C2×Q8C2×C4×D7311yescharacteristic
459C2×D4—2921no—
460C2×D4—731no—
461C2×D4—1461no—
462C2×D4—1462no—
463C2×D4C2×C4×D7311yescharacteristic
464C22×C4—21no—
465C22×C4—2922no—
466C22×C4—2922no—
467C22×C4—731no—
468C22×C4—731no—
469C22×C4—731no—
470C22×C4—1461no—
471C22×C4—1461no—
472C22×C4—1461no—
473C22×C4—1461no—
474C22×C4—1461no—
475C22×C4—1461no—
476SD16—1462no—
477SD16—1462no—
478SD16—1462no—
479SD16#1192401114yesdirect product factor
480M16—2922no—
481M16—2922no—
482M16—2922no—
483M16—2922no—
484M16—734no—
485M16—1462no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—42no—
490C2×C8—2921no—
491C2×C8—2922no—
492C2×C8—731no—
493C2×C8—731no—
494C2×C8—731no—
495C2×C8—731no—
496C2×C8—1461no—
497C2×C8—1461no—
498C2×C8—1461no—
499C2×C8—1462no—
500C2×C8C2×C4×D7311yescharacteristic
501C2×C8C2×C4×D7311yescharacteristic
502C2×C8D4×D7311yescharacteristic
503C2×C8D4×D7311yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—731no—
506C4⋊C4—731no—
507C4⋊C4—1461no—
508C4⋊C4—1461no—
509C4⋊C4—1461no—
510C4⋊C4—1461no—
511C4⋊C4—1461no—
512C4⋊C4C2×C4×D7311yescharacteristic
513C4⋊C4C2×C4×D7311yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—1461no—
516C22⋊C4—1461no—
517C22⋊C4—1461no—
518C42—21no—
519C42—731no—
520C42—731no—
521C42—731no—
522C42—1461no—
523C42—1461no—
524C42—1461no—
525C42C23×D7311yescharacteristic
526C23—21no—
527C23—2922no—
528C23—2922no—
529C23—5841no—
530C23—731no—
531C23—1461no—
532Q8—21no—
533Q8—2922no—
534Q8—1461no—
535Q8—1461no—
536Q8C2×#1192401112yescomplemented
537D4—21no—
538D4—2922no—
539D4—1461no—
540D4—1461no—
541D4C2×#1192401112yes—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—2922no—
548C2×C4—2921no—
549C2×C4—2922no—
550C2×C4—2922no—
551C2×C4—2922no—
552C2×C4—2921no—
553C2×C4—2921no—
554C2×C4—5841no—
555C2×C4—731no—
556C2×C4—732no—
557C2×C4—732no—
558C2×C4—731no—
559C2×C4—731no—
560C2×C4—1461no—
561C2×C4—1461no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4C22×C4×D7311yescharacteristic
566C2×C4C2×D4×D7311yescharacteristic
567C2×C4#41×D7311yescharacteristic
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—2921no—
574C8—2921no—
575C8—2921no—
576C8—732no—
577C8—1461no—
578C8—1461no—
579C8—1461no—
580C8C2×#1192401112yescomplemented
581C8SD16×D7312yescomplemented
582C22—22no—
583C22—41no—
584C22—41no—
585C22—2921no—
586C22—2921no—
587C22—2921no—
588C22—5844no—
589C22—732no—
590C22—1461no—
591C22—1461no—
592C22C4×D4×D7311yescharacteristic
593C4—22no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—2921no—
598C4—2921no—
599C4—2921no—
600C4—732no—
601C4—1461no—
602C4—1461no—
603C4C22×#1192401111yescharacteristic
604C4#1798935211yescharacteristic
605C4C2×SD16×D7311yescharacteristic
606C4#135×D7311yescharacteristic
607C2—42no—
608C2—5841no—
609C2—1462no—
610C2D4×#1192401111yescharacteristic
611C2C4×SD16×D7311yescharacteristic
612C2#2261884311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC8×SD16×C73C2
socleC22×C73C2×C4×D4
prime radicalC2×D4×D73C2×C4
cosocleC42×C73C24
hypercenterC8×SD16D73
hypocenterC73M16×SD16
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×#11924011C2semidirect
4. #22608823C2semidirect
5. #22608820C2semidirect
6. #22608774C2semidirect
7. #22608771C2semidirect
8. #22608767C2semidirect
9. #22608764C2semidirect
10. SD16×#10596831C2semidirect
11. #22608685C2semidirect
12. #22608358C2semidirect
14. C8×#11924011C2semidirect
15. C8×SD16×C73C2semidirect
21. #17988717C22semidirect
23. #17988714C22semidirect
24. Q8×#10596831C22semidirect
48. #17988338C22semidirect
49. #17988337C22semidirect
50. #17988337C22semidirect
51. #17988319C22semidirect
52. Q8⋊#10596831C22semidirect
53. #17988317C22semidirect
57. #17988309C22semidirect
58. #17988308C22semidirect
59. C8×#10596831C22semidirect
60. C8×Q8×C73C22semidirect
63. #334×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
66. C82×C73C22semidirect
174. #11924011SD16direct (N × H)
204. SD16×C73M16semidirect
226. Q8×C73C2×M16semidirect
266. C8×C73C2×M16semidirect
267. C8×C73C2×SD16semidirect
274. #10596831C2×SD16semidirect
317. C8×SD16D73semidirect
322. C73M16×SD16semidirect
332. C8×Q8C2×D73semidirect
361. #334C2×D73semidirect
365. Q8⋊C8C2×D73semidirect
373. C82C2×D73semidirect
479. SD16#11924011direct (N × H)
536. Q8C2×#11924011semidirect
580. C8C2×#11924011semidirect
581. C8SD16×D73semidirect

Maximal subgroups

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

subgroupindex
Q8×#119240112
C4×SD16×D732
D4×#119240112
#226088232
#226088202
#226087742
#226087712
#226087672
#226087642
SD16×#105968312
#226086852
#226083582
#226083542
C8×#119240112
C8×SD16×C732
M16×SD1673