Finite Group Databasebeta

← #15620043

Subgroups — #15620043

Order 2816.

1744 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082233C211yesmaximal, characteristic
2#13077768C213yesmaximal, complemented
3#13077761C213yesmaximal, complemented
4#13077747C211yesmaximal, characteristic, complemented
5#13077746C213yesmaximal, complemented
6#13077714C213yesmaximal, complemented
7#13077697C211yesmaximal, characteristic, complemented
8#13077695C211yesmaximal, characteristic, complemented
9#13077622C213yesmaximal, complemented
10#13077620C213yesmaximal, complemented
11#13077578C213yesmaximal, complemented
12C8×#4343C211yesmaximal, characteristic, complemented
13Q8×#4313C211yesmaximal, characteristic, complemented
14#13077547C213yesmaximal, complemented
15Q8×C11×M16C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17#10623348C411yescharacteristic
18Q8×C22⋊D11C411yescharacteristic
19#10623112C413yes—
20#10623111C2213yes—
21#10623109C2213yes—
22#10623107C411yescharacteristic
23C4×#4343C2211yescharacteristic
24C4×Q8×D11C2211yescharacteristic
25#10623100C411yescharacteristic
26#10623099C413yes—
27#10623044C413yes—
28#10623038C413yes—
29#10623010C2213yes—
30C4×#4339C2213yes—
31C11×#446C2213yes—
32C11×#446C2213yes—
33C8×Q8×C11C2211yescharacteristic
34C8×Q8×C11C2211yescharacteristic
35C11×#423C2213yes—
36C4×C11×M16C2213yes—
37#10622741C2216yes—
38#10622741C2211yescharacteristic
39#10622741C2213yes—
40#10622740C2213yes—
41#10622740C2213yes—
42Q8×C11⋊C8C2213yes—
43Q8×C11⋊C8C2211yescharacteristic
44Q8×C11⋊C8C2211yescharacteristic
45Q8×C11⋊C8C2213yes—
46#10622538C2213yes—
47#10622538C2213yes—
48#10622453C2216yes—
49#10622452C2216yes—
50#10622451C2213yes—
51#10622451C2216yes—
52#10622450C2213yes—
53#10622450C2213yes—
54#10622447C2213yes—
55#10622446C2213yes—
56#10622446C2213yes—
57#10622444C2213yes—
58#10622443C2213yes—
59#10622443C2216yes—
60#10622322C2216yes—
61#10622321C2216yes—
62#10622319C2213yes—
63#10622319C2213yes—
64#10622314C2213yes—
65#10622314C2213yes—
66#10622301C2213yes—
67C4×#4313C2213yes—
68C8×D44C2213yes—
69#10622298C2213yes—
70#10622298C2213yes—
71C4×C8×D11C2213yes—
72#10622292C2213yes—
73C8×Dic22C2213yes—
74C22×Q8×C11C2×C411yescharacteristic
75C2×#4343C2×C411yescharacteristic
76C2×Q8×D11C2×C411yescharacteristic
77C2×#4339C2×C413yes—
78C2×C11×M16C2311yescharacteristic
79C2×C11×M16C2313yes—
80C4×Q8×C11C2×C413yes—
81C4×Q8×C11C2×C411yescharacteristic
82C4×Q8×C11C2311yescharacteristic
83C4×Q8×C11C2313yes—
84C2×C11×C4⋊C4C2×C413yes—
85C2×C42×C11C2313yes—
86#67000C2×C413yes—
87#66999C2×C413yes—
88#66999C2×C413yes—
89Q8×Dic11C2×C411yescharacteristic
90Q8×Dic11C2×C411yescharacteristic
91#66997C2×C413yes—
92#66983C2×C413yes—
93#66982C2×C416yes—
94C4×C22⋊D11C2×C413yes—
95C4×C22⋊D11C2×C413yes—
96C4×C22⋊D11C2313yes—
97C4×C22⋊D11C2311yescharacteristic
98#66979C2×C413yes—
99#66977C2×C413yes—
100C2×#4313C2311yescharacteristic
101C2×#4313C2313yes—
102C2×#4313C2316yes—
103C2×C8×D11C2313yes—
104C2×C8×D11C2313yes—
105#66951C2×C416yes—
106#66950C2×C413yes—
107#66949C2×C416yes—
108#66948C2×C413yes—
109#66947C2×C416yes—
110#66946C2×C413yes—
111#66945C2×C413yes—
112C4⋊C4×D11C2×C413yes—
113#66943C2×C413yes—
114#66942C2×C416yes—
115#66941C2×C413yes—
116#66940C2×C413yes—
117#66929C2×C416yes—
118#66928C2×C413yes—
119C4×D44C2×C413yes—
120C4×D44C2313yes—
121C4×D44C2313yes—
122#66925C2×C413yes—
123#66925C2×C413yes—
124#66925C2316yes—
125C42×D11C2313yes—
126C42×D11C2313yes—
127#66923C2×C413yes—
128C4×Dic22C2×C413yes—
129C4×Dic22C2313yes—
130C4×Dic22C2313yes—
131C11×C4⋊C8C2313yes—
132C11×C4⋊C8C2313yes—
133C11×C4⋊C8C2316yes—
134C11×#97C2313yes—
135C11×#97C2313yes—
136C4×C8×C11C2313yes—
137C4×C8×C11C2313yes—
138C22⋊(C11⋊C8)C2311yescharacteristic
139C22⋊(C11⋊C8)C2313yes—
140(C2×D11)⋊C8C2313yes—
141(C2×D11)⋊C8C2313yes—
142(C2×D11)⋊C8C2311yescharacteristic
143(C2×D11)⋊C8C2313yes—
144(C2×D11)⋊C8C2316yes—
145#66879C2313yes—
146#66879C2313yes—
147Dic11⋊C8C2313yes—
148Dic11⋊C8C2313yes—
149Dic11⋊C8C2316yes—
150Dic11⋊C8C2311yescharacteristic
151Dic11⋊C8C2313yes—
152C8×Dic11C2316yes—
153C8×Dic11C2311yescharacteristic
154C8×Dic11C2313yes—
155C4⋊(C11⋊C8)C2313yes—
156C4⋊(C11⋊C8)C2313yes—
157C4⋊(C11⋊C8)C2313yes—
158C4⋊(C11⋊C8)C2313yes—
159C4×C11⋊C8C2313yes—
160C4×C11⋊C8C2313yes—
161C4×C11⋊C8C2316yes—
162#60345—111nomaximal, Sylow
163C2×Q8×C11—24no—
164C2×Q8×C11C22×C413yes—
165C2×Q8×C11C22×C411yescharacteristic
166C22×C4×C11C22×C413yes—
167C22×C4×C11C22×C413yes—
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11C22×C411yescharacteristic
170C2×C22⋊D11C22×C413yes—
171#4343—24no—
172Q8×D11—24no—
173#4339—46no—
174C2×D44C22×C413yes—
175C2×D44C22×C413yes—
176C2×C4×D11C22×C413yes—
177C2×C4×D11C22×C413yes—
178C2×C4×D11C22×C413yes—
179C2×C4×D11C22×C413yes—
180C2×C4×D11C2411yescharacteristic
181C2×C4×D11C2413yes—
182C2×Dic22C22×C413yes—
183C2×Dic22C22×C413yes—
184C11×M16—22no—
185C11×M16—43no—
186C2×C8×C11C2413yes—
187C2×C8×C11C2413yes—
188C2×C8×C11C2411yescharacteristic
189C2×C8×C11C2411yescharacteristic
190C11×C4⋊C4C22×C413yes—
191C11×C4⋊C4C22×C413yes—
192C11×C4⋊C4C22×C416yes—
193C42×C11C22×C413yes—
194C42×C11C22×C413yes—
195C42×C11C2413yes—
196C42×C11C2413yes—
197C22⋊Dic11C22×C413yes—
198C22⋊Dic11C22×C411yescharacteristic
199(C2×D11)⋊C4C22×C411yescharacteristic
200(C2×D11)⋊C4C22×C413yes—
201(C2×D11)⋊C4C22×C413yes—
202(C2×D11)⋊C4C22×C413yes—
203(C2×D11)⋊C4C22×C416yes—
204(C2×D11)⋊C4C22×C416yes—
205(C2×D11)⋊C4C22×C416yes—
206C4⋊Dic11C22×C413yes—
207C4⋊Dic11C22×C413yes—
208C4⋊Dic11C22×C413yes—
209C4⋊Dic11C22×C413yes—
210Dic11⋊C4C22×C411yescharacteristic
211Dic11⋊C4C22×C413yes—
212Dic11⋊C4C22×C413yes—
213Dic11⋊C4C22×C413yes—
214Dic11⋊C4C22×C416yes—
215Dic11⋊C4C22×C416yes—
216Dic11⋊C4C22×C416yes—
217C4×Dic11C22×C413yes—
218C4×Dic11C22×C413yes—
219C4×Dic11C22×C413yes—
220C4×Dic11C22×C413yes—
221C4×Dic11C2411yescharacteristic
222C4×Dic11C2413yes—
223C2×C11⋊C8C2413yes—
224C2×C11⋊C8C2411yescharacteristic
225C2×C11⋊C8C2413yes—
226C2×C11⋊C8C2411yescharacteristic
227#4313—22no—
228#4313—43no—
229#4313—46no—
230C8×D11—26no—
231C8×D11—43no—
232#3482—111no—
233#2993—113no—
234#2993—113no—
235#2991—111no—
236#2991—113no—
237#2986—113no—
238#2982—111no—
239#2982—111no—
240#2969—113no—
241#2969—113no—
242#2965—113no—
243C8×#41—111no—
244Q8×M16—111no—
245Q8×M16D1111yescharacteristic, complemented
246#2960—113no—
247C23×C11C23×C411yescharacteristic
248C22×D11C23×C413yes—
249C22×D11C23×C411yescharacteristic
250Q8×C11—26no—
251Q8×C11#13114yes—
252C2×C4×C11—26no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—43no—
256C2×C4×C11C23×C413yes—
257C2×C4×C11C23×C411yescharacteristic
258C2×C4×C11C23×C413yes—
259C2×C4×C11C23×C413yes—
260C2×C4×C11C23×C413yes—
261C2×C4×C11C2511yescharacteristic
262C22⋊D11—22no—
263C22⋊D11—43no—
264C2×Dic11C23×C411yescharacteristic
265C2×Dic11C23×C411yescharacteristic
266C2×Dic11C23×C413yes—
267C2×Dic11C23×C413yes—
268C2×Dic11C23×C413yes—
269C2×Dic11C23×C411yescharacteristic
270D44—26no—
271D44—43no—
272C4×D11—26no—
273C4×D11—26no—
274C4×D11—23no—
275C4×D11—21no—
276C4×D11—23no—
277C4×D11—21no—
278C4×D11—26no—
279C4×D11—43no—
280Dic22—26no—
281Dic22—26no—
282C8×C11—21no—
283C8×C11—23no—
284C8×C11—23no—
285C8×C112−1+412yes—
286C11⋊C8—23no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—23no—
290#557—111no—
291#556—113no—
292#552—113no—
293#552—113no—
294D4×Q8—111no—
295#548—111no—
296#548—111no—
297#547—113no—
298#533—113no—
299#529—113no—
300#529—113no—
301C4×#41—111no—
302C4×#41—113no—
303C2×C4×Q8—111no—
304C2×C4×Q8C2×D1111yescharacteristic
305#446—113no—
306#446—113no—
307#446—113no—
308#446—113no—
309#446C2×D1113yes—
310#446C2×D1113yes—
311C8×Q8—113no—
312C8×Q8—111no—
313C8×Q8—111no—
314C8×Q8—113no—
315C8×Q8—113no—
316C8×Q8—116no—
317C8×Q8—113no—
318C8×Q8C2×D1111yescharacteristic
319C8×Q8C2×D1111yescharacteristic
320#436—111no—
321#436—113no—
322#436—116no—
323#436—113no—
324#436—116no—
325#436—113no—
326#435—113no—
327#435—113no—
328#435—113no—
329#435—113no—
330C8×D4—113no—
331C8×D4—113no—
332#433—116no—
333#433—116no—
334#431—113no—
335#431—113no—
336#431—113no—
337#431—113no—
338#431—113no—
339#431—113no—
340#424—116no—
341#423—113no—
342#423—113no—
343#423C2×D1113yes—
344#405—116no—
345C4×M16—113no—
346C4×M16C2×D1113yes—
347C2×C4×C8—113no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11C24×C411yescharacteristic
352C2×D11—23no—
353C2×D11—21no—
354C2×D11—21no—
355C2×D11—23no—
356C2×D11—23no—
357C2×D11—21no—
358C4×C11—21no—
359C4×C11—23no—
360C4×C11—23no—
361C4×C11—23no—
362C4×C11C2×#13116yes—
363C4×C11C2×2−1+411yescharacteristic
364C4×C11#58511yescharacteristic
365Dic11—23no—
366Dic11—21no—
367Dic11—23no—
368Dic11—21no—
369Dic11—23no—
370Dic11#56812yes—
371C2×#41—111no—
372C2×#41—113no—
373C22×Q8—111no—
374C22×Q8C4×D1111yescharacteristic
375C2×M16—111no—
376C2×M16—113no—
377C2×M16—116no—
378C2×M16C22×D1111yescharacteristic
379C2×M16C22×D1113yes—
380C22×C8—113no—
381C22×C8—113no—
382C4⋊Q8—113no—
383C4⋊Q8—113no—
384#126—116no—
385#126—116no—
386#125—113no—
387#125—116no—
388#125—113no—
389#124—113no—
390#124—113no—
391#123—116no—
392#123—116no—
393C22⋊Q8—113no—
394C22⋊Q8—113no—
395C22⋊Q8—113no—
396C22⋊Q8—116no—
397C22⋊Q8—113no—
398#121—113no—
399#121—113no—
400C4×Q8—111no—
401C4×Q8—111no—
402C4×Q8—113no—
403C4×Q8—113no—
404C4×Q8—113no—
405C4×Q8—113no—
406C4×Q8C4×D1111yescharacteristic
407C4×Q8C4×D1113yes—
408C4×Q8C22×D1111yescharacteristic
409C4×Q8C22×D1113yes—
410C4×D4—113no—
411C4×D4—113no—
412C4×D4—111no—
413C4×D4—113no—
414C4×D4—113no—
415C4×D4—113no—
416C4×D4—113no—
417C4×D4—113no—
418#117—113no—
419#117—113no—
420#117—113no—
421#117—113no—
422#117—116no—
423C2×C4⋊C4—113no—
424C2×C4⋊C4C4×D1113yes—
425C2×C42—113no—
426C2×C42—113no—
427C2×C42C22×D1113yes—
428C4⋊C8—113no—
429C4⋊C8—116no—
430C4⋊C8—113no—
431C4⋊C8—111no—
432C4⋊C8—113no—
433C4⋊C8—113no—
434C4⋊C8—113no—
435C4⋊C8—113no—
436C4⋊C8—113no—
437C4⋊C8C22×D1113yes—
438C4⋊C8C22×D1113yes—
439C4⋊C8C22×D1116yes—
440C22⋊C8—111no—
441C22⋊C8—113no—
442C22⋊C8—111no—
443C22⋊C8—113no—
444C22⋊C8—116no—
445C22⋊C8—113no—
446C22⋊C8—113no—
447#97—113no—
448#97—113no—
449#97C22×D1113yes—
450#97C22×D1113yes—
451C4×C8—111no—
452C4×C8—113no—
453C4×C8—116no—
454C4×C8—113no—
455C4×C8—113no—
456C4×C8—116no—
457C4×C8C22×D1113yes—
458C4×C8C22×D1113yes—
459C2×C11—41no—
460C2×C11C4×2−1+411yescharacteristic
461C2×C11C22×#13111yescharacteristic
462C2×C11C2×#56811yescharacteristic
463D11—41no—
464D11—43no—
465#41—224no—
466#41—446no—
467C2×Q8—24no—
468C2×Q8—113no—
469C2×Q8—113no—
470C2×Q8—224no—
471C2×Q8C2×C4×D1113yes—
472C2×Q8C2×C4×D1111yescharacteristic
473C2×D4—111no—
474C2×D4—113no—
475C2×D4—113no—
476C2×D4—113no—
477C22×C4—113no—
478C22×C4—113no—
479C22×C4—113no—
480C22×C4—111no—
481C22×C4—113no—
482C22×C4—113no—
483C22×C4C2×C4×D1113yes—
484C22×C4C2×C4×D1113yes—
485C22×C4C23×D1111yescharacteristic
486M16—22no—
487M16—43no—
488M16—222no—
489M16—443no—
490M16—446no—
491C2×C8—113no—
492C2×C8—111no—
493C2×C8—111no—
494C2×C8—113no—
495C2×C8—226no—
496C2×C8—443no—
497C2×C8C23×D1113yes—
498C2×C8C23×D1113yes—
499C2×C8C23×D1111yescharacteristic
500C2×C8C23×D1111yescharacteristic
501C4⋊C4—113no—
502C4⋊C4—116no—
503C4⋊C4—111no—
504C4⋊C4—113no—
505C4⋊C4—113no—
506C4⋊C4—113no—
507C4⋊C4—113no—
508C4⋊C4—113no—
509C4⋊C4—113no—
510C4⋊C4—116no—
511C4⋊C4—116no—
512C4⋊C4C2×C4×D1113yes—
513C4⋊C4C2×C4×D1113yes—
514C4⋊C4C2×C4×D1116yes—
515C22⋊C4—111no—
516C22⋊C4—113no—
517C22⋊C4—111no—
518C22⋊C4—113no—
519C22⋊C4—116no—
520C22⋊C4—113no—
521C22⋊C4—113no—
522C22⋊C4—116no—
523C22⋊C4—116no—
524C42—113no—
525C42—113no—
526C42—113no—
527C42—113no—
528C42—111no—
529C42—113no—
530C42C2×C4×D1113yes—
531C42C2×C4×D1113yes—
532C42C23×D1113yes—
533C42C23×D1113yes—
534C11#6034511yescharacteristic, complemented, Sylow
535C23—113no—
536C23—111no—
537C23C22×C4×D1111yescharacteristic
538Q8—26no—
539Q8—226no—
540Q8—226no—
541Q8#6696014yes—
542D4—222no—
543D4—226no—
544D4—443no—
545D4—443no—
546C2×C4—26no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—43no—
550C2×C4—111no—
551C2×C4—111no—
552C2×C4—111no—
553C2×C4—113no—
554C2×C4—113no—
555C2×C4—113no—
556C2×C4—226no—
557C2×C4—226no—
558C2×C4—226no—
559C2×C4—223no—
560C2×C4—221no—
561C2×C4—223no—
562C2×C4—221no—
563C2×C4—443no—
564C2×C4C22×C4×D1113yes—
565C2×C4C22×C4×D1111yescharacteristic
566C2×C4C22×C4×D1113yes—
567C2×C4C22×C4×D1113yes—
568C2×C4C22×C4×D1113yes—
569C2×C4C24×D1111yescharacteristic
570C8—21no—
571C8—23no—
572C8—23no—
573C8—223no—
574C8—221no—
575C8—221no—
576C8—223no—
577C8#6704012yes—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—221no—
582C22—223no—
583C22—223no—
584C22—221no—
585C22—223no—
586C22—221no—
587C22C23×C4×D1111yescharacteristic
588C4—23no—
589C4—23no—
590C4—23no—
591C4—21no—
592C4—112no—
593C4—221no—
594C4—223no—
595C4—223no—
596C4—221no—
597C4—223no—
598C4C2×#6696016yes—
599C4C2×#6704011yescharacteristic
600C4#1062345311yescharacteristic
601C2—41no—
602C2—441no—
603C2—443no—
604C2C4×#6704011yescharacteristic
605C2C22×#6696011yescharacteristic
606C2D11×#56811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingQ8×C11×M16C2
prime radical#13082233C2
cosocleC2×C4×C11C25
hypercenterQ8×M16D11
hypocenterC11#60345
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
2. #13077768C2semidirect
3. #13077761C2semidirect
4. #13077747C2semidirect
5. #13077746C2semidirect
6. #13077714C2semidirect
7. #13077697C2semidirect
8. #13077695C2semidirect
9. #13077622C2semidirect
10. #13077620C2semidirect
11. #13077578C2semidirect
12. C8×#4343C2semidirect
13. Q8×#4313C2semidirect
14. #13077547C2semidirect
15. Q8×C11×M16C2semidirect
245. Q8×M16D11semidirect
534. C11#60345semidirect

Maximal subgroups

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

subgroupindex
#130822332
#130777682
#130777612
#130777472
#130777462
#130777142
#130776972
#130776952
#130776222
#130776202
#130775782
C8×#43432
Q8×#43132
#130775472
Q8×C11×M162
#6034511