Finite Group Databasebeta

← #14738841

Subgroups — #14738841

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079989C211yesmaximal, characteristic
2#13079158C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic
4#13068132C211yesmaximal, characteristic, complemented
5#13068127C211yesmaximal, characteristic, complemented
6#13068120C211yesmaximal, characteristic, complemented
7#13068113C211yesmaximal, characteristic, complemented
8#13068008C211yesmaximal, characteristic, complemented
9#13068003C211yesmaximal, characteristic, complemented
10#13067996C211yesmaximal, characteristic, complemented
11#13067989C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067327C211yesmaximal, characteristic, complemented
14#13067288C211yesmaximal, characteristic, complemented
15C11×#3218C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#497—21no—
20C11×#491—21no—
21C11×#462C2211yescharacteristic
22C11×#462C2211yescharacteristic
23C11×#461C2211yescharacteristic
24C11×#461C2211yescharacteristic
25C11×#451—21no—
26C11×#448—21no—
27C11×#432C2211yescharacteristic
28#10622693—21no—
29#10622693—21no—
30#10622692C2211yescharacteristic
31#10622692C2211yescharacteristic
32#10622691C2211yescharacteristic
33#10622691C2211yescharacteristic
34#10622676—21no—
35#10622667—21no—
36#10622665—21no—
37#10622655—21no—
38#10622644C2211yescharacteristic
39#10622637C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622632C2211yescharacteristic
43#10622625—21no—
44#10622625C2211yescharacteristic
45#10622624—21no—
46D4×C11⋊C8C2211yescharacteristic
47#10622621C2211yescharacteristic
48#10622613—21no—
49#10622610—21no—
50#10622577—21no—
51#10622577—21no—
52#10622538C2211yescharacteristic
53#10622537C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C22×Q8×C11—21no—
68C2×C11×Q16—21no—
69C2×C11×Q16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8—21no—
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×#126—21no—
78C11×#125D411yescharacteristic
79C11×#124D411yescharacteristic
80C11×#123—21no—
81C11×C22⋊Q8D411yescharacteristic
82C11×#121D411yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11C2311yescharacteristic
86C11×#117—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4326—21no—
91C2×#4324—21no—
92#66979—21no—
93#66977—21no—
94#66977—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318D411yescharacteristic
98C2×#4318D411yescharacteristic
99C22×C11⋊C8—21no—
100#66923—21no—
101#66922C2311yescharacteristic
102#66922C2311yescharacteristic
103C4×Dic22—21no—
104C4×Dic22—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#103—21no—
108C11×#103—21no—
109C11×#103—21no—
110C11×#103—21no—
111C11×C22⋊C8—21no—
112C11×#97—21no—
113#66899—21no—
114#66896—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118#66874—21no—
119#66874—21no—
120#66872—21no—
121#66872—21no—
122#66872—21no—
123#66872—21no—
124#66872—21no—
125#66871—21no—
126#66871—21no—
127#66871—21no—
128#66871—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19378—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—41no—
148C2×Q8×C11—81no—
149C2×Q8×C11—81no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11C2×D411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—41no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×Dic22—21no—
159C2×Dic22—21no—
160C11×Q16—81no—
161C11×Q16—81no—
162C11×SD16—81no—
163C11×SD16—81no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C42×C11—21no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—41no—
189#4326—81no—
190#4324—81no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195Dic11⋊C4—41no—
196Dic11⋊C4—41no—
197C4×Dic11—41no—
198#4318—22no—
199#4318—22no—
200#4318—42no—
201#4318—81no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—42no—
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211#3252—111no—
212#3218D1111yescharacteristic
213#3165—111no—
214#2969—111no—
215#1694—111no—
216#1693—111no—
217#1692—111no—
218#1691—111no—
219#1674—111no—
220#1673—111no—
221#1672—111no—
222#1671—111no—
223#1569—111no—
224#1554—111no—
225#1546—111no—
226C23×C11—21no—
227C23×C11#12111yescharacteristic
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—82no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—81no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—82no—
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×Dic11—41no—
258C2×Dic11—41no—
259Dic22—41no—
260Dic22—41no—
261Dic22—81no—
262C8×C11—41no—
263C8×C11—41no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8#13712yes—
271C11⋊C8#13712yes—
272#533—111no—
273C2×C4⋊Q8C2×D1111yescharacteristic
274#529C2×D1111yescharacteristic
275#501—221no—
276#501—221no—
277#500—111no—
278#500—111no—
279#498—111no—
280#498—111no—
281#497—21no—
282#491—21no—
283#479—221no—
284#477—111no—
285#476—111no—
286#470—221no—
287#468—221no—
288#464—221no—
289#462—111no—
290#462C2×D1111yescharacteristic
291#462C2×D1111yescharacteristic
292#461—111no—
293#461C2×D1111yescharacteristic
294#461C2×D1111yescharacteristic
295#451—21no—
296#448—21no—
297#446—111no—
298C8×Q8—111no—
299#436—111no—
300#436—221no—
301#435—221no—
302C8×D4—111no—
303#433—221no—
304#432C2×D1111yescharacteristic
305#431—111no—
306#428—221no—
307#428—221no—
308#423—111no—
309#405—221no—
310C4×M16—111no—
311#335—111no—
312#335—111no—
313#334—111no—
314#334—111no—
315#333—111no—
316#333—111no—
317#332—111no—
318#332—111no—
319#332—111no—
320#332—111no—
321#332—111no—
322#332—111no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11C2×#12111yescharacteristic
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11C2×#13711yescharacteristic
340C4×C11C2×#13711yescharacteristic
341C4×C11#57611yescharacteristic
342C4×C11#57711yescharacteristic
343Dic11—81no—
344Dic11—81no—
345C22×Q8—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—221no—
349C2×SD16—21no—
350C2×SD16—21no—
351C2×SD16—221no—
352C2×M16—111no—
353C2×M16—111no—
354C2×M16—221no—
355C2×M16—221no—
356C22×C8—221no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—111no—
361C4⋊Q8—111no—
362C4⋊Q8C22×D1111yescharacteristic
363C4⋊Q8C22×D1111yescharacteristic
364#126—21no—
365#125—221no—
366#125C22⋊D1111yescharacteristic
367#124C22⋊D1111yescharacteristic
368#123—21no—
369C22⋊Q8—221no—
370C22⋊Q8—221no—
371C22⋊Q8C22⋊D1111yescharacteristic
372#121C22⋊D1111yescharacteristic
373C4×Q8—221no—
374C4×Q8—221no—
375C4×Q8C22×D1111yescharacteristic
376C4×D4—21no—
377C4×D4C22×D1111yescharacteristic
378#117—21no—
379#117—221no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C42C22×D1111yescharacteristic
383#107—221no—
384#107—221no—
385#107—221no—
386#107—221no—
387#107—221no—
388#106—221no—
389#106—221no—
390#106—221no—
391#106—221no—
392#106—221no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8—221no—
400C4⋊C8C22×D1111yescharacteristic
401C4⋊C8C22×D1111yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—221no—
407#103—221no—
408#103—221no—
409#102—221no—
410C22⋊C8—21no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413C22⋊C8—221no—
414#97—21no—
415#97—111no—
416#97—111no—
417#97—221no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—221no—
421C4×C8—221no—
422C2×C11—41no—
423C2×C11—81no—
424C2×C11#303911yescharacteristic
425C2×C11#306211yescharacteristic
426C2×C11#306911yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—81no—
431C2×Q8—81no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8C2×C22⋊D1111yescharacteristic
435C2×D4—21no—
436C2×D4C2×C22⋊D1111yescharacteristic
437C22×C4—21no—
438C22×C4—41no—
439C22×C4D4×D1111yescharacteristic
440C22×C4#434111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442Q16—81no—
443Q16—81no—
444Q16—881no—
445SD16—81no—
446SD16—81no—
447SD16—881no—
448M16—222no—
449M16—222no—
450M16—442no—
451M16—881no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—442no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—441no—
478C4⋊C4—441no—
479C4⋊C4C2×C22⋊D1111yescharacteristic
480C4⋊C4C2×C22⋊D1111yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—441no—
487C42—21no—
488C42—441no—
489C42D4×D1111yescharacteristic
490C42#434111yescharacteristic
491C42C2×C22⋊D1111yescharacteristic
492C42C23×D1111yescharacteristic
493C11#1937811yescharacteristic, complemented, Sylow
494C23—21no—
495C23#6699211yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—82no—
503Q8—441no—
504Q8—441no—
505Q8—881no—
506D4—21no—
507D4—21no—
508D4—81no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4#6699211yescharacteristic
525C2×C4#6699211yescharacteristic
526C2×C4#6699211yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4C2×#434111yescharacteristic
529C2×C4C22×C22⋊D1111yescharacteristic
530C8—41no—
531C8—41no—
532C8—112no—
533C8—112no—
534C8—221no—
535C8—221no—
536C8—441no—
537C8—441no—
538C8—441no—
539C8—441no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×#6699211yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4—81no—
556C4—881no—
557C4—881no—
558C4D11×#13711yescharacteristic
559C4D11×#13711yescharacteristic
560C4#1062336611yescharacteristic
561C4#1062336711yescharacteristic
562C2—41no—
563C2—81no—
564C2#1307810111yescharacteristic
565C2#1307829211yescharacteristic
566C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3218C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#3218D11
hypocenterC11#19378
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3218

Complements

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

NH ≅ G/Ntype
2. #13079158C2semidirect
4. #13068132C2semidirect
5. #13068127C2semidirect
6. #13068120C2semidirect
7. #13068113C2semidirect
8. #13068008C2semidirect
9. #13068003C2semidirect
10. #13067996C2semidirect
11. #13067989C2semidirect
12. #13067384C2semidirect
13. #13067327C2semidirect
14. #13067288C2semidirect
493. C11#19378semidirect

Maximal subgroups

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

subgroupindex
#130799892
#130791582
#130776212
#130681322
#130681272
#130681202
#130681132
#130680082
#130680032
#130679962
#130679892
#130673842
#130673272
#130672882
C11×#32182
#1937811