Finite Group Databasebeta

← #14743990

Subgroups — #14743990

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081524C211yesmaximal, characteristic
2Q8×#4326C211yesmaximal, characteristic, complemented
3#13080492C211yesmaximal, characteristic
4#13068290C211yesmaximal, characteristic, complemented
5#13068119C211yesmaximal, characteristic, complemented
6#13068072C211yesmaximal, characteristic, complemented
7#13068020C211yesmaximal, characteristic, complemented
8#13068013C211yesmaximal, characteristic
9#13067836C211yesmaximal, characteristic, complemented
10#13067781C211yesmaximal, characteristic
11#13067756C211yesmaximal, characteristic, complemented
12#13067748C211yesmaximal, characteristic
13#13067466C211yesmaximal, characteristic, complemented
14SD16⋊(C11⋊C8)C211yesmaximal, characteristic
15Q8×C11×SD16C211yesmaximal, characteristic
16Q82×C11C2211yescharacteristic
17D4×Q8×C11C2211yescharacteristic
18Q8×Dic22C2211yescharacteristic
19#10623074C2211yescharacteristic
20C11×#498—21no—
21C11×#498C2211yescharacteristic
22C11×#476—21no—
23C11×#476C2211yescharacteristic
24C11×#475—21no—
25C11×#475C2211yescharacteristic
26C8×Q8×C11C2211yescharacteristic
27C4×C11×SD16—21no—
28C4×C11×SD16C2211yescharacteristic
29#10622841—21no—
30C2×#66899—21no—
31#10622777—21no—
32#10622706C2211yescharacteristic
33#10622705C2211yescharacteristic
34#10622704—21no—
35#10622704C2211yescharacteristic
36#10622703C2211yescharacteristic
37#10622694C2211yescharacteristic
38#10622691—21no—
39#10622691C2211yescharacteristic
40#10622664—21no—
41#10622657—21no—
42C4×#4326—21no—
43C4×#4326C2211yescharacteristic
44Q8×C11⋊C8C2211yescharacteristic
45#10622634—21no—
46#10622634C2211yescharacteristic
47#10622634C2211yescharacteristic
48#10622634C2211yescharacteristic
49D4×C11⋊C8C2211yescharacteristic
50#10622621C2211yescharacteristic
51#10622469—21no—
52#10622409—21no—
53#10622372—21no—
54#10622295C2211yescharacteristic
55#10622292C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59Q8⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622122C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622119C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622096C2211yescharacteristic
66#10622093C2211yescharacteristic
67C22×Q8×C11—21no—
68C2×C11×SD16D411yescharacteristic
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—41no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—41no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11C2311yescharacteristic
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11C2311yescharacteristic
83Q8×Dic11—21no—
84C2×#4326—21no—
85C2×#4326—41no—
86C2×#4326D411yescharacteristic
87D4×Dic11—21no—
88C2×C4⋊Dic11—21no—
89#66977—21no—
90C22×C11⋊C8—21no—
91#66943—21no—
92#66941—21no—
93#66941—41no—
94#66931—41no—
95#66922—21no—
96#66922C2311yescharacteristic
97#66922C2311yescharacteristic
98C4×Dic22—21no—
99C4×Dic22C2311yescharacteristic
100C11×#106—21no—
101C11×#106—21no—
102C11×#106—21no—
103C11×#106—21no—
104C11×#106D411yescharacteristic
105C11×C4⋊C8—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×#103—21no—
108C11×#103D411yescharacteristic
109C11×#102—21no—
110C11×#102D411yescharacteristic
111C4×C8×C11—21no—
112C4×C8×C11C2311yescharacteristic
113#66899—21no—
114#66899—21no—
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66899—21no—
119#66899D411yescharacteristic
120#66896—21no—
121C22⋊(C11⋊C8)—21no—
122#66882—21no—
123#66882—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126#66874—21no—
127#66874—41no—
128#66874D411yescharacteristic
129#66872—21no—
130#66871—21no—
131#66871—21no—
132#66871—21no—
133#66871—21no—
134#66871—21no—
135#66871—21no—
136#66871D411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19813—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—41no—
148C2×Q8×C11—41no—
149C2×Q8×C11—42no—
150C2×Q8×C11—81no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11C2×D411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—41no—
156C22×Dic11—41no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—41no—
160C2×Dic22C2×D411yescharacteristic
161C11×SD16Q1614yescomplemented
162C2×C8×C11—21no—
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—41no—
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C22⋊C4—21no—
178C11×C22⋊C4—41no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—41no—
182C42×C11C2411yescharacteristic
183C22⋊Dic11—41no—
184#4326—22no—
185#4326—81no—
186#4326—82no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—41no—
192C4⋊Dic11—41no—
193C4⋊Dic11C2×D411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—41no—
196Dic11⋊C4—41no—
197C4×Dic11—21no—
198C4×Dic11—41no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—81no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206#3385—111no—
207Q8×Q16—111no—
208Q8×SD16D1111yescharacteristic
209#3299—111no—
210#1723—111no—
211#1692—111no—
212#1684—111no—
213#1676—111no—
214#1675—111no—
215#1645—111no—
216#1637—111no—
217#1633—111no—
218#1632—111no—
219#1584—111no—
220SD16⋊C8—111no—
221C23×C11—21no—
222Q8×C11—21no—
223Q8×C11—21no—
224Q8×C11—41no—
225Q8×C11—41no—
226Q8×C11—82no—
227Q8×C11—81no—
228Q8×C11—161no—
229Q8×C11C2×Q1612yes—
230Q8×C11#13712yes—
231D4×C11—21no—
232D4×C11C2×Q1612yes—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—82no—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—161no—
251Dic22—21no—
252Dic22—21no—
253Dic22—81no—
254Dic22—81no—
255Dic22—161no—
256C8×C11—21no—
257C8×C11—41no—
258C8×C11C2×Q1612yes—
259C11⋊C8—21no—
260C11⋊C8—21no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265Q82—111no—
266Q82C2×D1111yescharacteristic
267#554—111no—
268D4×Q8C2×D1111yescharacteristic
269#501—221no—
270#500—111no—
271#500—111no—
272#500—221no—
273#498—21no—
274#498C2×D1111yescharacteristic
275#494—111no—
276#487—111no—
277#487—111no—
278#484—221no—
279#479—221no—
280#477—111no—
281#477—111no—
282#477—111no—
283#477—111no—
284#477—221no—
285#477—221no—
286#476—21no—
287#476—111no—
288#476C2×D1111yescharacteristic
289#475—21no—
290#475C2×D1111yescharacteristic
291#474—221no—
292#467—221no—
293#462—111no—
294#451—221no—
295#446—111no—
296C8×Q8—111no—
297C8×Q8C2×D1111yescharacteristic
298#440—221no—
299C4×Q16—111no—
300C4×Q16—221no—
301C4×SD16—21no—
302C4×SD16C2×D1111yescharacteristic
303C8×D4—111no—
304C2×#103—221no—
305#335—111no—
306#335—111no—
307#333—111no—
308#333—111no—
309#333—111no—
310#332—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314D4⋊C8—111no—
315#322—111no—
316C22×C11—22no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11D4211yescharacteristic
320C4×C11—22no—
321C4×C11—22no—
322C4×C11—21no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—81no—
327C4×C11—81no—
328C4×C11C22×Q1611yescharacteristic
329C4×C11C2×#13711yescharacteristic
330C4×C11#57711yescharacteristic
331C4×C11#57811yescharacteristic
332Dic11—41no—
333Dic11—41no—
334Dic11—81no—
335Dic11—81no—
336C22×Q8—21no—
337C2×Q16—111no—
338C2×Q16—221no—
339C2×Q16—441no—
340C2×SD16C22⋊D1111yescharacteristic
341C22×C8—221no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—41no—
346C4⋊Q8—111no—
347C4⋊Q8—111no—
348C4⋊Q8—221no—
349C4⋊Q8—221no—
350C4⋊Q8—441no—
351C4⋊Q8C22×D1111yescharacteristic
352C4⋊Q8C22×D1111yescharacteristic
353#125—221no—
354C22⋊Q8—21no—
355C22⋊Q8—41no—
356C22⋊Q8—221no—
357C22⋊Q8—441no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—111no—
361C4×Q8—221no—
362C4×Q8—221no—
363C4×Q8C22×D1111yescharacteristic
364C4×Q8C22×D1111yescharacteristic
365C4×D4—21no—
366C4×D4—221no—
367C4×D4C22×D1111yescharacteristic
368C2×C4⋊C4—221no—
369#107—111no—
370#107—221no—
371#107—221no—
372#107—221no—
373#107—221no—
374#107—221no—
375#107—221no—
376#107—221no—
377#107—221no—
378#106—21no—
379#106—21no—
380#106—21no—
381#106—21no—
382#106—221no—
383#106C22⋊D1111yescharacteristic
384C4⋊C8—21no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8C22×D1111yescharacteristic
391#103—21no—
392#103—111no—
393#103—111no—
394#103—221no—
395#103—221no—
396#103—221no—
397#103—221no—
398#103—221no—
399#103—221no—
400#103—221no—
401#103—441no—
402#103C22⋊D1111yescharacteristic
403#102—21no—
404#102—221no—
405#102C22⋊D1111yescharacteristic
406C22⋊C8—221no—
407#97—221no—
408C4×C8—21no—
409C4×C8—111no—
410C4×C8—111no—
411C4×C8—221no—
412C4×C8C22×D1111yescharacteristic
413C2×C11—42no—
414C2×C11#326611yescharacteristic
415C2×C11D4×Q1611yescharacteristic
416C2×C11#328811yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8—42no—
422C2×Q8—81no—
423C2×Q8—111no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—441no—
427C2×Q8D4×D1111yescharacteristic
428C2×Q8C2×C22⋊D1111yescharacteristic
429C2×D4C2×C22⋊D1111yescharacteristic
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—441no—
433Q16—222no—
434Q16—881no—
435Q16—882no—
436SD16#432614yescomplemented
437C2×C8—21no—
438C2×C8—111no—
439C2×C8—111no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—881no—
445C2×C8C2×C22⋊D1111yescharacteristic
446C2×C8C2×C22⋊D1111yescharacteristic
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—111no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—441no—
463C4⋊C4—441no—
464C4⋊C4—441no—
465C4⋊C4—441no—
466C4⋊C4D4×D1111yescharacteristic
467C4⋊C4C2×C22⋊D1111yescharacteristic
468C4⋊C4C2×C22⋊D1111yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—41no—
471C22⋊C4—441no—
472C42—21no—
473C42—21no—
474C42—41no—
475C42—221no—
476C42—441no—
477C42C23×D1111yescharacteristic
478C11#1981311yescharacteristic, complemented, Sylow
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—41no—
483Q8—41no—
484Q8—82no—
485Q8—81no—
486Q8—161no—
487Q8—221no—
488Q8—221no—
489Q8—881no—
490Q8—881no—
491Q8—1761no—
492Q8#6696812yes—
493Q8C2×#432612yes—
494D4—21no—
495D4C2×#432612yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—82no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—1761no—
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4#6703711yescharacteristic
513C2×C4C22×C22⋊D1111yescharacteristic
514C8—21no—
515C8—41no—
516C8—221no—
517C8—221no—
518C8—441no—
519C8—441no—
520C8—441no—
521C8—441no—
522C8C2×#432612yes—
523C22—22no—
524C22—41no—
525C22—41no—
526C22D4×C22⋊D1111yescharacteristic
527C4—22no—
528C4—21no—
529C4—22no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—81no—
534C4—81no—
535C4—441no—
536C4—441no—
537C4—881no—
538C4—881no—
539C4C2×#6696811yescharacteristic
540C4#1062329311yescharacteristic
541C4C22×#432611yescharacteristic
542C4#1062336911yescharacteristic
543C2—42no—
544C2#1308012611yescharacteristic
545C2D4×#432611yescharacteristic
546C2#1308037811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingQ8×C11×SD16C2
socleC22×C11D42
prime radicalC2×D4×C11C2×D4
hypercenterQ8×SD16D11
hypocenterC11#19813
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ Q8×SD16

Complements

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

NH ≅ G/Ntype
2. Q8×#4326C2semidirect
4. #13068290C2semidirect
5. #13068119C2semidirect
6. #13068072C2semidirect
7. #13068020C2semidirect
9. #13067836C2semidirect
11. #13067756C2semidirect
13. #13067466C2semidirect
161. C11×SD16Q16semidirect
436. SD16#4326semidirect
478. C11#19813semidirect

Maximal subgroups

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

subgroupindex
#130815242
Q8×#43262
#130804922
#130682902
#130681192
#130680722
#130680202
#130680132
#130678362
#130677812
#130677562
#130677482
#130674662
SD16⋊(C11⋊C8)2
Q8×C11×SD162
#1981311