Finite Group Databasebeta

← #14910614

Subgroups — #14910614

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080980C211yesmaximal, characteristic, complemented
2#13080301C211yesmaximal, characteristic
3#13070846C211yesmaximal, characteristic, complemented
4#13070813C211yesmaximal, characteristic, complemented
5#13070805C211yesmaximal, characteristic, complemented
6#13070771C211yesmaximal, characteristic, complemented
7#13070711C211yesmaximal, characteristic, complemented
8#13070707C211yesmaximal, characteristic, complemented
9#13070677C211yesmaximal, characteristic, complemented
10#13070557C211yesmaximal, characteristic, complemented
11#13070545C211yesmaximal, characteristic, complemented
12#13070471C211yesmaximal, characteristic, complemented
13C16×C22⋊D11C211yesmaximal, characteristic, complemented
14#13070320C211yesmaximal, characteristic, complemented
15C2×C11×#357C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17#10623337—21no—
18C2×#66965C2211yescharacteristic
19#10623044—21no—
20C22×C11×C16C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622831—21no—
23#10622771—21no—
24#10622770C2211yescharacteristic
25#10622768C2211yescharacteristic
26#10622766—21no—
27D8×Dic11C2211yescharacteristic
28C2×#66891C2211yescharacteristic
29C2×#66891C2211yescharacteristic
30#10622729C2211yescharacteristic
31#10622729C2211yescharacteristic
32C8×C22⋊D11C2211yescharacteristic
33#10622584—21no—
34C2×Dic88C2211yescharacteristic, complemented
35C2×C16×D11C2211yescharacteristic, complemented
36#10622501—21no—
37#10622500C2211yescharacteristic, complemented
38#10622493C2211yescharacteristic, complemented
39#10622491C2211yescharacteristic, complemented
40#10622490—21no—
41#10622486C2211yescharacteristic, complemented
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic, complemented
50#10622142C2211yescharacteristic, complemented
51#10622141C2211yescharacteristic, complemented
52#10622141C2211yescharacteristic, complemented
53Dic11⋊C16C2211yescharacteristic, complemented
54C16×Dic11C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622130C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622128C2211yescharacteristic, complemented
59C22×D4×C11—21no—
60C2×#4341—21no—
61C2×C11×D8—22no—
62C2×C11×D8—21no—
63C2×C11×D8—41no—
64C2×C11×D8C2311yescharacteristic
65C2×C11×D8C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68#67006—41no—
69C2×C22⋊Dic11—41no—
70#66992—41no—
71#66991—21no—
72#66989—21no—
73#66988—41no—
74D4×Dic11—21no—
75C2×#4324—21no—
76C2×#4324—21no—
77#66982—41no—
78C4×C22⋊D11D411yescharacteristic
79#66979—41no—
80#66977—21no—
81#66977—21no—
82#66965—22no—
83#66965—41no—
84C2×Dic44C2311yescharacteristic
85C2×Dic44C2311yescharacteristic
86C2×C8×D11C2311yescharacteristic
87#66951—41no—
88#66950—21no—
89#66945—21no—
90#66943—21no—
91#66942—41no—
92#66940—21no—
93C2×C11×C16—41no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107—21no—
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99#66896—21no—
100#66896—21no—
101C22⋊(C11⋊C8)D411yescharacteristic
102#66891—22no—
103#66891—41no—
104(C2×D11)⋊C8D411yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66880—21no—
108#66880—21no—
109Dic11⋊C8D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66874—21no—
114#66874—21no—
115#66872—21no—
116#66872—21no—
117Dic88—41no—
118C16×D11—41no—
119#33863—111nomaximal, Sylow
120C24×C11—41no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—42no—
124C2×D4×C11—41no—
125C2×D4×C11—81no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11D811yescharacteristic
131C22×Dic11—41no—
132C22×Dic11—41no—
133#4341—42no—
134#4341—81no—
135C2×C4×D11C2×D411yescharacteristic
136C2×Dic22—21no—
137C2×Dic22—21no—
138C11×D8—21no—
139C11×D8—21no—
140C11×D8—21no—
141C11×D8—42no—
142C11×D8#4112yes—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2411yescharacteristic
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153C22⋊Dic11—41no—
154C22⋊Dic11—41no—
155C22⋊Dic11—41no—
156C22⋊Dic11D811yescharacteristic
157#4324—42no—
158#4324—81no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4D811yescharacteristic
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—41no—
165C4⋊Dic11—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4D811yescharacteristic
171C4×Dic11—41no—
172C4×Dic11—41no—
173C4×Dic11C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176Dic44—21no—
177Dic44—21no—
178Dic44—21no—
179Dic44—21no—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3336—111no—
187#3280—111no—
188#2242—111no—
189#2235—111no—
190#2234—111no—
191#2228—111no—
192#2217—111no—
193#2216—111no—
194#2211—111no—
195#2189—111no—
196#2187—111no—
197C4×SD32—111no—
198D4×C16—111no—
199#2138—111no—
200C2×#357D1111yescharacteristic, complemented
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—82no—
204C23×C11—82no—
205C23×C11—161no—
206C23×C11C2×D811yescharacteristic
207C22×D11C2×D811yescharacteristic
208D4×C11—22no—
209D4×C11—41no—
210D4×C11—41no—
211D4×C11—41no—
212D4×C11—82no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—82no—
218C2×C4×C11C2×D811yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C22⋊D11—22no—
221C22⋊D11—82no—
222C22⋊D11—161no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—82no—
228C2×Dic11—161no—
229C2×Dic11C2×D811yescharacteristic
230C2×Dic11C2×D811yescharacteristic
231C2×Dic11C2×D811yescharacteristic
232C4×D11—21no—
233C4×D11—21no—
234Dic22—41no—
235Dic22—41no—
236Dic22—41no—
237Dic22—41no—
238C8×C11—21no—
239C8×C11C2×#4111yescharacteristic
240C8×C11H(5,𝔽2)11yescharacteristic
241C11⋊C8—21no—
242C11⋊C8—21no—
243C2×#135—111no—
244C22×D8C2×D1111yescharacteristic
245#552—221no—
246#546—221no—
247C2×Q32—111no—
248C2×SD32—111no—
249C2×SD32—111no—
250C22×C16—111no—
251C22×C16C2×D1111yescharacteristic
252#499—111no—
253#495—111no—
254#485—221no—
255#483—221no—
256#479—221no—
257#467—111no—
258#467—111no—
259#467—111no—
260#466—111no—
261#463—221no—
262#450—221no—
263#449—221no—
264C4×Q16—111no—
265C4×D8—111no—
266C8×D4—111no—
267#427—111no—
268C2×#107C2×D1111yescharacteristic
269#367—111no—
270#367—111no—
271#366—111no—
272C4⋊C16—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#357—111no—
278#357—111no—
279#357C2×D1111yescharacteristic
280#357C2×D1111yescharacteristic
281#357C2×D1111yescharacteristic
282#357C2×D1111yescharacteristic
283C22⋊C16—111no—
284C22⋊C16—111no—
285C4×C16—111no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—42no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—164no—
295C22×C11#50812yes—
296C22×C11C22×D811yescharacteristic
297C2×D11—21no—
298C2×D11—21no—
299C2×D11—21no—
300C4×C11—21no—
301C4×C11—81no—
302C4×C11—81no—
303C4×C11#54611yescharacteristic
304C4×C11#57711yescharacteristic
305Dic11—21no—
306Dic11—21no—
307Dic11—21no—
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311Dic11—81no—
312C2×#41—221no—
313C22×D4—21no—
314#135—222no—
315#135—441no—
316C2×Q16—111no—
317C2×Q16—111no—
318C2×SD16—221no—
319C2×SD16—221no—
320C2×D8—22no—
321C2×D8—21no—
322C2×D8—41no—
323C2×D8C22×D1111yescharacteristic
324C2×D8C22×D1111yescharacteristic
325C22×C8—111no—
326C22×C8C22×D1111yescharacteristic
327#126—441no—
328#125—221no—
329#125—441no—
330#124—221no—
331#123—441no—
332#123—441no—
333C22⋊Q8—221no—
334C22⋊Q8—221no—
335C22⋊Q8—221no—
336#121—221no—
337#121—441no—
338#120—441no—
339C4×Q8—221no—
340C4×D4—111no—
341C4×D4—221no—
342#117—221no—
343#117—441no—
344C2×C4⋊C4—21no—
345C2×C22⋊C4—441no—
346Q32—441no—
347SD32—222no—
348SD32—441no—
349C2×C16—41no—
350C2×C16—111no—
351C2×C16—111no—
352C2×C16—441no—
353C2×C16C22×D1111yescharacteristic
354C2×C16C22×D1111yescharacteristic
355#107—21no—
356#107—111no—
357#107—111no—
358#107C22×D1111yescharacteristic
359#107C22×D1111yescharacteristic
360#106—221no—
361#106—221no—
362C4⋊C8—111no—
363#103—221no—
364#103—221no—
365#103—221no—
366#103—221no—
367#102—221no—
368#102—221no—
369C22⋊C8—111no—
370C22⋊C8—111no—
371C4×C8—111no—
372C2×C11—22no—
373C2×C11—82no—
374C2×C11—161no—
375C2×C11#329411yescharacteristic
376C2×C11C2×#50811yescharacteristic
377C2×C11#341611yescharacteristic
378D11—41no—
379C24—41no—
380#41—442no—
381#41—881no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—42no—
387C2×D4—41no—
388C2×D4—81no—
389C2×D4—111no—
390C2×D4—441no—
391C2×D4—441no—
392C22×C4—41no—
393C22×C4—111no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4D4×D1111yescharacteristic
397Q16—221no—
398Q16—221no—
399Q16—221no—
400Q16—221no—
401SD16—442no—
402SD16—881no—
403D8—21no—
404D8—21no—
405D8—21no—
406D8—42no—
407D8#433912yes—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—111no—
411C2×C8—111no—
412C2×C8—221no—
413C2×C8—221no—
414C2×C8D4×D1111yescharacteristic
415C2×C8C23×D1111yescharacteristic
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—41no—
419C4⋊C4—111no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4—441no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C22⋊C4—111no—
429C22⋊C4—111no—
430C22⋊C4—441no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C42—111no—
439C42—441no—
440C42—441no—
441C16—21no—
442C16—21no—
443C16—221no—
444C16—221no—
445C11#3386311yescharacteristic, complemented, Sylow
446C23—41no—
447C23—41no—
448C23—82no—
449C23—82no—
450C23—111no—
451C23—161no—
452C23D8×D1111yescharacteristic
453Q8—441no—
454Q8—441no—
455Q8—441no—
456Q8—441no—
457D4—22no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—82no—
462D4—222no—
463D4—882no—
464D4—1761no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—82no—
470C2×C4—111no—
471C2×C4—111no—
472C2×C4—111no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—882no—
480C2×C4—1761no—
481C2×C4D8×D1111yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C8—21no—
484C8—221no—
485C8—221no—
486C8C2×#433911yescharacteristic
487C8#6703711yescharacteristic
488C22—21no—
489C22—21no—
490C22—42no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—81no—
496C22—164no—
497C22—221no—
498C22—221no—
499C22—221no—
500C22#1062252512yes—
501C22C2×D8×D1111yescharacteristic
502C4—21no—
503C4—81no—
504C4—81no—
505C4—221no—
506C4—221no—
507C4—221no—
508C4—881no—
509C4—881no—
510C4—881no—
511C4—881no—
512C4#1062302111yescharacteristic
513C4#1062329311yescharacteristic
514C2—22no—
515C2—82no—
516C2—161no—
517C2—441no—
518C2#1308042511yescharacteristic
519C2C2×#1062252511yescharacteristic
520C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#357C2
socleC22×C11C22×D8
prime radical#13080301C2
hypercenterC2×#357D11
hypocenterC11#33863
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
1. #13080980C2semidirect
3. #13070846C2semidirect
4. #13070813C2semidirect
5. #13070805C2semidirect
6. #13070771C2semidirect
7. #13070711C2semidirect
8. #13070707C2semidirect
9. #13070677C2semidirect
10. #13070557C2semidirect
11. #13070545C2semidirect
12. #13070471C2semidirect
13. C16×C22⋊D11C2semidirect
14. #13070320C2semidirect
15. C2×C11×#357C2semidirect
34. C2×Dic88C22semidirect
35. C2×C16×D11C22semidirect
37. #10622500C22semidirect
38. #10622493C22semidirect
39. #10622491C22semidirect
41. #10622486C22semidirect
49. (C2×D11)⋊C16C22semidirect
50. #10622142C22semidirect
51. #10622141C22semidirect
52. #10622141C22semidirect
53. Dic11⋊C16C22semidirect
54. C16×Dic11C22semidirect
55. #10622130C22semidirect
56. #10622130C22semidirect
57. #10622128C22semidirect
58. #10622128C22semidirect
200. C2×#357D11semidirect
445. C11#33863semidirect

Maximal subgroups

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

subgroupindex
#130809802
#130803012
#130708462
#130708132
#130708052
#130707712
#130707112
#130707072
#130706772
#130705572
#130705452
#130704712
C16×C22⋊D112
#130703202
C2×C11×#3572
#3386311