Finite Group Databasebeta

← #14910644

Subgroups — #14910644

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080961C211yesmaximal, characteristic
2Q16×C22⋊D11C211yesmaximal, characteristic, complemented
3#13070842C211yesmaximal, characteristic, complemented
4#13070813C211yesmaximal, characteristic, complemented
5#13070812C211yesmaximal, characteristic, complemented
6#13070756C211yesmaximal, characteristic, complemented
7#13070715C211yesmaximal, characteristic, complemented
8#13070712C211yesmaximal, characteristic, complemented
9#13070660C211yesmaximal, characteristic, complemented
10#13070534C211yesmaximal, characteristic, complemented
11#13070533C211yesmaximal, characteristic, complemented
12#13070465C211yesmaximal, characteristic, complemented
13C16×C22⋊D11C211yesmaximal, characteristic, complemented
14D11×#358C211yesmaximal, characteristic, complemented
15C2×C11×#358C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17Q8×C22⋊D11—21no—
18C2×Q16×D11C2211yescharacteristic
19#10623038—21no—
20C22×C11×C16C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622841—21no—
23#10622801C2211yescharacteristic
24#10622799—21no—
25Q16×Dic11C2211yescharacteristic
26#10622795—21no—
27#10622794C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29C2×#66892C2211yescharacteristic
30#10622729C2211yescharacteristic
31#10622728C2211yescharacteristic
32C8×C22⋊D11C2211yescharacteristic
33#10622580—21no—
34C2×#66864C2211yescharacteristic
35C2×C16×D11C2211yescharacteristic
36#10622503—21no—
37#10622496C2211yescharacteristic
38#10622495—21no—
39D11×#107C2211yescharacteristic
40#10622487C2211yescharacteristic
41#10622485C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#358C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622147C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622141C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622128C2211yescharacteristic
59C22×Q8×C11—21no—
60C2×Q8×D11—21no—
61C2×#4339—41no—
62C2×C11×Q16—22no—
63C2×C11×Q16—21no—
64C2×C11×Q16—41no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×Q16C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—21no—
69#66999—21no—
70#66999—41no—
71Q8×Dic11—21no—
72#66997—21no—
73#66997—41no—
74C2×#4326—21no—
75C2×#4326—21no—
76#66983—21no—
77#66982—41no—
78C4×C22⋊D11—41no—
79C4×C22⋊D11D411yescharacteristic
80#66977—21no—
81#66977—41no—
82Q16×D11—22no—
83Q16×D11—41no—
84C2×Dic44C2311yescharacteristic
85C2×D88C2311yescharacteristic
86C2×C8×D11C2311yescharacteristic
87#66949—41no—
88#66948—21no—
89#66947—41no—
90#66946—21no—
91C4⋊C4×D11—21no—
92#66941—21no—
93C2×C11×C16—41no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107—21no—
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99#66899—21no—
100#66899—21no—
101C22⋊(C11⋊C8)D411yescharacteristic
102#66892—22no—
103#66892—41no—
104#66885—21no—
105(C2×D11)⋊C8D411yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66880—21no—
109Dic11⋊C8D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66873—21no—
114#66873—21no—
115#66871—21no—
116#66871—21no—
117#66864—41no—
118C16×D11—41no—
119#33865—111nomaximal, Sylow
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—42no—
123C2×Q8×C11—41no—
124C2×Q8×C11—81no—
125C22×C4×C11—41no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11D811yescharacteristic
130Q8×D11—42no—
131Q8×D11—81no—
132#4339—84no—
133C2×D44—21no—
134C2×D44—41no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11C2×D411yescharacteristic
139C2×Dic22—21no—
140C2×Dic22—41no—
141C2×Dic22—41no—
142C11×Q16—21no—
143C11×Q16—21no—
144C11×Q16—21no—
145C11×Q16—42no—
146C11×Q16#4112yescomplemented
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2411yescharacteristic
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—41no—
154C22⋊Dic11—41no—
155C22⋊Dic11D811yescharacteristic
156#4326—42no—
157#4326—81no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4D811yescharacteristic
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4—41no—
172Dic11⋊C4D811yescharacteristic
173C4×Dic11—41no—
174C4×Dic11C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176C2×C11⋊C8C2×D411yescharacteristic
177Dic44—21no—
178Dic44—21no—
179D88—21no—
180D88—21no—
181C8×D11—21no—
182C8×D11—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3334—111no—
188D4×Q16—111no—
189#2241—111no—
190#2235—111no—
191#2235—111no—
192#2225—111no—
193#2217—111no—
194#2217—111no—
195#2208—111no—
196#2185—111no—
197#2185—111no—
198C4×SD32—111no—
199D4×C16—111no—
200C2×#358—111no—
201C2×#358D1111yescharacteristic, complemented
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11C2×D811yescharacteristic
205Q8×C11—22no—
206Q8×C11—41no—
207Q8×C11—41no—
208Q8×C11—41no—
209Q8×C11—82no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—82no—
217C2×C4×C11—82no—
218C2×C4×C11C2×D811yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C22⋊D11—82no—
221C22⋊D11SD3214yescomplemented
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11C2×D811yescharacteristic
226C2×Dic11C2×D811yescharacteristic
227C2×Dic11C2×D811yescharacteristic
228D44—41no—
229D44—41no—
230D44—82no—
231C4×D11—21no—
232C4×D11—21no—
233C4×D11—82no—
234C4×D11—82no—
235C4×D11—82no—
236Dic22—41no—
237Dic22—41no—
238Dic22—82no—
239Dic22—82no—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11H(5,𝔽2)11yescharacteristic
243C11⋊C8—21no—
244C11⋊C8—21no—
245C22×Q16—111no—
246C22×Q16C2×D1111yescharacteristic
247D4×Q8—221no—
248#547—221no—
249C2×SD32—111no—
250C2×SD32—111no—
251C2×SD32—111no—
252C22×C16—111no—
253C22×C16C2×D1111yescharacteristic
254#500—111no—
255#494—111no—
256#480—221no—
257#480—221no—
258#474—221no—
259#467—111no—
260#467—111no—
261#466—111no—
262#466—111no—
263#462—221no—
264#451—221no—
265#451—221no—
266C4×Q16—111no—
267C4×D8—111no—
268C8×D4—111no—
269C2×#107—111no—
270C2×#107C2×D1111yescharacteristic
271#367—111no—
272#367—111no—
273#367—111no—
274C4⋊C16—111no—
275#358—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#358—111no—
280#358C2×D1111yescharacteristic
281#358C2×D1111yescharacteristic
282#358C2×D1111yescharacteristic
283#358C2×D1111yescharacteristic
284#357—111no—
285C22⋊C16—111no—
286C22⋊C16—111no—
287C4×C16—111no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11C2×SD3212yes—
291C22×C11C22×D811yescharacteristic
292C2×D11—21no—
293C2×D11—21no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11C2×SD3212yes—
298C4×C11—21no—
299C4×C11—42no—
300C4×C11—81no—
301C4×C11—81no—
302C4×C11—81no—
303C4×C11#54611yescharacteristic
304C4×C11#57711yescharacteristic
305Dic11—21no—
306Dic11—21no—
307Dic11—81no—
308Dic11—81no—
309Dic11—81no—
310Dic11C2×SD3212yes—
311C2×#41—441no—
312C22×Q8—21no—
313C22×Q8—221no—
314C2×Q16—22no—
315C2×Q16—21no—
316C2×Q16—41no—
317C2×Q16—111no—
318C2×Q16—221no—
319C2×Q16—221no—
320C2×Q16—222no—
321C2×Q16—441no—
322C2×Q16C22×D1111yescharacteristic
323C2×Q16C22×D1111yescharacteristic
324C2×D8—111no—
325C22×C8—111no—
326C22×C8C22×D1111yescharacteristic
327C4⋊Q8—221no—
328C4⋊Q8—221no—
329C4⋊Q8—441no—
330#123—441no—
331#123—441no—
332C22⋊Q8—221no—
333C22⋊Q8—221no—
334C22⋊Q8—441no—
335C22⋊Q8—441no—
336C22⋊Q8—441no—
337#121—221no—
338#121—221no—
339C4×Q8—221no—
340C4×D4—111no—
341C4×D4—221no—
342C4×D4—441no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—221no—
345SD32—222no—
346SD32—441no—
347SD32—441no—
348C2×C16—41no—
349C2×C16—111no—
350C2×C16—111no—
351C2×C16—441no—
352C2×C16C22×D1111yescharacteristic
353C2×C16C22×D1111yescharacteristic
354#107—21no—
355#107—111no—
356#107—111no—
357#107—221no—
358#107—221no—
359#107C22×D1111yescharacteristic
360#107C22×D1111yescharacteristic
361C4⋊C8—111no—
362#103—221no—
363#103—221no—
364#103—221no—
365#102—221no—
366#102—221no—
367#102—221no—
368C22⋊C8—111no—
369C22⋊C8—111no—
370C4×C8—111no—
371C2×C11—22no—
372C2×C11#329411yescharacteristic
373C2×C11C22×SD3211yescharacteristic
374C2×C11#341711yescharacteristic
375D11—22no—
376D11—161no—
377#41—884no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—42no—
381C2×Q8—41no—
382C2×Q8—81no—
383C2×Q8—221no—
384C2×Q8—441no—
385C2×Q8—441no—
386C2×Q8—442no—
387C2×Q8—881no—
388C2×D4—111no—
389C2×D4—221no—
390C2×D4—441no—
391C2×D4—441no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—111no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4—441no—
398C22×C4D4×D1111yescharacteristic
399Q16—21no—
400Q16—21no—
401Q16—21no—
402Q16—42no—
403Q16—221no—
404Q16—221no—
405Q16—442no—
406Q16—881no—
407Q16#433912yescomplemented
408D8—221no—
409D8—221no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—111no—
413C2×C8—111no—
414C2×C8—221no—
415C2×C8—221no—
416C2×C8D4×D1111yescharacteristic
417C2×C8C23×D1111yescharacteristic
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—41no—
421C4⋊C4—111no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C22⋊C4—111no—
432C22⋊C4—111no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C42—111no—
439C42—441no—
440C16—21no—
441C16—21no—
442C16—221no—
443C16—221no—
444C11#3386511yescharacteristic, complemented, Sylow
445C23—111no—
446C23—441no—
447C23D8×D1111yescharacteristic
448Q8—22no—
449Q8—41no—
450Q8—41no—
451Q8—41no—
452Q8—82no—
453Q8—441no—
454Q8—441no—
455Q8—882no—
456Q8—882no—
457D4—114no—
458D4—441no—
459D4—441no—
460D4—882no—
461D4—882no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—82no—
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—882no—
479C2×C4—882no—
480C2×C4—882no—
481C2×C4D8×D1111yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C8—21no—
484C8—221no—
485C8—221no—
486C8C2×#433911yescharacteristic
487C8#6703711yescharacteristic
488C22—21no—
489C22—21no—
490C22—112no—
491C22—221no—
492C22—221no—
493C22—881no—
494C22—881no—
495C22—881no—
496C22D11×SD3212yes—
497C22C2×D8×D1111yescharacteristic
498C4—21no—
499C4—42no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4—112no—
504C4—221no—
505C4—221no—
506C4—881no—
507C4—881no—
508C4—881no—
509C4#1062302111yescharacteristic
510C4#1062329311yescharacteristic
511C2—22no—
512C2—222no—
513C2—1761no—
514C2#1308042511yescharacteristic
515C2C2×D11×SD3211yescharacteristic
516C2#1308176511yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#358C2
socleC22×C11C22×D8
prime radical#13080961C2
hypercenterC2×#358D11
hypocenterC11#33865
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. Q16×C22⋊D11C2semidirect
3. #13070842C2semidirect
4. #13070813C2semidirect
5. #13070812C2semidirect
6. #13070756C2semidirect
7. #13070715C2semidirect
8. #13070712C2semidirect
9. #13070660C2semidirect
10. #13070534C2semidirect
11. #13070533C2semidirect
12. #13070465C2semidirect
13. C16×C22⋊D11C2semidirect
14. D11×#358C2semidirect
15. C2×C11×#358C2semidirect
146. C11×Q16#41semidirect
201. C2×#358D11semidirect
221. C22⋊D11SD32semidirect
407. Q16#4339semidirect
444. C11#33865semidirect

Maximal subgroups

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

subgroupindex
#130809612
Q16×C22⋊D112
#130708422
#130708132
#130708122
#130707562
#130707152
#130707122
#130706602
#130705342
#130705332
#130704652
C16×C22⋊D112
D11×#3582
C2×C11×#3582
#3386511