Finite Group Databasebeta

← #14910641

Subgroups — #14910641

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#13080960C211yesmaximal, characteristic
2Q16×C22⋊D11C211yesmaximal, characteristic, complemented
3#13070842C211yesmaximal, characteristic, complemented
4#13070814C211yesmaximal, characteristic, complemented
5#13070812C211yesmaximal, characteristic, complemented
6#13070756C211yesmaximal, characteristic, complemented
7#13070710C211yesmaximal, characteristic, complemented
8#13070709C211yesmaximal, characteristic, complemented
9#13070659C211yesmaximal, characteristic, complemented
10#13070531C211yesmaximal, characteristic, complemented
11SD32×Dic11C211yesmaximal, characteristic, complemented
12(C22⋊D11)⋊C16C211yesmaximal, characteristic, complemented
13C2×#10622202C211yesmaximal, characteristic, complemented
14D11×#358C211yesmaximal, characteristic, complemented
15C11×#2185C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17Q8×C22⋊D11—21no—
18C2×Q16×D11C2211yescharacteristic
19#10623142—21no—
20C2×C11×SD32C2211yescharacteristic
21C2×C11×SD32C2211yescharacteristic
22C11×#466C2211yescharacteristic
23#10622841—21no—
24#10622801C2211yescharacteristic
25#10622799—21no—
26Q16×Dic11C2211yescharacteristic
27#10622795—21no—
28#10622794C2211yescharacteristic
29#10622770C2211yescharacteristic
30D8×Dic11C2211yescharacteristic
31C2×#66891C2211yescharacteristic
32#10622729C2211yescharacteristic
33C8×C22⋊D11C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C22×C11⋊C16C2211yescharacteristic
36#10622646—21no—
37C2×C16×D11C2211yescharacteristic
38D11×#107C2211yescharacteristic
39#10622487C2211yescharacteristic
40#10622387—21no—
41#10622372—21no—
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622202C2211yescharacteristic
49#10622200C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622143C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622141C2211yescharacteristic
55Dic11⋊C16C2211yescharacteristic
56C16×Dic11C2211yescharacteristic
57#10622130C2211yescharacteristic
58#10622128C2211yescharacteristic
59C22×Q8×C11—21no—
60C2×Q8×D11—21no—
61C2×#4341—41no—
62C2×C11×Q16—22no—
63C2×C11×Q16—21no—
64C2×C11×Q16—41no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×Q16C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#121—21no—
70#66999—21no—
71#66999—41no—
72Q8×Dic11—21no—
73#66997—21no—
74#66997—41no—
75C2×#4326—21no—
76C2×#4326—21no—
77#66991—21no—
78#66988—41no—
79D4×Dic11—21no—
80C4×C22⋊D11—41no—
81C4×C22⋊D11D411yescharacteristic
82C2×C4⋊Dic11—21no—
83#66977—21no—
84#66977—41no—
85Q16×D11—22no—
86Q16×D11—41no—
87C2×Dic44C2311yescharacteristic
88C2×C8×D11C2311yescharacteristic
89C4⋊C4×D11—21no—
90#66941—21no—
91#66936—41no—
92#66931—41no—
93C11×SD32—22no—
94C11×SD32—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#102—21no—
99#66899—21no—
100#66899—21no—
101#66896—21no—
102#66896—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66891—41no—
105(C2×D11)⋊C8D411yescharacteristic
106#66882—21no—
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66880—21no—
111Dic11⋊C8D411yescharacteristic
112C8×Dic11C2311yescharacteristic
113C2×C11⋊C16—41no—
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#66871—21no—
117#66871—21no—
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—
125C2×D4×C11—21no—
126C2×D4×C11—41no—
127C22×C4×C11—41no—
128C22×C4×C11C2×D411yescharacteristic
129C2×C22⋊D11—41no—
130C2×C22⋊D11D811yescharacteristic
131C22×Dic11—41no—
132C22×Dic11—41no—
133Q8×D11—42no—
134Q8×D11—81no—
135#4341—84no—
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
147C11×D8—21no—
148C11×D8—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11C2×D411yescharacteristic
152C2×C8×C11C2411yescharacteristic
153C11×C4⋊C4—21no—
154C11×C22⋊C4—41no—
155C22⋊Dic11—41no—
156C22⋊Dic11—41no—
157C22⋊Dic11—41no—
158C22⋊Dic11D811yescharacteristic
159#4326—42no—
160#4326—81no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4D811yescharacteristic
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—41no—
167C4⋊Dic11—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4—41no—
172Dic11⋊C4—41no—
173Dic11⋊C4—41no—
174Dic11⋊C4D811yescharacteristic
175C4×Dic11—41no—
176C4×Dic11C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178C2×C11⋊C8C2×D411yescharacteristic
179Dic44—21no—
180Dic44—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#2185D1111yescharacteristic, complemented
198C4×SD32—111no—
199D4×C16—111no—
200C2×#358—111no—
201C2×#358—111no—
202C23×C11—41no—
203C23×C11C2×D811yescharacteristic
204C22×D11C2×D811yescharacteristic
205Q8×C11—22no—
206Q8×C11—41no—
207Q8×C11—41no—
208Q8×C11—41no—
209Q8×C11—82no—
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—41no—
218C2×C4×C11—82no—
219C2×C4×C11C2×D811yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C22⋊D11—82no—
222C22⋊D11SD3214yescomplemented
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—82no—
228C2×Dic11—82no—
229C2×Dic11C2×D811yescharacteristic
230C2×Dic11C2×D811yescharacteristic
231C2×Dic11C2×D811yescharacteristic
232C4×D11—21no—
233C4×D11—21no—
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×SD32C2×D1111yescharacteristic
251C2×SD32C2×D1111yescharacteristic
252C22×C16—111no—
253C22×C16—111no—
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#466C2×D1111yescharacteristic
263#462—221no—
264#451—221no—
265#451—221no—
266C4×Q16—111no—
267C4×D8—111no—
268C8×D4—111no—
269C2×#107—111no—
270C2×#107—111no—
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#358—111no—
281#358—111no—
282#358C2×D1111yescharacteristic
283#358C2×D1111yescharacteristic
284#357—111no—
285C22⋊C16—111no—
286C22⋊C16C2×D1111yescharacteristic
287C4×C16—111no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11C2×SD3212yes—
294C22×C11C22×D811yescharacteristic
295C2×D11—21no—
296C2×D11—21no—
297C2×D11C2×SD3212yes—
298C4×C11—21no—
299C4×C11—42no—
300C4×C11—81no—
301C4×C11—81no—
302C4×C11#54611yescharacteristic
303C4×C11#57711yescharacteristic
304Dic11—21no—
305Dic11—21no—
306Dic11—81no—
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×D8C22×D1111yescharacteristic
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—21no—
338#121—221no—
339C4×Q8—221no—
340C4×D4—111no—
341C4×D4—221no—
342C4×D4—441no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345SD32—22no—
346SD32—41no—
347SD32—441no—
348C2×C16—111no—
349C2×C16—111no—
350C2×C16—441no—
351C2×C16—441no—
352C2×C16C22×D1111yescharacteristic
353C2×C16C22×D1111yescharacteristic
354#107—111no—
355#107—111no—
356#107—111no—
357#107—221no—
358#107—221no—
359#107—221no—
360#107C22×D1111yescharacteristic
361C4⋊C8—111no—
362#103—221no—
363#103—221no—
364#103—221no—
365#102—21no—
366#102—221no—
367#102—221no—
368C22⋊C8—111no—
369C22⋊C8—111no—
370C4×C8—111no—
371C2×C11—22no—
372C2×C11—161no—
373C2×C11#329411yescharacteristic
374C2×C11C22×SD3211yescharacteristic
375C2×C11#341711yescharacteristic
376D11—22no—
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—21no—
389C2×D4—41no—
390C2×D4—111no—
391C2×D4—441no—
392C22×C4—41no—
393C22×C4—111no—
394C22×C4—441no—
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#434112yescomplemented
408D8—21no—
409D8—21no—
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—111no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C22⋊C4—41no—
432C22⋊C4—111no—
433C22⋊C4—111no—
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—41no—
446C23—111no—
447C23D8×D1111yescharacteristic
448Q8—22no—
449Q8—41no—
450Q8—41no—
451Q8—41no—
452Q8—82no—
453Q8—441no—
454Q8—441no—
455Q8—882no—
456Q8—882no—
457D4—41no—
458D4—41no—
459D4—82no—
460D4—114no—
461D4—882no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—82no—
468C2×C4—111no—
469C2×C4—111no—
470C2×C4—111no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—882no—
478C2×C4—882no—
479C2×C4—882no—
480C2×C4—882no—
481C2×C4D8×D1111yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C8—21no—
484C8—221no—
485C8—221no—
486C8C2×#434111yescharacteristic
487C8#6703711yescharacteristic
488C22—21no—
489C22—21no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—112no—
494C22—221no—
495C22—221no—
496C22D11×SD3212yes—
497C22C2×D8×D1111yescharacteristic
498C4—21no—
499C4—42no—
500C4—81no—
501C4—81no—
502C4—112no—
503C4—221no—
504C4—221no—
505C4—881no—
506C4—881no—
507C4—881no—
508C4—881no—
509C4#1062312211yescharacteristic
510C4#1062330611yescharacteristic
511C2—22no—
512C2—161no—
513C2—222no—
514C2#1308042211yescharacteristic
515C2C2×D11×SD3211yescharacteristic
516C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2185C2
socleC22×C11C22×D8
prime radical#13080960C2
hypercenter#2185D11
hypocenterC11#33865
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2185

Complements

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

NH ≅ G/Ntype
2. Q16×C22⋊D11C2semidirect
3. #13070842C2semidirect
4. #13070814C2semidirect
5. #13070812C2semidirect
6. #13070756C2semidirect
7. #13070710C2semidirect
8. #13070709C2semidirect
9. #13070659C2semidirect
10. #13070531C2semidirect
11. SD32×Dic11C2semidirect
12. (C22⋊D11)⋊C16C2semidirect
13. C2×#10622202C2semidirect
14. D11×#358C2semidirect
15. C11×#2185C2semidirect
146. C11×Q16#41semidirect
197. #2185D11semidirect
222. C22⋊D11SD32semidirect
407. Q16#4341semidirect
444. C11#33865semidirect

Maximal subgroups

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

subgroupindex
#130809602
Q16×C22⋊D112
#130708422
#130708142
#130708122
#130707562
#130707102
#130707092
#130706592
#130705312
SD32×Dic112
(C22⋊D11)⋊C162
C2×#106222022
D11×#3582
C11×#21852
#3386511