Finite Group Databasebeta

← #14910672

Subgroups — #14910672

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080985C211yesmaximal, characteristic, complemented
2#13080359C211yesmaximal, characteristic
3#13070848C211yesmaximal, characteristic, complemented
4#13070825C211yesmaximal, characteristic, complemented
5#13070797C211yesmaximal, characteristic, complemented
6#13070781C211yesmaximal, characteristic, complemented
7#13070712C211yesmaximal, characteristic, complemented
8#13070707C211yesmaximal, characteristic, complemented
9#13070679C211yesmaximal, characteristic, complemented
10#13070558C211yesmaximal, characteristic, complemented
11#13070552C211yesmaximal, characteristic, complemented
12C4×Dic88C211yesmaximal, characteristic, complemented
13#13070324C211yesmaximal, characteristic, complemented
14C2×#10622141C211yesmaximal, characteristic, complemented
15D4×C11×C16C211yesmaximal, characteristic, complemented
16C22×Dic44C2211yescharacteristic
17C2×#66957C2211yescharacteristic
18#10623083—21no—
19#10623072—21no—
20C22×C11×C16C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622729C2211yescharacteristic
25#10622729C2211yescharacteristic
26#10622728C2211yescharacteristic
27#10622719C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×Dic88C2211yescharacteristic
30C2×Dic88C2211yescharacteristic
31C2×#66864C2211yescharacteristic
32#10622458—21no—
33#10622442—21no—
34#10622351—21no—
35#10622346—21no—
36#10622336—21no—
37#10622334—21no—
38C4×Dic44C2211yescharacteristic
39C4×Dic44C2211yescharacteristic
40#10622309C2211yescharacteristic
41#10622296C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45C4×C11×C16C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622142C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622141C2211yescharacteristic
55#10622141C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C2×#4339—21no—
60C22×Dic22—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C4×D4×C11D411yescharacteristic
64#66992—41no—
65#66988—41no—
66#66983—21no—
67#66979—21no—
68C2×C4⋊Dic11—21no—
69#66977—21no—
70#66977—21no—
71#66977—21no—
72C2×Dic44—22no—
73C2×Dic44—21no—
74C2×Dic44—41no—
75C2×Dic44C2311yescharacteristic
76C2×Dic44C2311yescharacteristic
77C2×Dic44C2311yescharacteristic
78#66957—22no—
79#66957—41no—
80C2×D88C2311yescharacteristic
81C2×#4314—21no—
82C2×#4314—21no—
83#66949—41no—
84#66942—41no—
85#66938—41no—
86(C22⋊D11)⋊C4—41no—
87#66932—41no—
88#66930—41no—
89#66928—21no—
90#66923—21no—
91C4×Dic22—21no—
92C4×Dic22—21no—
93C2×C11×C16—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C2×C11×C16C2311yescharacteristic
98C2×C11×C16C2311yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C22⋊C8D411yescharacteristic
101C11×C22⋊C8D411yescharacteristic
102C4×C8×C11C2311yescharacteristic
103#66885—21no—
104#66882—21no—
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66881—21no—
110#66881—21no—
111#66880—21no—
112#66880—21no—
113#66880—21no—
114#66880—21no—
115#66880—21no—
116Dic88—22no—
117Dic88—41no—
118#66864—41no—
119#33867—111nomaximal, Sylow
120C2×D4×C11D811yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C22×Dic11—41no—
126C22×Dic11—41no—
127#4339—42no—
128#4339—81no—
129C2×D44—21no—
130C2×C4×D11—41no—
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—42no—
135C2×Dic22—41no—
136C2×Dic22—81no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2411yescharacteristic
145C11×C4⋊C4D811yescharacteristic
146C11×C22⋊C4D811yescharacteristic
147C11×C22⋊C4D811yescharacteristic
148C42×C11C2×D411yescharacteristic
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168C4×Dic11—41no—
169C4×Dic11—41no—
170C4×Dic11—41no—
171Dic44—21no—
172Dic44—21no—
173Dic44—21no—
174Dic44—21no—
175Dic44—21no—
176Dic44—42no—
177Dic44#4112yes—
178D88—21no—
179D88—21no—
180#4314—42no—
181#4314—81no—
182C11×C16—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11×C16—21no—
186#3336—111no—
187#3285—111no—
188#2242—111no—
189#2237—111no—
190#2232—111no—
191#2229—111no—
192#2217—111no—
193#2216—111no—
194#2211—111no—
195#2189—111no—
196#2188—111no—
197C4×Q32—111no—
198D4×C16D1111yescharacteristic, complemented
199#2138—111no—
200C2×#358—111no—
201C23×C11C2×D811yescharacteristic
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204D4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—82no—
215C22⋊D11—82no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—82no—
224C2×Dic11—82no—
225D44—41no—
226D44—41no—
227C4×D11—82no—
228Dic22—22no—
229Dic22—41no—
230Dic22—41no—
231Dic22—41no—
232Dic22—41no—
233Dic22—41no—
234Dic22—82no—
235C8×C11—21no—
236C8×C11—21no—
237C8×C11—21no—
238C8×C11C2×#4111yescharacteristic
239C8×C11H(5,𝔽2)11yescharacteristic
240C2×#135—111no—
241C22×Q16—111no—
242#552—221no—
243#548—221no—
244C2×Q32—111no—
245C2×Q32—111no—
246C2×SD32—111no—
247C22×C16C2×D1111yescharacteristic
248C22×C16C2×D1111yescharacteristic
249#499—111no—
250#495—111no—
251#485—221no—
252#483—221no—
253#479—221no—
254#467—111no—
255#467—111no—
256#467—111no—
257#466—111no—
258#464—221no—
259#452—221no—
260#448—221no—
261C4×Q16—111no—
262C4×Q16—111no—
263C8×D4C2×D1111yescharacteristic
264#427—111no—
265C2×#107—111no—
266#367—111no—
267#366—111no—
268#366—111no—
269C4⋊C16C2×D1111yescharacteristic
270#358—111no—
271#358—111no—
272#358—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#357—111no—
278#357—111no—
279#357—111no—
280C22⋊C16C2×D1111yescharacteristic
281C22⋊C16C2×D1111yescharacteristic
282C4×C16C2×D1111yescharacteristic
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11#50812yes—
289C22×C11C22×D811yescharacteristic
290C2×D11—81no—
291C2×D11—81no—
292C2×D11—81no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11#54611yescharacteristic
298C4×C11#57711yescharacteristic
299Dic11—42no—
300Dic11—81no—
301Dic11—81no—
302Dic11—81no—
303Dic11—81no—
304Dic11—81no—
305Dic11—81no—
306C2×#41—221no—
307C22×Q8—221no—
308#135—222no—
309#135—441no—
310C2×Q16—111no—
311C2×Q16—111no—
312C2×Q16—111no—
313C2×Q16—222no—
314C2×Q16—221no—
315C2×Q16—441no—
316C2×SD16—221no—
317C2×SD16—221no—
318C2×D8—111no—
319C22×C8C22×D1111yescharacteristic
320C22×C8C22×D1111yescharacteristic
321#126—441no—
322#125—221no—
323#125—441no—
324#124—221no—
325#124—441no—
326#123—441no—
327C22⋊Q8—221no—
328C22⋊Q8—221no—
329C22⋊Q8—221no—
330C22⋊Q8—441no—
331#121—221no—
332#121—441no—
333C4×Q8—221no—
334C4×Q8—221no—
335C4×D4—441no—
336C4×D4D4411yescharacteristic
337#117—221no—
338#117—441no—
339C2×C4⋊C4—221no—
340Q32—222no—
341Q32—441no—
342SD32—441no—
343C2×C16—41no—
344C2×C16—41no—
345C2×C16C22×D1111yescharacteristic
346C2×C16C22×D1111yescharacteristic
347C2×C16C22×D1111yescharacteristic
348C2×C16C22×D1111yescharacteristic
349#107—111no—
350#107—111no—
351#107—111no—
352#107—111no—
353#107—221no—
354#106—221no—
355#106—221no—
356C4⋊C8D4411yescharacteristic
357#103—221no—
358#103—221no—
359#103—221no—
360#103—221no—
361#103—221no—
362#102—221no—
363C22⋊C8D4411yescharacteristic
364C22⋊C8D4411yescharacteristic
365C4×C8C22×D1111yescharacteristic
366C2×C11—22no—
367C2×C11—41no—
368C2×C11#329411yescharacteristic
369C2×C11C2×#50811yescharacteristic
370C2×C11#341711yescharacteristic
371D11—161no—
372#41—442no—
373#41—881no—
374C2×Q8—221no—
375C2×Q8—221no—
376C2×Q8—221no—
377C2×Q8—442no—
378C2×Q8—441no—
379C2×Q8—881no—
380C2×D4—221no—
381C2×D4—441no—
382C2×D4—441no—
383C2×D4D8811yescharacteristic
384C22×C4—441no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4C2×D4411yescharacteristic
388C22×C4C2×D4411yescharacteristic
389Q16—112no—
390Q16—221no—
391Q16—221no—
392Q16—221no—
393Q16—221no—
394Q16—221no—
395Q16—442no—
396SD16—442no—
397SD16—881no—
398D8—221no—
399D8—221no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8C2×D4411yescharacteristic
405C2×C8C2×D4411yescharacteristic
406C2×C8C2×D4411yescharacteristic
407C2×C8C23×D1111yescharacteristic
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—441no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C4⋊C4—441no—
419C4⋊C4—441no—
420C4⋊C4D8811yescharacteristic
421C22⋊C4—441no—
422C22⋊C4—441no—
423C22⋊C4—441no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C22⋊C4D8811yescharacteristic
429C22⋊C4D8811yescharacteristic
430C42—441no—
431C42—441no—
432C42—441no—
433C42C2×D4411yescharacteristic
434C16—21no—
435C16—21no—
436C16—21no—
437C16—21no—
438C11#3386711yescharacteristic, complemented, Sylow
439C23—441no—
440C23C2×D8811yescharacteristic
441C23C2×D8811yescharacteristic
442Q8—222no—
443Q8—441no—
444Q8—441no—
445Q8—441no—
446Q8—441no—
447Q8—441no—
448Q8—882no—
449D4—22no—
450D4—441no—
451D4—441no—
452D4—882no—
453D4—882no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—882no—
466C2×C4—882no—
467C2×C4—882no—
468C2×C4C2×D8811yescharacteristic
469C2×C4C2×D8811yescharacteristic
470C2×C4C2×D8811yescharacteristic
471C2×C4C2×D8811yescharacteristic
472C2×C4C22×D4411yescharacteristic
473C8—21no—
474C8—21no—
475C8—21no—
476C8#6703711yescharacteristic
477C8#41×D1111yescharacteristic
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—881no—
484C22—881no—
485C22—881no—
486C22#1062251712yes—
487C22C22×D8811yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—442no—
493C4—881no—
494C4—881no—
495C4—881no—
496C4—881no—
497C4—881no—
498C4—881no—
499C4#1062308511yescharacteristic
500C4#1062328211yescharacteristic
501C2—22no—
502C2—41no—
503C2—1761no—
504C2#1308043011yescharacteristic
505C2C2×#1062251711yescharacteristic
506C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×C16C2
socleC22×C11C22×D8
prime radical#13080359C2
hypercenterD4×C16D11
hypocenterC11#33867
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #13080985C2semidirect
3. #13070848C2semidirect
4. #13070825C2semidirect
5. #13070797C2semidirect
6. #13070781C2semidirect
7. #13070712C2semidirect
8. #13070707C2semidirect
9. #13070679C2semidirect
10. #13070558C2semidirect
11. #13070552C2semidirect
12. C4×Dic88C2semidirect
13. #13070324C2semidirect
14. C2×#10622141C2semidirect
15. D4×C11×C16C2semidirect
198. D4×C16D11semidirect
438. C11#33867semidirect

Maximal subgroups

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

subgroupindex
#130809852
#130803592
#130708482
#130708252
#130707972
#130707812
#130707122
#130707072
#130706792
#130705582
#130705522
C4×Dic882
#130703242
C2×#106221412
D4×C11×C162
#3386711