Finite Group Databasebeta

← #14910876

Subgroups — #14910876

Order 2816.

542 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#13080983C211yesmaximal, characteristic, complemented
2#13080337C211yesmaximal, characteristic
3#13070863C211yesmaximal, characteristic, complemented
4#13070827C211yesmaximal, characteristic, complemented
5#13070820C211yesmaximal, characteristic, complemented
6#13070725C211yesmaximal, characteristic, complemented
7#13070708C211yesmaximal, characteristic, complemented
8#13070667C211yesmaximal, characteristic, complemented
9#13070557C211yesmaximal, characteristic, complemented
10#13070557C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12#13070440C211yesmaximal, characteristic, complemented
13#13070325C211yesmaximal, characteristic, complemented
14#13070320C211yesmaximal, characteristic, complemented
15C11×#2228C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C2×#66965C2211yescharacteristic
18#10623225—21no—
19#10623086—21no—
20C11×#499C2211yescharacteristic
21C4×C11×D8C2211yescharacteristic
22C2×#66891C2211yescharacteristic
23#10622676—21no—
24#10622632—21no—
25C2×Dic88C2211yescharacteristic
26C2×Dic88C2211yescharacteristic
27C2×#66862C2211yescharacteristic
28C2×C16×D11C2211yescharacteristic
29#10622500C2211yescharacteristic
30#10622500C2211yescharacteristic
31#10622500C2211yescharacteristic
32#10622500C2211yescharacteristic
33#10622493C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622480—21no—
36#10622475—21no—
37#10622396—21no—
38#10622396—21no—
39#10622312C2211yescharacteristic
40C4×Dic44C2211yescharacteristic
41C8×D44C2211yescharacteristic
42C11×#367C2211yescharacteristic
43C11×#366C2211yescharacteristic
44C11×C4⋊C16C2211yescharacteristic
45C11×#357C2211yescharacteristic
46C11×#357C2211yescharacteristic
47#10622200C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×#4341—21no—
60C2×#4341—21no—
61C2×C11×D8C2311yescharacteristic
62C11×#125—21no—
63C4×D4×C11—21no—
64C2×#4324—21no—
65C2×#4324—21no—
66#66983—41no—
67C2×C4⋊Dic11—41no—
68#66965—22no—
69#66965—22no—
70#66965—41no—
71#66965—41no—
72C2×Dic44—21no—
73C2×Dic44C2311yescharacteristic
74C2×Dic44C2311yescharacteristic
75C2×Dic44C2311yescharacteristic
76C2×C8×D11C2311yescharacteristic
77C2×C8×D11C2311yescharacteristic
78#66951—41no—
79#66950—21no—
80#66950—21no—
81#66950—21no—
82#66950—21no—
83#66947—41no—
84#66945—21no—
85#66945—41no—
86C4⋊C4×D11—21no—
87#66943—41no—
88#66939—41no—
89#66939—41no—
90C4×D44D411yescharacteristic
91#66922—21no—
92C4×Dic22—21no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#106—21no—
99C11×#102—21no—
100C4×C8×C11C2311yescharacteristic
101#66891—22no—
102(C2×D11)⋊C8D411yescharacteristic
103(C2×D11)⋊C8D411yescharacteristic
104#66882C2311yescharacteristic
105#66880—21no—
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66874—21no—
110#66874—21no—
111#66874—21no—
112#66872—21no—
113#66871—21no—
114C4⋊(C11⋊C8)D411yescharacteristic
115Dic88—41no—
116Dic88—41no—
117#66862—41no—
118C16×D11—41no—
119#33882—111nomaximal, Sylow
120C2×D4×C11—21no—
121C22×C4×C11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126#4341—42no—
127#4341—42no—
128#4341—81no—
129#4341—81no—
130C2×D44D811yescharacteristic
131C2×C4×D11—41no—
132C2×C4×D11C2×D411yescharacteristic
133C2×C4×D11C2×D411yescharacteristic
134C2×Dic22—21no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C11×D8—21no—
138C11×D8#4112yes—
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2411yescharacteristic
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C22⋊C4—41no—
147C42×C11C2×D411yescharacteristic
148#4324—42no—
149#4324—42no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4D811yescharacteristic
156(C2×D11)⋊C4D811yescharacteristic
157C4⋊Dic11—21no—
158C4⋊Dic11—41no—
159C4⋊Dic11—41no—
160C4⋊Dic11—41no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163C4⋊Dic11—41no—
164C4⋊Dic11D811yescharacteristic
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167C4×Dic11—41no—
168C4×Dic11—41no—
169C2×C11⋊C8C2×D411yescharacteristic
170C2×C11⋊C8C2×D411yescharacteristic
171Dic44—21no—
172Dic44—21no—
173Dic44—21no—
174Dic44—21no—
175Dic44—21no—
176Dic44—21no—
177Dic44—81no—
178C8×D11—21no—
179C8×D11—21no—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3336—111no—
187#3283—111no—
188#2245—111no—
189#2237—111no—
190#2236—111no—
191#2228D1111yescharacteristic, complemented
192#2219—111no—
193#2216—111no—
194#2209—111no—
195#2189—111no—
196#2189—111no—
197#2175—111no—
198#2168—111no—
199#2139—111no—
200#2138—111no—
201C23×C11—41no—
202C22×D11C2×D811yescharacteristic
203C22×D11C2×D811yescharacteristic
204D4×C11—22no—
205D4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—82no—
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C22⋊D11—82no—
214C22⋊D11—82no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—82no—
220C2×Dic11—82no—
221C2×Dic11C2×D811yescharacteristic
222C2×Dic11C2×D811yescharacteristic
223D44—41no—
224C4×D11—21no—
225C4×D11—21no—
226C4×D11—21no—
227C4×D11—21no—
228C4×D11—82no—
229Dic22—41no—
230Dic22—41no—
231Dic22—41no—
232Dic22—41no—
233Dic22—41no—
234Dic22—41no—
235C8×C11—21no—
236C8×C11C2×#4111yescharacteristic
237C8×C11H(5,𝔽2)11yescharacteristic
238C11⋊C8—21no—
239C11⋊C8—21no—
240C2×#135—111no—
241C2×#135—111no—
242#552—221no—
243#547—221no—
244C2×Q32—111no—
245C2×Q32—111no—
246C2×SD32—111no—
247C2×M32—111no—
248C22×C16—111no—
249#499C2×D1111yescharacteristic
250#494—111no—
251#485—221no—
252#483—221no—
253#479—221no—
254#467—111no—
255#467—111no—
256#467—111no—
257#467—111no—
258#461—221no—
259#452—221no—
260#452—221no—
261C4×Q16—111no—
262C4×D8C2×D1111yescharacteristic
263C8×D4—111no—
264#427—111no—
265C2×#107—111no—
266#367C2×D1111yescharacteristic
267#366—111no—
268#366C2×D1111yescharacteristic
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#357C2×D1111yescharacteristic
279#357C2×D1111yescharacteristic
280C22⋊C16—111no—
281C22⋊C16—111no—
282#346—111no—
283C22×C11—42no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11C22×D811yescharacteristic
287C2×D11—21no—
288C2×D11—21no—
289C2×D11—21no—
290C2×D11—21no—
291C2×D11—21no—
292C2×D11—21no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—81no—
296C4×C11—81no—
297C4×C11—81no—
298C4×C11#54611yescharacteristic
299C4×C11#57711yescharacteristic
300Dic11—21no—
301Dic11—21no—
302Dic11—81no—
303Dic11—81no—
304Dic11—81no—
305Dic11—81no—
306C2×#41—221no—
307C2×#41—221no—
308#135—222no—
309#135—222no—
310#135—441no—
311#135—441no—
312C2×Q16—111no—
313C2×Q16—111no—
314C2×Q16—111no—
315C2×Q16—221no—
316C2×SD16—221no—
317C2×SD16—221no—
318C2×D8C22×D1111yescharacteristic
319C22×C8—111no—
320C22×C8—111no—
321C4⋊Q8—221no—
322#126—441no—
323#125—21no—
324#125—441no—
325#123—441no—
326#123—441no—
327#123—441no—
328C22⋊Q8—221no—
329C22⋊Q8—221no—
330C22⋊Q8—221no—
331C22⋊Q8—221no—
332#121—441no—
333C4×Q8—221no—
334C4×D4—21no—
335C4×D4—111no—
336#117—221no—
337#117—441no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—441no—
340Q32—441no—
341Q32—441no—
342SD32—222no—
343M32—441no—
344C2×C16—111no—
345C2×C16—111no—
346C2×C16—441no—
347C2×C16C22×D1111yescharacteristic
348C2×C16C22×D1111yescharacteristic
349#107—111no—
350#107—221no—
351#107C22×D1111yescharacteristic
352#107C22×D1111yescharacteristic
353#107C22×D1111yescharacteristic
354#106—21no—
355#106—221no—
356C4⋊C8—111no—
357#103—221no—
358#103—221no—
359#103—221no—
360#103—221no—
361#103—221no—
362#102—21no—
363C22⋊C8—111no—
364C22⋊C8—111no—
365C4×C8C22×D1111yescharacteristic
366C2×C11—82no—
367C2×C11#329411yescharacteristic
368C2×C11#341411yescharacteristic
369C2×C11#341711yescharacteristic
370D11—41no—
371D11—41no—
372#41—442no—
373#41—442no—
374#41—881no—
375#41—881no—
376C2×Q8—221no—
377C2×Q8—221no—
378C2×Q8—221no—
379C2×D4—21no—
380C2×D4—111no—
381C2×D4—441no—
382C2×D4—441no—
383C22×C4—41no—
384C22×C4—111no—
385C22×C4—111no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389Q16—221no—
390Q16—221no—
391Q16—221no—
392Q16—221no—
393Q16—221no—
394Q16—221no—
395Q16—881no—
396SD16—442no—
397SD16—442no—
398D8—21no—
399D8#434312yes—
400C2×C8—111no—
401C2×C8—111no—
402C2×C8—221no—
403C2×C8—221no—
404C2×C8—221no—
405C2×C8—221no—
406C2×C8D4×D1111yescharacteristic
407C2×C8C23×D1111yescharacteristic
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—111no—
414C4⋊C4—221no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C4⋊C4—441no—
419C4⋊C4—441no—
420C4⋊C4—441no—
421C4⋊C4—441no—
422C4⋊C4—441no—
423C22⋊C4—41no—
424C22⋊C4—111no—
425C22⋊C4—111no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C22⋊C4—441no—
429C22⋊C4—441no—
430C22⋊C4—441no—
431C42—441no—
432C42—441no—
433C42D4×D1111yescharacteristic
434C16—21no—
435C16—21no—
436C16—221no—
437C16—221no—
438C11#3388211yescharacteristic, complemented, Sylow
439C23—41no—
440C23—111no—
441C23—111no—
442Q8—441no—
443Q8—441no—
444Q8—441no—
445Q8—441no—
446Q8—441no—
447Q8—441no—
448D4—22no—
449D4—41no—
450D4—441no—
451D4—882no—
452D4—882no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—82no—
457C2×C4—111no—
458C2×C4—111no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—221no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—882no—
468C2×C4—882no—
469C2×C4—882no—
470C2×C4D8×D1111yescharacteristic
471C2×C4D8×D1111yescharacteristic
472C2×C4C2×D4×D1111yescharacteristic
473C8—21no—
474C8—221no—
475C8—221no—
476C8C2×#434311yescharacteristic
477C8#6704211yescharacteristic
478C22—42no—
479C22—81no—
480C22—81no—
481C22—221no—
482C22—221no—
483C22—221no—
484C22—221no—
485C22—221no—
486C22—221no—
487C22C2×D8×D1111yescharacteristic
488C4—21no—
489C4—21no—
490C4—81no—
491C4—81no—
492C4—81no—
493C4—221no—
494C4—221no—
495C4—881no—
496C4—881no—
497C4—881no—
498C4—881no—
499C4#1062316111yescharacteristic
500C4#1062330911yescharacteristic
501C2—82no—
502C2—441no—
503C2—441no—
504C2#1308042611yescharacteristic
505C2#1308174811yescharacteristic
506C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2228C2
socleC22×C11C22×D8
prime radical#13080337C2
hypercenter#2228D11
hypocenterC11#33882
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #13080983C2semidirect
3. #13070863C2semidirect
4. #13070827C2semidirect
5. #13070820C2semidirect
6. #13070725C2semidirect
7. #13070708C2semidirect
8. #13070667C2semidirect
9. #13070557C2semidirect
10. #13070557C2semidirect
11. #13070480C2semidirect
12. #13070440C2semidirect
13. #13070325C2semidirect
14. #13070320C2semidirect
15. C11×#2228C2semidirect
191. #2228D11semidirect
438. C11#33882semidirect

Maximal subgroups

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

subgroupindex
#130809832
#130803372
#130708632
#130708272
#130708202
#130707252
#130707082
#130706672
#130705572
#130704802
#130704402
#130703252
#130703202
C11×#22282
#3388211