Finite Group Databasebeta

← #14910833

Subgroups — #14910833

Order 2816.

536 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080983C211yesmaximal, characteristic
2#13080366C211yesmaximal, characteristic
3#13070822C211yesmaximal, characteristic, complemented
4#13070812C211yesmaximal, characteristic, complemented
5#13070777C211yesmaximal, characteristic, complemented
6#13070723C211yesmaximal, characteristic, complemented
7#13070706C211yesmaximal, characteristic, complemented
8#13070663C211yesmaximal, characteristic, complemented
9#13070551C211yesmaximal, characteristic, complemented
10#13070551C211yesmaximal, characteristic, complemented
11#13070488C211yesmaximal, characteristic, complemented
12#13070443C211yesmaximal, characteristic
13#13070334C211yesmaximal, characteristic, complemented
14D11×#358C211yesmaximal, characteristic, complemented
15C11×#2245C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic
18#10623258—21no—
19#10623225—21no—
20C11×#499C2211yescharacteristic
21C11×#494C2211yescharacteristic
22#10622801C2211yescharacteristic
23#10622801C2211yescharacteristic
24#10622799—21no—
25#10622799—21no—
26C2×#66893C2211yescharacteristic
27C2×#66893C2211yescharacteristic
28#10622703—21no—
29#10622676—21no—
30C2×Dic88C2211yescharacteristic
31C2×#66862C2211yescharacteristic
32C2×C16×D11C2211yescharacteristic
33#10622500C2211yescharacteristic
34#10622500C2211yescharacteristic
35#10622493C2211yescharacteristic
36D11×#107C2211yescharacteristic
37#10622480—21no—
38#10622475—21no—
39C4×Dic44C2211yescharacteristic
40C4×Dic44C2211yescharacteristic
41C8×D44C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#358C2211yescharacteristic
46C11×#346C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622202C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×Q8×D11—21no—
60C2×Q8×D11—21no—
61C2×C11×Q16—21no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×Q16C2311yescharacteristic
64C11×C4⋊Q8—21no—
65C11×#125—21no—
66#66999—21no—
67#66999—21no—
68C2×#4326—21no—
69C2×#4326—21no—
70Q16×D11—22no—
71Q16×D11—22no—
72Q16×D11—41no—
73Q16×D11—41no—
74C2×Dic44C2311yescharacteristic
75C2×Dic44C2311yescharacteristic
76C2×C8×D11C2311yescharacteristic
77C2×C8×D11C2311yescharacteristic
78#66951—41no—
79#66950—21no—
80#66950—21no—
81#66949—41no—
82#66949—41no—
83#66947—41no—
84#66946—41no—
85#66945—21no—
86#66945—41no—
87C4⋊C4×D11—21no—
88#66943—41no—
89#66941—41no—
90C4×D44D411yescharacteristic
91C4×Dic22—21no—
92C4×Dic22—21no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#106—21no—
98C4×C8×C11C2311yescharacteristic
99#66899—21no—
100#66899—21no—
101#66893—41no—
102#66893—41no—
103(C2×D11)⋊C8D411yescharacteristic
104(C2×D11)⋊C8D411yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66880—21no—
108#66880—21no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111#66874—21no—
112#66874—21no—
113#66872—21no—
114#66871—21no—
115C4⋊(C11⋊C8)D411yescharacteristic
116Dic88—22no—
117#66862—41no—
118C16×D11—41no—
119#33879—111nomaximal, Sylow
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122Q8×D11—42no—
123Q8×D11—42no—
124Q8×D11—81no—
125Q8×D11—81no—
126C2×D44D811yescharacteristic
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×C4×D11—41no—
130C2×C4×D11C2×D411yescharacteristic
131C2×C4×D11C2×D411yescharacteristic
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—41no—
135C2×Dic22—41no—
136C11×Q16—21no—
137C11×Q16—21no—
138C11×Q16—21no—
139C11×Q16—21no—
140C11×Q16—81no—
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2411yescharacteristic
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4—41no—
149C42×C11C2×D411yescharacteristic
150#4326—42no—
151#4326—42no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4D811yescharacteristic
158(C2×D11)⋊C4D811yescharacteristic
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163C4⋊Dic11D811yescharacteristic
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169C4×Dic11—41no—
170C4×Dic11—41no—
171C4×Dic11—41no—
172C2×C11⋊C8C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174Dic44—21no—
175Dic44—21no—
176Dic44—21no—
177Dic44#4112yes—
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—
187D4×Q16—111no—
188#2245D1111yescharacteristic, complemented
189#2237—111no—
190#2235—111no—
191#2229—111no—
192#2219—111no—
193#2216—111no—
194#2209—111no—
195#2188—111no—
196#2188—111no—
197#2176—111no—
198#2168—111no—
199#2141—111no—
200C2×#358—111no—
201C22×D11C2×D811yescharacteristic
202C22×D11C2×D811yescharacteristic
203Q8×C11—41no—
204Q8×C11—41no—
205Q8×C11—41no—
206Q8×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11C2×D811yescharacteristic
219C2×Dic11C2×D811yescharacteristic
220D44—22no—
221C4×D11—21no—
222C4×D11—21no—
223C4×D11—21no—
224C4×D11—21no—
225C4×D11—82no—
226C4×D11—82no—
227C4×D11—82no—
228Dic22—22no—
229Dic22—41no—
230Dic22—41no—
231Dic22—41no—
232Dic22—82no—
233Dic22—82no—
234C8×C11—21no—
235C8×C11C2×#4111yescharacteristic
236C8×C11H(5,𝔽2)11yescharacteristic
237C11⋊C8—21no—
238C11⋊C8—21no—
239C22×Q16—111no—
240C22×Q16—111no—
241#552—221no—
242D4×Q8—221no—
243C2×Q32—111no—
244C2×Q32—111no—
245C2×Q32—111no—
246C2×M32—111no—
247C22×C16—111no—
248#499C2×D1111yescharacteristic
249#494C2×D1111yescharacteristic
250#485—221no—
251#483—221no—
252#479—221no—
253#467—111no—
254#467—111no—
255#467—111no—
256#467—111no—
257#462—221no—
258#451—221no—
259#451—221no—
260C4×Q16—111no—
261C4×Q16—111no—
262C8×D4—111no—
263#427—111no—
264C2×#107—111no—
265#367—111no—
266#367—111no—
267#366—111no—
268C4⋊C16—111no—
269#358—111no—
270#358—111no—
271#358—111no—
272#358—111no—
273#358—111no—
274#358—111no—
275#358C2×D1111yescharacteristic
276#358C2×D1111yescharacteristic
277#358C2×D1111yescharacteristic
278#358C2×D1111yescharacteristic
279C22⋊C16—111no—
280C22⋊C16—111no—
281#346C2×D1111yescharacteristic
282C22×C11C22×D811yescharacteristic
283C2×D11—21no—
284C2×D11—21no—
285C2×D11—21no—
286C2×D11—21no—
287C2×D11—21no—
288C2×D11#51012yes—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—81no—
292C4×C11—81no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11#54611yescharacteristic
296C4×C11#57711yescharacteristic
297Dic11—21no—
298Dic11—21no—
299Dic11—42no—
300Dic11—81no—
301Dic11—81no—
302Dic11—81no—
303C22×Q8—221no—
304C22×Q8—221no—
305C2×Q16—21no—
306C2×Q16—111no—
307C2×Q16—111no—
308C2×Q16—221no—
309C2×Q16—221no—
310C2×Q16—222no—
311C2×Q16—222no—
312C2×Q16—441no—
313C2×Q16—441no—
314C2×Q16C22×D1111yescharacteristic
315C2×Q16C22×D1111yescharacteristic
316C22×C8—111no—
317C22×C8—111no—
318C4⋊Q8—21no—
319C4⋊Q8—441no—
320#126—441no—
321#125—21no—
322#125—441no—
323#123—441no—
324C22⋊Q8—221no—
325C22⋊Q8—221no—
326C22⋊Q8—221no—
327C22⋊Q8—221no—
328C22⋊Q8—441no—
329C22⋊Q8—441no—
330C4×Q8—221no—
331C4×Q8—221no—
332C4×D4—111no—
333C4×D4—441no—
334#117—221no—
335#117—441no—
336C2×C4⋊C4—221no—
337Q32—222no—
338Q32—441no—
339Q32—441no—
340M32—441no—
341C2×C16—111no—
342C2×C16—111no—
343C2×C16—441no—
344C2×C16C22×D1111yescharacteristic
345C2×C16C22×D1111yescharacteristic
346#107—111no—
347#107—111no—
348#107—221no—
349#107C22×D1111yescharacteristic
350#107C22×D1111yescharacteristic
351#106—21no—
352#106—221no—
353C4⋊C8—111no—
354#103—221no—
355#103—221no—
356#103—221no—
357#103—221no—
358#103—221no—
359#103—221no—
360C22⋊C8—111no—
361C22⋊C8—111no—
362C4×C8C22×D1111yescharacteristic
363C2×C11#329411yescharacteristic
364C2×C11C2×#51011yescharacteristic
365C2×C11#341711yescharacteristic
366D11—22no—
367D11—41no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—221no—
371C2×Q8—221no—
372C2×Q8—441no—
373C2×Q8—441no—
374C2×Q8—442no—
375C2×Q8—442no—
376C2×Q8—881no—
377C2×Q8—881no—
378C2×D4—111no—
379C22×C4—111no—
380C22×C4—111no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384Q16—21no—
385Q16—21no—
386Q16—21no—
387Q16—21no—
388Q16—81no—
389Q16—112no—
390Q16—221no—
391Q16—221no—
392Q16—221no—
393Q16—442no—
394Q16—442no—
395C2×C8—111no—
396C2×C8—111no—
397C2×C8—221no—
398C2×C8—221no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8D4×D1111yescharacteristic
402C2×C8C23×D1111yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—111no—
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—
419C22⋊C4—111no—
420C22⋊C4—111no—
421C22⋊C4—441no—
422C22⋊C4—441no—
423C22⋊C4—441no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C42—441no—
427C42—441no—
428C42—441no—
429C42D4×D1111yescharacteristic
430C16—21no—
431C16—21no—
432C16—221no—
433C16—221no—
434C11#3387911yescharacteristic, complemented, Sylow
435C23—111no—
436C23—111no—
437Q8—41no—
438Q8—41no—
439Q8—41no—
440Q8—41no—
441Q8—222no—
442Q8—441no—
443Q8—441no—
444Q8—441no—
445Q8—882no—
446Q8—882no—
447D4—222no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—111no—
453C2×C4—111no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—882no—
463C2×C4—882no—
464C2×C4—882no—
465C2×C4D8×D1111yescharacteristic
466C2×C4D8×D1111yescharacteristic
467C2×C4C2×D4×D1111yescharacteristic
468C8—21no—
469C8—221no—
470C8—221no—
471C8#41×D1111yescharacteristic
472C8#6704211yescharacteristic
473C22—112no—
474C22—221no—
475C22—221no—
476C22—221no—
477C22—221no—
478C22—221no—
479C22C2×D8×D1111yescharacteristic
480C4—21no—
481C4—21no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4—221no—
487C4—221no—
488C4—442no—
489C4—881no—
490C4—881no—
491C4—881no—
492C4#1062320711yescharacteristic
493C4#1062329311yescharacteristic
494C2—222no—
495C2—441no—
496C2#1308042811yescharacteristic
497C2D11×#51011yescharacteristic
498C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2245C2
socleC22×C11C22×D8
prime radicalC2×D44D8
hypercenter#2245D11
hypocenterC11#33879
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2245

Complements

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

NH ≅ G/Ntype
3. #13070822C2semidirect
4. #13070812C2semidirect
5. #13070777C2semidirect
6. #13070723C2semidirect
7. #13070706C2semidirect
8. #13070663C2semidirect
9. #13070551C2semidirect
10. #13070551C2semidirect
11. #13070488C2semidirect
13. #13070334C2semidirect
14. D11×#358C2semidirect
15. C11×#2245C2semidirect
188. #2245D11semidirect
434. C11#33879semidirect

Maximal subgroups

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

subgroupindex
#130809832
#130803662
#130708222
#130708122
#130707772
#130707232
#130707062
#130706632
#130705512
#130704882
#130704432
#130703342
D11×#3582
C11×#22452
#3387911