Finite Group Databasebeta

← #14910839

Subgroups — #14910839

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#13080986C211yesmaximal, characteristic
2Q16×D44C211yesmaximal, characteristic
3#13070862C211yesmaximal, characteristic, complemented
4#13070827C211yesmaximal, characteristic, complemented
5#13070815C211yesmaximal, characteristic, complemented
6#13070780C211yesmaximal, characteristic, complemented
7#13070723C211yesmaximal, characteristic, complemented
8#13070706C211yesmaximal, characteristic, complemented
9#13070666C211yesmaximal, characteristic, complemented
10#13070548C211yesmaximal, characteristic, complemented
11#13070548C211yesmaximal, characteristic, complemented
12#13070443C211yesmaximal, characteristic
13#13070334C211yesmaximal, characteristic, complemented
14D11×#358C211yesmaximal, characteristic, complemented
15C11×#2176C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic
18#10623112—21no—
19Q8×D44—21no—
20C2×C11×Q32C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22C4×C11×Q16C2211yescharacteristic
23#10622801C2211yescharacteristic
24#10622801C2211yescharacteristic
25C2×#66893C2211yescharacteristic
26C2×#66893C2211yescharacteristic
27#10622644—21no—
28#10622635—21no—
29C2×#66862C2211yescharacteristic
30C2×C16×D11C2211yescharacteristic
31#10622500C2211yescharacteristic
32#10622500C2211yescharacteristic
33#10622493C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622428—21no—
36#10622421—21no—
37#10622421—21no—
38#10622418—21no—
39#10622312C2211yescharacteristic
40C8×D44C2211yescharacteristic
41#10622296C2211yescharacteristic
42C11×#367C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#346C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
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×Q16C2311yescharacteristic
62C2×C11×Q16C2311yescharacteristic
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65#66999—21no—
66#66999—21no—
67C2×#4326—21no—
68C2×#4326—21no—
69Q16×D11—22no—
70Q16×D11—22no—
71Q16×D11—41no—
72Q16×D11—41no—
73C2×Dic44—21no—
74C2×Dic44C2311yescharacteristic
75C2×Dic44C2311yescharacteristic
76C2×C8×D11C2311yescharacteristic
77C2×C8×D11C2311yescharacteristic
78#66950—21no—
79#66950—21no—
80#66950—41no—
81#66950—41no—
82#66947—41no—
83#66945—21no—
84C4⋊C4×D11—21no—
85#66942—41no—
86#66929—41no—
87C4×D44—41no—
88C4×D44D411yescharacteristic
89#66925—41no—
90#66923—21no—
91#66922—21no—
92#66922—41no—
93C11×Q32—22no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#103—21no—
99C11×#103—21no—
100C4×C8×C11C2311yescharacteristic
101#66899—21no—
102#66899—21no—
103#66893—41no—
104#66893—41no—
105(C2×D11)⋊C8D411yescharacteristic
106(C2×D11)⋊C8D411yescharacteristic
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66881—21no—
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112#66874—21no—
113#66874—21no—
114#66872—21no—
115#66871—21no—
116C4⋊(C11⋊C8)D411yescharacteristic
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#4112yes—
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2411yescharacteristic
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C42×C11—41no—
147C42×C11—41no—
148C42×C11C2×D411yescharacteristic
149#4326—42no—
150#4326—42no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4D811yescharacteristic
157(C2×D11)⋊C4D811yescharacteristic
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—41no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163C4⋊Dic11—41no—
164C4⋊Dic11D811yescharacteristic
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170C4×Dic11—41no—
171C2×C11⋊C8C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
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—
187D4×Q16—111no—
188#2245—111no—
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#2176D1111yescharacteristic, complemented
198#2168—111no—
199#2141—111no—
200C2×#358—111no—
201C22×D11C2×D811yescharacteristic
202C22×D11C2×D811yescharacteristic
203Q8×C11—22no—
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—41no—
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×Q32C2×D1111yescharacteristic
246C2×M32—111no—
247C22×C16—111no—
248#499—111no—
249#494—111no—
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×Q16C2×D1111yescharacteristic
261C4×Q16C2×D1111yescharacteristic
262C8×D4—111no—
263#427—111no—
264C2×#107—111no—
265#367—111no—
266#367C2×D1111yescharacteristic
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#358—111no—
276#358—111no—
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—42no—
292C4×C11—81no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11#54611yescharacteristic
296C4×C11#57711yescharacteristic
297Dic11—21no—
298Dic11—21no—
299Dic11—81no—
300Dic11—81no—
301Dic11—81no—
302Dic11—81no—
303C22×Q8—221no—
304C22×Q8—221no—
305C2×Q16—111no—
306C2×Q16—111no—
307C2×Q16—221no—
308C2×Q16—221no—
309C2×Q16—222no—
310C2×Q16—222no—
311C2×Q16—221no—
312C2×Q16—441no—
313C2×Q16—441no—
314C2×Q16C22×D1111yescharacteristic
315C2×Q16C22×D1111yescharacteristic
316C22×C8—111no—
317C22×C8—111no—
318C4⋊Q8—221no—
319C4⋊Q8—441no—
320#126—441no—
321#125—221no—
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—21no—
331C4×Q8—21no—
332C4×D4—111no—
333C4×D4—441no—
334#117—221no—
335#117—441no—
336C2×C4⋊C4—221no—
337Q32—22no—
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—221no—
352#106—221no—
353C4⋊C8—111no—
354#103—21no—
355#103—21no—
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—221no—
388Q16—221no—
389Q16—221no—
390Q16—221no—
391Q16—442no—
392Q16—442no—
393Q16—881no—
394Q16#433912yes—
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—111no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4—441no—
411C4⋊C4—441no—
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—41no—
427C42—41no—
428C42—441no—
429C42D4×D1111yescharacteristic
430C16—21no—
431C16—21no—
432C16—221no—
433C16—221no—
434C11#3387911yescharacteristic, complemented, Sylow
435C23—111no—
436C23—111no—
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—41no—
441Q8—441no—
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—
471C8C2×#433911yescharacteristic
472C8#6704211yescharacteristic
473C22—112no—
474C22—221no—
475C22—221no—
476C22—221no—
477C22—221no—
478C22—221no—
479C22C2×D8×D1111yescharacteristic
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4—221no—
487C4—221no—
488C4—881no—
489C4—881no—
490C4—881no—
491C4—881no—
492C4#1062308111yescharacteristic
493C4#1062330111yescharacteristic
494C2—222no—
495C2—441no—
496C2#1308043111yescharacteristic
497C2D11×#51011yescharacteristic
498C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2176C2
socleC22×C11C22×D8
prime radicalC2×D44D8
hypercenter#2176D11
hypocenterC11#33879
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2176

Complements

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

NH ≅ G/Ntype
3. #13070862C2semidirect
4. #13070827C2semidirect
5. #13070815C2semidirect
6. #13070780C2semidirect
7. #13070723C2semidirect
8. #13070706C2semidirect
9. #13070666C2semidirect
10. #13070548C2semidirect
11. #13070548C2semidirect
13. #13070334C2semidirect
14. D11×#358C2semidirect
15. C11×#2176C2semidirect
197. #2176D11semidirect
434. C11#33879semidirect

Maximal subgroups

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

subgroupindex
#130809862
Q16×D442
#130708622
#130708272
#130708152
#130707802
#130707232
#130707062
#130706662
#130705482
#130704432
#130703342
D11×#3582
C11×#21762
#3387911