Finite Group Databasebeta

← #14910834

Subgroups — #14910834

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#13080985C211yesmaximal, characteristic
2#13070861C211yesmaximal, characteristic, complemented
3#13070821C211yesmaximal, characteristic, complemented
4#13070811C211yesmaximal, characteristic, complemented
5#13070780C211yesmaximal, characteristic, complemented
6#13070722C211yesmaximal, characteristic, complemented
7#13070705C211yesmaximal, characteristic, complemented
8#13070663C211yesmaximal, characteristic, complemented
9#13070550C211yesmaximal, characteristic, complemented
10#13070550C211yesmaximal, characteristic, complemented
11#13070485C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic
13#13070336C211yesmaximal, characteristic, complemented
14C2×#10622202C211yesmaximal, characteristic, complemented
15D4×C11×Q16C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18D4×Q8×C11—21no—
19#10623072—21no—
20C11×#494C2211yescharacteristic
21C11×#467C2211yescharacteristic
22C11×#467C2211yescharacteristic
23C11×#462—21no—
24C11×#451—21no—
25C11×#451—21no—
26C4×C11×Q16C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C2×#66893C2211yescharacteristic
29C2×#66893C2211yescharacteristic
30C2×#66893C2211yescharacteristic
31#10622729C2211yescharacteristic
32#10622729C2211yescharacteristic
33#10622719C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622442—21no—
38#10622336—21no—
39#10622334—21no—
40C4×Dic44C2211yescharacteristic
41#10622296C2211yescharacteristic
42#10622202C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622202C2211yescharacteristic
49#10622202C2211yescharacteristic
50#10622202C2211yescharacteristic
51C22⋊(C11⋊C16)C2211yescharacteristic
52C22⋊(C11⋊C16)C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×Q8×C11—21no—
61C2×C11×Q16—22no—
62C2×C11×Q16—22no—
63C2×C11×Q16—21no—
64C2×C11×Q16—21no—
65C2×C11×Q16—21no—
66C2×C11×Q16—41no—
67C2×C11×Q16—41no—
68C2×C11×Q16C2311yescharacteristic
69C2×C11×Q16C2311yescharacteristic
70C2×C11×Q16C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8—41no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—41no—
78C11×C22⋊Q8—41no—
79C4×Q8×C11—21no—
80C4×D4×C11—41no—
81C4×D4×C11D411yescharacteristic
82#66988—41no—
83#66979—21no—
84C2×C4⋊Dic11—21no—
85#66977—21no—
86#66977—21no—
87C2×Dic44C2311yescharacteristic
88#66942—41no—
89#66932—41no—
90#66930—41no—
91#66923—21no—
92C4×Dic22—21no—
93C11×#107C2311yescharacteristic
94C11×C4⋊C8D411yescharacteristic
95C11×#103—21no—
96C11×#103—21no—
97C11×#103—21no—
98C11×C22⋊C8D411yescharacteristic
99C11×C22⋊C8D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66893—22no—
102#66893—41no—
103#66893—41no—
104#66882—21no—
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66881—21no—
109#66881—21no—
110#66880—21no—
111#66880—21no—
112#66880—21no—
113#66876—41no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#33879—111nomaximal, Sylow
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—42no—
124C2×Q8×C11—42no—
125C2×Q8×C11—41no—
126C2×Q8×C11—41no—
127C2×Q8×C11—81no—
128C2×Q8×C11—81no—
129C2×D4×C11D811yescharacteristic
130C22×C4×C11—41no—
131C22×C4×C11—41no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×Dic11—41no—
135C2×Dic22—21no—
136C11×Q16—21no—
137C11×Q16—21no—
138C11×Q16—21no—
139C11×Q16—21no—
140C11×Q16—21no—
141C11×Q16—42no—
142C11×Q16—42no—
143C11×Q16—81no—
144C11×Q16#4112yes—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2×D411yescharacteristic
151C2×C8×C11C2×D411yescharacteristic
152C2×C8×C11C2411yescharacteristic
153C11×C4⋊C4—21no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4D811yescharacteristic
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4D811yescharacteristic
163C11×C22⋊C4D811yescharacteristic
164C42×C11—41no—
165C42×C11C2×D411yescharacteristic
166C22⋊Dic11—41no—
167C22⋊Dic11—41no—
168C22⋊Dic11—41no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—41no—
173Dic11⋊C4—41no—
174Dic11⋊C4—41no—
175Dic11⋊C4—41no—
176Dic11⋊C4—41no—
177Dic11⋊C4—41no—
178C4×Dic11—41no—
179C4×Dic11—41no—
180Dic44—21no—
181Dic44—21no—
182C11⋊C16—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3336—111no—
187D4×Q16D1111yescharacteristic
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#2176—111no—
198#2168—111no—
199#2141—111no—
200C2×#358—111no—
201C23×C11C2×D811yescharacteristic
202C23×C11C2×D811yescharacteristic
203Q8×C11—22no—
204Q8×C11—41no—
205Q8×C11—41no—
206Q8×C11—41no—
207Q8×C11—41no—
208Q8×C11—41no—
209Q8×C11—82no—
210Q8×C11—82no—
211D4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—82no—
221C2×C4×C11—82no—
222C2×C4×C11C2×D811yescharacteristic
223C2×C4×C11C2×D811yescharacteristic
224C2×C4×C11C2×D811yescharacteristic
225C2×C4×C11C2×D811yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—82no—
232Dic22—41no—
233Dic22—41no—
234C8×C11—21no—
235C8×C11—21no—
236C8×C11—21no—
237C8×C11C2×#4111yescharacteristic
238C8×C11H(5,𝔽2)11yescharacteristic
239C22×Q16C2×D1111yescharacteristic
240C22×Q16C2×D1111yescharacteristic
241#552—221no—
242D4×Q8—21no—
243C2×Q32—111no—
244C2×Q32—111no—
245C2×Q32—111no—
246C2×M32—111no—
247C22×C16—111no—
248#499—111no—
249#494C2×D1111yescharacteristic
250#485—221no—
251#483—221no—
252#479—221no—
253#467—111no—
254#467—111no—
255#467C2×D1111yescharacteristic
256#467C2×D1111yescharacteristic
257#462—21no—
258#451—21no—
259#451—21no—
260C4×Q16—111no—
261C4×Q16C2×D1111yescharacteristic
262C8×D4C2×D1111yescharacteristic
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#358—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279C22⋊C16—111no—
280C22⋊C16—111no—
281#346—111no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11#51012yes—
288C22×C11C22×D811yescharacteristic
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—42no—
294C4×C11—81no—
295C4×C11—81no—
296C4×C11—81no—
297C4×C11#54611yescharacteristic
298C4×C11#57711yescharacteristic
299Dic11—81no—
300Dic11—81no—
301Dic11—81no—
302Dic11—81no—
303C22×Q8—21no—
304C22×Q8—21no—
305C2×Q16—22no—
306C2×Q16—22no—
307C2×Q16—21no—
308C2×Q16—21no—
309C2×Q16—21no—
310C2×Q16—41no—
311C2×Q16—41no—
312C2×Q16—111no—
313C2×Q16C22×D1111yescharacteristic
314C2×Q16C22×D1111yescharacteristic
315C2×Q16C22×D1111yescharacteristic
316C22×C8C22×D1111yescharacteristic
317C22×C8C22×D1111yescharacteristic
318C4⋊Q8—21no—
319C4⋊Q8—41no—
320#126—441no—
321#125—221no—
322#125—441no—
323#123—441no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—41no—
327C22⋊Q8—41no—
328C22⋊Q8—221no—
329C22⋊Q8—221no—
330C4×Q8—21no—
331C4×Q8—221no—
332C4×D4—41no—
333C4×D4C22⋊D1111yescharacteristic
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—111no—
344C2×C16—111no—
345C2×C16—441no—
346#107—111no—
347#107—111no—
348#107—111no—
349#107—221no—
350#107C22×D1111yescharacteristic
351#106—221no—
352#106—221no—
353C4⋊C8C22⋊D1111yescharacteristic
354#103—21no—
355#103—21no—
356#103—21no—
357#103—221no—
358#103—221no—
359#103—221no—
360C22⋊C8C22⋊D1111yescharacteristic
361C22⋊C8C22⋊D1111yescharacteristic
362C4×C8C22×D1111yescharacteristic
363C2×C11—22no—
364C2×C11—41no—
365C2×C11#329411yescharacteristic
366C2×C11C2×#51011yescharacteristic
367C2×C11#341711yescharacteristic
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—42no—
372C2×Q8—42no—
373C2×Q8—41no—
374C2×Q8—41no—
375C2×Q8—81no—
376C2×Q8—81no—
377C2×Q8—221no—
378C2×D4#432311yescharacteristic
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—441no—
382C22×C4C2×C22⋊D1111yescharacteristic
383C22×C4C2×C22⋊D1111yescharacteristic
384Q16—21no—
385Q16—21no—
386Q16—21no—
387Q16—21no—
388Q16—21no—
389Q16—42no—
390Q16—42no—
391Q16—81no—
392Q16—221no—
393Q16—221no—
394Q16#434112yes—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8C2×C22⋊D1111yescharacteristic
400C2×C8C2×C22⋊D1111yescharacteristic
401C2×C8C2×C22⋊D1111yescharacteristic
402C2×C8C23×D1111yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
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#432311yescharacteristic
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—441no—
422C22⋊C4—441no—
423C22⋊C4—441no—
424C22⋊C4#432311yescharacteristic
425C22⋊C4#432311yescharacteristic
426C42—41no—
427C42—441no—
428C42—441no—
429C42C2×C22⋊D1111yescharacteristic
430C16—221no—
431C16—221no—
432C16—221no—
433C16—221no—
434C11#3387911yescharacteristic, complemented, Sylow
435C23C2×#432311yescharacteristic
436C23C2×#432311yescharacteristic
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—82no—
444Q8—82no—
445Q8—441no—
446Q8—441no—
447D4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—882no—
463C2×C4C2×#432311yescharacteristic
464C2×C4C2×#432311yescharacteristic
465C2×C4C2×#432311yescharacteristic
466C2×C4C2×#432311yescharacteristic
467C2×C4C22×C22⋊D1111yescharacteristic
468C8—21no—
469C8—21no—
470C8—21no—
471C8C2×#434111yescharacteristic
472C8#6703711yescharacteristic
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22#1062279212yes—
479C22C22×#432311yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—42no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—881no—
489C4—881no—
490C4—881no—
491C4—881no—
492C4#1062333711yescharacteristic
493C4#1062336711yescharacteristic
494C2—22no—
495C2—41no—
496C2#1308042911yescharacteristic
497C2C2×#1062279211yescharacteristic
498C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×Q16C2
socleC22×C11C22×D8
prime radicalC2×D4×C11D8
hypercenterD4×Q16D11
hypocenterC11#33879
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×Q16

Complements

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

NH ≅ G/Ntype
2. #13070861C2semidirect
3. #13070821C2semidirect
4. #13070811C2semidirect
5. #13070780C2semidirect
6. #13070722C2semidirect
7. #13070705C2semidirect
8. #13070663C2semidirect
9. #13070550C2semidirect
10. #13070550C2semidirect
11. #13070485C2semidirect
13. #13070336C2semidirect
14. C2×#10622202C2semidirect
434. C11#33879semidirect

Maximal subgroups

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

subgroupindex
#130809852
#130708612
#130708212
#130708112
#130707802
#130707222
#130707052
#130706632
#130705502
#130704852
#130704422
#130703362
C2×#106222022
D4×C11×Q162
#3387911