Finite Group Databasebeta

← #14910776

Subgroups — #14910776

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080964C211yesmaximal, characteristic, complemented
2#13080359C211yesmaximal, characteristic, complemented
3#13070853C211yesmaximal, characteristic, complemented
4#13070819C211yesmaximal, characteristic, complemented
5#13070797C211yesmaximal, characteristic, complemented
6#13070769C211yesmaximal, characteristic, complemented
7#13070729C211yesmaximal, characteristic, complemented
8#13070702C211yesmaximal, characteristic, complemented
9#13070672C211yesmaximal, characteristic, complemented
10#13070541C211yesmaximal, characteristic, complemented
11#13070535C211yesmaximal, characteristic, complemented
12#13070482C211yesmaximal, characteristic, complemented
13#13070329C211yesmaximal, characteristic, complemented
14C2×#10622141C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16C22×Dic44C2211yescharacteristic
17C2×#66957C2211yescharacteristic
18#10623086—21no—
19#10623083—21no—
20C2×C11×M32C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622728C2211yescharacteristic
25#10622728C2211yescharacteristic
26#10622728C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66864C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31C2×D176C2211yescharacteristic
32#10622459—21no—
33#10622458—21no—
34#10622351—21no—
35#10622349—21no—
36#10622349—21no—
37#10622346—21no—
38C4×Dic44C2211yescharacteristic
39#10622309C2211yescharacteristic
40C4×D88C2211yescharacteristic
41#10622295C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45C11×#346C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622142C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622141C2211yescharacteristic
55#10622141C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C2×#4341—41no—
60C2×#4339—21no—
61C22×Dic22—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C4×D4×C11D411yescharacteristic
65#66992—41no—
66#66983—21no—
67#66983—21no—
68#66983—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71#66977—21no—
72C2×Dic44—22no—
73C2×Dic44—21no—
74C2×Dic44—41no—
75C2×Dic44C2311yescharacteristic
76C2×Dic44C2311yescharacteristic
77#66957—22no—
78#66957—41no—
79C2×D88C2311yescharacteristic
80C2×D88C2311yescharacteristic
81C2×#4314—21no—
82C2×#4314—21no—
83#66950—41no—
84#66949—41no—
85#66939—41no—
86#66939—41no—
87#66938—41no—
88(C22⋊D11)⋊C4—41no—
89#66928—21no—
90C4×D44—21no—
91#66922—21no—
92C4×Dic22—21no—
93C11×M32—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#66885—21no—
105#66885—21no—
106#66885—21no—
107#66882—21no—
108#66882—21no—
109#66882—21no—
110#66882C2311yescharacteristic
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66882C2311yescharacteristic
114#66880—21no—
115#66880—21no—
116#66864—22no—
117#66864—41no—
118D176—41no—
119#33875—111nomaximal, Sylow
120C2×D4×C11D811yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C22×Dic11—41no—
128C22×Dic11—41no—
129C22×Dic11—41no—
130#4341—84no—
131#4339—42no—
132#4339—81no—
133C2×D44—21no—
134C2×D44—21no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—42no—
140C2×Dic22—41no—
141C2×Dic22—41no—
142C2×Dic22—81no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2×D411yescharacteristic
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2411yescharacteristic
151C11×C4⋊C4D811yescharacteristic
152C11×C22⋊C4D811yescharacteristic
153C11×C22⋊C4D811yescharacteristic
154C42×C11C2×D411yescharacteristic
155C22⋊Dic11—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—41no—
167C4⋊Dic11—41no—
168C4⋊Dic11—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171C4×Dic11—41no—
172Dic44—21no—
173Dic44—21no—
174Dic44—21no—
175Dic44—42no—
176Dic44#4112yescomplemented
177D88—21no—
178D88—21no—
179D88—21no—
180D88—21no—
181#4314—42no—
182#4314—81no—
183C11×C16—21no—
184C11×C16—21no—
185C11×C16—21no—
186C11×C16—21no—
187#3334—111no—
188#3285—111no—
189#2243—111no—
190#2236—111no—
191#2232—111no—
192#2227—111no—
193#2220—111no—
194#2215—111no—
195#2210—111no—
196#2186—111no—
197#2185—111no—
198#2175—111no—
199#2168D1111yescharacteristic, complemented
200#2139—111no—
201C2×#358—111no—
202C23×C11C2×D811yescharacteristic
203C23×C11C2×D811yescharacteristic
204C22×D11—41no—
205C22×D11—41no—
206D4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C22⋊D11—82no—
217C22⋊D11—82no—
218C22⋊D11—82no—
219C22⋊D11—82no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—82no—
227C2×Dic11—82no—
228C2×Dic11—82no—
229D44—41no—
230D44—41no—
231D44—41no—
232D44—41no—
233C4×D11—82no—
234C4×D11—82no—
235Dic22—22no—
236Dic22—41no—
237Dic22—41no—
238Dic22—41no—
239Dic22—82no—
240Dic22—82no—
241C8×C11—21no—
242C8×C11—21no—
243C8×C11—21no—
244C8×C11C2×#4111yescharacteristic
245C8×C11H(5,𝔽2)11yescharacteristic
246C2×#135—111no—
247C22×Q16—111no—
248#548—221no—
249#547—221no—
250C2×SD32—111no—
251C2×SD32—111no—
252C2×D16—111no—
253C2×M32C2×D1111yescharacteristic
254C22×C16C2×D1111yescharacteristic
255#500—111no—
256#495—111no—
257#480—221no—
258#480—221no—
259#474—221no—
260#467—111no—
261#466—111no—
262#466—111no—
263#466—111no—
264#464—221no—
265#452—221no—
266#448—221no—
267C4×Q16—111no—
268C4×D8—111no—
269C8×D4C2×D1111yescharacteristic
270C2×#107—111no—
271C2×#107—111no—
272#366—111no—
273#366—111no—
274#366—111no—
275C4⋊C16C2×D1111yescharacteristic
276#358—111no—
277#358—111no—
278#358—111no—
279#358—111no—
280#358—111no—
281#358—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357—111no—
286C22⋊C16C2×D1111yescharacteristic
287C22⋊C16C2×D1111yescharacteristic
288#346C2×D1111yescharacteristic
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11#50912yes—
295C22×C11C22×D811yescharacteristic
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—21no—
306C4×C11#54611yescharacteristic
307C4×C11#57711yescharacteristic
308Dic11—42no—
309Dic11—81no—
310Dic11—81no—
311Dic11—81no—
312Dic11—81no—
313Dic11—81no—
314C2×#41—221no—
315C2×#41—441no—
316C22×Q8—221no—
317#135—222no—
318#135—441no—
319C2×Q16—111no—
320C2×Q16—111no—
321C2×Q16—222no—
322C2×Q16—221no—
323C2×Q16—441no—
324C2×SD16—221no—
325C2×SD16—221no—
326C2×D8—111no—
327C2×D8—111no—
328C22×C8C22×D1111yescharacteristic
329C22×C8C22×D1111yescharacteristic
330C4⋊Q8—221no—
331#124—221no—
332#124—441no—
333#123—441no—
334#123—441no—
335C22⋊Q8—221no—
336C22⋊Q8—441no—
337C22⋊Q8—441no—
338#121—221no—
339#121—221no—
340#121—221no—
341#121—441no—
342C4×Q8—221no—
343C4×D4—221no—
344C4×D4—441no—
345C4×D4D4411yescharacteristic
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348SD32—222no—
349SD32—441no—
350D16—441no—
351M32—41no—
352C2×C16—41no—
353C2×C16C22×D1111yescharacteristic
354C2×C16C22×D1111yescharacteristic
355C2×C16C22×D1111yescharacteristic
356C2×C16C22×D1111yescharacteristic
357#107—111no—
358#107—111no—
359#107—111no—
360#107—111no—
361#107—221no—
362#107—221no—
363#107—221no—
364C4⋊C8D4411yescharacteristic
365#103—221no—
366#103—221no—
367#102—221no—
368#102—221no—
369#102—221no—
370#102—221no—
371C22⋊C8D4411yescharacteristic
372C22⋊C8D4411yescharacteristic
373C4×C8C22×D1111yescharacteristic
374C2×C11—22no—
375C2×C11—41no—
376C2×C11#329411yescharacteristic
377C2×C11C2×#50911yescharacteristic
378C2×C11#341711yescharacteristic
379D11—161no—
380D11—161no—
381#41—442no—
382#41—881no—
383#41—884no—
384C2×Q8—221no—
385C2×Q8—221no—
386C2×Q8—442no—
387C2×Q8—441no—
388C2×Q8—441no—
389C2×Q8—881no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—441no—
393C2×D4—441no—
394C2×D4—441no—
395C2×D4—441no—
396C2×D4D8811yescharacteristic
397C22×C4—441no—
398C22×C4—441no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—441no—
402C22×C4C2×D4411yescharacteristic
403C22×C4C2×D4411yescharacteristic
404Q16—112no—
405Q16—221no—
406Q16—221no—
407Q16—221no—
408Q16—442no—
409SD16—442no—
410SD16—881no—
411D8—221no—
412D8—221no—
413D8—221no—
414D8—221no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8C2×D4411yescharacteristic
420C2×C8C2×D4411yescharacteristic
421C2×C8C2×D4411yescharacteristic
422C2×C8C23×D1111yescharacteristic
423C4⋊C4—221no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—441no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C4⋊C4D8811yescharacteristic
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C22⋊C4—441no—
440C22⋊C4D8811yescharacteristic
441C22⋊C4D8811yescharacteristic
442C42—441no—
443C42C2×D4411yescharacteristic
444C16—21no—
445C16—21no—
446C16—21no—
447C16—21no—
448C11#3387511yescharacteristic, complemented, Sylow
449C23—441no—
450C23—441no—
451C23C2×D8811yescharacteristic
452C23C2×D8811yescharacteristic
453Q8—222no—
454Q8—441no—
455Q8—441no—
456Q8—441no—
457Q8—882no—
458Q8—882no—
459D4—22no—
460D4—441no—
461D4—441no—
462D4—441no—
463D4—441no—
464D4—882no—
465D4—882no—
466D4—882no—
467D4—882no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—882no—
479C2×C4—882no—
480C2×C4—882no—
481C2×C4—882no—
482C2×C4—882no—
483C2×C4C2×D8811yescharacteristic
484C2×C4C2×D8811yescharacteristic
485C2×C4C2×D8811yescharacteristic
486C2×C4C2×D8811yescharacteristic
487C2×C4C22×D4411yescharacteristic
488C8—21no—
489C8—21no—
490C8—21no—
491C8#6703711yescharacteristic
492C8#41×D1111yescharacteristic
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—881no—
499C22—881no—
500C22—881no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22#1062252112yes—
505C22C22×D8811yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—442no—
511C4—881no—
512C4—881no—
513C4—881no—
514C4—881no—
515C4—881no—
516C4#1062308511yescharacteristic
517C4#1062328211yescharacteristic
518C2—22no—
519C2—41no—
520C2—1761no—
521C2—1761no—
522C2#1308043011yescharacteristic
523C2C2×#1062252111yescharacteristic
524C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
hypercenter#2168D11
hypocenterC11#33875
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. #13080964C2semidirect
2. #13080359C2semidirect
3. #13070853C2semidirect
4. #13070819C2semidirect
5. #13070797C2semidirect
6. #13070769C2semidirect
7. #13070729C2semidirect
8. #13070702C2semidirect
9. #13070672C2semidirect
10. #13070541C2semidirect
11. #13070535C2semidirect
12. #13070482C2semidirect
13. #13070329C2semidirect
14. C2×#10622141C2semidirect
15. C11×#2168C2semidirect
176. Dic44#41semidirect
199. #2168D11semidirect
448. C11#33875semidirect

Maximal subgroups

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

subgroupindex
#130809642
#130803592
#130708532
#130708192
#130707972
#130707692
#130707292
#130707022
#130706722
#130705412
#130705352
#130704822
#130703292
C2×#106221412
C11×#21682
#3387511