Finite Group Databasebeta

← #14765636

Subgroups — #14765636

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078529C211yesmaximal, characteristic
2#13077310C211yesmaximal, characteristic
3#13069366C212yesmaximal, complemented
4#13069326C212yesmaximal, complemented
5#13069212C212yesmaximal, complemented
6#13068918C211yesmaximal, characteristic
7#13068890C212yesmaximal, complemented
8#13068821C211yesmaximal, characteristic, complemented
9#13068715C211yesmaximal, characteristic, complemented
10#13068392C211yesmaximal, characteristic, complemented
11C2×C11×#424C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15#10623322C2211yescharacteristic
16C2×#66954C2211yescharacteristic
17C11×#424—21no—
18C11×#424—21no—
19C11×#424C2212yes—
20C11×#424C2212yes—
21C2×C11×C4⋊C8—21no—
22C2×C11×C4⋊C8—21no—
23C4×C22⋊Dic11C2211yescharacteristic
24#10622820C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66889C2212yes—
27C2×#66886C2212yes—
28#10622724—21no—
29#10622724—21no—
30#10622723C2211yescharacteristic
31C8×C22⋊D11—21no—
32C8×C22⋊D11—21no—
33#10622715C2211yescharacteristic
34#10622714C2211yescharacteristic
35C2×#66879C2212yes—
36#10622616C412yescomplemented
37#10622615C2212yes—
38#10622611C2212yes—
39#10622609C412yescomplemented
40#10622584C411yescharacteristic, complemented
41#10622583C411yescharacteristic, complemented
42#10622581C411yescharacteristic, complemented
43#10622580C411yescharacteristic, complemented
44#10622196C2212yes—
45#10622193C2212yes—
46#10622188C2212yes—
47#10622170C2212yes—
48#10622170C2212yes—
49C23×C4×C11C2311yescharacteristic
50C2×#4339C2311yescharacteristic
51C2×C11×M16—21no—
52C2×C11×M16—42no—
53C2×C11×M16C2312yes—
54C22×C8×C11—21no—
55C22×C8×C11—42no—
56C22×C8×C11D411yescharacteristic
57C22×C8×C11D411yescharacteristic
58C22×C8×C11D411yescharacteristic
59C22×C8×C11D411yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×#117—21no—
63C11×#117—21no—
64C11×#117C2×C412yes—
65C11×#117C2312yes—
66C2×C11×C4⋊C4C2×C411yescharacteristic
67C2×C11×C4⋊C4C2×C411yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C42×C11—21no—
70#67006—21no—
71C2×C22⋊Dic11—21no—
72#66983C2×C411yescharacteristic
73#66983C2×C411yescharacteristic
74#66982—21no—
75C4×C22⋊D11—21no—
76C4×C22⋊D11—21no—
77#66979C2311yescharacteristic
78#66977C2×C411yescharacteristic
79#66977C2×C411yescharacteristic
80C2×C4×Dic11C2312yes—
81C2×#4318C2311yescharacteristic
82C2×#4318C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84#66954—42no—
85C2×#4313—21no—
86C2×C8×D11—21no—
87C11×C4⋊C8—22no—
88C11×C4⋊C8—22no—
89C11×C4⋊C8—22no—
90C11×C4⋊C8—22no—
91C11⋊#95—21no—
92C22⋊(C11⋊C8)—21no—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)C2×C411yescharacteristic
95C22⋊(C11⋊C8)C2×C411yescharacteristic
96C22⋊(C11⋊C8)C2×C412yes—
97#66889—42no—
98#66886—42no—
99(C2×D11)⋊C8—21no—
100(C2×D11)⋊C8—21no—
101#66879—21no—
102#66879—42no—
103Dic11⋊C8—21no—
104Dic11⋊C8—21no—
105C8×Dic11—21no—
106#66874C2×C412yes—
107#66874C2×C412yes—
108#66873C2×C412yes—
109#66873C2×C412yes—
110#66872C2×C412yes—
111#66872C2×C412yes—
112#66871C2×C412yes—
113#66871C2×C412yes—
114#22096—111nomaximal, Sylow
115C24×C11#4111yescharacteristic
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—21no—
127C2×C22⋊D11—21no—
128C2×C22⋊D11—21no—
129C22×Dic11—22no—
130#4339—22no—
131#4339—22no—
132C2×D44C22×C411yescharacteristic
133C2×C4×D11—21no—
134C2×Dic22C22×C411yescharacteristic
135C11×M16—22no—
136C11×M16—22no—
137C11×M16—42no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—41no—
142C2×C8×C11—41no—
143C2×C8×C11—41no—
144C2×C8×C11—41no—
145C2×C8×C11—42no—
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2×D411yescharacteristic
149C2×C8×C11C2×D411yescharacteristic
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4C22×C412yes—
153C11×C4⋊C4C22×C412yes—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C42×C11—22no—
157C42×C11—22no—
158C22⋊Dic11—21no—
159C22⋊Dic11—21no—
160C22⋊Dic11—21no—
161C22⋊Dic11—42no—
162(C2×D11)⋊C4—21no—
163(C2×D11)⋊C4—21no—
164C4⋊Dic11C22×C411yescharacteristic
165C4⋊Dic11C22×C411yescharacteristic
166Dic11⋊C4—21no—
167Dic11⋊C4—21no—
168C4×Dic11—21no—
169C4×Dic11—22no—
170C4×Dic11—22no—
171#4318—22no—
172#4318—22no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8C22×C412yes—
178C2×C11⋊C8C22×C412yes—
179#4313—42no—
180C8×D11—42no—
181#3091—111no—
182#2929—111no—
183C2×#424D1111yescharacteristic, complemented
184#1946—112no—
185#1938—112no—
186#1922—112no—
187#1871—111no—
188#1866—112no—
189#1855—111no—
190#1826—111no—
191#1752—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—41no—
195C23×C11C4×D411yescharacteristic
196C23×C11C4×D411yescharacteristic
197C23×C11C2×#4111yescharacteristic
198C22×D11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11C4×D411yescharacteristic
211C2×C4×C11C4×D411yescharacteristic
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11H(5,𝔽2)12yes—
215C2×C4×C112−1+412yes—
216C22⋊D11—42no—
217C22⋊D11—42no—
218C22⋊D11—42no—
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225D44—22no—
226C4×D11—41no—
227C4×D11—41no—
228Dic22—22no—
229C8×C11—21no—
230C8×C11—21no—
231C8×C11—21no—
232C8×C11—21no—
233C8×C11—42no—
234C11⋊C8—22no—
235C11⋊C8—22no—
236C11⋊C8—41no—
237C11⋊C8—41no—
238C2×#131—111no—
239C22×M16C2×D1111yescharacteristic
240C23×C8C2×D1111yescharacteristic
241#525—111no—
242C2×#117C2×D1111yescharacteristic
243#485—112no—
244#484—111no—
245#483—111no—
246#482—112no—
247#481—111no—
248#480—111no—
249#435—221no—
250#435—221no—
251C8×D4—221no—
252C8×D4—221no—
253C2×#108—112no—
254#427—112no—
255#424—21no—
256#424—21no—
257#424—111no—
258#424C2×D1112yes—
259#424C2×D1112yes—
260C2×C4⋊C8—21no—
261C2×C4⋊C8—21no—
262C2×#104—112no—
263#416—112no—
264#408—111no—
265#407—111no—
266C2×C22⋊C8—111no—
267#405—111no—
268C2×#97—112no—
269C4×C22⋊C4—111no—
270#341—112no—
271#339—112no—
272#339—112no—
273#339—112no—
274#336—112no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—44no—
283C22×C11#44412yes—
284C22×C11C2×C4×D411yescharacteristic
285C22×C11#53912yes—
286C2×D11—41no—
287C2×D11—41no—
288C2×D11—41no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11#52012yes—
294C4×C11#53411yescharacteristic
295C4×C11#53611yescharacteristic
296Dic11—41no—
297Dic11—41no—
298Dic11—41no—
299Dic11—82no—
300C2×#41—111no—
301C23×C4C22×D1111yescharacteristic
302#131—442no—
303C2×M16—21no—
304C2×M16—42no—
305C2×M16—111no—
306C2×M16—111no—
307C2×M16—221no—
308C2×M16C22×D1112yes—
309C22×C8—21no—
310C22×C8—42no—
311C22×C8—112no—
312C22×C8—221no—
313C22×C8C22⋊D1111yescharacteristic
314C22×C8C22⋊D1111yescharacteristic
315C22×C8C22⋊D1111yescharacteristic
316C22×C8C22⋊D1111yescharacteristic
317C22×C8C22×D1111yescharacteristic
318C22×C8C22×D1111yescharacteristic
319#123—221no—
320C22⋊Q8—111no—
321C22⋊Q8—111no—
322#121—111no—
323#121—111no—
324#120—221no—
325C4×D4—221no—
326C4×D4—221no—
327#117—21no—
328#117—21no—
329#117—111no—
330#117C4×D1112yes—
331#117C22×D1112yes—
332C2×C4⋊C4C4×D1111yescharacteristic
333C2×C4⋊C4C4×D1111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—221no—
336C2×C42—21no—
337C2×C42—112no—
338#108—442no—
339#107—112no—
340#107—112no—
341#106—112no—
342#106—112no—
343C4⋊C8—22no—
344C4⋊C8—22no—
345C4⋊C8—22no—
346C4⋊C8—22no—
347C4⋊C8—221no—
348C4⋊C8—221no—
349#104—442no—
350#103—112no—
351#103—112no—
352#102—112no—
353#102—112no—
354C22⋊C8—111no—
355C22⋊C8—111no—
356C22⋊C8—112no—
357C22⋊C8—221no—
358C22⋊C8—221no—
359C22⋊C8—221no—
360C22⋊C8—221no—
361#97—221no—
362#97—442no—
363C4×C8—221no—
364#95—221no—
365C2×C11—22no—
366C2×C11—22no—
367C2×C11—41no—
368C2×C11#232211yescharacteristic
369C2×C11C2×#44411yescharacteristic
370C2×C11#295511yescharacteristic
371D11—81no—
372C24#433911yescharacteristic
373#41—222no—
374#41—222no—
375C2×Q8—111no—
376C2×D4—111no—
377C2×D4—221no—
378C2×D4—221no—
379C2×D4—221no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—221no—
385C22×C4—222no—
386C22×C4C2×C4×D1111yescharacteristic
387C22×C4C2×C4×D1111yescharacteristic
388C22×C4#433911yescharacteristic
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392M16—22no—
393M16—22no—
394M16—42no—
395M16—222no—
396M16—222no—
397M16—442no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—42no—
406C2×C8—112no—
407C2×C8—112no—
408C2×C8—222no—
409C2×C8—222no—
410C2×C8—221no—
411C2×C8—221no—
412C2×C8—442no—
413C2×C8C2×C22⋊D1111yescharacteristic
414C2×C8C2×C22⋊D1111yescharacteristic
415C2×C8C2×C22⋊D1111yescharacteristic
416C2×C8C2×C22⋊D1111yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—111no—
420C4⋊C4—111no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4C2×C4×D1112yes—
424C4⋊C4C2×C4×D1112yes—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—221no—
428C22⋊C4—221no—
429C22⋊C4—221no—
430C22⋊C4—221no—
431C22⋊C4—221no—
432C22⋊C4—442no—
433C42—22no—
434C42—22no—
435C42—221no—
436C42—222no—
437C42—222no—
438C11#2209611yescharacteristic, complemented, Sylow
439C23—22no—
440C23—22no—
441C23—41no—
442C23—221no—
443C23C4×C22⋊D1111yescharacteristic
444C23C4×C22⋊D1111yescharacteristic
445C23C2×#433911yescharacteristic
446Q8—222no—
447D4—222no—
448D4—442no—
449D4—442no—
450D4—442no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—221no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4C4×C22⋊D1111yescharacteristic
471C2×C4C4×C22⋊D1111yescharacteristic
472C2×C4C22×C4×D1111yescharacteristic
473C2×C4#6703712yes—
474C2×C4#6704012yes—
475C2×C4C22×C22⋊D1111yescharacteristic
476C8—21no—
477C8—21no—
478C8—21no—
479C8—21no—
480C8—42no—
481C8—222no—
482C8—222no—
483C8—441no—
484C8—441no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—44no—
493C22—441no—
494C22—441no—
495C22—441no—
496C22#1062275812yes—
497C22#1062304612yes—
498C22C2×C4×C22⋊D1111yescharacteristic
499C4—21no—
500C4—21no—
501C4—42no—
502C4—42no—
503C4—441no—
504C4—441no—
505C4—441no—
506C4—882no—
507C4#1062303512yes—
508C4#1062333511yescharacteristic
509C4#1062334711yescharacteristic
510C2—22no—
511C2—22no—
512C2—41no—
513C2—881no—
514C2#1307128511yescharacteristic
515C2C2×#1062275811yescharacteristic
516C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#424C2
socleC22×C11C2×C4×D4
prime radical#10623322C22
cosocleC22×C4×C11C24
hypercenterC2×#424D11
hypocenterC11#22096
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
3. #13069366C2semidirect
4. #13069326C2semidirect
5. #13069212C2semidirect
7. #13068890C2semidirect
8. #13068821C2semidirect
9. #13068715C2semidirect
10. #13068392C2semidirect
11. C2×C11×#424C2semidirect
36. #10622616C4semidirect
39. #10622609C4semidirect
40. #10622584C4semidirect
41. #10622583C4semidirect
42. #10622581C4semidirect
43. #10622580C4semidirect
183. C2×#424D11semidirect
438. C11#22096semidirect

Maximal subgroups

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

subgroupindex
#130785292
#130773102
#130693662
#130693262
#130692122
#130689182
#130688902
#130688212
#130687152
#130683922
C2×C11×#4242
#2209611