Finite Group Databasebeta

← #14810757

Subgroups — #14810757

Order 2816.

996 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622682C211yesmaximal, characteristic
2C2×#10622644C211yesmaximal, characteristic
3#13073828C211yesmaximal, characteristic
4#13069764C212yesmaximal
5#13069754C212yesmaximal
6#13069574C211yesmaximal, characteristic
7#13069557C211yesmaximal, characteristic
8#13068957C212yesmaximal
9#13068957C212yesmaximal
10#13068446C211yesmaximal, characteristic
11C2×C11×#557C211yesmaximal, characteristic
12C11×#557—24no—
13C11×#557—24no—
14C2×C11×C4⋊Q8—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×#125—21no—
18C2×C11×#125C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C22×#4326C2212yes—
26C2×#66922C2211yescharacteristic
27#10622843—21no—
28C2×#66899C2212yes—
29#10622682—24no—
30#10622644—24no—
31#10622599—21no—
32#10622599—21no—
33#10622590—21no—
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36C2×#66874C2212yes—
37C4×C4⋊Dic11C2211yescharacteristic
38#10622542C2212yes—
39#10622542C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622162C2212yes—
46#10622162C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11D411yescharacteristic
49C22×Q8×C11C2311yescharacteristic
50C22×Dic22C2312yes—
51C11×C4⋊Q8—28no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C11×#125—28no—
55C11×#125—28no—
56C11×#125—22no—
57C11×#125—22no—
58C11×#125—22no—
59C11×#125D414yes—
60C4×Q8×C11—28no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11D414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×#4326—24no—
90C2×#4326—28no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2312yes—
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2312yes—
96C22×C11⋊C8C2312yes—
97#66922—22no—
98#66922—22no—
99#66899—24no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C11⋊#95—21no—
105#66874—24no—
106#66874—24no—
107#66874—24no—
108C4⋊(C11⋊C8)—22no—
109#66867—22no—
110#25943—111nomaximal, Sylow
111C2×Q8×C11—24no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—41no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11#4114yes—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—22no—
133C22×Dic11—22no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—24no—
137C2×Dic22—24no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4C2×D412yes—
153C11×C4⋊C4C2×D412yes—
154C11×C4⋊C4C2×D412yes—
155C42×C11—24no—
156C42×C11—24no—
157C42×C11—24no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164#4326—48no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—42no—
168C4⋊Dic11—42no—
169C4×Dic11—42no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—24no—
174C2×C11⋊C8—22no—
175C2×#557D1111yescharacteristic
176C2×#491—111no—
177C2×#462—111no—
178#2568—111no—
179#2026—112no—
180#2024—112no—
181#1989—111no—
182#1985—111no—
183#1878—112no—
184#1878—112no—
185#1763—111no—
186C23×C11C22×D411yescharacteristic
187Q8×C11—22no—
188Q8×C11—24no—
189Q8×C11—44no—
190Q8×C11—48no—
191Q8×C11#12414yes—
192C2×C4×C11—22no—
193C2×C4×C11—21no—
194C2×C4×C11—24no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11#12012yes—
215C2×C4×C11#12012yes—
216C2×C4×C11#13712yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4112yes—
220C2×C4×C112−1+412yes—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—44no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226Dic22—42no—
227Dic22—42no—
228Dic22—44no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231C22×Q16—112no—
232#557—24no—
233#557—24no—
234C2×C4⋊Q8—21no—
235C2×C4⋊Q8—111no—
236C2×C4⋊Q8C2×D1111yescharacteristic
237C2×#125—21no—
238C2×#125—21no—
239C2×#125C2×D1111yescharacteristic
240C2×#125C2×D1111yescharacteristic
241C2×C4×Q8—21no—
242C2×C4×Q8C2×D1111yescharacteristic
243C2×C4×Q8C2×D1111yescharacteristic
244C2×C4×Q8C2×D1111yescharacteristic
245C2×C4×Q8C2×D1111yescharacteristic
246#491—224no—
247#462—224no—
248C2×C4⋊C8—111no—
249C2×#103—112no—
250C2×#103—112no—
251C2×#103—112no—
252C2×#103—112no—
253C2×#97—111no—
254#400—221no—
255#400—221no—
256#391—112no—
257#391—112no—
258#391—221no—
259#382—221no—
260C4×C4⋊C4—111no—
261#340—112no—
262#340—112no—
263#340—112no—
264#336—112no—
265#336—112no—
266C22×C11C2×#12011yescharacteristic
267C22×C11#54812yes—
268C22×C11C2×#13711yescharacteristic
269C22×C11#57511yescharacteristic
270C22×C11#57812yes—
271C4×C11—24no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—22no—
275C4×C11—41no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—42no—
281C4×C11C2×#12411yescharacteristic
282C4×C11#53611yescharacteristic
283C4×C11#54812yes—
284Dic11—82no—
285Dic11—82no—
286C22×Q8—21no—
287C22×Q8—112no—
288C22×Q8C22⋊D1111yescharacteristic
289C22×Q8C22×D1111yescharacteristic
290C2×Q16—228no—
291C2×Q16—224no—
292C22×C8—112no—
293C22×C8—112no—
294C4⋊Q8—28no—
295C4⋊Q8—22no—
296C4⋊Q8—22no—
297C4⋊Q8—222no—
298C4⋊Q8—222no—
299#125—28no—
300#125—28no—
301#125—22no—
302#125—22no—
303#125—22no—
304#125C22⋊D1114yes—
305C4×Q8—28no—
306C4×Q8—22no—
307C4×Q8—22no—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×Q8—22no—
312C4×Q8—22no—
313C4×Q8C22⋊D1114yes—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4C22⋊D1111yescharacteristic
326C2×C4⋊C4C22⋊D1111yescharacteristic
327C2×C4⋊C4C22⋊D1111yescharacteristic
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C4⋊C4C22×D1111yescharacteristic
330C2×C4⋊C4C22×D1111yescharacteristic
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—221no—
335C2×C42C22×D1111yescharacteristic
336C2×C42C22×D1111yescharacteristic
337C2×C42C22×D1111yescharacteristic
338C4⋊C8—222no—
339#103—224no—
340#103—224no—
341#103—224no—
342#103—224no—
343#97—222no—
344#95—221no—
345#95—222no—
346#95—222no—
347#95—222no—
348#95—222no—
349C2×C11#243611yescharacteristic
350C2×C11#300711yescharacteristic
351C2×C11#301111yescharacteristic
352C2×C11#337412yes—
353C2×C11#337712yes—
354C2×Q8—24no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—41no—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×Q8—224no—
363C2×Q8—224no—
364C2×Q8—222no—
365C2×Q8—222no—
366C2×Q8#434314yes—
367C2×Q8C2×C22⋊D1112yes—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4C2×C22⋊D1111yescharacteristic
375C22×C4C2×C22⋊D1111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377C22×C4C2×C22⋊D1111yescharacteristic
378C22×C4C2×C22⋊D1111yescharacteristic
379C22×C4C2×C22⋊D1111yescharacteristic
380C22×C4C23×D1111yescharacteristic
381Q16—448no—
382C2×C8—222no—
383C2×C8—224no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—222no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—222no—
402C4⋊C4—222no—
403C4⋊C4—442no—
404C4⋊C4—442no—
405C4⋊C4C2×C22⋊D1112yes—
406C4⋊C4C2×C22⋊D1112yes—
407C4⋊C4C2×C22⋊D1112yes—
408C42—24no—
409C42—24no—
410C42—24no—
411C42—21no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42—442no—
416C42C2×C22⋊D1112yes—
417C42C2×C22⋊D1112yes—
418C11#2594311yescharacteristic, complemented, Sylow
419C23C22×C22⋊D1111yescharacteristic
420Q8—22no—
421Q8—24no—
422Q8—44no—
423Q8—48no—
424Q8—442no—
425Q8—442no—
426Q8—444no—
427Q8#6700014yes—
428C2×C4—24no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—442no—
451C2×C4—444no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4#6700412yes—
456C2×C4#6700612yes—
457C2×C4#6700612yes—
458C2×C4C2×#434312yes—
459C2×C4#6704012yes—
460C2×C4C22×C22⋊D1111yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—442no—
463C8—442no—
464C22#1062334812yes—
465C22#1062335311yescharacteristic
466C22C2×#6700411yescharacteristic
467C22#1062336912yes—
468C22C2×#6700611yescharacteristic
469C4—22no—
470C4—22no—
471C4—24no—
472C4—22no—
473C4—41no—
474C4—42no—
475C4—42no—
476C4—41no—
477C4—41no—
478C4—42no—
479C4—882no—
480C4—882no—
481C4C2×#6700011yescharacteristic
482C4#1062334711yescharacteristic
483C4#1062334812yes—
484C2#1307227011yescharacteristic
485C2#1307787611yescharacteristic
486C2#1307791111yescharacteristic
487C2#1308141912yes—
488C2#1308145812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#557C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×#557D11
hypocenterC11#25943
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
418. C11#25943semidirect

Maximal subgroups

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

subgroupindex
C2×#106226822
C2×#106226442
#130738282
#130697642
#130697542
#130695742
#130695572
#130689572
#130684462
C2×C11×#5572
#2594311