Finite Group Databasebeta

← #14788737

Subgroups — #14788737

Order 2816.

1036 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623101C211yesmaximal, characteristic
2C2×#10622644C211yesmaximal, characteristic
3C2×#10622643C211yesmaximal, characteristic
4#13069862C212yesmaximal
5#13069715C212yesmaximal
6#13069557C211yesmaximal, characteristic
7#13069435C211yesmaximal, characteristic
8#13068960C212yesmaximal
9#13068883C212yesmaximal
10#13068628C211yesmaximal, characteristic
11C11×#2581C211yesmaximal, characteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×Q8×Dic11—21no—
15C22×#4326C2211yescharacteristic
16C22×#4326C2212yes—
17#10623101—24no—
18#10623101—24no—
19C2×#66943—22no—
20C2×#66943—21no—
21C2×#66922C2212yes—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22C2212yes—
24C2×C4×Dic22C2211yescharacteristic
25C11×#400—21no—
26C11×#395—21no—
27C11×#391C2212yes—
28C11×#389C2212yes—
29C11×#387—22no—
30C11×#382C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622644—24no—
33#10622643—24no—
34C2×#66874C2211yescharacteristic
35C2×#66874C2212yes—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39C2×#66872C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×Dic22C2312yes—
48C22×Dic22C2311yescharacteristic
49C4×Q8×C11—22no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C42×C11—21no—
60C2×C42×C11C2312yes—
61C2×C42×C11C2311yescharacteristic
62Q8×Dic11—28no—
63C2×#4326—22no—
64C2×#4326—22no—
65C2×#4326—24no—
66C2×#4326—24no—
67C2×#4326—22no—
68C2×#4326—42no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—21no—
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2311yescharacteristic
81#66943—216no—
82#66943—28no—
83#66922—24no—
84#66922—24no—
85#66922—22no—
86#66922D414yes—
87C4×Dic22—24no—
88C4×Dic22—22no—
89C4×Dic22—24no—
90C4×Dic22D414yes—
91C11×#95—21no—
92C11×#95—21no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95—22no—
96#66899—22no—
97#66874—22no—
98#66874—24no—
99#66874—24no—
100#66874—42no—
101#66874—42no—
102#66872—22no—
103C4⋊(C11⋊C8)—22no—
104#66867—22no—
105#24203—111nomaximal, Sylow
106C2×Q8×C11—22no—
107C2×Q8×C11—24no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11#4112yes—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—21no—
123C22×Dic11—22no—
124C22×Dic11—21no—
125C2×Dic22—22no—
126C2×Dic22—21no—
127C2×Dic22—22no—
128C2×Dic22—21no—
129C2×Dic22—22no—
130C2×Dic22—21no—
131C2×Dic22—21no—
132C2×Dic22—22no—
133C2×Dic22—21no—
134C2×Dic22—22no—
135C2×Dic22C2×D414yes—
136C2×Dic22C2×D412yes—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—44no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11—42no—
148C42×C11C2×D412yes—
149C42×C11C2×D412yes—
150#4326—28no—
151#4326—48no—
152C4⋊Dic11—28no—
153C4⋊Dic11—28no—
154C4⋊Dic11—24no—
155C4⋊Dic11—24no—
156C4⋊Dic11—21no—
157C4⋊Dic11C2×D412yes—
158Dic11⋊C4—28no—
159Dic11⋊C4—24no—
160C4×Dic11—28no—
161C4×Dic11—24no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8#4112yes—
171C2×#557—111no—
172C2×#462—111no—
173C2×#441—111no—
174#2581D1111yescharacteristic
175#2043—112no—
176#2016—112no—
177#1985—111no—
178#1960—111no—
179#1878—112no—
180#1865—112no—
181#1805—111no—
182C23×C11C22×D411yescharacteristic
183Q8×C11—28no—
184Q8×C11—22no—
185Q8×C11—22no—
186Q8×C11—41no—
187Q8×C11—41no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11#12012yes—
203C2×C4×C11#12012yes—
204C2×C4×C11#13714yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)11yescharacteristic
210C2×C4×C112−1+411yescharacteristic
211C2×Dic11—22no—
212C2×Dic11—24no—
213C2×Dic11—22no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—41no—
218C2×Dic11—42no—
219Dic22—22no—
220Dic22—22no—
221Dic22—24no—
222Dic22—24no—
223Dic22—42no—
224Dic22—42no—
225Dic22—41no—
226Dic22—41no—
227C11⋊C8—22no—
228C11⋊C8—41no—
229C11⋊C8—42no—
230C22×Q16—111no—
231C22×Q16—112no—
232#557—224no—
233#557—224no—
234C2×C4⋊Q8—111no—
235C2×C4⋊Q8—112no—
236C2×#125—222no—
237C2×#125—221no—
238C2×C4×Q8—111no—
239C2×C4×Q8—112no—
240C2×C4×Q8—221no—
241C2×C4×Q8C2×D1111yescharacteristic
242C2×C4×Q8C2×D1111yescharacteristic
243#462—224no—
244#441—224no—
245C2×#106—111no—
246C2×C4⋊C8—111no—
247C2×#103—111no—
248C2×#103—112no—
249C2×#103—112no—
250C2×#103—111no—
251C2×#103—112no—
252C2×#103—112no—
253C2×#97—111no—
254#400—21no—
255#395—21no—
256#391C2×D1112yes—
257#389C2×D1112yes—
258#387—22no—
259#382C2×D1111yescharacteristic
260#340—112no—
261#336—112no—
262#336—112no—
263C22×C11C2×#12011yescharacteristic
264C22×C11#54811yescharacteristic
265C22×C11#55011yescharacteristic
266C22×C11C2×#13712yes—
267C22×C11#57812yes—
268C4×C11—22no—
269C4×C11—24no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—82no—
274C4×C11—81no—
275C4×C11#52511yescharacteristic
276C4×C11#53711yescharacteristic
277C4×C11#54611yescharacteristic
278C4×C11#54711yescharacteristic
279Dic11—42no—
280Dic11—44no—
281Dic11—42no—
282C22×Q8—111no—
283C22×Q8—112no—
284C22×Q8C22⋊D1111yescharacteristic
285C22×Q8C22×D1111yescharacteristic
286C2×Q16—222no—
287C2×Q16—222no—
288C2×Q16—222no—
289C2×Q16—224no—
290C2×Q16—224no—
291C2×Q16—442no—
292C22×C8—111no—
293C22×C8—112no—
294C22×C8—111no—
295C4⋊Q8—114no—
296C4⋊Q8—224no—
297C4⋊Q8—224no—
298C4⋊Q8—222no—
299#125—2216no—
300#125—228no—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8—22no—
305C4×Q8—114no—
306C4×Q8—224no—
307C4×Q8—224no—
308C4×Q8—228no—
309C4×Q8—222no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4C22⋊D1112yes—
320C2×C4⋊C4C22⋊D1111yescharacteristic
321C2×C4⋊C4C22×D1111yescharacteristic
322C2×C4⋊C4C22×D1112yes—
323C2×C42—21no—
324C2×C42—222no—
325C2×C42—221no—
326C2×C42C22×D1112yes—
327C2×C42C22×D1111yescharacteristic
328#106—222no—
329C4⋊C8—222no—
330#103—224no—
331#103—222no—
332#103—224no—
333#103—222no—
334#103—442no—
335#103—442no—
336#97—222no—
337#95—21no—
338#95—21no—
339#95—22no—
340#95—22no—
341#95—22no—
342C2×C11#240711yescharacteristic
343C2×C11#300411yescharacteristic
344C2×C11#301111yescharacteristic
345C2×C11#337412yes—
346C2×C11#339812yes—
347C2×Q8—22no—
348C2×Q8—24no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—112no—
355C2×Q8—114no—
356C2×Q8—222no—
357C2×Q8—221no—
358C2×Q8—221no—
359C2×Q8—222no—
360C2×Q8—221no—
361C2×Q8—222no—
362C2×Q8—222no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×Q8—222no—
366C2×Q8#434312yes—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—221no—
371C22×C4—222no—
372C22×C4—221no—
373C22×C4C2×C22⋊D1112yes—
374C22×C4C2×C22⋊D1111yescharacteristic
375C22×C4C2×C22⋊D1111yescharacteristic
376C22×C4C2×C22⋊D1112yes—
377C22×C4C23×D1111yescharacteristic
378Q16—228no—
379Q16—448no—
380C2×C8—112no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—221no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8—222no—
389C4⋊C4—24no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—42no—
396C4⋊C4—44no—
397C4⋊C4—112no—
398C4⋊C4—228no—
399C4⋊C4—228no—
400C4⋊C4—228no—
401C4⋊C4—224no—
402C4⋊C4—224no—
403C4⋊C4—224no—
404C4⋊C4—221no—
405C42—22no—
406C42—22no—
407C42—42no—
408C42—228no—
409C42—224no—
410C42D4×D1112yes—
411C42D4×D1112yes—
412C11#2420311yescharacteristic, complemented, Sylow
413C23C22×C22⋊D1111yescharacteristic
414Q8—28no—
415Q8—22no—
416Q8—22no—
417Q8—41no—
418Q8—41no—
419Q8—222no—
420Q8—222no—
421Q8—224no—
422Q8—224no—
423Q8—442no—
424Q8—442no—
425Q8—441no—
426Q8—441no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—222no—
442C2×C4—224no—
443C2×C4—222no—
444C2×C4—441no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—441no—
448C2×C4—442no—
449C2×C4#6699012yes—
450C2×C4#6699012yes—
451C2×C4#6700414yes—
452C2×C4C2×D4×D1111yescharacteristic
453C2×C4C2×D4×D1111yescharacteristic
454C2×C4C2×#434311yescharacteristic
455C2×C4#6704011yescharacteristic
456C2×C4#41×D1111yescharacteristic
457C2×C4#6704211yescharacteristic
458C8—222no—
459C8—441no—
460C8—442no—
461C22C2×#6699011yescharacteristic
462C22#1062334811yescharacteristic
463C22C2×#6700412yes—
464C22#1062336511yescharacteristic
465C22#1062336912yes—
466C4—22no—
467C4—24no—
468C4—22no—
469C4—42no—
470C4—42no—
471C4—82no—
472C4—81no—
473C4—442no—
474C4—444no—
475C4—442no—
476C4#1062315811yescharacteristic
477C4#1062316011yescharacteristic
478C4#1062316111yescharacteristic
479C4#1062316211yescharacteristic
480C2#1307196311yescharacteristic
481C2#1307784911yescharacteristic
482C2#1307790911yescharacteristic
483C2#1308141912yes—
484C2#1308164712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2581C2
socle, prime radicalC23×C11C22×D4
hypercenter#2581D11
hypocenterC11#24203
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2581

Complements

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

NH ≅ G/Ntype
412. C11#24203semidirect

Maximal subgroups

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

subgroupindex
C2×#106231012
C2×#106226442
C2×#106226432
#130698622
#130697152
#130695572
#130694352
#130689602
#130688832
#130686282
C11×#25812
#2420311