Finite Group Databasebeta

← #14788729

Subgroups — #14788729

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×#10622703C211yesmaximal, characteristic
2C2×#10622643C211yesmaximal, characteristic
3#13073982C211yesmaximal, characteristic
4#13069859C212yesmaximal
5#13069716C212yesmaximal
6#13069557C211yesmaximal, characteristic
7#13069437C211yesmaximal, characteristic
8#13068957C212yesmaximal
9#13068884C212yesmaximal
10#13068631C211yesmaximal, characteristic
11C2×C11×#557C211yesmaximal, characteristic
12C11×#557—24no—
13C11×#557—24no—
14C2×C11×C4⋊Q8C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—22no—
17C2×C11×#125—21no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C22×#4326C2212yes—
24C2×C4×Dic22C2211yescharacteristic
25#10622842—21no—
26C2×#66899C2211yescharacteristic
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31#10622703—24no—
32#10622643—24no—
33#10622595—21no—
34#10622591—22no—
35C2×#66874C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37#10622549C2211yescharacteristic
38#10622542C2212yes—
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2312yes—
47C22×Q8×C11C2311yescharacteristic
48C22×Dic22C2311yescharacteristic
49C11×C4⋊Q8—24no—
50C11×C4⋊Q8—24no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8D414yes—
53C11×#125—216no—
54C11×#125—28no—
55C4×Q8×C11—28no—
56C4×Q8×C11—24no—
57C4×Q8×C11—24no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11D414yes—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—22no—
72C2×C42×C11—21no—
73C2×C42×C11C2312yes—
74C2×C42×C11C2311yescharacteristic
75C2×#4326—22no—
76C2×#4326—22no—
77C2×#4326—24no—
78C2×#4326—24no—
79C2×#4326—22no—
80C2×#4326—42no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2312yes—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—22no—
85C2×C4×Dic11—21no—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2311yescharacteristic
89C4×Dic22—22no—
90C4×Dic22—22no—
91#66899—22no—
92#66899—24no—
93#66899—24no—
94#66899—42no—
95#66899—42no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101#66874—22no—
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—22no—
109C2×Q8×C11—21no—
110C2×Q8×C11—22no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11C2×D414yes—
119C2×Q8×C11C2×D412yes—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—21no—
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—21no—
135C2×Dic22—21no—
136C2×Dic22#4112yes—
137C11×C4⋊C4—28no—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4C2×D412yes—
147C42×C11—28no—
148C42×C11—24no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11C2×D412yes—
152C42×C11C2×D412yes—
153#4326—28no—
154#4326—48no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159Dic11⋊C4—42no—
160Dic11⋊C4—44no—
161C4×Dic11—42no—
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×#557D1111yescharacteristic
172C2×#462—111no—
173C2×#441—111no—
174#2581—111no—
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—24no—
187Q8×C11—24no—
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—41no—
191Q8×C11—41no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11#12012yes—
207C2×C4×C11#12012yes—
208C2×C4×C11#13714yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11H(5,𝔽2)11yescharacteristic
214C2×C4×C112−1+411yescharacteristic
215C2×Dic11—22no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223Dic22—22no—
224Dic22—22no—
225Dic22—41no—
226Dic22—41no—
227C11⋊C8—22no—
228C11⋊C8—41no—
229C11⋊C8—42no—
230C22×Q16—111no—
231C22×Q16—112no—
232#557—24no—
233#557—24no—
234C2×C4⋊Q8C2×D1112yes—
235C2×C4⋊Q8C2×D1111yescharacteristic
236C2×#125—22no—
237C2×#125—21no—
238C2×C4×Q8—21no—
239C2×C4×Q8—111no—
240C2×C4×Q8C2×D1112yes—
241C2×C4×Q8C2×D1111yescharacteristic
242C2×C4×Q8C2×D1111yescharacteristic
243#462—224no—
244#441—224no—
245C2×#106—111no—
246C2×C4⋊C8—111no—
247C2×#103—112no—
248C2×#103—112no—
249C2×#103—111no—
250C2×#103—111no—
251C2×#103—112no—
252C2×#103—112no—
253C2×#97—111no—
254#400—221no—
255#395—221no—
256#391—112no—
257#389—112no—
258#387—222no—
259#382—111no—
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—44no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11#52511yescharacteristic
276C4×C11#53711yescharacteristic
277C4×C11#54611yescharacteristic
278C4×C11#54711yescharacteristic
279Dic11—42no—
280Dic11—82no—
281Dic11—81no—
282C22×Q8—111no—
283C22×Q8C22⋊D1111yescharacteristic
284C22×Q8C22×D1112yes—
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—24no—
296C4⋊Q8—24no—
297C4⋊Q8—22no—
298C4⋊Q8C22⋊D1114yes—
299#125—216no—
300#125—28no—
301C4×Q8—28no—
302C4×Q8—24no—
303C4×Q8—24no—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×Q8—22no—
307C4×Q8—222no—
308C4×Q8—222no—
309C4×Q8C22⋊D1114yes—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4C22⋊D1112yes—
321C2×C4⋊C4C22⋊D1111yescharacteristic
322C2×C4⋊C4C22×D1111yescharacteristic
323C2×C42—22no—
324C2×C42—21no—
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—221no—
338#95—221no—
339#95—222no—
340#95—222no—
341#95—222no—
342C2×C11#240711yescharacteristic
343C2×C11#300411yescharacteristic
344C2×C11#301111yescharacteristic
345C2×C11#337412yes—
346C2×C11#339812yes—
347C2×Q8—24no—
348C2×Q8—22no—
349C2×Q8—21no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—21no—
353C2×Q8—22no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—112no—
360C2×Q8—221no—
361C2×Q8—221no—
362C2×Q8—221no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×Q8C2×C22⋊D1114yes—
366C2×Q8C2×C22⋊D1112yes—
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⋊D1112yes—
375C22×C4C2×C22⋊D1111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377C22×C4C23×D1111yescharacteristic
378Q16—228no—
379Q16—448no—
380C2×C8—112no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—222no—
384C2×C8—221no—
385C2×C8—222no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8—222no—
389C4⋊C4—28no—
390C4⋊C4—28no—
391C4⋊C4—28no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—222no—
399C4⋊C4—222no—
400C4⋊C4—221no—
401C4⋊C4—221no—
402C4⋊C4—444no—
403C4⋊C4—442no—
404C4⋊C4C2×C22⋊D1112yes—
405C42—28no—
406C42—24no—
407C42—22no—
408C42—22no—
409C42—442no—
410C42C2×C22⋊D1112yes—
411C42C2×C22⋊D1112yes—
412C11#2420311yescharacteristic, complemented, Sylow
413C23C22×C22⋊D1111yescharacteristic
414Q8—28no—
415Q8—24no—
416Q8—22no—
417Q8—24no—
418Q8—22no—
419Q8—41no—
420Q8—42no—
421Q8—41no—
422Q8—42no—
423Q8—222no—
424Q8—222no—
425Q8—441no—
426Q8—441no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—222no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—441no—
449C2×C4#6699514yes—
450C2×C4#6700612yes—
451C2×C4#6700612yes—
452C2×C4#41×D1111yescharacteristic
453C2×C4#41×D1111yescharacteristic
454C2×C4#6704211yescharacteristic
455C2×C4#6704311yescharacteristic
456C2×C4C22×C22⋊D1111yescharacteristic
457C2×C4C22×C22⋊D1111yescharacteristic
458C8—222no—
459C8—442no—
460C8—441no—
461C22C2×#6699512yes—
462C22#1062336211yescharacteristic
463C22#1062336511yescharacteristic
464C22#1062336912yes—
465C22C2×#6700611yescharacteristic
466C4—24no—
467C4—22no—
468C4—22no—
469C4—44no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—442no—
474C4—882no—
475C4—881no—
476C4#1062335511yescharacteristic
477C4#1062335911yescharacteristic
478C4#1062336011yescharacteristic
479C4#1062336411yescharacteristic
480C2#1307195511yescharacteristic
481C2#1307785011yescharacteristic
482C2#1307791111yescharacteristic
483C2#1308141512yes—
484C2#1308164312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#557C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×#557D11
hypocenterC11#24203
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
412. C11#24203semidirect

Maximal subgroups

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

subgroupindex
C2×#106227032
C2×#106226432
#130739822
#130698592
#130697162
#130695572
#130694372
#130689572
#130688842
#130686312
C2×C11×#5572
#2420311