Finite Group Databasebeta

← #14775653

Subgroups — #14775653

Order 2816.

886 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic
2C4⋊C4×D44C211yesmaximal, characteristic
3#13069578C211yesmaximal, characteristic, complemented
4#13069374C211yesmaximal, characteristic, complemented
5#13069356C212yesmaximal, complemented
6#13069201C212yesmaximal, complemented
7#13068862C212yesmaximal
8#13068485C211yesmaximal, characteristic, complemented
9#13068444C212yesmaximal
10C4×#66873C211yesmaximal, characteristic
11C11×#2369C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4⋊C4×D11—21no—
14C2×C4×D44C2212yes—
15C2×C4×D44C2211yescharacteristic
16C11×#391—22no—
17C11×#389—21no—
18C11×#389C2212yes—
19C4×C11×C4⋊C4—21no—
20C4×C11×C4⋊C4C2211yescharacteristic
21C4×C11×C4⋊C4C2212yes—
22C4×C11×C4⋊C4C2211yescharacteristic
23#10622697C418yescomplemented
24#10622600—21no—
25C2×#66873C2211yescharacteristic
26C2×#66873C2212yes—
27C2×#66873C2211yescharacteristic
28C2×#66872C2212yes—
29C2×#66871C2212yes—
30#10622548C2211yescharacteristic
31#10622541C2212yes—
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33C2×#66867C2212yes—
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622281—22no—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622162C2212yes—
42C22×Q8×C11—21no—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×C4×D11—22no—
46C11×C4⋊Q8—22no—
47C11×C4⋊Q8C2×C414yescomplemented
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11—22no—
57C2×C42×C11C2312yes—
58C2×C42×C11C2311yescharacteristic
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×Dic11⋊C4—22no—
66C22×C11⋊C8C2311yescharacteristic
67C22×C11⋊C8C2312yes—
68C22×C11⋊C8C2311yescharacteristic
69C4⋊C4×D11—44no—
70C4×D44—22no—
71C4×D44—24no—
72C4×D44—42no—
73C4×D44C2×C414yes—
74C11×#95—22no—
75C11×#95—22no—
76C11×#95—21no—
77C11×#95D412yes—
78C11⋊#95—22no—
79#66873—22no—
80#66873C2×C418yes—
81#66873Q814yescomplemented
82#66872C2×C418yescomplemented
83#66871—42no—
84C4⋊(C11⋊C8)C2×C414yescomplemented
85#66867—42no—
86C4×C11⋊C8—22no—
87#22969—111nomaximal, Sylow
88C23×D11—21no—
89C2×Q8×C11—24no—
90C2×Q8×C11—81no—
91C2×Q8×C11—81no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—22no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44C22×C412yes—
106C2×D44C2×Q812yes—
107C2×D44#4112yes—
108C2×C4×D11—24no—
109C2×C4×D11—44no—
110C2×C4×D11—44no—
111C2×C4×D11—42no—
112C2×C4×D11—42no—
113C2×C4×D11—82no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—82no—
122C11×C4⋊C4C22×C414yes—
123C11×C4⋊C4C2×Q812yes—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11—42no—
127C42×C11—82no—
128C42×C11C22×C412yes—
129C42×C11#4112yes—
130(C2×D11)⋊C4—24no—
131(C2×D11)⋊C4—44no—
132C4⋊Dic11—21no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—42no—
136C4⋊Dic11—81no—
137C4⋊Dic11C22×C412yes—
138Dic11⋊C4—44no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8C22×C414yes—
147C2×C11⋊C8C2×Q812yes—
148C2×#476—111no—
149#2369D1111yescharacteristic, complemented
150D4×C4⋊C4—111no—
151#1990—111no—
152#1947—111no—
153#1944—112no—
154#1920—112no—
155#1862—112no—
156#1770—111no—
157#1762—112no—
158C4×#102—111no—
159C23×C11C22×D411yescharacteristic
160C22×D11—22no—
161C22×D11—22no—
162C22×D11—22no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167Q8×C11—84no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—24no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11C4×D412yes—
186C2×C4×C11C4×D412yes—
187C2×C4×C11AGL(1,ℤ/8)12yes—
188C2×C4×C11#13712yes—
189C2×C4×C11C23×C411yescharacteristic
190C2×C4×C11C22×Q811yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11H(5,𝔽2)11yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C2×Dic11—22no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201D44—22no—
202D44—22no—
203D44—22no—
204D44C4×Q814yes—
205C4×D11—48no—
206C4×D11—88no—
207C11⋊C8—24no—
208C11⋊C8—22no—
209C11⋊C8—41no—
210C2×C4⋊Q8C2×D1111yescharacteristic
211C2×C4×D4—111no—
212C2×C4×D4—112no—
213C22×C4⋊C4—221no—
214#476—118no—
215C2×#107—112no—
216C2×#106—112no—
217C2×C4⋊C8—111no—
218C2×#102—112no—
219C2×#102—111no—
220C2×#102—111no—
221C2×#97—112no—
222C2×C4×C8—111no—
223#391—22no—
224#389—21no—
225#389—112no—
226#389C2×D1112yes—
227#385—222no—
228#384—111no—
229#380—221no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4C2×D1112yes—
232C4×C4⋊C4C2×D1111yescharacteristic
233C4×C4⋊C4C2×D1111yescharacteristic
234#340—112no—
235#340—111no—
236#340—112no—
237#340—111no—
238#340—112no—
239#336—112no—
240C22×C11C2×C4×D411yescharacteristic
241C22×C11#54611yescharacteristic
242C22×C11D4×Q811yescharacteristic
243C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
244C22×C11C2×#13711yescharacteristic
245C22×C11#57611yescharacteristic
246C22×C11#57711yescharacteristic
247C2×D11—24no—
248C2×D11—42no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—42no—
254C4×C11—22no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—44no—
258C4×C11—42no—
259C4×C11—81no—
260C4×C11#44014yes—
261C4×C11C2×C4×Q811yescharacteristic
262C4×C11#52011yescharacteristic
263C4×C11#55211yescharacteristic
264C4×C11#55411yescharacteristic
265Dic11—42no—
266Dic11—82no—
267C22×Q8—21no—
268C22×D4—111no—
269C23×C4—221no—
270C23×C4—222no—
271C22×C8—112no—
272C22×C8—111no—
273C22×C8—111no—
274C4⋊Q8—22no—
275C4⋊Q8C4×D1114yescomplemented
276C4×D4—114no—
277C4×D4—224no—
278C4×D4—222no—
279C4×D4—442no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—111no—
283C2×C4⋊C4—112no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—222no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—444no—
288C2×C4⋊C4C22⋊D1111yescharacteristic
289C2×C4⋊C4C22⋊D1111yescharacteristic
290C2×C4⋊C4C22×D1111yescharacteristic
291C2×C4⋊C4C22×D1112yes—
292C2×C4⋊C4C22×D1111yescharacteristic
293C2×C22⋊C4—221no—
294C2×C22⋊C4—222no—
295C2×C42—21no—
296C2×C42—22no—
297C2×C42C22×D1112yes—
298C2×C42C22×D1111yescharacteristic
299#107—442no—
300#106—118no—
301C4⋊C8—114no—
302#102—118no—
303#102—114no—
304#102—222no—
305#97—442no—
306C4×C8—222no—
307#95—22no—
308#95—22no—
309#95—21no—
310#95—222no—
311#95C22⋊D1112yes—
312C2×C11#236011yescharacteristic
313C2×C11C2×#44011yescharacteristic
314C2×C11#294611yescharacteristic
315C2×C11#332511yescharacteristic
316C2×C11#333111yescharacteristic
317C2×C11#338411yescharacteristic
318C2×C11#338511yescharacteristic
319D11—44no—
320C24—221no—
321C2×Q8—24no—
322C2×Q8—81no—
323C2×Q8—81no—
324C2×D4—112no—
325C2×D4—112no—
326C2×D4—112no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—221no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—221no—
334C22×C4—224no—
335C22×C4—222no—
336C22×C4—444no—
337C22×C4—444no—
338C22×C4—442no—
339C22×C4—442no—
340C22×C4—882no—
341C22×C4C2×C22⋊D1112yes—
342C22×C4C2×C22⋊D1112yes—
343C22×C4C2×C22⋊D1111yescharacteristic
344C22×C4C2×C22⋊D1111yescharacteristic
345C22×C4C23×D1111yescharacteristic
346C2×C8—114no—
347C2×C8—112no—
348C2×C8—221no—
349C2×C8—222no—
350C2×C8—221no—
351C2×C8—222no—
352C2×C8—221no—
353C2×C8—221no—
354C2×C8—221no—
355C4⋊C4—24no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—82no—
363C4⋊C4—112no—
364C4⋊C4—221no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—444no—
368C4⋊C4—442no—
369C4⋊C4—881no—
370C4⋊C4C2×C4×D1114yes—
371C4⋊C4Q8×D1112yes—
372C22⋊C4—224no—
373C22⋊C4—444no—
374C42—22no—
375C42—22no—
376C42—42no—
377C42—82no—
378C42C2×C4×D1112yes—
379C42#433912yes—
380C11#2296911yescharacteristic, complemented, Sylow
381C23—222no—
382C23—222no—
383C23—222no—
384C23—441no—
385C23—441no—
386C23—441no—
387C23—441no—
388C23C22×C22⋊D1111yescharacteristic
389Q8—84no—
390D4—114no—
391D4—222no—
392D4—222no—
393D4—222no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—24no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—222no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—448no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—888no—
419C2×C4C4×C22⋊D1112yes—
420C2×C4C4×C22⋊D1112yes—
421C2×C4#6699512yes—
422C2×C4#6700212yes—
423C2×C4C22×C4×D1111yescharacteristic
424C2×C4C2×#433911yescharacteristic
425C2×C4C2×Q8×D1111yescharacteristic
426C2×C4#6704011yescharacteristic
427C2×C4#41×D1111yescharacteristic
428C2×C4#6704211yescharacteristic
429C8—224no—
430C8—222no—
431C8—441no—
432C22—224no—
433C22—442no—
434C22—442no—
435C22—442no—
436C22—442no—
437C22—442no—
438C22—442no—
439C22C2×C4×C22⋊D1111yescharacteristic
440C22C2×#6699511yescharacteristic
441C22Q8×C22⋊D1111yescharacteristic
442C22C2×#6700211yescharacteristic
443C22#1062336011yescharacteristic
444C22#1062336611yescharacteristic
445C22#1062336711yescharacteristic
446C4—22no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—44no—
451C4—81no—
452C4—442no—
453C4—882no—
454C4#1062263914yes—
455C4C4×Q8×D1111yescharacteristic
456C4#1062310511yescharacteristic
457C4#1062311011yescharacteristic
458C4#1062311211yescharacteristic
459C2—444no—
460C2#1307161711yescharacteristic
461C2C2×#1062263911yescharacteristic
462C2#1307744811yescharacteristic
463C2#1308085211yescharacteristic
464C2#1308092611yescharacteristic
465C2#1308151511yescharacteristic
466C2#1308152211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2369C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2369D11
hypocenterC11#22969
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2369

Complements

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

NH ≅ G/Ntype
3. #13069578C2semidirect
4. #13069374C2semidirect
5. #13069356C2semidirect
6. #13069201C2semidirect
8. #13068485C2semidirect
11. C11×#2369C2semidirect
23. #10622697C4semidirect
47. C11×C4⋊Q8C2×C4semidirect
81. #66873Q8semidirect
82. #66872C2×C4semidirect
84. C4⋊(C11⋊C8)C2×C4semidirect
149. #2369D11semidirect
275. C4⋊Q8C4×D11semidirect
380. C11#22969semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C4⋊C4×D442
#130695782
#130693742
#130693562
#130692012
#130688622
#130684852
#130684442
C4×#668732
C11×#23692
#2296911