Finite Group Databasebeta

← #14767626

Subgroups — #14767626

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622673C211yesmaximal, characteristic
2#13071335C211yesmaximal, characteristic, complemented
3#13069428C211yesmaximal, characteristic
4#13069417C211yesmaximal, characteristic, complemented
5#13068974C212yesmaximal
6#13068960C212yesmaximal, complemented
7#13068957C212yesmaximal, complemented
8#13068950C212yesmaximal
9#13068751C211yesmaximal, characteristic, complemented
10#13068368C211yesmaximal, characteristic, complemented
11C11×#2326C211yesmaximal, characteristic
12C2×C11×#124C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C22×#4326C2212yes—
16C22×#4324C2212yes—
17C2×#66922C2211yescharacteristic
18C2×C4×Dic22C2212yes—
19C11×#391C2211yescharacteristic
20C11×#390C2211yescharacteristic
21C11×#388—22no—
22C11×#385—22no—
23C11×#384C2211yescharacteristic
24C11×#376C2211yescharacteristic
25C2×#66899C2212yes—
26C2×#66896C2212yes—
27#10622673C418yescomplemented
28C2×#66874C2212yes—
29C2×#66874C2212yes—
30#10622549C2211yescharacteristic
31#10622542C2212yes—
32C2×#66867C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622266—22no—
35#10622266—22no—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622162C2212yes—
39#10622162C2212yes—
40C22×Q8×C11C2311yescharacteristic
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11—21no—
43C22×Dic22C2312yes—
44C11×#124—22no—
45C11×#124C2×C414yes—
46C4×Q8×C11—42no—
47C4×D4×C11—42no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—22no—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2311yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×#4326—42no—
60C2×#4326—42no—
61C2×#4326C2×C418yescomplemented
62C2×#4324—42no—
63C2×#4324—42no—
64C2×#4324C2×C418yes—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11C2312yes—
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—22no—
69C22×C11⋊C8C2312yes—
70C22×C11⋊C8C2312yes—
71#66922—22no—
72#66922C2×C414yescomplemented
73C4×Dic22—42no—
74C4×Dic22—42no—
75C11×#95—22no—
76C11×#95D412yes—
77C11×#95D412yes—
78#66899—42no—
79#66896—42no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83#66874—42no—
84#66874—42no—
85#66867C2×C414yescomplemented
86C4×C11⋊C8—22no—
87#22278—111nomaximal, Sylow
88C24×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11C22×C412yes—
93C2×D4×C11—21no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11C22×C412yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—42no—
101C22×C4×C11—82no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—22no—
108C22×Dic11—22no—
109C2×Dic22—22no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22—22no—
114C2×Dic22C22×C414yes—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—82no—
119C11×C22⋊C4—28no—
120C11×C22⋊C4—42no—
121C11×C22⋊C4—82no—
122C42×C11—22no—
123C42×C11—22no—
124C42×C11—42no—
125C42×C11C22×C412yes—
126C42×C11#4112yes—
127#4326—48no—
128#4324—48no—
129C4⋊Dic11—28no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132Dic11⋊C4—44no—
133C4×Dic11—44no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8C22×C414yes—
140C2×#497—111no—
141#2327—111no—
142#2326D1111yescharacteristic
143#1958—111no—
144#1956—111no—
145#1880—112no—
146#1878—112no—
147#1878—112no—
148#1877—112no—
149#1836—111no—
150#1746—111no—
151C23×C11—22no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11C22×D411yescharacteristic
157Q8×C11—24no—
158Q8×C11—42no—
159D4×C11—24no—
160D4×C11—42no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—84no—
178C2×C4×C11C4×D414yes—
179C2×C4×C11C23×C411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11H(5,𝔽2)12yes—
182C2×C4×C11H(5,𝔽2)12yes—
183C2×Dic11—24no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189Dic22—24no—
190Dic22—24no—
191Dic22—42no—
192Dic22—42no—
193C11⋊C8—24no—
194C11⋊C8—42no—
195C22×Q16—112no—
196C22×SD16—112no—
197C2×C4⋊Q8—111no—
198C2×#124C2×D1111yescharacteristic
199C2×C4×Q8—112no—
200C2×C4×Q8C2×D1111yescharacteristic
201C2×C4×D4C2×D1111yescharacteristic
202#497—118no—
203C2×#103—112no—
204C2×#103—112no—
205C2×#103—112no—
206C2×#102—112no—
207C2×#97—111no—
208C2×C4×C8—111no—
209#391—112no—
210#391C2×D1111yescharacteristic
211#390C2×D1111yescharacteristic
212#388—22no—
213#387—222no—
214#387—222no—
215#385—22no—
216#384C2×D1111yescharacteristic
217#382—111no—
218#376C2×D1111yescharacteristic
219#340—112no—
220#340—112no—
221#336—112no—
222#336—112no—
223C22×C11—42no—
224C22×C11—44no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—82no—
228C22×C11C2×C4×D411yescharacteristic
229C22×C11#53511yescharacteristic
230C22×C11#53511yescharacteristic
231C22×C11#57712yes—
232C22×C11#57812yes—
233C4×C11—24no—
234C4×C11—42no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11—42no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11#51812yes—
241C4×C11#54012yes—
242Dic11—44no—
243Dic11—82no—
244C22×Q8—112no—
245C22×Q8C22×D1111yescharacteristic
246C22×D4C22×D1111yescharacteristic
247C23×C4—21no—
248C2×Q16—118no—
249C2×Q16—442no—
250C2×Q16—442no—
251C2×SD16—118no—
252C2×SD16—442no—
253C2×SD16—442no—
254C22×C8—112no—
255C22×C8—112no—
256C4⋊Q8—114no—
257C4⋊Q8—222no—
258#124—22no—
259#124C4×D1114yes—
260C4×Q8—42no—
261C4×Q8—442no—
262C4×Q8—442no—
263C4×D4—42no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—112no—
267C2×C4⋊C4—222no—
268C2×C4⋊C4—222no—
269C2×C4⋊C4C22×D1111yescharacteristic
270C2×C4⋊C4C22×D1111yescharacteristic
271C2×C22⋊C4—22no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—22no—
274C2×C42—21no—
275C2×C42—222no—
276C2×C42C22×D1111yescharacteristic
277C2×C42C22×D1111yescharacteristic
278C2×C42C22×D1111yescharacteristic
279#103—442no—
280#103—442no—
281#103—442no—
282#102—442no—
283#97—114no—
284C4×C8—222no—
285#95—22no—
286#95—222no—
287#95—222no—
288#95—222no—
289#95C22⋊D1112yes—
290#95C22⋊D1112yes—
291C2×C11—82no—
292C2×C11#232811yescharacteristic
293C2×C11#294712yes—
294C2×C11#322211yescharacteristic
295C2×C11#322311yescharacteristic
296C2×C11#322512yes—
297C24—21no—
298C2×Q8—21no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—114no—
302C2×Q8—222no—
303C2×Q8—222no—
304C2×Q8—222no—
305C2×Q8—222no—
306C2×Q8—222no—
307C2×Q8C2×C4×D1112yes—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4C2×C4×D1112yes—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—42no—
316C22×C4—82no—
317C22×C4—222no—
318C22×C4—222no—
319C22×C4C2×C22⋊D1112yes—
320C22×C4C2×C22⋊D1111yescharacteristic
321C22×C4C2×C22⋊D1111yescharacteristic
322C22×C4C2×C22⋊D1112yes—
323C22×C4C23×D1111yescharacteristic
324Q16—448no—
325SD16—448no—
326C2×C8—114no—
327C2×C8—222no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—222no—
331C2×C8—222no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—42no—
335C4⋊C4—82no—
336C4⋊C4—228no—
337C4⋊C4—222no—
338C4⋊C4—222no—
339C4⋊C4—444no—
340C22⋊C4—28no—
341C22⋊C4—42no—
342C22⋊C4—82no—
343C42—22no—
344C42—22no—
345C42—42no—
346C42—444no—
347C42C2×C4×D1112yes—
348C42#433912yes—
349C11#2227811yescharacteristic, complemented, Sylow
350C23—22no—
351C23—41no—
352C23—41no—
353C23—42no—
354C23—42no—
355C23C22×C22⋊D1111yescharacteristic
356Q8—24no—
357Q8—42no—
358Q8—224no—
359Q8—224no—
360Q8—442no—
361Q8—442no—
362D4—24no—
363D4—42no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—84no—
381C2×C4—224no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4C4×C22⋊D1114yes—
388C2×C4C22×C4×D1111yescharacteristic
389C2×C4C2×#433911yescharacteristic
390C2×C4#6703712yes—
391C2×C4#6704212yes—
392C8—224no—
393C8—442no—
394C22—44no—
395C22—42no—
396C22—81no—
397C22—81no—
398C22—82no—
399C22C2×C4×C22⋊D1111yescharacteristic
400C22#1062333611yescharacteristic
401C22#1062336111yescharacteristic
402C22#1062336712yes—
403C22#1062336912yes—
404C4—24no—
405C4—41no—
406C4—41no—
407C4—42no—
408C4—42no—
409C4—81no—
410C4—81no—
411C4—444no—
412C4—882no—
413C4#1062307612yes—
414C4#1062309312yes—
415C2—82no—
416C2#1307133811yescharacteristic
417C2#1307745512yes—
418C2#1307968811yescharacteristic
419C2#1307969911yescharacteristic
420C2#1307971912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2326C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#2326D11
hypocenterC11#22278
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2326

Complements

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

NH ≅ G/Ntype
2. #13071335C2semidirect
4. #13069417C2semidirect
6. #13068960C2semidirect
7. #13068957C2semidirect
9. #13068751C2semidirect
10. #13068368C2semidirect
27. #10622673C4semidirect
61. C2×#4326C2×C4semidirect
72. #66922C2×C4semidirect
85. #66867C2×C4semidirect
349. C11#22278semidirect

Maximal subgroups

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

subgroupindex
C2×#106226732
#130713352
#130694282
#130694172
#130689742
#130689602
#130689572
#130689502
#130687512
#130683682
C11×#23262
#2227811