Finite Group Databasebeta

← #14853492

Subgroups — #14853492

Order 2816.

706 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
1#13077001C211yesmaximal, characteristic, complemented
2C4×#67000C211yesmaximal, characteristic
3#13070188C212yesmaximal, complemented
4#13069853C212yesmaximal
5#13069314C212yesmaximal
6#13069308C212yesmaximal, complemented
7#13068631C211yesmaximal, characteristic, complemented
8#13068627C211yesmaximal, characteristic
9#13068623C211yesmaximal, characteristic
10#13068471C211yesmaximal, characteristic, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000C2211yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103C2212yes—
17C11×#382C2211yescharacteristic
18#10622843C2211yescharacteristic
19C2×#66899C2212yes—
20C2×#66885C2212yes—
21C2×#66879C2212yes—
22#10622603—22no—
23#10622601C2211yescharacteristic
24#10622598C2212yes—
25#10622590C2211yescharacteristic
26#10622586C2212yes—
27C2×#66873C2212yes—
28C4×(C2×D11)⋊C4—22no—
29#10622549C2211yescharacteristic
30C42×Dic11C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622268—22no—
33#10622267—22no—
34C11×#340C2212yes—
35#10622189C2212yes—
36#10622188C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39C22×Q8×C11C2311yescharacteristic
40C22×D44C2311yescharacteristic
41C22×C4×D11—21no—
42C22×C8×C11C2312yes—
43C4×Q8×C11—22no—
44C4×Q8×C11—22no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4C2311yescharacteristic
47C2×C11×C4⋊C4C2312yes—
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50#67000—22no—
51#67000—22no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11C2312yes—
57C2×C4⋊Dic11C2311yescharacteristic
58C2×Dic11⋊C4—22no—
59C2×C4×Dic11D412yes—
60C2×C4×Dic11D412yes—
61C2×C4×Dic11C2311yescharacteristic
62C2×C4×Dic11C2311yescharacteristic
63C22×C11⋊C8C2312yes—
64C4×D44—22no—
65C4×D44—22no—
66C11×C4⋊C8—22no—
67C11×#103—24no—
68C11×#95—21no—
69C11×#95—21no—
70#66899—42no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77#66885—42no—
78#66879—42no—
79#66873—24no—
80C4⋊(C11⋊C8)—22no—
81#29128—111nomaximal, Sylow
82C23×D11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11#4112yes—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2411yescharacteristic
95C22×Dic11—22no—
96C22×Dic11—21no—
97C22×Dic11C2×D412yes—
98C22×Dic11C2×D412yes—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44#4112yes—
105C2×C4×D11—44no—
106C2×C4×D11—42no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—42no—
115C42×C11—42no—
116C42×C11#4112yes—
117C42×C11#4112yes—
118(C2×D11)⋊C4—28no—
119(C2×D11)⋊C4—44no—
120(C2×D11)⋊C4—42no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—44no—
126Dic11⋊C4—44no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131C4×Dic11—42no—
132C4×Dic11—42no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136#2864—111no—
137C4×#124—111no—
138#2101—112no—
139#2042—112no—
140#1936—112no—
141#1935—112no—
142#1805—111no—
143#1805D1111yescharacteristic, complemented
144#1804—111no—
145#1804—111no—
146#1767—111no—
147C23×C11C22×D411yescharacteristic
148C22×D11—22no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—42no—
152C22×D11—42no—
153Q8×C11—22no—
154Q8×C11—22no—
155Q8×C11—41no—
156Q8×C11—41no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11#12412yes—
168C2×C4×C11#12412yes—
169C2×C4×C11C2×#4111yescharacteristic
170C2×C4×C11C2×#4111yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172C2×C4×C11C2×#4111yescharacteristic
173C2×C4×C11H(5,𝔽2)11yescharacteristic
174C2×C4×C112−1+411yescharacteristic
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—41no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186D44—22no—
187D44—22no—
188D44—41no—
189D44—41no—
190C4×D11—84no—
191C8×C11—42no—
192C11⋊C8—42no—
193C2×#124—111no—
194C2×C4×Q8C2×D1111yescharacteristic
195C2×C4×D4—111no—
196C2×C4⋊C8—111no—
197C2×C4⋊C8C2×D1111yescharacteristic
198C2×#103—112no—
199C2×#103C2×D1112yes—
200C2×#102—112no—
201C2×#102—112no—
202C2×#97—112no—
203#391—111no—
204#390—111no—
205#389—112no—
206#389—112no—
207#388—222no—
208#387—222no—
209#387—222no—
210#382—111no—
211#382—111no—
212#382C2×D1111yescharacteristic
213C4×C22⋊C4—222no—
214C43—111no—
215#340—112no—
216#340—112no—
217#340—112no—
218#340C2×D1112yes—
219#336—112no—
220C22×C11#52511yescharacteristic
221C22×C11C2×#12411yescharacteristic
222C22×C11#53711yescharacteristic
223C22×C11#57512yes—
224C22×C11#57512yes—
225C2×D11—42no—
226C2×D11—44no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—82no—
230C4×C11—22no—
231C4×C11—22no—
232C4×C11—42no—
233C4×C11—82no—
234C4×C11—81no—
235C4×C11#55211yescharacteristic
236C4×C11#55211yescharacteristic
237C4×C11#55311yescharacteristic
238C4×C11#55311yescharacteristic
239Dic11—42no—
240Dic11—42no—
241Dic11—81no—
242Dic11—82no—
243C22×Q8C22×D1111yescharacteristic
244C22×D4—111no—
245C23×C4—221no—
246C22×C8—112no—
247C22×C8C22×D1112yes—
248#124—222no—
249#124—222no—
250C4×Q8—22no—
251C4×Q8—22no—
252C4×D4—222no—
253C4×D4—222no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—222no—
259C2×C4⋊C4C22×D1111yescharacteristic
260C2×C4⋊C4C22×D1112yes—
261C2×C22⋊C4—222no—
262C2×C22⋊C4—222no—
263C2×C22⋊C4—221no—
264C2×C42—21no—
265C2×C42—111no—
266C2×C42—111no—
267C2×C42—112no—
268C2×C42—112no—
269C2×C42C22×D1111yescharacteristic
270C4⋊C8—22no—
271C4⋊C8—222no—
272#103—24no—
273#103—442no—
274#102—224no—
275#102—442no—
276#97—442no—
277#95—21no—
278#95—21no—
279#95—222no—
280#95—222no—
281#95—222no—
282#95—222no—
283#95—221no—
284#95—221no—
285C2×C11#256211yescharacteristic
286C2×C11#311112yes—
287C2×C11#313511yescharacteristic
288C2×C11#314011yescharacteristic
289C2×C11#325612yes—
290D11—82no—
291C24—221no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8#434112yes—
298C2×D4—112no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—221no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—112no—
308C22×C4—112no—
309C22×C4—221no—
310C22×C4—222no—
311C22×C4—444no—
312C22×C4—442no—
313C22×C4D4×D1111yescharacteristic
314C22×C4D4×D1111yescharacteristic
315C22×C4C23×D1111yescharacteristic
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—222no—
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—42no—
327C4⋊C4—221no—
328C4⋊C4—221no—
329C4⋊C4—222no—
330C4⋊C4—222no—
331C4⋊C4—444no—
332C4⋊C4—444no—
333C22⋊C4—228no—
334C22⋊C4—444no—
335C22⋊C4—442no—
336C42—42no—
337C42—221no—
338C42—221no—
339C42—221no—
340C42—221no—
341C42—442no—
342C42—442no—
343C42#433912yes—
344C42#434112yes—
345C11#2912811yescharacteristic, complemented, Sylow
346C23—222no—
347C23—441no—
348C23—442no—
349C23—442no—
350C23—441no—
351C23C2×D4×D1111yescharacteristic
352Q8—22no—
353Q8—22no—
354Q8—41no—
355Q8—41no—
356D4—222no—
357D4—222no—
358D4—441no—
359D4—441no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—222no—
376C2×C4—441no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—884no—
382C2×C4#6693812yes—
383C2×C4#6693812yes—
384C2×C4C2×#433911yescharacteristic
385C2×C4C2×#434111yescharacteristic
386C2×C4C2×#434111yescharacteristic
387C2×C4#6704011yescharacteristic
388C2×C4#41×D1111yescharacteristic
389C2×C4#6704211yescharacteristic
390C8—42no—
391C8—442no—
392C22—442no—
393C22—444no—
394C22—881no—
395C22—882no—
396C22—881no—
397C22C2×#6693811yescharacteristic
398C22#1062313711yescharacteristic
399C22#1062316011yescharacteristic
400C22#1062329912yes—
401C22#1062330812yes—
402C4—22no—
403C4—22no—
404C4—42no—
405C4—81no—
406C4—82no—
407C4—442no—
408C4—442no—
409C4—882no—
410C4—881no—
411C4#1062304411yescharacteristic
412C4#1062306111yescharacteristic
413C4#1062314911yescharacteristic
414C4#1062317011yescharacteristic
415C2—882no—
416C2#1307377911yescharacteristic
417C2#1307872412yes—
418C2#1307895911yescharacteristic
419C2#1307900411yescharacteristic
420C2#1308001912yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1805C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1805D11
hypocenterC11#29128
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
1. #13077001C2semidirect
3. #13070188C2semidirect
6. #13069308C2semidirect
7. #13068631C2semidirect
10. #13068471C2semidirect
11. C11×#1805C2semidirect
143. #1805D11semidirect
345. C11#29128semidirect

Maximal subgroups

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

subgroupindex
#130770012
C4×#670002
#130701882
#130698532
#130693142
#130693082
#130686312
#130686272
#130686232
#130684712
C11×#18052
#2912811