Finite Group Databasebeta

← #14853490

Subgroups — #14853490

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
1C4×#66928C211yesmaximal, characteristic
2#13070184C212yesmaximal, complemented
3#13069857C212yesmaximal
4#13069312C212yesmaximal
5#13069305C212yesmaximal, complemented
6#13068628C211yesmaximal, characteristic, complemented
7#13068628C211yesmaximal, characteristic, complemented
8#13068623C211yesmaximal, characteristic
9#13068623C211yesmaximal, characteristic
10#13068469C211yesmaximal, characteristic, complemented
11C11×#2864C211yesmaximal, characteristic, complemented
12C2×#66928C2211yescharacteristic
13C2×C4×D44C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C11×#389C2212yes—
16C11×#389C2212yes—
17C11×#387—22no—
18C11×#387—22no—
19C11×#382C2211yescharacteristic
20C11×#382C2211yescharacteristic
21C43×C11C2211yescharacteristic
22C2×#66874C2212yes—
23C2×#66874C2212yes—
24C2×#66873C2212yes—
25C2×#66873C2212yes—
26#10622553—22no—
27#10622552C2211yescharacteristic
28C4×(C2×D11)⋊C4—22no—
29#10622549C2211yescharacteristic
30#10622542C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33C2×#66867C2212yes—
34#10622167C2212yes—
35#10622167C2212yes—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622162C2212yes—
39C22×D44C2311yescharacteristic
40C22×C4×D11—21no—
41C22×Dic22C2311yescharacteristic
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C4⋊C4C2312yes—
46C2×C42×C11D412yes—
47C2×C42×C11D412yes—
48C2×C42×C11C2311yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—22no—
54C2×C4⋊Dic11C2311yescharacteristic
55C2×C4⋊Dic11C2311yescharacteristic
56C2×Dic11⋊C4—21no—
57C2×C4×Dic11—21no—
58C22×C11⋊C8C2312yes—
59C22×C11⋊C8C2312yes—
60#66928—22no—
61#66928—22no—
62C4×D44—22no—
63C4×D44—22no—
64C4×Dic22—22no—
65C4×Dic22—22no—
66C11×#95—21no—
67C11×#95—21no—
68C11×#95—21no—
69C11×#95—21no—
70C11×#95—22no—
71C11×#95—22no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74#66874—24no—
75#66874—42no—
76#66873—24no—
77#66873—42no—
78C4⋊(C11⋊C8)—22no—
79C4⋊(C11⋊C8)—22no—
80#66867—42no—
81#29128—111nomaximal, Sylow
82C23×D11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2411yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44#4112yes—
99C2×C4×D11—44no—
100C2×C4×D11—42no—
101C2×Dic22—21no—
102C2×Dic22—21no—
103C2×Dic22—21no—
104C2×Dic22—21no—
105C2×Dic22—21no—
106C2×Dic22#4112yes—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—44no—
112C11×C4⋊C4—44no—
113C42×C11—21no—
114C42×C11—21no—
115C42×C11—21no—
116C42×C11—21no—
117C42×C11—42no—
118C42×C11—42no—
119C42×C11#4112yes—
120C42×C11#4112yes—
121(C2×D11)⋊C4—28no—
122(C2×D11)⋊C4—44no—
123(C2×D11)⋊C4—42no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128Dic11⋊C4—42no—
129C4×Dic11—42no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136#2864D1111yescharacteristic, complemented
137C4×#124—111no—
138#2101—112no—
139#2042—112no—
140#1936—112no—
141#1935—112no—
142#1805—111no—
143#1805—111no—
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—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
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—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182D44—22no—
183D44—22no—
184D44—41no—
185D44—41no—
186C4×D11—84no—
187Dic22—22no—
188Dic22—22no—
189Dic22—41no—
190Dic22—41no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193C2×#124—111no—
194C2×C4×Q8—111no—
195C2×C4×D4—111no—
196C2×C4⋊C8—111no—
197C2×C4⋊C8—111no—
198C2×#103—112no—
199C2×#103—112no—
200C2×#102—112no—
201C2×#102—112no—
202C2×#97—112no—
203#391—111no—
204#390—111no—
205#389C2×D1112yes—
206#389C2×D1112yes—
207#388—222no—
208#387—22no—
209#387—22no—
210#382—111no—
211#382C2×D1111yescharacteristic
212#382C2×D1111yescharacteristic
213C4×C22⋊C4—222no—
214C43C2×D1111yescharacteristic
215#340—112no—
216#340—112no—
217#340—112no—
218#340—112no—
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—42no—
234C4×C11—82no—
235C4×C11—82no—
236C4×C11#55211yescharacteristic
237C4×C11#55211yescharacteristic
238C4×C11#55311yescharacteristic
239C4×C11#55311yescharacteristic
240Dic11—42no—
241Dic11—81no—
242Dic11—81no—
243C22×Q8—111no—
244C22×D4—111no—
245C23×C4—221no—
246C22×C8—112no—
247C22×C8—112no—
248#124—222no—
249#124—222no—
250C4×Q8—222no—
251C4×Q8—222no—
252C4×D4—222no—
253C4×D4—222no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4C22×D1112yes—
260C2×C4⋊C4C22×D1112yes—
261C2×C22⋊C4—222no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—222no—
264C2×C42—221no—
265C2×C42C22⋊D1112yes—
266C2×C42C22⋊D1112yes—
267C2×C42C22×D1111yescharacteristic
268C2×C42C22×D1111yescharacteristic
269C2×C42C22×D1111yescharacteristic
270C4⋊C8—222no—
271C4⋊C8—222no—
272#103—224no—
273#103—442no—
274#102—224no—
275#102—442no—
276#97—442no—
277#95—21no—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—22no—
282#95—22no—
283#95—222no—
284#95—222no—
285C2×C11#256211yescharacteristic
286C2×C11#311112yes—
287C2×C11#313511yescharacteristic
288C2×C11#314011yescharacteristic
289C2×C11#325612yes—
290D11—82no—
291C24—221no—
292C2×Q8—112no—
293C2×Q8—221no—
294C2×Q8—221no—
295C2×Q8—221no—
296C2×Q8—221no—
297C2×Q8—221no—
298C2×D4—112no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—221no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—444no—
310C22×C4—442no—
311C22×C4C2×C22⋊D1112yes—
312C22×C4C2×C22⋊D1112yes—
313C22×C4C2×C22⋊D1111yescharacteristic
314C22×C4C2×C22⋊D1111yescharacteristic
315C22×C4C23×D1111yescharacteristic
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—222no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—44no—
327C4⋊C4—44no—
328C4⋊C4—221no—
329C4⋊C4—221no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—442no—
333C22⋊C4—228no—
334C22⋊C4—444no—
335C22⋊C4—442no—
336C42—21no—
337C42—21no—
338C42—21no—
339C42—21no—
340C42—42no—
341C42—42no—
342C42—442no—
343C42#434312yes—
344C42#434312yes—
345C11#2912811yescharacteristic, complemented, Sylow
346C23—222no—
347C23—441no—
348C23—442no—
349C23—442no—
350C23—441no—
351C23C22×C22⋊D1111yescharacteristic
352Q8—222no—
353Q8—222no—
354Q8—441no—
355Q8—441no—
356D4—222no—
357D4—222no—
358D4—441no—
359D4—441no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—222no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—884no—
382C2×C4#6700012yes—
383C2×C4#6700012yes—
384C2×C4C2×#434311yescharacteristic
385C2×C4C2×#434311yescharacteristic
386C2×C4#41×D1111yescharacteristic
387C2×C4#41×D1111yescharacteristic
388C2×C4#6704211yescharacteristic
389C2×C4#6704311yescharacteristic
390C8—442no—
391C8—442no—
392C22—442no—
393C22—444no—
394C22—881no—
395C22—882no—
396C22—881no—
397C22C2×#6700011yescharacteristic
398C22#1062335312yes—
399C22#1062335312yes—
400C22#1062335911yescharacteristic
401C22#1062336411yescharacteristic
402C4—22no—
403C4—22no—
404C4—42no—
405C4—42no—
406C4—82no—
407C4—82no—
408C4—442no—
409C4—881no—
410C4—881no—
411C4#1062322511yescharacteristic
412C4#1062322511yescharacteristic
413C4#1062322611yescharacteristic
414C4#1062322611yescharacteristic
415C2—882no—
416C2#1307378311yescharacteristic
417C2#1307871912yes—
418C2#1307896411yescharacteristic
419C2#1307900511yescharacteristic
420C2#1308001212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2864C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2864D11
hypocenterC11#29128
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2864

Complements

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

NH ≅ G/Ntype
2. #13070184C2semidirect
5. #13069305C2semidirect
6. #13068628C2semidirect
7. #13068628C2semidirect
10. #13068469C2semidirect
11. C11×#2864C2semidirect
136. #2864D11semidirect
345. C11#29128semidirect

Maximal subgroups

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

subgroupindex
C4×#669282
#130701842
#130698572
#130693122
#130693052
#130686282
#130686232
#130684692
C11×#28642
#2912811