Finite Group Databasebeta

← #14650584

Subgroups — #14650584

Order 2816.

514 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078767C211yesmaximal, characteristic
2#13067226C211yesmaximal, characteristic, complemented
3#13067050C211yesmaximal, characteristic, complemented
4#13067034C211yesmaximal, characteristic, complemented
5#13066515C211yesmaximal, characteristic, complemented
6#13066488C211yesmaximal, characteristic, complemented
7C11×#2875C211yesmaximal, characteristic, complemented
8C2×C11×#131—21no—
9C4×C11×#41C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#405—21no—
12C11×#405—22no—
13C4×C11×M16—21no—
14C4×C11×M16C2211yescharacteristic
15C2×C11×#97—21no—
16C2×C11×#97C2211yescharacteristic
17#10622851—21no—
18#10622640C411yescharacteristic
19#10622639—21no—
20#10622633C411yescharacteristic
21#10622628C411yescharacteristic
22#10622627—21no—
23#10622620C411yescharacteristic
24#10622616—21no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27#10622538C2211yescharacteristic
28Q8⋊(C11⋊C8)—21no—
29D4⋊(C11⋊C8)—21no—
30#10622102—21no—
31#10622102—21no—
32#10622097—22no—
33C2×C11×#41D411yescharacteristic
34C2×#4339—21no—
35C11×#131—24no—
36C11×#131—24no—
37C2×C11×M16—22no—
38C2×C11×M16—21no—
39C22×C8×C11—22no—
40C22×C8×C11—21no—
41C4×Q8×C11C2×C411yescharacteristic
42C4×Q8×C11D411yescharacteristic
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11C2×C411yescharacteristic
46C4×D4×C11D411yescharacteristic
47C11×#117—21no—
48C11×#117D411yescharacteristic
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4325—21no—
52C2×#4323—21no—
53#66983—21no—
54#66983—21no—
55#66928—21no—
56#66927C2×C411yescharacteristic
57C4×D44—21no—
58C4×D44—21no—
59#66922C2×C411yescharacteristic
60C11×#97—22no—
61C11×#97—21no—
62C11×#97—21no—
63C11×#97D411yescharacteristic
64C11×#97D411yescharacteristic
65C4×C8×C11—22no—
66C4×C8×C11D412yes—
67#66899—21no—
68#66896—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72#66873—21no—
73#66873—21no—
74#66872—21no—
75#66871—21no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)C2×C411yescharacteristic
79C4⋊(C11⋊C8)C2×C411yescharacteristic
80#66867—21no—
81#66867—21no—
82C4×C11⋊C8—21no—
83#9311—111nomaximal, Sylow
84C11×#41—22no—
85C11×#41—22no—
86C2×Q8×C11C22⋊C411yescharacteristic
87C2×D4×C11—21no—
88C2×D4×C11C22⋊C411yescharacteristic
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C2×C22⋊D11—41no—
96#4339—82no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×C4×D11—41no—
101C2×Dic22—21no—
102C11×M16—28no—
103C11×M16—22no—
104C11×M16—22no—
105C2×C8×C11—28no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—21no—
109C2×C8×C11—22no—
110C2×C8×C11—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4C22⋊C411yescharacteristic
114C11×C4⋊C4C22⋊C411yescharacteristic
115C11×C22⋊C4—21no—
116C11×C22⋊C4—21no—
117C11×C22⋊C4—21no—
118C42×C11—21no—
119C42×C11—21no—
120C42×C11—21no—
121C42×C11C22×C411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125#4325—42no—
126#4323—42no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135#3115—111no—
136#2875D1111yescharacteristic, complemented
137#1530—111no—
138#1488—111no—
139#1484—111no—
140#1302—111no—
141#1291—111no—
142C23×C11—21no—
143C23×C11#12311yescharacteristic
144C22×D11—41no—
145Q8×C11—21no—
146Q8×C11#10412yes—
147D4×C11—24no—
148D4×C11—21no—
149D4×C11#10412yes—
150C2×C4×C11—24no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11C2×C22⋊C411yescharacteristic
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C22⋊D11—82no—
167C2×Dic11—41no—
168D44—42no—
169D44—41no—
170D44—41no—
171D44—81no—
172C4×D11—82no—
173Dic22—81no—
174C8×C11—22no—
175C8×C11—22no—
176C8×C11—24no—
177C11⋊C8—41no—
178C11⋊C8—41no—
179C11⋊C8—81no—
180C11⋊C8—81no—
181C2×#131—21no—
182#532—111no—
183C4×#41C2×D1111yescharacteristic
184#482—221no—
185#475—111no—
186#474—111no—
187#460—111no—
188#459—111no—
189#449—221no—
190#442—221no—
191#440—221no—
192#432—111no—
193#432—111no—
194#431—111no—
195#405—21no—
196#405—22no—
197C4×M16—21no—
198C4×M16C2×D1111yescharacteristic
199C2×#97—21no—
200C2×#97C2×D1111yescharacteristic
201#329—221no—
202#329—221no—
203Q8⋊C8—221no—
204D4⋊C8—221no—
205D4⋊C8—222no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—22no—
209C22×C11—21no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11#38611yescharacteristic
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—81no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—22no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—41no—
223C4×C11—41no—
224C4×C11C2×#10411yescharacteristic
225C4×C11C2×#10411yescharacteristic
226Dic11—81no—
227C2×#41—221no—
228C2×#41C22⋊D1111yescharacteristic
229C2×SD16—221no—
230C2×D8—221no—
231#131—24no—
232#131—24no—
233C2×M16—22no—
234C2×M16—21no—
235C22×C8—22no—
236C22×C8—21no—
237C4⋊Q8—111no—
238#127—111no—
239#124—221no—
240#121—221no—
241#121—221no—
242C4×Q8C4×D1111yescharacteristic
243C4×Q8D4411yescharacteristic
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—221no—
247C4×D4—221no—
248C4×D4C4×D1111yescharacteristic
249C4×D4D4411yescharacteristic
250#117—21no—
251#117C22⋊D1111yescharacteristic
252C2×C42—21no—
253C2×C42C22×D1111yescharacteristic
254#107—221no—
255#106—221no—
256C4⋊C8—111no—
257C4⋊C8—111no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260#103—221no—
261#102—221no—
262#102—221no—
263#102—221no—
264C22⋊C8—221no—
265C22⋊C8—221no—
266C22⋊C8—221no—
267#97—22no—
268#97—21no—
269#97—21no—
270#97—221no—
271#97—221no—
272#97C22⋊D1111yescharacteristic
273#97C22⋊D1111yescharacteristic
274C4×C8—22no—
275C4×C8—221no—
276C4×C8C22⋊D1112yes—
277C2×C11—41no—
278C2×C11—42no—
279C2×C11#188111yescharacteristic
280C2×C11#189611yescharacteristic
281C2×C11#190311yescharacteristic
282D11—161no—
283#41—22no—
284#41—22no—
285#41—882no—
286C2×Q8—221no—
287C2×Q8(C2×D11)⋊C411yescharacteristic
288C2×D4—21no—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4—221no—
292C2×D4—441no—
293C2×D4(C2×D11)⋊C411yescharacteristic
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—441no—
298C22×C4#433911yescharacteristic
299C22×C4#433911yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301SD16—442no—
302D8—442no—
303M16—28no—
304M16—22no—
305M16—22no—
306C2×C8—28no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—21no—
310C2×C8—22no—
311C2×C8—21no—
312C2×C8—221no—
313C2×C8—221no—
314C2×C8—441no—
315C2×C8—441no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C4⋊C4(C2×D11)⋊C411yescharacteristic
321C4⋊C4(C2×D11)⋊C411yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C42—21no—
328C42—21no—
329C42—21no—
330C42C2×C4×D1111yescharacteristic
331C42C2×D4411yescharacteristic
332C42C2×C22⋊D1111yescharacteristic
333C42C2×C22⋊D1111yescharacteristic
334C11#931111yescharacteristic, complemented, Sylow
335C23—21no—
336C23—441no—
337C23#6698211yescharacteristic
338Q8—21no—
339Q8—881no—
340Q8#6686912yes—
341D4—24no—
342D4—21no—
343D4—442no—
344D4—441no—
345D4—441no—
346D4—881no—
347D4—882no—
348D4#6686912yes—
349C2×C4—24no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—441no—
360C2×C4—882no—
361C2×C4C2×(C2×D11)⋊C411yescharacteristic
362C2×C4C4×C22⋊D1111yescharacteristic
363C2×C4C4×C22⋊D1111yescharacteristic
364C2×C4#6698311yescharacteristic
365C2×C4#6698311yescharacteristic
366C2×C4#6700611yescharacteristic
367C8—22no—
368C8—22no—
369C8—24no—
370C8—441no—
371C8—441no—
372C8—881no—
373C8—881no—
374C22—21no—
375C22—22no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—881no—
381C22—881no—
382C22—881no—
383C22#1062282611yescharacteristic
384C4—21no—
385C4—22no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—881no—
393C4C2×#6686911yescharacteristic
394C4C2×#6686911yescharacteristic
395C2—41no—
396C2—42no—
397C2—1761no—
398C2#1306897811yescharacteristic
399C2#1306905911yescharacteristic
400C2#1306909611yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2875C2
socleC22×C11#386
prime radical#13078767C2
cosocleC2×C42×C11C23
hypercenter#2875D11
hypocenterC11#9311
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2875

Complements

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

NH ≅ G/Ntype
2. #13067226C2semidirect
3. #13067050C2semidirect
4. #13067034C2semidirect
5. #13066515C2semidirect
6. #13066488C2semidirect
7. C11×#2875C2semidirect
136. #2875D11semidirect
334. C11#9311semidirect

Maximal subgroups

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

subgroupindex
#130787672
#130672262
#130670502
#130670342
#130665152
#130664882
C11×#28752
#931111