Finite Group Databasebeta

← #14650616

Subgroups — #14650616

Order 2816.

512 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078099C211yesmaximal, characteristic
2#13077724C211yesmaximal, characteristic
3#13069569C211yesmaximal, characteristic, complemented
4#13068633C211yesmaximal, characteristic
5#13066518C211yesmaximal, characteristic, complemented
6#13066490C211yesmaximal, characteristic, complemented
7C11×#1546C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66995—21no—
10C4×#4339C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622838—21no—
14C2×#66889—21no—
15#10622703—21no—
16#10622703C412yescomplemented
17#10622696—21no—
18#10622696C412yescomplemented
19C4×C4⋊Dic11C2211yescharacteristic
20#10622537C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22#10622446—21no—
23D11×C4⋊C8—21no—
24(C22⋊D11)⋊C8—22no—
25C8×D44—21no—
26C8×Dic22—21no—
27C11×#332—21no—
28C11×#332—21no—
29#10622193—21no—
30#10622167—22no—
31C22×Q8×C11—21no—
32C2×#4339D411yescharacteristic
33C2×C11×M16—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8C2×C412yes—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4326—22no—
42#66995—42no—
43#66995—42no—
44C2×#4325—22no—
45C4×C22⋊D11—21no—
46C4×C22⋊D11—21no—
47#66979D411yescharacteristic
48C2×C4⋊Dic11—21no—
49C2×C4×Dic11—21no—
50C2×#4318—21no—
51C22×C11⋊C8D412yes—
52C2×C8×D11—22no—
53C4×D44C2×C411yescharacteristic
54C4×D44D411yescharacteristic
55#66925—21no—
56C42×D11—21no—
57C4×Dic22C2×C411yescharacteristic
58C4×Dic22D411yescharacteristic
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8D411yescharacteristic
62C11×C4⋊C8D411yescharacteristic
63C11×C22⋊C8—21no—
64C4×C8×C11—21no—
65#66899—22no—
66#66899—22no—
67C11⋊#95—21no—
68#66889—42no—
69(C2×D11)⋊C8—22no—
70Dic11⋊C8—22no—
71C8×Dic11—22no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)C2×C412yes—
76#9316—111nomaximal, Sylow
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C2×C22⋊D11—21no—
88C22×Dic11—41no—
89#4339—21no—
90#4339—21no—
91#4339D812yes—
92#4339SD1612yes—
93C2×D44C22⋊C411yescharacteristic
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×Dic22C22⋊C411yescharacteristic
98C11×M16—41no—
99C11×M16—41no—
100C2×C8×C11—21no—
101C2×C8×C11—21no—
102C2×C8×C11—41no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C42×C11C22×C411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C22⋊Dic11—21no—
112#4326—44no—
113#4325—44no—
114(C2×D11)⋊C4—21no—
115(C2×D11)⋊C4—21no—
116C4⋊Dic11—22no—
117C4⋊Dic11—41no—
118C4⋊Dic11C22⋊C411yescharacteristic
119C4⋊Dic11C22⋊C411yescharacteristic
120Dic11⋊C4—21no—
121Dic11⋊C4—21no—
122C4×Dic11—21no—
123C4×Dic11—21no—
124C4×Dic11—21no—
125C4×Dic11—41no—
126C4×Dic11—41no—
127#4318—41no—
128#4318—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132C8×D11—82no—
133#3039—111no—
134#2988—111no—
135#1988—111no—
136#1806—111no—
137#1546D1111yescharacteristic, complemented
138#1303—111no—
139#1292—111no—
140C23×C11#12111yescharacteristic
141C22×D11—21no—
142Q8×C11—42no—
143Q8×C11—42no—
144Q8×C11—81no—
145Q8×C11—81no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11C2×C22⋊C411yescharacteristic
153C2×C4×C11C4×D411yescharacteristic
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12311yescharacteristic
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C2×SD1611yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C2×C4×C11#13511yescharacteristic
162C22⋊D11—22no—
163C22⋊D11—22no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—42no—
168C2×Dic11—81no—
169C2×Dic11—81no—
170D44—21no—
171D44#10212yes—
172C4×D11—22no—
173C4×D11—22no—
174C4×D11—41no—
175C4×D11—41no—
176C4×D11—81no—
177Dic22—21no—
178Dic22#10212yes—
179C8×C11—41no—
180C8×C11—41no—
181C8×C11—81no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C2×#137—221no—
185C2×C4⋊Q8C2×D1111yescharacteristic
186C4×#41—111no—
187#462—112no—
188#462—221no—
189#461—112no—
190#461—221no—
191C8×Q8—221no—
192C8×D4—221no—
193C8×D4—222no—
194#431—221no—
195#431C2×D1111yescharacteristic
196#423—111no—
197#423C2×D1111yescharacteristic
198C2×C4⋊C8—111no—
199C2×C4⋊C8—221no—
200C2×#104—221no—
201#419—221no—
202C4×C4⋊C4—111no—
203#340—222no—
204#339—221no—
205#332—21no—
206#332—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11#38611yescharacteristic
210C22×C11#46511yescharacteristic
211C22×C11#46611yescharacteristic
212C2×D11—22no—
213C2×D11—41no—
214C2×D11—41no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—82no—
219C4×C11C2×#10211yescharacteristic
220C4×C11#41611yescharacteristic
221C4×C11#45511yescharacteristic
222C4×C11#45611yescharacteristic
223C4×C11#46511yescharacteristic
224C4×C11#46611yescharacteristic
225Dic11—22no—
226Dic11—41no—
227Dic11—41no—
228Dic11—82no—
229C2×#41—111no—
230C22×Q8—21no—
231#137—442no—
232#137—442no—
233C2×Q16—222no—
234C2×SD16—222no—
235C2×M16—21no—
236C2×M16—221no—
237C22×C8—112no—
238C22×C8—222no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8C4×D1112yes—
243C4×Q8—111no—
244C4×Q8—111no—
245C4×D4—111no—
246C4×D4—111no—
247C4×D4—221no—
248C4×D4—221no—
249#117—111no—
250#117—221no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—221no—
254C2×C42—221no—
255C2×C42—221no—
256C2×C42C22×D1111yescharacteristic
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—112no—
260C4⋊C8—222no—
261C4⋊C8—221no—
262C4⋊C8—221no—
263C4⋊C8—221no—
264C4⋊C8C22⋊D1111yescharacteristic
265C4⋊C8C22⋊D1111yescharacteristic
266#104—442no—
267#103—222no—
268#103—222no—
269C22⋊C8—21no—
270C22⋊C8—222no—
271C4×C8—21no—
272C4×C8—222no—
273#95—221no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11#188211yescharacteristic
277C2×C11#189311yescharacteristic
278C2×C11#190211yescharacteristic
279D11—42no—
280#41—112no—
281#41—112no—
282#41—221no—
283#41—221no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—111no—
291C2×D4—111no—
292C2×D4—221no—
293C22×C4—41no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—441no—
298C22×C4#433911yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301Q16—444no—
302SD16—444no—
303M16—41no—
304M16—41no—
305M16—441no—
306M16—441no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—41no—
310C2×C8—222no—
311C2×C8—222no—
312C2×C8—442no—
313C2×C8—882no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—111no—
319C4⋊C4—111no—
320C4⋊C4—222no—
321C4⋊C4—221no—
322C4⋊C4—221no—
323C4⋊C4—441no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C42—221no—
328C42—221no—
329C42—221no—
330C42—441no—
331C42—441no—
332C42C2×C4×D1111yescharacteristic
333C42D4×D1111yescharacteristic
334C42#434111yescharacteristic
335C42C2×C22⋊D1111yescharacteristic
336C11#931611yescharacteristic, complemented, Sylow
337C23—221no—
338C23#6693711yescharacteristic
339Q8—42no—
340Q8—42no—
341Q8—81no—
342Q8—81no—
343Q8—112no—
344Q8—221no—
345D4—112no—
346D4—222no—
347D4—222no—
348D4—221no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—221no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—442no—
363C2×C4—881no—
364C2×C4—881no—
365C2×C4—881no—
366C2×C4C22⋊C4×D1111yescharacteristic
367C2×C4(C22⋊D11)⋊C411yescharacteristic
368C2×C4#6693611yescharacteristic
369C2×C4D8×D1111yescharacteristic
370C2×C4#6696511yescharacteristic
371C2×C4SD16×D1111yescharacteristic
372C2×C4#6696911yescharacteristic
373C2×C4C4×C22⋊D1111yescharacteristic
374C2×C4#6699011yescharacteristic
375C2×C4#6699111yescharacteristic
376C8—41no—
377C8—41no—
378C8—81no—
379C8—442no—
380C8—442no—
381C22—21no—
382C22—21no—
383C22—222no—
384C22—441no—
385C22—441no—
386C22#1062238811yescharacteristic
387C22#1062239111yescharacteristic
388C22#1062256911yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—82no—
393C4—222no—
394C4—441no—
395C4—441no—
396C4—882no—
397C4D11×#10211yescharacteristic
398C4#1062238511yescharacteristic
399C4#1062277011yescharacteristic
400C4#1062278411yescharacteristic
401C4#1062281511yescharacteristic
402C4#1062281811yescharacteristic
403C2—21no—
404C2—21no—
405C2—442no—
406C2#1306898211yescharacteristic
407C2#1306904111yescharacteristic
408C2#1306909211yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#386
prime radicalC2×#4339D4
cosocleC2×C42×C11C23
hypercenter#1546D11
hypocenterC11#9316
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. #13069569C2semidirect
5. #13066518C2semidirect
6. #13066490C2semidirect
7. C11×#1546C2semidirect
16. #10622703C4semidirect
18. #10622696C4semidirect
137. #1546D11semidirect
336. C11#9316semidirect

Maximal subgroups

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

subgroupindex
#130780992
#130777242
#130695692
#130686332
#130665182
#130664902
C11×#15462
#931611