Finite Group Databasebeta

← #14908441

Subgroups — #14908441

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#500C211yesmaximal, characteristic, complemented
2C4×#66972C211yesmaximal, characteristic
3#13070766C212yesmaximal, complemented
4#13070762C212yesmaximal, complemented
5#13070758C211yesmaximal, characteristic, complemented
6#13070754C211yesmaximal, characteristic, complemented
7#13070750C211yesmaximal, characteristic, complemented
8#13070403C212yesmaximal, complemented
9#13070370C211yesmaximal, characteristic, complemented
10#13070327C212yesmaximal
11C11×#2225C211yesmaximal, characteristic, complemented
12C2×#66972C2211yescharacteristic
13D11×C4⋊Q8—21no—
14C4×#4343—21no—
15C11×#500C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17Q16×Dic11C2211yescharacteristic
18#10622691—21no—
19C4×#4325—21no—
20C2×#66862C2212yes—
21#10622493C2211yescharacteristic
22D11×#107—21no—
23D11×#107C2212yes—
24#10622487—21no—
25#10622487C2212yes—
26#10622485C2211yescharacteristic
27#10622417—21no—
28#10622401—21no—
29C4×D88C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622295C2211yescharacteristic
32C11×#367C2212yes—
33C11×C4⋊C16C2211yescharacteristic
34C11×#358C2212yes—
35#10622202C2212yes—
36#10622147C2212yes—
37#10622142C2212yes—
38Dic11⋊C16C2212yes—
39#10622129C2212yes—
40#10622128C2212yes—
41#10622127C2212yes—
42C4⋊(C11⋊C16)C2211yescharacteristic
43C2×#4343—21no—
44C2×Q8×D11—41no—
45C2×C11×Q16C2311yescharacteristic
46C11×C4⋊Q8—21no—
47C4×Q8×C11—21no—
48Q8×Dic11—21no—
49#66997—41no—
50C2×#4325—21no—
51#66972—22no—
52#66972Q814yescomplemented
53C2×D88C2311yescharacteristic
54C2×C8×D11D411yescharacteristic
55C2×C8×D11C2311yescharacteristic
56#66946—21no—
57#66946—41no—
58#66945—21no—
59#66945—41no—
60C4⋊C4×D11—22no—
61C4⋊C4×D11—41no—
62#66941—22no—
63#66941—41no—
64C4×D44—21no—
65C4×D44—41no—
66C42×D11—41no—
67C42×D11D411yescharacteristic
68#66922—21no—
69C2×C11×C16C2312yes—
70C11×#107—21no—
71C11×#107C2312yes—
72C11×#107C2311yescharacteristic
73C11×#103—21no—
74C4×C8×C11C2311yescharacteristic
75#66899—21no—
76#66885—21no—
77#66882—21no—
78#66882C2312yes—
79#66882C2311yescharacteristic
80C8×Dic11D411yescharacteristic
81C8×Dic11C2311yescharacteristic
82C2×C11⋊C16C2312yes—
83#66873—21no—
84#66872—21no—
85#66871—22no—
86#66871—22no—
87C4×C11⋊C8D411yescharacteristic
88#66862—24no—
89#33629—111nomaximal, Sylow
90C2×Q8×C11—21no—
91C2×Q8×C11—41no—
92#4343—24no—
93#4343—42no—
94Q8×D11—84no—
95C2×D44—21no—
96C2×D44—41no—
97C2×C4×D11—41no—
98C2×C4×D11—41no—
99C2×C4×D11—42no—
100C2×C4×D11—41no—
101C2×C4×D11D811yescharacteristic
102C2×C4×D11D811yescharacteristic
103C2×C4×D11C2×D411yescharacteristic
104C2×Dic22—42no—
105C2×Dic22—41no—
106C11×Q16—21no—
107C11×Q16C2×Q812yescomplemented
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2411yescharacteristic
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C42×C11—41no—
115C42×C11C2×D411yescharacteristic
116#4325—24no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124Dic11⋊C4—42no—
125Dic11⋊C4—42no—
126C4×Dic11—41no—
127C4×Dic11—41no—
128C4×Dic11D811yescharacteristic
129C4×Dic11D811yescharacteristic
130C4×Dic11C2×D411yescharacteristic
131C2×C11⋊C8C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133D88—21no—
134D88C2×Q812yescomplemented
135C8×D11—22no—
136C8×D11C2×Q812yes—
137C8×D11#4112yes—
138C11×C16—22no—
139C11⋊C16—22no—
140C2×#500—111no—
141C4×#135—111no—
142#2227—112no—
143#2226—112no—
144#2225—111no—
145#2225D1111yescharacteristic, complemented
146#2224—111no—
147#2224—111no—
148#2159—112no—
149#2150—111no—
150#2139—112no—
151C22×D11—41no—
152C22×D11C2×D811yescharacteristic
153Q8×C11—22no—
154Q8×C11—41no—
155Q8×C11—82no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C2×Dic11—41no—
163C2×Dic11—42no—
164C2×Dic11C2×D811yescharacteristic
165C2×Dic11C2×D811yescharacteristic
166C2×Dic11C2×D811yescharacteristic
167D44—22no—
168D44—44no—
169D44—41no—
170C4×D11—22no—
171C4×D11—22no—
172C4×D11—44no—
173C4×D11—84no—
174C4×D11—82no—
175C4×D11—82no—
176C4×D11C22⋊Q812yes—
177C4×D11#13712yes—
178Dic22—84no—
179Dic22—82no—
180C8×C11—21no—
181C8×C11C22×Q811yescharacteristic
182C8×C11C2×#4111yescharacteristic
183C11⋊C8—21no—
184C11⋊C8C22⋊Q812yes—
185C2×#135—111no—
186C2×C4⋊Q8—221no—
187C4×#41—221no—
188C2×M32—112no—
189#500—112no—
190#500—111no—
191#500—221no—
192#500—221no—
193#500C2×D1111yescharacteristic
194C4×Q16—111no—
195C4×Q16C2×D1111yescharacteristic
196C4×SD16—221no—
197C4×SD16—221no—
198C4×D8—111no—
199C4×D8—111no—
200#427—111no—
201C2×#107—112no—
202C2×#107—221no—
203#416—221no—
204C2×C4×C8—111no—
205#367—112no—
206#367C2×D1112yes—
207#366—112no—
208#366—112no—
209C4⋊C16—112no—
210C4⋊C16—111no—
211C4⋊C16C2×D1111yescharacteristic
212#358—112no—
213#358C2×D1112yes—
214#357—112no—
215#357—112no—
216C22×C11C22×D811yescharacteristic
217C2×D11—21no—
218C2×D11—21no—
219C2×D11—42no—
220C2×D11—81no—
221C2×D11—81no—
222C2×D11#47412yes—
223C4×C11—21no—
224C4×C11—42no—
225C4×C11—82no—
226C4×C11—81no—
227C4×C11#50912yes—
228C4×C11C2×C22⋊Q811yescharacteristic
229C4×C11C2×#13711yescharacteristic
230Dic11—21no—
231Dic11—82no—
232Dic11—81no—
233Dic11#47412yes—
234Dic11#51012yes—
235C2×#41—221no—
236C22×Q8—441no—
237#135—114no—
238#135—222no—
239C2×Q16C22×D1111yescharacteristic
240C2×SD16—221no—
241C2×D8—111no—
242C22×C8—111no—
243C22×C8—111no—
244C4⋊Q8—21no—
245C4⋊Q8—222no—
246C4⋊Q8—221no—
247C4⋊Q8—441no—
248C4⋊Q8—441no—
249C4×Q8—21no—
250C4×Q8—221no—
251C4×D4—221no—
252C4×D4—221no—
253C4×D4—441no—
254C4×D4—441no—
255#117—221no—
256#117—441no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—441no—
259C2×C42—111no—
260C2×C42—441no—
261M32—224no—
262C2×C16—112no—
263C2×C16C22×D1112yes—
264#107—21no—
265#107—112no—
266#107—111no—
267#107—222no—
268#107—222no—
269#107—221no—
270#107C22×D1112yes—
271#107C22×D1111yescharacteristic
272#106—221no—
273#103—21no—
274#103—221no—
275#102—221no—
276#102—221no—
277C4×C8—111no—
278C4×C8—111no—
279C4×C8—111no—
280C4×C8C22×D1111yescharacteristic
281C2×C11C2×#47411yescharacteristic
282C2×C11C2×#50911yescharacteristic
283C2×C11C2×#51011yescharacteristic
284D11—22no—
285D11—82no—
286#41—224no—
287#41—442no—
288C2×Q8—21no—
289C2×Q8—41no—
290C2×Q8—442no—
291C2×Q8—441no—
292C2×Q8—884no—
293C2×D4—221no—
294C2×D4—441no—
295C22×C4—111no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—441no—
299C22×C4—441no—
300C22×C4—442no—
301C22×C4—441no—
302Q16—21no—
303Q16Q8×D1112yescomplemented
304SD16—224no—
305D8—112no—
306D8—221no—
307C2×C8—111no—
308C2×C8—112no—
309C2×C8—112no—
310C2×C8—111no—
311C2×C8—222no—
312C2×C8D4×D1111yescharacteristic
313C2×C8C23×D1111yescharacteristic
314C4⋊C4—21no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—221no—
319C4⋊C4—222no—
320C4⋊C4—442no—
321C4⋊C4—442no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C22⋊C4—441no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C42—41no—
328C42—111no—
329C42—111no—
330C42—111no—
331C42—441no—
332C42—441no—
333C42D4×D1111yescharacteristic
334C16—22no—
335C16—222no—
336C11#3362911yescharacteristic, complemented, Sylow
337C23—111no—
338C23—441no—
339Q8—22no—
340Q8—41no—
341Q8—82no—
342Q8—884no—
343Q8—882no—
344D4—222no—
345D4—444no—
346D4—441no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—111no—
351C2×C4—111no—
352C2×C4—112no—
353C2×C4—112no—
354C2×C4—111no—
355C2×C4—222no—
356C2×C4—222no—
357C2×C4—444no—
358C2×C4—441no—
359C2×C4—442no—
360C2×C4—882no—
361C2×C4—884no—
362C2×C4—882no—
363C2×C4D8×D1111yescharacteristic
364C2×C4D8×D1111yescharacteristic
365C2×C4C2×D4×D1111yescharacteristic
366C8—21no—
367C8—112no—
368C8—221no—
369C8C2×Q8×D1111yescharacteristic
370C8#41×D1111yescharacteristic
371C22—112no—
372C22—221no—
373C22—221no—
374C22—442no—
375C22—881no—
376C22—881no—
377C22C2×D8×D1111yescharacteristic
378C4—21no—
379C4—42no—
380C4—82no—
381C4—81no—
382C4—112no—
383C4—112no—
384C4—221no—
385C4—882no—
386C4—881no—
387C4#1062252712yes—
388C4D11×C22⋊Q811yescharacteristic
389C4D11×#13711yescharacteristic
390C2—222no—
391C2—882no—
392C2D11×#47411yescharacteristic
393C2C2×#1062252711yescharacteristic
394C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2225C2
socleC22×C11C22×D8
prime radicalC2×#66972C22
hypercenter#2225D11
hypocenterC11#33629
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

Complements

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

NH ≅ G/Ntype
1. D11×#500C2semidirect
3. #13070766C2semidirect
4. #13070762C2semidirect
5. #13070758C2semidirect
6. #13070754C2semidirect
7. #13070750C2semidirect
8. #13070403C2semidirect
9. #13070370C2semidirect
11. C11×#2225C2semidirect
52. #66972Q8semidirect
107. C11×Q16C2×Q8semidirect
134. D88C2×Q8semidirect
145. #2225D11semidirect
303. Q16Q8×D11semidirect
336. C11#33629semidirect

Maximal subgroups

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

subgroupindex
D11×#5002
C4×#669722
#130707662
#130707622
#130707582
#130707542
#130707502
#130704032
#130703702
#130703272
C11×#22252
#3362911