Finite Group Databasebeta

← #14908239

Subgroups — #14908239

Order 2816.

690 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
1C2×#10622807C211yesmaximal, characteristic, complemented
2C22×#66862C211yesmaximal, characteristic, complemented
3#13078198C211yesmaximal, characteristic, complemented
4#13078193C211yesmaximal, characteristic, complemented
5#13070732C212yesmaximal, complemented
6#13070728C212yesmaximal, complemented
7#13070723C212yesmaximal, complemented
8#13070718C212yesmaximal, complemented
9#13070398C211yesmaximal, characteristic, complemented
10#13070324C211yesmaximal, characteristic, complemented
11C11×#2138C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#10623359—21no—
14C2×#66957C2211yescharacteristic
15C22×C8×D11C2211yescharacteristic
16#10623055—21no—
17C22×C11×C16C2211yescharacteristic
18C11×#427C2211yescharacteristic
19#10622846—21no—
20#10622807—24no—
21#10622801C2212yes—
22C2×#66893C2211yescharacteristic, complemented
23C2×#66892C2211yescharacteristic, complemented
24#10622784—22no—
25#10622770C2212yes—
26C2×#66891C2211yescharacteristic, complemented
27C2×#66890C2211yescharacteristic, complemented
28#10622719C2211yescharacteristic
29C22×C11⋊C16C2211yescharacteristic
30#10622615—21no—
31C2×#66862—24no—
32C2×#66862C2212yes—
33C2×#66862C2212yes—
34#10622500C2212yes—
35#10622496C2212yes—
36#10622477—22no—
37C11×#358C2212yescomplemented
38C11×#357C2212yescomplemented
39#10622147C2212yescomplemented
40#10622141C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C2×C11×#41—21no—
44C2×#4339—21no—
45C22×C4×D11D411yescharacteristic
46C11×#135—22no—
47C11×#135—22no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×#117—21no—
53#66999—22no—
54#66991—22no—
55#66990—41no—
56#66988—41no—
57C4×C22⋊D11—42no—
58#66979—21no—
59C22×C11⋊C8D411yescharacteristic
60C2×Dic44C2311yescharacteristic
61#66957—22no—
62#66957—22no—
63C2×D88C2311yescharacteristic
64C2×#4314—21no—
65C2×C8×D11—22no—
66C2×C8×D11—22no—
67C2×C8×D11D412yes—
68C2×C8×D11C2312yes—
69#66950—22no—
70#66948—22no—
71#66939—41no—
72#66935—41no—
73C4×D44—42no—
74C2×C11×C16—22no—
75C2×C11×C16C2312yes—
76C11×#107C2312yes—
77C11×#106—21no—
78#66899—22no—
79#66896—22no—
80#66893—22no—
81#66892—22no—
82#66891—22no—
83#66890—22no—
84#66882C2312yes—
85#66881—21no—
86C2×C11⋊C16D414yescomplemented
87C2×C11⋊C16C2311yescharacteristic
88C2×C11⋊C16C2311yescharacteristic
89#66874—22no—
90#66873—22no—
91#66862—24no—
92#66862—24no—
93#33604—111nomaximal, Sylow
94C23×D11D811yescharacteristic
95C11×#41—42no—
96C11×#41—42no—
97C2×Q8×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103C2×C22⋊D11—42no—
104C22×Dic11D811yescharacteristic
105#4339—42no—
106#4339—42no—
107C2×D44—21no—
108C2×D44—42no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—41no—
112C2×C4×D11D812yes—
113C2×C4×D11C2×D412yes—
114C2×Dic22—21no—
115C11×Q16—21no—
116C11×Q16—21no—
117C11×SD16—42no—
118C11×D8—21no—
119C11×D8—21no—
120C2×C8×C11C2×D412yes—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11#4112yes—
123C2×C8×C11C2411yescharacteristic
124C11×C4⋊C4—22no—
125C11×C22⋊C4—41no—
126C42×C11—41no—
127C22⋊Dic11—42no—
128C22⋊Dic11—41no—
129(C2×D11)⋊C4—42no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—42no—
132C4⋊Dic11—22no—
133C4⋊Dic11—42no—
134Dic11⋊C4—42no—
135C4×Dic11—41no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8C2×D412yes—
138Dic44—21no—
139Dic44—21no—
140D88—21no—
141D88—21no—
142#4314—42no—
143C8×D11—24no—
144C8×D11—22no—
145C8×D11—22no—
146C11×C16—22no—
147C11⋊C16C2×D412yes—
148C11⋊C16C2×D412yes—
149C2×#508—111no—
150C22×M32—111no—
151#3050—111no—
152#3050—111no—
153#2220—112no—
154#2220—112no—
155#2219—112no—
156#2218—112no—
157#2158—111no—
158#2138—111no—
159#2138D1111yescharacteristic, complemented
160C23×C11—41no—
161C23×C11C2×D811yescharacteristic
162C22×D11—22no—
163C22×D11—42no—
164C22×D11—41no—
165C22×D11C2×D812yes—
166Q8×C11—41no—
167Q8×C11—41no—
168D4×C11—41no—
169D4×C11—41no—
170D4×C11—82no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—82no—
174C2×C4×C11#12112yes—
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11#13512yes—
177C2×C4×C11C22×D411yescharacteristic
178C22⋊D11—84no—
179C22⋊D11—82no—
180C2×Dic11—22no—
181C2×Dic11—42no—
182C2×Dic11—41no—
183C2×Dic11C2×D812yes—
184D44—41no—
185D44—41no—
186D44—84no—
187C4×D11—22no—
188C4×D11—22no—
189C4×D11—24no—
190C4×D11—82no—
191Dic22—41no—
192Dic22—41no—
193C8×C11#12112yes—
194C8×C11C22×D411yescharacteristic
195C8×C11C2×#4111yescharacteristic
196C11⋊C8—22no—
197C2×#135—111no—
198C2×#135C2×D1111yescharacteristic
199C23×C8—111no—
200#525—221no—
201#525—221no—
202#508—224no—
203C2×Q32—111no—
204C2×SD32—111no—
205C2×SD32—111no—
206C2×D16—111no—
207C2×M32—112no—
208C2×M32—112no—
209C2×M32—224no—
210C22×C16—111no—
211C22×C16C2×D1111yescharacteristic
212#467—112no—
213#467—112no—
214#466—112no—
215#466—112no—
216#465—222no—
217#465—222no—
218#427—111no—
219#427C2×D1111yescharacteristic
220#416—221no—
221#416—221no—
222#367—112no—
223#366—112no—
224#358—112no—
225#358C2×D1112yescomplemented
226#357—112no—
227#357C2×D1112yescomplemented
228C22×C11—22no—
229C22×C11—82no—
230C22×C11—81no—
231C22×C11#46612yes—
232C22×C11C22×D811yescharacteristic
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—22no—
236C2×D11—44no—
237C2×D11—82no—
238C2×D11—81no—
239C4×C11—82no—
240C4×C11—81no—
241C4×C11#46612yes—
242C4×C11C2×#12111yescharacteristic
243C4×C11C2×#13511yescharacteristic
244Dic11—22no—
245Dic11—82no—
246Dic11—81no—
247C2×#41—21no—
248C2×#41—221no—
249C23×C4—111no—
250#135—22no—
251#135—22no—
252#135—222no—
253#135—222no—
254C2×Q16—111no—
255C2×Q16C22×D1111yescharacteristic
256C2×SD16—21no—
257C2×SD16—221no—
258C2×D8—111no—
259C2×D8C22×D1111yescharacteristic
260C22×C8—111no—
261C22×C8—112no—
262C22×C8—112no—
263C22×C8—222no—
264C22×C8—222no—
265C22×C8C22×D1111yescharacteristic
266#123—441no—
267#123—441no—
268C22⋊Q8—222no—
269C22⋊Q8—222no—
270#121—222no—
271#121—222no—
272#120—441no—
273#120—441no—
274C4×D4—442no—
275C4×D4—442no—
276#117—21no—
277#117—221no—
278Q32—222no—
279SD32—222no—
280SD32—222no—
281D16—222no—
282M32—224no—
283M32—224no—
284C2×C16—22no—
285C2×C16—114no—
286C2×C16—111no—
287C2×C16—111no—
288C2×C16C22×D1112yes—
289#107—112no—
290#107C22×D1112yes—
291#106—21no—
292#106—221no—
293#103—222no—
294#103—222no—
295#102—222no—
296#102—222no—
297C2×C11—22no—
298C2×C11—161no—
299C2×C11C2×#46611yescharacteristic
300C2×C11#341412yes—
301D11—42no—
302D11—161no—
303C24—111no—
304#41—42no—
305#41—42no—
306#41—442no—
307#41—442no—
308C2×Q8—21no—
309C2×Q8—221no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4—221no—
313C2×D4—442no—
314C2×D4—442no—
315C2×D4—441no—
316C22×C4—41no—
317C22×C4—111no—
318C22×C4—112no—
319C22×C4—112no—
320C22×C4—222no—
321C22×C4—222no—
322C22×C4—441no—
323C22×C4D4×D1111yescharacteristic
324Q16—21no—
325Q16—21no—
326Q16—221no—
327Q16—221no—
328SD16—42no—
329SD16—442no—
330D8—21no—
331D8—21no—
332D8—221no—
333D8—221no—
334C2×C8—112no—
335C2×C8—222no—
336C2×C8—224no—
337C2×C8—222no—
338C2×C8—222no—
339C2×C8#433912yes—
340C2×C8D4×D1111yescharacteristic
341C2×C8D4×D1112yes—
342C2×C8C23×D1111yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—222no—
345C4⋊C4—442no—
346C4⋊C4—442no—
347C22⋊C4—41no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C22⋊C4—442no—
351C22⋊C4—442no—
352C22⋊C4—441no—
353C42—41no—
354C42—441no—
355C16—22no—
356C16—112no—
357C16—112no—
358C11#3360411yescharacteristic, complemented, Sylow
359C23—41no—
360C23—112no—
361C23—222no—
362C23—442no—
363C23—441no—
364C23D8×D1111yescharacteristic
365Q8—41no—
366Q8—41no—
367Q8—441no—
368Q8—441no—
369D4—41no—
370D4—41no—
371D4—82no—
372D4—441no—
373D4—441no—
374D4—884no—
375D4—884no—
376D4—882no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—82no—
380C2×C4—112no—
381C2×C4—222no—
382C2×C4—222no—
383C2×C4—222no—
384C2×C4—224no—
385C2×C4—442no—
386C2×C4—441no—
387C2×C4—882no—
388C2×C4#6693712yes—
389C2×C4D8×D1111yescharacteristic
390C2×C4#6696912yes—
391C2×C4C2×D4×D1111yescharacteristic
392C8—222no—
393C8#6693712yes—
394C8C2×#433911yescharacteristic
395C8C2×D4×D1111yescharacteristic
396C22—22no—
397C22—82no—
398C22—81no—
399C22—222no—
400C22—222no—
401C22—222no—
402C22—444no—
403C22—882no—
404C22—881no—
405C22#1062238812yes—
406C22C2×D8×D1111yescharacteristic
407C4—82no—
408C4—81no—
409C4—222no—
410C4—882no—
411C4—881no—
412C4#1062238812yes—
413C4C2×#6693711yescharacteristic
414C4C2×#6696911yescharacteristic
415C2—22no—
416C2—161no—
417C2—442no—
418C2—1761no—
419C2C2×#1062238811yescharacteristic
420C2#1308174912yes—
subgroupG/H
centerC2×C4D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2138C2
socleC22×C11C22×D8
hypercenter#2138D11
hypocenterC11#33604
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2138

Complements

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

NH ≅ G/Ntype
1. C2×#10622807C2semidirect
2. C22×#66862C2semidirect
3. #13078198C2semidirect
4. #13078193C2semidirect
5. #13070732C2semidirect
6. #13070728C2semidirect
7. #13070723C2semidirect
8. #13070718C2semidirect
9. #13070398C2semidirect
10. #13070324C2semidirect
11. C11×#2138C2semidirect
22. C2×#66893C22semidirect
23. C2×#66892C22semidirect
26. C2×#66891C22semidirect
27. C2×#66890C22semidirect
37. C11×#358C22semidirect
38. C11×#357C22semidirect
39. #10622147C22semidirect
40. #10622141C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
86. C2×C11⋊C16D4semidirect
159. #2138D11semidirect
225. #358C2×D11semidirect
227. #357C2×D11semidirect
358. C11#33604semidirect

Maximal subgroups

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

subgroupindex
C2×#106228072
C22×#668622
#130781982
#130781932
#130707322
#130707282
#130707232
#130707182
#130703982
#130703242
C11×#21382
#3360411