Finite Group Databasebeta

← #14908314

Subgroups — #14908314

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622806C211yesmaximal, characteristic, complemented
2C2×#10622514C211yesmaximal, characteristic, complemented
3#13078282C211yesmaximal, characteristic, complemented
4#13078265C211yesmaximal, characteristic, complemented
5#13070732C212yesmaximal, complemented
6#13070718C212yesmaximal, complemented
7#13070715C212yesmaximal, complemented
8#13070701C212yesmaximal, complemented
9#13070405C211yesmaximal, characteristic, complemented
10C2×#10622147C211yesmaximal, characteristic, complemented
11C11×#2138C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#10623364—21no—
14C22×D88C2211yescharacteristic
15C2×#66954C2211yescharacteristic
16#10623056—21no—
17C22×C11×C16C2211yescharacteristic
18C11×#427C2211yescharacteristic
19#10622845—21no—
20#10622806—24no—
21#10622801C2212yescomplemented
22C2×#66892C2212yes—
23#10622787—22no—
24#10622770C2212yescomplemented
25C2×#66890C2212yes—
26C2×#66882C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28#10622614—21no—
29#10622514—24no—
30C2×#66862C2212yescomplemented
31C2×C16×D11C2212yescomplemented
32#10622496C2212yes—
33#10622496C2212yes—
34#10622478—22no—
35C11×#358C2211yescharacteristic, complemented
36C11×#358C2211yescharacteristic, complemented
37C11×#357C2211yescharacteristic, complemented
38C11×#357C2211yescharacteristic, complemented
39#10622147C2212yes—
40#10622147C2212yes—
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C2×C11×#41—21no—
44C2×#4339D411yescharacteristic
45C22×D44—21no—
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#66992—42no—
55#66991—22no—
56#66983—41no—
57C2×C4⋊Dic11—21no—
58#66977—41no—
59C2×#4318D411yescharacteristic
60C2×D88—22no—
61C2×D88—22no—
62C2×D88—21no—
63C2×D88C2312yes—
64#66954—22no—
65#66954—22no—
66C2×#4313D412yes—
67C2×C8×D11C2312yes—
68#66948—22no—
69#66948—22no—
70#66935—42no—
71#66928—41no—
72#66927—41no—
73C2×C11×C16—22no—
74C2×C11×C16C2311yescharacteristic
75C2×C11×C16C2311yescharacteristic
76C11×#107C2311yescharacteristic
77C11×#107C2311yescharacteristic
78C11×#106—21no—
79#66899—22no—
80#66896—22no—
81#66892—24no—
82#66890—24no—
83#66882—21no—
84#66882C2312yes—
85#66876D414yescomplemented
86C2×C11⋊C16C2312yes—
87#66873—22no—
88#66873—22no—
89#66862—24no—
90C16×D11—24no—
91#33612—111nomaximal, Sylow
92C23×D11—41no—
93C11×#41—42no—
94C11×#41—42no—
95C2×Q8×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C2×C22⋊D11—42no—
101C2×C22⋊D11D812yes—
102C22×Dic11—41no—
103#4339—22no—
104#4339—22no—
105C2×D44—22no—
106C2×D44—42no—
107C2×D44—42no—
108C2×D44—42no—
109C2×D44—41no—
110C2×D44—42no—
111C2×D44D811yescharacteristic
112C2×C4×D11C2×D412yes—
113C2×Dic22D811yescharacteristic
114C11×Q16—21no—
115C11×Q16—21no—
116C11×SD16—42no—
117C11×D8—21no—
118C11×D8—21no—
119C2×C8×C11C2×D412yes—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11#4112yes—
122C2×C8×C11C2411yescharacteristic
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C22⋊C4—41no—
126C42×C11—41no—
127C22⋊Dic11—42no—
128(C2×D11)⋊C4—42no—
129(C2×D11)⋊C4—42no—
130(C2×D11)⋊C4—42no—
131C4⋊Dic11—22no—
132C4⋊Dic11—41no—
133Dic11⋊C4—42no—
134#4318—22no—
135C2×C11⋊C8C2×D412yes—
136D88—22no—
137D88—22no—
138D88—42no—
139#4313—24no—
140C8×D11—22no—
141C8×D11—22no—
142C11×C16—21no—
143C11×C16—21no—
144C11⋊C16C2×D414yes—
145C2×#509—111no—
146C2×#504—111no—
147#3061—111no—
148#3058—111no—
149#2220—112no—
150#2218—112no—
151#2217—112no—
152#2215—112no—
153#2159—111no—
154#2138D1111yescharacteristic, complemented
155C2×#357—111no—
156C23×C11—41no—
157C23×C11C2×D811yescharacteristic
158C22×D11—42no—
159C22×D11—82no—
160C22×D11—161no—
161C22×D11—161no—
162C22×D11C2×D812yes—
163Q8×C11—41no—
164Q8×C11—41no—
165D4×C11—41no—
166D4×C11—41no—
167D4×C11—82no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—82no—
172C2×C4×C11#12112yes—
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11#13512yes—
175C2×C4×C11C22×D411yescharacteristic
176C22⋊D11—24no—
177C22⋊D11—162no—
178C2×Dic11—42no—
179C2×Dic11—161no—
180C2×Dic11C2×D812yes—
181D44—22no—
182D44—42no—
183D44—42no—
184D44—82no—
185D44—162no—
186D44—162no—
187C4×D11—22no—
188C4×D11—22no—
189Dic22—22no—
190C8×C11#12112yes—
191C8×C11C22×D411yescharacteristic
192C8×C11C2×#4111yescharacteristic
193C11⋊C8—22no—
194C2×#135C2×D1111yescharacteristic
195C22×D8—111no—
196C2×#131—111no—
197#537—221no—
198#535—221no—
199#509—224no—
200C2×SD32—112no—
201C2×D16—112no—
202#504—224no—
203C2×M32—111no—
204C2×M32—112no—
205C22×C16—112no—
206C22×C16C2×D1111yescharacteristic
207#469—222no—
208#468—222no—
209#467—112no—
210#466—112no—
211#466—112no—
212#466—112no—
213#427C2×D1111yescharacteristic
214C2×#107—111no—
215#418—221no—
216#417—221no—
217#367—112no—
218#366—112no—
219#358C2×D1111yescharacteristic, complemented
220#358C2×D1111yescharacteristic, complemented
221#357—112no—
222#357—112no—
223#357C2×D1111yescharacteristic, complemented
224#357C2×D1111yescharacteristic, complemented
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11#46612yes—
231C22×C11C22×D811yescharacteristic
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—82no—
236C2×D11—82no—
237C2×D11—82no—
238C2×D11—164no—
239C4×C11—81no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11#46612yes—
243C4×C11C2×#12111yescharacteristic
244C4×C11C2×#13511yescharacteristic
245Dic11—22no—
246Dic11—82no—
247C2×#41—21no—
248C2×#41—111no—
249C22×D4—221no—
250#135—22no—
251#135—22no—
252C2×Q16C22×D1111yescharacteristic
253C2×SD16—21no—
254C2×D8—112no—
255C2×D8—222no—
256C2×D8—222no—
257C2×D8—221no—
258C2×D8C22×D1111yescharacteristic
259#131—222no—
260#131—222no—
261C2×M16—111no—
262C2×M16—112no—
263C22×C8—112no—
264C22×C8C22×D1111yescharacteristic
265#127—441no—
266#124—441no—
267C22⋊Q8—222no—
268C22⋊Q8—441no—
269#121—222no—
270#121—222no—
271#121—222no—
272#121—441no—
273#121—442no—
274#120—442no—
275#117—21no—
276C2×C4⋊C4—221no—
277SD32—224no—
278D16—224no—
279M32—114no—
280M32—224no—
281C2×C16—22no—
282C2×C16—112no—
283C2×C16—224no—
284C2×C16C22×D1111yescharacteristic
285C2×C16C22×D1111yescharacteristic
286#107—112no—
287#107—221no—
288#107C22×D1111yescharacteristic
289#107C22×D1111yescharacteristic
290#106—21no—
291#103—222no—
292#102—222no—
293#102—222no—
294#102—222no—
295C2×C11—22no—
296C2×C11—161no—
297C2×C11C2×#46611yescharacteristic
298C2×C11#341511yescharacteristic
299C2×C11#341611yescharacteristic
300D11—42no—
301D11—162no—
302C24—441no—
303#41—42no—
304#41—42no—
305#41—222no—
306#41—222no—
307C2×Q8—21no—
308C2×Q8—111no—
309C2×D4—21no—
310C2×D4—41no—
311C2×D4—112no—
312C2×D4—111no—
313C2×D4—222no—
314C2×D4—442no—
315C2×D4—442no—
316C2×D4—442no—
317C2×D4—442no—
318C2×D4—441no—
319C2×D4—442no—
320C22×C4—41no—
321C22×C4—112no—
322C22×C4—441no—
323C22×C4D4×D1111yescharacteristic
324Q16—21no—
325Q16—21no—
326SD16—42no—
327D8—21no—
328D8—21no—
329D8—222no—
330D8—222no—
331D8—442no—
332M16—222no—
333M16—224no—
334C2×C8—112no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8#433912yes—
338C2×C8D4×D1111yescharacteristic
339C2×C8D4×D1112yes—
340C2×C8C23×D1111yescharacteristic
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—222no—
344C4⋊C4—442no—
345C4⋊C4—441no—
346C22⋊C4—41no—
347C22⋊C4—442no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C22⋊C4—442no—
351C42—41no—
352C16—21no—
353C16—21no—
354C16—114no—
355C11#3361211yescharacteristic, complemented, Sylow
356C23—41no—
357C23—112no—
358C23—442no—
359C23—882no—
360C23—1761no—
361C23—1761no—
362C23D8×D1111yescharacteristic
363Q8—41no—
364Q8—41no—
365Q8—222no—
366D4—41no—
367D4—41no—
368D4—82no—
369D4—224no—
370D4—222no—
371D4—442no—
372D4—442no—
373D4—882no—
374D4—1762no—
375D4—1762no—
376D4—1762no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—82no—
381C2×C4—112no—
382C2×C4—222no—
383C2×C4—222no—
384C2×C4—442no—
385C2×C4—1761no—
386C2×C4#6693712yes—
387C2×C4D8×D1111yescharacteristic
388C2×C4#6696912yes—
389C2×C4C2×D4×D1111yescharacteristic
390C8—222no—
391C8#6693712yes—
392C8C2×#433911yescharacteristic
393C8C2×D4×D1111yescharacteristic
394C22—21no—
395C22—21no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—222no—
400C22—222no—
401C22—222no—
402C22—882no—
403C22—882no—
404C22—882no—
405C22—1764no—
406C22#1062238812yes—
407C22C2×D8×D1111yescharacteristic
408C4—81no—
409C4—81no—
410C4—81no—
411C4—222no—
412C4—882no—
413C4#1062238812yes—
414C4C2×#6693711yescharacteristic
415C4C2×#6696911yescharacteristic
416C2—22no—
417C2—161no—
418C2—442no—
419C2—1762no—
420C2C2×#1062238811yescharacteristic
421C2#1308175411yescharacteristic
422C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2138C2
socleC22×C11C22×D8
hypercenter#2138D11
hypocenterC11#33612
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2138

Complements

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

NH ≅ G/Ntype
1. C2×#10622806C2semidirect
2. C2×#10622514C2semidirect
3. #13078282C2semidirect
4. #13078265C2semidirect
5. #13070732C2semidirect
6. #13070718C2semidirect
7. #13070715C2semidirect
8. #13070701C2semidirect
9. #13070405C2semidirect
10. C2×#10622147C2semidirect
11. C11×#2138C2semidirect
21. #10622801C22semidirect
24. #10622770C22semidirect
30. C2×#66862C22semidirect
31. C2×C16×D11C22semidirect
35. C11×#358C22semidirect
36. C11×#358C22semidirect
37. C11×#357C22semidirect
38. C11×#357C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
85. #66876D4semidirect
154. #2138D11semidirect
219. #358C2×D11semidirect
220. #358C2×D11semidirect
223. #357C2×D11semidirect
224. #357C2×D11semidirect
355. C11#33612semidirect

Maximal subgroups

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

subgroupindex
C2×#106228062
C2×#106225142
#130782822
#130782652
#130707322
#130707182
#130707152
#130707012
#130704052
C2×#106221472
C11×#21382
#3361211