Finite Group Databasebeta

← #14908131

Subgroups — #14908131

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×#10622792C211yesmaximal, characteristic, complemented
2C2×#10622807C211yesmaximal, characteristic
3#13077493C211yesmaximal, characteristic, complemented
4#13070675C212yesmaximal, complemented
5#13070668C212yesmaximal, complemented
6#13070663C212yesmaximal, complemented
7#13070658C212yesmaximal, complemented
8#13070375C211yesmaximal, characteristic, complemented
9#13070328C211yesmaximal, characteristic, complemented
10C2×#10622202C211yesmaximal, characteristic, complemented
11C11×#3156C211yesmaximal, characteristic, complemented
12C2×C11×#137—21no—
13C2×C11×#135C2211yescharacteristic
14C22×C11×Q16C2211yescharacteristic
15C11×#536—21no—
16C2×#66957C2211yescharacteristic
17#10623054—21no—
18C11×#497—22no—
19C11×#495C2212yes—
20C11×#494C2212yes—
21C11×#405C2211yescharacteristic
22#10622807—24no—
23C2×#66893C2211yescharacteristic
24C2×#66893C2212yes—
25#10622792—24no—
26C2×#66892C2211yescharacteristic
27C2×#66892C2212yes—
28C2×#66891C2211yescharacteristic
29C2×#66890C2211yescharacteristic
30#10622746—21no—
31C2×#66882C2211yescharacteristic
32C2×#66876C2211yescharacteristic
33C22×C11⋊C16C2211yescharacteristic
34#10622323—22no—
35C4×Dic44C2212yes—
36C4×D88C2212yes—
37#10622202C2212yes—
38#10622202C2212yes—
39#10622202C2212yes—
40#10622200C2212yes—
41C4⋊(C11⋊C16)C2212yes—
42C4⋊(C11⋊C16)C2212yes—
43C2×C11×#41—21no—
44C22×Q8×C11—21no—
45C2×#4339—21no—
46C11×#137—44no—
47C11×#135—22no—
48C11×#135—22no—
49C2×C11×Q16—22no—
50C2×C11×Q16—22no—
51C2×C11×Q16—21no—
52C2×C11×Q16—22no—
53C2×C11×Q16C2311yescharacteristic
54C2×C11×Q16C2312yes—
55C2×C11×SD16—22no—
56C2×C11×SD16—21no—
57C2×C11×D8C2311yescharacteristic
58C2×C11×M16D411yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—22no—
61C11×#124—22no—
62C11×#123—42no—
63C11×C22⋊Q8—41no—
64C11×C22⋊Q8—41no—
65C11×#117D411yescharacteristic
66C2×C4⋊Dic11—21no—
67C2×Dic44C2311yescharacteristic
68#66957—22no—
69#66957D414yes—
70C2×D88C2311yescharacteristic
71C2×#4314—21no—
72#66945—41no—
73C4⋊C4×D11—41no—
74(C22⋊D11)⋊C4—42no—
75C4×D44—22no—
76C4×Dic22—22no—
77C11×#97D412yes—
78C4×C8×C11C2312yes—
79#66893—24no—
80#66893—22no—
81#66892—24no—
82#66892—22no—
83#66891—22no—
84#66890—22no—
85#66885—22no—
86#66882—21no—
87#66882C2312yes—
88#66880—22no—
89#66876—22no—
90C2×C11⋊C16—22no—
91C2×C11⋊C16C2311yescharacteristic
92C2×C11⋊C16C2311yescharacteristic
93C2×C11⋊C16C2312yes—
94#33590—111nomaximal, Sylow
95C11×#41—42no—
96C11×#41—42no—
97C2×Q8×C11—22no—
98C2×Q8×C11—21no—
99C2×Q8×C11—41no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C2×D4×C11—21no—
103C2×D4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11C2×D411yescharacteristic
107C2×C22⋊D11—41no—
108C22×Dic11—41no—
109#4339—24no—
110#4339—42no—
111C2×D44—21no—
112C2×C4×D11—41no—
113C2×C4×D11—42no—
114C2×Dic22—21no—
115C11×Q16—22no—
116C11×Q16—21no—
117C11×Q16—22no—
118C11×Q16—21no—
119C11×Q16—44no—
120C11×Q16—42no—
121C11×SD16—44no—
122C11×SD16—42no—
123C11×D8—21no—
124C11×D8—21no—
125C11×M16—22no—
126C2×C8×C11C2×D412yes—
127C2×C8×C11C2×D412yes—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11#4112yes—
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4—42no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4D811yescharacteristic
134C11×C4⋊C4D811yescharacteristic
135C11×C22⋊C4—42no—
136C11×C22⋊C4—42no—
137C11×C22⋊C4D812yes—
138C42×C11C2×D412yes—
139(C2×D11)⋊C4—42no—
140C4⋊Dic11—22no—
141C4⋊Dic11—41no—
142Dic11⋊C4—42no—
143C4×Dic11—42no—
144Dic44—21no—
145Dic44C2×D412yes—
146D88—21no—
147D88C2×D412yes—
148#4314—24no—
149C11⋊C16—21no—
150C11⋊C16—21no—
151C11⋊C16—22no—
152C2×#510—111no—
153C2×#508—111no—
154#3156D1111yescharacteristic, complemented
155#2951—111no—
156#2211—112no—
157#2210—112no—
158#2209—112no—
159#2208—112no—
160#2151—111no—
161#2139—111no—
162C2×#358—111no—
163C23×C11—41no—
164C23×C11C2×D811yescharacteristic
165C22×D11—41no—
166Q8×C11—41no—
167Q8×C11—42no—
168Q8×C11—42no—
169Q8×C11—41no—
170Q8×C11—82no—
171D4×C11—41no—
172D4×C11—41no—
173D4×C11—82no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—82no—
177C2×C4×C11—82no—
178C2×C4×C11#12112yes—
179C2×C4×C11C2×D812yes—
180C2×C4×C11C2×D812yes—
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11AGL(1,ℤ/8)12yes—
183C2×C4×C11C22×D411yescharacteristic
184C22⋊D11—44no—
185C2×Dic11—41no—
186C2×Dic11—42no—
187C2×Dic11—161no—
188D44—22no—
189D44—41no—
190C4×D11—44no—
191C4×D11—162no—
192Dic22—22no—
193Dic22—41no—
194C8×C11—22no—
195C8×C11#12112yes—
196C8×C11C22×D411yescharacteristic
197C8×C11C2×#4111yescharacteristic
198C2×#137—21no—
199C2×#135—111no—
200C2×#135C2×D1111yescharacteristic
201C22×Q16C2×D1111yescharacteristic
202#536—21no—
203#520—221no—
204#510—224no—
205#508—224no—
206C2×Q32—111no—
207C2×Q32—112no—
208C2×SD32—111no—
209C2×SD32—112no—
210C2×SD32—111no—
211C2×D16—111no—
212C2×M32—111no—
213C22×C16—111no—
214#497—22no—
215#495C2×D1112yes—
216#494C2×D1112yes—
217#440—222no—
218C4×Q16—112no—
219C4×D8—112no—
220C2×#107—111no—
221#417—221no—
222#405C2×D1111yescharacteristic
223C4⋊C16—112no—
224C4⋊C16—112no—
225#358—112no—
226#358—112no—
227#358—112no—
228#357—112no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11#45912yes—
235C22×C11C22×D811yescharacteristic
236C2×D11—42no—
237C2×D11—81no—
238C2×D11—81no—
239C4×C11—22no—
240C4×C11—22no—
241C4×C11—81no—
242C4×C11—82no—
243C4×C11#45912yes—
244C4×C11C2×#12111yescharacteristic
245C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
246Dic11—42no—
247Dic11—82no—
248C2×#41—21no—
249C2×#41—221no—
250C22×Q8—21no—
251#137—44no—
252#135—22no—
253#135—22no—
254#135—114no—
255#135—222no—
256C2×Q16—22no—
257C2×Q16—22no—
258C2×Q16—21no—
259C2×Q16—22no—
260C2×Q16—111no—
261C2×Q16C22×D1112yes—
262C2×Q16C22×D1111yescharacteristic
263C2×SD16—21no—
264C2×SD16—22no—
265C2×SD16—221no—
266C2×D8—111no—
267C2×D8C22×D1111yescharacteristic
268C2×M16C22⋊D1111yescharacteristic
269C22×C8C22×D1111yescharacteristic
270C4⋊Q8—22no—
271#124—22no—
272#123—42no—
273C22⋊Q8—41no—
274C22⋊Q8—41no—
275C4×Q8—222no—
276C4×D4—222no—
277C4×D4—442no—
278#117—441no—
279#117C22⋊D1111yescharacteristic
280C2×C4⋊C4—221no—
281C2×C4⋊C4—441no—
282Q32—222no—
283Q32—224no—
284SD32—222no—
285SD32—222no—
286SD32—224no—
287D16—222no—
288M32—222no—
289C2×C16—112no—
290C2×C16—111no—
291C2×C16—111no—
292C2×C16—222no—
293#107—112no—
294#107—221no—
295#103—222no—
296#102—222no—
297#97C22⋊D1112yes—
298C4×C8C22×D1112yes—
299C2×C11—22no—
300C2×C11—161no—
301C2×C11C2×#45911yescharacteristic
302C2×C11#341611yescharacteristic
303C2×C11#341711yescharacteristic
304D11—82no—
305#41—42no—
306#41—42no—
307#41—224no—
308#41—442no—
309C2×Q8—22no—
310C2×Q8—21no—
311C2×Q8—41no—
312C2×Q8—42no—
313C2×Q8—42no—
314C2×Q8—221no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—221no—
318C2×D4—441no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—441no—
322C22×C4—441no—
323C22×C4—442no—
324C22×C4C2×C22⋊D1111yescharacteristic
325Q16—22no—
326Q16—21no—
327Q16—22no—
328Q16—21no—
329Q16—44no—
330Q16—42no—
331Q16—112no—
332Q16—221no—
333SD16—44no—
334SD16—42no—
335SD16—224no—
336D8—21no—
337D8—21no—
338D8—112no—
339D8—221no—
340M16—22no—
341C2×C8D4×D1112yes—
342C2×C8#434112yes—
343C2×C8C2×C22⋊D1112yes—
344C2×C8C2×C22⋊D1111yescharacteristic
345C2×C8C23×D1111yescharacteristic
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—222no—
349C4⋊C4—441no—
350C4⋊C4—442no—
351C4⋊C4#432311yescharacteristic
352C4⋊C4#432311yescharacteristic
353C22⋊C4—42no—
354C22⋊C4—42no—
355C22⋊C4—442no—
356C22⋊C4#432312yes—
357C42—442no—
358C42C2×C22⋊D1112yes—
359C16—221no—
360C16—221no—
361C16—222no—
362C11#3359011yescharacteristic, complemented, Sylow
363C23—41no—
364C23—441no—
365C23C2×#432311yescharacteristic
366Q8—42no—
367Q8—41no—
368Q8—41no—
369Q8—42no—
370Q8—82no—
371Q8—222no—
372Q8—441no—
373D4—41no—
374D4—41no—
375D4—82no—
376D4—222no—
377D4—444no—
378D4—441no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—441no—
384C2×C4—444no—
385C2×C4—442no—
386C2×C4—1762no—
387C2×C4—1761no—
388C2×C4C2×#432312yes—
389C2×C4C2×#432312yes—
390C2×C4C2×#432311yescharacteristic
391C2×C4#6698512yes—
392C2×C4#6699112yes—
393C2×C4C22×C22⋊D1111yescharacteristic
394C8—22no—
395C8#6699112yes—
396C8C2×D4×D1111yescharacteristic
397C8C2×#434111yescharacteristic
398C22—21no—
399C22—21no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—442no—
404C22—881no—
405C22—881no—
406C22#1062268512yes—
407C22C22×#432311yescharacteristic
408C4—22no—
409C4—22no—
410C4—81no—
411C4—82no—
412C4—442no—
413C4—882no—
414C4#1062268512yes—
415C4C2×#6698511yescharacteristic
416C4C2×#6699111yescharacteristic
417C2—22no—
418C2—161no—
419C2—882no—
420C2C2×#1062268511yescharacteristic
421C2#1308176011yescharacteristic
422C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3156C2
socleC22×C11C22×D8
prime radicalC2×#10622807C2
hypercenter#3156D11
hypocenterC11#33590
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3156

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
3. #13077493C2semidirect
4. #13070675C2semidirect
5. #13070668C2semidirect
6. #13070663C2semidirect
7. #13070658C2semidirect
8. #13070375C2semidirect
9. #13070328C2semidirect
10. C2×#10622202C2semidirect
11. C11×#3156C2semidirect
154. #3156D11semidirect
362. C11#33590semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
C2×#106228072
#130774932
#130706752
#130706682
#130706632
#130706582
#130703752
#130703282
C2×#106222022
C11×#31562
#3359011