Finite Group Databasebeta

← #14908413

Subgroups — #14908413

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66957C211yesmaximal, characteristic
2#13070777C212yesmaximal, complemented
3#13070770C212yesmaximal, complemented
4#13070765C211yesmaximal, characteristic, complemented
5#13070760C211yesmaximal, characteristic, complemented
6#13070755C211yesmaximal, characteristic, complemented
7#13070750C211yesmaximal, characteristic, complemented
8#13070398C212yesmaximal, complemented
9C2×C4⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
10#13070321C212yesmaximal
11C11×#3160C211yesmaximal, characteristic, complemented
12C11×#533—21no—
13C2×#66957C2211yescharacteristic
14C4×#4339—21no—
15C11×#500C2211yescharacteristic
16C11×#500C2211yescharacteristic
17C11×#499—21no—
18C11×#499C2212yes—
19C11×#498—21no—
20C11×#427—21no—
21C11×#427C2212yes—
22C2×C4×C8×C11C2211yescharacteristic
23#10622726—21no—
24#10622719C2211yescharacteristic
25C22×C11⋊C16C2212yes—
26C4×Dic44C2211yescharacteristic
27C4×Dic44C2211yescharacteristic
28C4×D88C2211yescharacteristic
29C4×D88C2211yescharacteristic
30C4×#4314—21no—
31C4×#4314—21no—
32#10622130C2212yes—
33#10622130C2212yes—
34#10622129C2212yes—
35#10622129C2212yes—
36#10622128C2212yes—
37#10622128C2212yes—
38#10622127C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C4⋊(C11⋊C16)C2211yescharacteristic
42C4⋊(C11⋊C16)C2212yes—
43C2×#4339—21no—
44C22×C8×C11D411yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×#125—22no—
49C11×C22⋊Q8—41no—
50C11×C22⋊Q8—41no—
51C4×Q8×C11—41no—
52C4×Q8×C11—41no—
53C11×#117—22no—
54C2×C42×C11D411yescharacteristic
55C4×C22⋊D11—41no—
56C4×C22⋊D11—41no—
57#66979—21no—
58C2×Dic44C2311yescharacteristic
59#66957—22no—
60#66957Q814yescomplemented
61C2×D88C2311yescharacteristic
62C2×#4314—21no—
63C4×D44—21no—
64C4×D44—21no—
65#66925—41no—
66C42×D11—41no—
67C4×Dic22—21no—
68C4×Dic22—21no—
69C11×#107—21no—
70C11×#107—21no—
71C11×#107C2312yes—
72C11×#107C2312yes—
73C11×#106—22no—
74C11×#106—22no—
75C4×C8×C11D411yescharacteristic
76C4×C8×C11D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#66885—21no—
80#66885—21no—
81#66882C2311yescharacteristic
82#66882C2311yescharacteristic
83#66881—21no—
84#66880—21no—
85#66880—21no—
86C2×C11⋊C16—24no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33626—111nomaximal, Sylow
90C2×Q8×C11—41no—
91C2×Q8×C11—41no—
92C22×C4×C11D811yescharacteristic
93C22×C4×C11D811yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—41no—
96#4339—24no—
97#4339—42no—
98C2×D44—21no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×Dic22—21no—
103C2×C8×C11—22no—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×Q812yes—
108C2×C8×C11#4112yes—
109C2×C8×C11C2411yescharacteristic
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4—42no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—42no—
117C42×C11—42no—
118C42×C11D811yescharacteristic
119C42×C11D811yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C22⋊Dic11—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129C4×Dic11—41no—
130C4×Dic11—41no—
131C4×Dic11—41no—
132Dic44—21no—
133Dic44C2×Q812yes—
134D88—21no—
135D88C2×Q812yes—
136#4314—24no—
137C11⋊C16—22no—
138C11⋊C16—22no—
139#3160D1111yescharacteristic, complemented
140C4×#135—111no—
141#2229—112no—
142#2228—112no—
143#2227—111no—
144#2226—111no—
145#2225—111no—
146#2224—111no—
147#2158—112no—
148C2×C4⋊C16—111no—
149#2138—112no—
150C23×C11C2×D811yescharacteristic
151C22×D11—41no—
152Q8×C11—82no—
153Q8×C11—82no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11C22⋊Q812yes—
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C2×D811yescharacteristic
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11#13712yes—
165C2×C4×C11C22×D411yescharacteristic
166C22⋊D11—44no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170D44—22no—
171D44—41no—
172C4×D11—44no—
173C4×D11—82no—
174C4×D11—82no—
175Dic22—22no—
176Dic22—41no—
177C8×C11—21no—
178C8×C11—21no—
179C8×C11C22⋊Q812yes—
180C8×C11C22×Q811yescharacteristic
181C8×C11C2×#4111yescharacteristic
182C2×#135—111no—
183#533—21no—
184C4×#41—221no—
185C22×C16—112no—
186#500C2×D1111yescharacteristic
187#500C2×D1111yescharacteristic
188#499—21no—
189#499C2×D1112yes—
190#498—21no—
191C4×Q16—111no—
192C4×Q16—111no—
193C4×SD16—221no—
194C4×SD16—221no—
195C4×D8—111no—
196C4×D8—111no—
197#427—21no—
198#427—111no—
199#427C2×D1112yes—
200#416—221no—
201C2×C4×C8C2×D1111yescharacteristic
202#367—112no—
203#367—112no—
204#366—112no—
205#366—112no—
206C4⋊C16—111no—
207C4⋊C16—111no—
208C4⋊C16—112no—
209#358—112no—
210#358—112no—
211#357—112no—
212#357—112no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11#47412yes—
216C22×C11C22×D811yescharacteristic
217C2×D11—42no—
218C2×D11—81no—
219C2×D11—81no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—82no—
224C4×C11—82no—
225C4×C11#47412yes—
226C4×C11#50812yes—
227C4×C11C2×C22⋊Q811yescharacteristic
228C4×C11C2×#13711yescharacteristic
229Dic11—42no—
230Dic11—81no—
231Dic11—81no—
232C2×#41—221no—
233#135—114no—
234#135—222no—
235C2×Q16—111no—
236C2×SD16—221no—
237C2×D8—111no—
238C22×C8C22⋊D1111yescharacteristic
239C22×C8C22×D1111yescharacteristic
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242#125—22no—
243C22⋊Q8—41no—
244C22⋊Q8—41no—
245C4×Q8—41no—
246C4×Q8—41no—
247C4×Q8—221no—
248C4×Q8—221no—
249C4×D4—221no—
250C4×D4—221no—
251C4×D4—441no—
252C4×D4—441no—
253#117—22no—
254#117—221no—
255#117—441no—
256C2×C42—441no—
257C2×C42C22⋊D1111yescharacteristic
258C2×C16—112no—
259C2×C16—112no—
260C2×C16—224no—
261#107—21no—
262#107—21no—
263#107—111no—
264#107—111no—
265#107C22×D1112yes—
266#107C22×D1112yes—
267#106—22no—
268#106—22no—
269#106—221no—
270#103—221no—
271#103—221no—
272#102—221no—
273#102—221no—
274C4×C8C22⋊D1111yescharacteristic
275C4×C8C22⋊D1111yescharacteristic
276C4×C8C22×D1111yescharacteristic
277C4×C8C22×D1111yescharacteristic
278C2×C11—22no—
279C2×C11C2×#47411yescharacteristic
280C2×C11C2×#50811yescharacteristic
281C2×C11#341411yescharacteristic
282D11—82no—
283#41—224no—
284#41—442no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—221no—
288C2×D4—221no—
289C2×D4—441no—
290C22×C4—441no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4#432311yescharacteristic
294C22×C4#432311yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296Q16—112no—
297Q16—221no—
298SD16—224no—
299D8—112no—
300D8—221no—
301C2×C8—22no—
302C2×C8Q8×D1112yes—
303C2×C8#434312yes—
304C2×C8C2×C22⋊D1111yescharacteristic
305C2×C8C2×C22⋊D1111yescharacteristic
306C2×C8C2×C22⋊D1111yescharacteristic
307C2×C8C23×D1111yescharacteristic
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C22⋊C4—42no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C42—42no—
323C42—441no—
324C42—441no—
325C42—441no—
326C42#432311yescharacteristic
327C42#432311yescharacteristic
328C42C2×C22⋊D1111yescharacteristic
329C42C2×C22⋊D1111yescharacteristic
330C16—222no—
331C16—222no—
332C11#3362611yescharacteristic, complemented, Sylow
333C23—441no—
334C23C2×#432311yescharacteristic
335Q8—82no—
336Q8—82no—
337Q8—222no—
338Q8—441no—
339D4—222no—
340D4—444no—
341D4—441no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—441no—
347C2×C4—444no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—882no—
351C2×C4—882no—
352C2×C4C2×#432311yescharacteristic
353C2×C4C2×#432311yescharacteristic
354C2×C4C2×#432311yescharacteristic
355C2×C4C2×#432311yescharacteristic
356C2×C4C2×#432311yescharacteristic
357C2×C4#6699512yes—
358C2×C4#6699912yes—
359C2×C4C22×C22⋊D1111yescharacteristic
360C8—21no—
361C8—21no—
362C8#6699912yes—
363C8C2×Q8×D1111yescharacteristic
364C8C2×#434311yescharacteristic
365C22—21no—
366C22—21no—
367C22—442no—
368C22—881no—
369C22—881no—
370C22#1062270012yes—
371C22C22×#432311yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—82no—
376C4—82no—
377C4—442no—
378C4—881no—
379C4—881no—
380C4#1062270012yes—
381C4#1062280712yes—
382C4C2×#6699511yescharacteristic
383C4C2×#6699911yescharacteristic
384C2—22no—
385C2—882no—
386C2C2×#1062270011yescharacteristic
387C2C2×#1062280711yescharacteristic
388C2#1308175011yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3160C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#3160D11
hypocenterC11#33626
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3160

Complements

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

NH ≅ G/Ntype
2. #13070777C2semidirect
3. #13070770C2semidirect
4. #13070765C2semidirect
5. #13070760C2semidirect
6. #13070755C2semidirect
7. #13070750C2semidirect
8. #13070398C2semidirect
9. C2×C4⋊(C11⋊C16)C2semidirect
11. C11×#3160C2semidirect
60. #66957Q8semidirect
139. #3160D11semidirect
332. C11#33626semidirect

Maximal subgroups

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

subgroupindex
C4×#669572
#130707772
#130707702
#130707652
#130707602
#130707552
#130707502
#130703982
C2×C4⋊(C11⋊C16)2
#130703212
C11×#31602
#3362611