Finite Group Databasebeta

← #14910413

Subgroups — #14910413

Order 2816.

674 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
1C2×#10622792C212yesmaximal, complemented
2#13080376C211yesmaximal, characteristic
3#13070873C211yesmaximal, characteristic, complemented
4#13070731C212yesmaximal, complemented
5#13070663C211yesmaximal, characteristic, complemented
6#13070656C211yesmaximal, characteristic, complemented
7#13070554C212yesmaximal, complemented
8#13070533C212yesmaximal, complemented
9C4×#66893C211yesmaximal, characteristic, complemented
10#13070448C211yesmaximal, characteristic, complemented
11D4×C11×Q16C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2212yes—
13D4×Q8×C11—21no—
14C2×#66957C2212yes—
15#10623084—21no—
16C11×#494C2211yescharacteristic
17C11×#467C2212yes—
18C11×#462—21no—
19C11×#451—22no—
20C4×C11×Q16C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22C2×#66893C2212yes—
23C2×#66893C2211yescharacteristic
24#10622792—28no—
25C2×#66892C2212yes—
26C2×#66892C2212yes—
27C2×#66892C2212yes—
28#10622728C2212yes—
29C2×#66876C2212yes—
30#10622461—21no—
31#10622347—22no—
32C4×Dic44C2211yescharacteristic
33#10622308C2211yescharacteristic
34#10622202C2212yes—
35#10622202C2211yescharacteristic
36C22⋊(C11⋊C16)C2212yes—
37#10622130C2211yescharacteristic
38#10622129C2212yes—
39#10622127C2211yescharacteristic
40C4⋊(C11⋊C16)C2211yescharacteristic
41C4×C11⋊C16C2211yescharacteristic
42C22×Q8×C11—22no—
43C2×#4339—22no—
44C2×C11×Q16—24no—
45C2×C11×Q16—22no—
46C2×C11×Q16—21no—
47C2×C11×Q16—42no—
48C2×C11×Q16C2312yes—
49C2×C11×Q16C2311yescharacteristic
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—41no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—42no—
55C4×Q8×C11—21no—
56C4×D4×C11—41no—
57C4×D4×C11D411yescharacteristic
58#66993—41no—
59#66983—22no—
60C2×Dic44C2311yescharacteristic
61#66957—24no—
62#66957—42no—
63C2×D88—21no—
64C2×D88C2312yes—
65C2×#4314—22no—
66#66946—41no—
67#66937—42no—
68#66927—21no—
69C4×Dic22—21no—
70C11×#107C2311yescharacteristic
71C11×C4⋊C8D411yescharacteristic
72C11×#103—21no—
73C11×#103—22no—
74C11×C22⋊C8D412yes—
75C4×C8×C11C2311yescharacteristic
76#66893—24no—
77#66893D414yescomplemented
78#66892—24no—
79#66892—24no—
80#66892—42no—
81#66885—22no—
82#66882C2311yescharacteristic
83#66880—21no—
84#66876—24no—
85C2×C11⋊C16C2311yescharacteristic
86C2×C11⋊C16C2312yes—
87C2×C11⋊C16C2311yescharacteristic
88#33844—111nomaximal, Sylow
89C2×Q8×C11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—44no—
92C2×Q8×C11—42no—
93C2×Q8×C11—82no—
94C2×D4×C11D811yescharacteristic
95C22×C4×C11—42no—
96C22×C4×C11C2×D412yes—
97C2×C22⋊D11—42no—
98C2×C22⋊D11—42no—
99#4339—44no—
100#4339—82no—
101C2×D44—22no—
102C2×D44—41no—
103C2×D44—41no—
104C2×C4×D11—42no—
105C2×Dic22—21no—
106C11×Q16—21no—
107C11×Q16—22no—
108C11×Q16—22no—
109C11×Q16—44no—
110C11×Q16—81no—
111C11×Q16C2×D412yes—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D412yes—
116C2×C8×C11C2411yescharacteristic
117C11×C4⋊C4—21no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—42no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4D811yescharacteristic
123C11×C22⋊C4—42no—
124C11×C22⋊C4D812yes—
125C42×C11—41no—
126C42×C11C2×D411yescharacteristic
127(C2×D11)⋊C4—42no—
128C4⋊Dic11—21no—
129Dic11⋊C4—41no—
130C4×Dic11—41no—
131Dic44—21no—
132Dic44C2×D412yes—
133D88—22no—
134D88—22no—
135D88—81no—
136#4314—44no—
137C11⋊C16—22no—
138C11⋊C16—21no—
139C11⋊C16C2×D412yes—
140C2×#510—112no—
141#3287—111no—
142D4×Q16D1111yescharacteristic, complemented
143#2248—111no—
144#2220—112no—
145#2209—111no—
146#2207—111no—
147#2189—112no—
148#2185—112no—
149C4×Q32—111no—
150#2169—111no—
151C23×C11C2×D812yes—
152C22×D11—42no—
153Q8×C11—22no—
154Q8×C11—41no—
155Q8×C11—42no—
156Q8×C11—42no—
157Q8×C11—84no—
158D4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—84no—
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C2×D812yes—
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C22⋊D11—84no—
170C22⋊D11—162no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173D44—42no—
174D44—42no—
175D44—82no—
176D44—161no—
177C4×D11—84no—
178Dic22—22no—
179Dic22—41no—
180C8×C11—22no—
181C8×C11—21no—
182C8×C11C22×D411yescharacteristic
183C8×C11H(5,𝔽2)11yescharacteristic
184C2×#135—112no—
185C22×Q16C2×D1112yes—
186#550—221no—
187D4×Q8—21no—
188#510—228no—
189C2×Q32—111no—
190C2×Q32—112no—
191C2×SD32—112no—
192C2×SD32—112no—
193C2×SD32—112no—
194C2×M32—112no—
195#494C2×D1111yescharacteristic
196#493—111no—
197#467C2×D1112yes—
198#466—112no—
199#462—21no—
200#460—221no—
201#451—22no—
202#449—222no—
203C4×Q16—111no—
204C4×Q16C2×D1111yescharacteristic
205C8×D4C2×D1111yescharacteristic
206#366—111no—
207C4⋊C16—111no—
208#358—111no—
209#358—112no—
210#358—111no—
211#357—112no—
212C22⋊C16—112no—
213C4×C16—111no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11C22×D811yescharacteristic
218C2×D11—82no—
219C2×D11—82no—
220C2×D11—82no—
221C4×C11—21no—
222C4×C11—22no—
223C4×C11—42no—
224C4×C11—81no—
225C4×C11—82no—
226C4×C11#51012yescomplemented
227C4×C11D4211yescharacteristic
228C4×C11#57611yescharacteristic
229Dic11—42no—
230Dic11—81no—
231C2×#41—222no—
232C22×Q8—22no—
233#135—224no—
234#135—442no—
235C2×Q16—24no—
236C2×Q16—22no—
237C2×Q16—21no—
238C2×Q16—42no—
239C2×Q16—111no—
240C2×Q16C22×D1112yes—
241C2×Q16C22×D1111yescharacteristic
242C2×SD16—222no—
243C2×D8—112no—
244C2×D8—221no—
245C22×C8C22×D1112yes—
246C4⋊Q8—21no—
247C4⋊Q8—41no—
248#127—221no—
249#127—441no—
250C22⋊Q8—22no—
251C22⋊Q8—42no—
252#121—222no—
253#121—442no—
254C4×Q8—21no—
255C4×Q8—221no—
256C4×D4—41no—
257C4×D4—441no—
258C4×D4C22⋊D1111yescharacteristic
259Q32—114no—
260Q32—224no—
261SD32—224no—
262SD32—224no—
263SD32—442no—
264M32—224no—
265C2×C16—111no—
266C2×C16—111no—
267C2×C16—112no—
268#107—111no—
269#107C22×D1111yescharacteristic
270C4⋊C8C22⋊D1111yescharacteristic
271#103—21no—
272#103—22no—
273#103—221no—
274#102—222no—
275C22⋊C8C22⋊D1112yes—
276C4×C8C22×D1111yescharacteristic
277C2×C11—42no—
278C2×C11D4×D811yescharacteristic
279C2×C11C2×#51011yescharacteristic
280C2×C11#341611yescharacteristic
281D11—162no—
282#41—444no—
283#41—882no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—44no—
287C2×Q8—42no—
288C2×Q8—82no—
289C2×Q8—221no—
290C2×D4—222no—
291C2×D4—442no—
292C2×D4—442no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4#432311yescharacteristic
296C22×C4—42no—
297C22×C4—442no—
298C22×C4C2×C22⋊D1112yes—
299Q16—22no—
300Q16—21no—
301Q16—22no—
302Q16—44no—
303Q16—81no—
304Q16—112no—
305Q16—221no—
306Q16D4×D1112yes—
307SD16—444no—
308D8—222no—
309D8—222no—
310D8—881no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8C2×C22⋊D1111yescharacteristic
314C2×C8C2×C22⋊D1112yes—
315C2×C8C23×D1111yescharacteristic
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—221no—
322C4⋊C4—441no—
323C4⋊C4#432311yescharacteristic
324C22⋊C4—42no—
325C22⋊C4—442no—
326C22⋊C4#432312yes—
327C42—41no—
328C42—441no—
329C42C2×C22⋊D1111yescharacteristic
330C16—112no—
331C16—222no—
332C16—221no—
333C11#3384411yescharacteristic, complemented, Sylow
334C23—442no—
335C23C2×#432312yes—
336Q8—22no—
337Q8—41no—
338Q8—42no—
339Q8—42no—
340Q8—84no—
341Q8—222no—
342Q8—441no—
343D4—22no—
344D4—442no—
345D4—442no—
346D4—884no—
347D4—882no—
348D4—1761no—
349D4—1762no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—84no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—884no—
359C2×C4C2×#432311yescharacteristic
360C2×C4C2×#432312yes—
361C2×C4C2×#432311yescharacteristic
362C2×C4C22×C22⋊D1111yescharacteristic
363C8—22no—
364C8—21no—
365C8C2×D4×D1111yescharacteristic
366C8#6703711yescharacteristic
367C22—22no—
368C22—22no—
369C22—22no—
370C22—882no—
371C22—882no—
372C22—882no—
373C22C22×#432311yescharacteristic
374C4—21no—
375C4—22no—
376C4—42no—
377C4—81no—
378C4—82no—
379C4—442no—
380C4—881no—
381C4#1062279212yescomplemented
382C4D4×C22⋊D1111yescharacteristic
383C4#1062336611yescharacteristic
384C2—42no—
385C2—1762no—
386C2D4×#432311yescharacteristic
387C2C2×#1062279211yescharacteristic
388C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×Q16C2
socleC22×C11C22×D8
prime radical#13080376C2
hypercenterD4×Q16D11
hypocenterC11#33844
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
3. #13070873C2semidirect
4. #13070731C2semidirect
5. #13070663C2semidirect
6. #13070656C2semidirect
7. #13070554C2semidirect
8. #13070533C2semidirect
9. C4×#66893C2semidirect
10. #13070448C2semidirect
11. D4×C11×Q16C2semidirect
77. #66893D4semidirect
142. D4×Q16D11semidirect
226. C4×C11#510semidirect
333. C11#33844semidirect
381. C4#10622792semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
#130803762
#130708732
#130707312
#130706632
#130706562
#130705542
#130705332
C4×#668932
#130704482
D4×C11×Q162
#3384411