Finite Group Databasebeta

← #14908821

Subgroups — #14908821

Order 2816.

586 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079196C211yesmaximal, characteristic
2C4×Q16×D11C211yesmaximal, characteristic, complemented
3#13070798C212yesmaximal, complemented
4#13070765C211yesmaximal, characteristic, complemented
5#13070657C211yesmaximal, characteristic, complemented
6#13070656C211yesmaximal, characteristic, complemented
7#13070534C212yesmaximal, complemented
8#13070483C212yesmaximal, complemented
9#13070479C212yesmaximal, complemented
10#13070418C211yesmaximal, characteristic, complemented
11C11×#2227C211yesmaximal, characteristic, complemented
12C2×Q16×D11C2211yescharacteristic
13#10623256—21no—
14C4×Q8×D11—21no—
15C11×#500C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17Q16×Dic11C2211yescharacteristic
18C2×#66892C2212yes—
19#10622701—21no—
20C4×#4326—21no—
21C2×#66864C2212yes—
22#10622496—21no—
23#10622496C2212yes—
24D11×#107C2211yescharacteristic
25#10622486C2211yescharacteristic
26#10622485—21no—
27#10622485C2212yes—
28D11×#103—21no—
29#10622403—21no—
30C4×Dic44C2211yescharacteristic
31#10622308C2211yescharacteristic
32C4×C8×D11C2211yescharacteristic
33C11×#366C2212yes—
34C11×C4⋊C16C2211yescharacteristic
35C11×#358C2212yes—
36#10622147C2212yes—
37(C2×D11)⋊C16C2212yes—
38#10622140C2212yes—
39#10622130C2212yes—
40#10622129C2212yes—
41#10622127C2212yes—
42C4⋊(C11⋊C16)C2211yescharacteristic
43C2×#4343—41no—
44C2×Q8×D11—21no—
45C2×C11×Q16C2311yescharacteristic
46C11×C4⋊Q8—21no—
47C4×Q8×C11—21no—
48#67000—41no—
49Q8×Dic11—21no—
50C2×#4326—21no—
51Q16×D11—22no—
52Q16×D11—22no—
53C2×Dic44C2311yescharacteristic
54C2×D88—21no—
55C2×D88C2312yes—
56C2×C8×D11D411yescharacteristic
57C2×C8×D11C2311yescharacteristic
58#66948—22no—
59#66948—41no—
60#66946—22no—
61#66946—41no—
62C4⋊C4×D11—21no—
63C4⋊C4×D11—41no—
64#66940—21no—
65#66940—41no—
66#66927—21no—
67C42×D11—41no—
68C42×D11D411yescharacteristic
69C4×Dic22—21no—
70C4×Dic22—41no—
71C2×C11×C16C2312yes—
72C11×#107—21no—
73C11×#107C2312yes—
74C11×#107C2311yescharacteristic
75C11×#103—21no—
76C4×C8×C11C2311yescharacteristic
77#66899—21no—
78#66892—24no—
79#66882C2311yescharacteristic
80#66880—21no—
81C8×Dic11D411yescharacteristic
82C8×Dic11C2311yescharacteristic
83C2×C11⋊C16C2312yes—
84#66874—21no—
85#66873—22no—
86#66873—22no—
87#66871—21no—
88C4×C11⋊C8D411yescharacteristic
89#66864—24no—
90#33672—111nomaximal, Sylow
91C2×Q8×C11—21no—
92C2×Q8×C11—41no—
93#4343—84no—
94Q8×D11—24no—
95Q8×D11—42no—
96C2×D44—22no—
97C2×D44—42no—
98C2×D44—41no—
99C2×D44—41no—
100C2×C4×D11—42no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11D811yescharacteristic
104C2×C4×D11D811yescharacteristic
105C2×C4×D11C2×D411yescharacteristic
106C2×Dic22—21no—
107C2×Dic22—41no—
108C11×Q16—21no—
109C11×Q16#4112yescomplemented
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2411yescharacteristic
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C42×C11—41no—
117C42×C11C2×D411yescharacteristic
118#4326—24no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—42no—
121C4⋊Dic11—21no—
122C4⋊Dic11—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126C4×Dic11—41no—
127C4×Dic11—41no—
128C4×Dic11—41no—
129C4×Dic11D811yescharacteristic
130C4×Dic11D811yescharacteristic
131C4×Dic11C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134Dic44—21no—
135Dic44#4112yescomplemented
136D88—22no—
137D88—22no—
138D88—42no—
139C8×D11—21no—
140C8×D11—21no—
141C8×D11—41no—
142C11×C16—22no—
143C11⋊C16—22no—
144#3169—111no—
145C2×C4×Q16—111no—
146#2232—112no—
147#2227—111no—
148#2227D1111yescharacteristic, complemented
149#2207—111no—
150#2207—111no—
151#2185—112no—
152#2175—112no—
153#2175—112no—
154#2163—111no—
155C22×D11—42no—
156C22×D11C2×D811yescharacteristic
157Q8×C11—22no—
158Q8×C11—41no—
159Q8×C11—82no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11C2×D811yescharacteristic
169C2×Dic11C2×D811yescharacteristic
170C2×Dic11C2×D811yescharacteristic
171D44—42no—
172D44—42no—
173D44—82no—
174D44—84no—
175D44—82no—
176C4×D11—22no—
177C4×D11—21no—
178C4×D11—21no—
179C4×D11—22no—
180C4×D11—44no—
181C4×D11—84no—
182C4×D11—82no—
183Dic22—22no—
184Dic22—44no—
185Dic22—41no—
186C8×C11—21no—
187C8×C11C2×#4111yescharacteristic
188C8×C11C2×#4111yescharacteristic
189C11⋊C8—21no—
190C11⋊C8—21no—
191C22×Q16—111no—
192#532—221no—
193C2×C4×Q8—221no—
194C2×SD32—112no—
195C2×SD32—112no—
196#500C2×D1111yescharacteristic
197#493—111no—
198#486—221no—
199#466—112no—
200#466—221no—
201C4×Q16—111no—
202C4×Q16—111no—
203C4×Q16—111no—
204C4×Q16—221no—
205C4×Q16—221no—
206C4×Q16C2×D1111yescharacteristic
207C4×D8—112no—
208C4×D8—221no—
209C2×#107—111no—
210C2×#103—221no—
211C2×C4×C8—111no—
212#366—112no—
213#366C2×D1112yes—
214C4⋊C16—111no—
215C4⋊C16C2×D1111yescharacteristic
216#358—112no—
217#358C2×D1112yes—
218#357—112no—
219#357—112no—
220C22⋊C16—112no—
221#346—112no—
222C22×C11C22×D811yescharacteristic
223C2×D11—21no—
224C2×D11—21no—
225C2×D11—82no—
226C2×D11—82no—
227C2×D11—82no—
228C2×D11#50912yes—
229C4×C11—21no—
230C4×C11—42no—
231C4×C11—82no—
232C4×C11—81no—
233C4×C11#51012yes—
234C4×C11#52511yescharacteristic
235C4×C11#57511yescharacteristic
236Dic11—21no—
237Dic11—21no—
238Dic11—21no—
239Dic11—42no—
240Dic11—81no—
241C2×#41—441no—
242C22×Q8—221no—
243C2×Q16—111no—
244C2×Q16—221no—
245C2×Q16—222no—
246C2×Q16—222no—
247C2×Q16C22×D1111yescharacteristic
248C2×D8—112no—
249C2×D8—221no—
250C22×C8—111no—
251C22×C8—111no—
252C4⋊Q8—21no—
253#127—221no—
254#124—441no—
255#121—222no—
256#121—441no—
257C4×Q8—21no—
258C4×Q8—221no—
259C4×Q8—221no—
260C4×Q8—221no—
261C4×Q8—441no—
262C4×Q8—441no—
263C4×D4—222no—
264C4×D4—441no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—441no—
267C2×C42—111no—
268C2×C42—441no—
269SD32—224no—
270SD32—224no—
271C2×C16—112no—
272C2×C16C22×D1112yes—
273#107—21no—
274#107—111no—
275#107—221no—
276#107C22×D1111yescharacteristic
277#107C22×D1112yes—
278#103—21no—
279#103—221no—
280#103—221no—
281#103—221no—
282#102—222no—
283#102—222no—
284C4×C8—111no—
285C4×C8—111no—
286C4×C8—111no—
287C4×C8C22×D1111yescharacteristic
288C2×C11#310011yescharacteristic
289C2×C11C2×#50911yescharacteristic
290C2×C11C2×#51011yescharacteristic
291D11—22no—
292D11—162no—
293#41—884no—
294C2×Q8—21no—
295C2×Q8—41no—
296C2×Q8—224no—
297C2×Q8—221no—
298C2×Q8—441no—
299C2×Q8—442no—
300C2×D4—222no—
301C2×D4—442no—
302C2×D4—441no—
303C2×D4—441no—
304C22×C4—111no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—442no—
308C22×C4—441no—
309C22×C4—441no—
310Q16—21no—
311Q16—112no—
312Q16—224no—
313Q16—221no—
314Q16#434312yescomplemented
315D8—222no—
316D8—222no—
317D8—442no—
318C2×C8—111no—
319C2×C8—111no—
320C2×C8—221no—
321C2×C8—221no—
322C2×C8—441no—
323C2×C8D4×D1111yescharacteristic
324C2×C8C23×D1111yescharacteristic
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—221no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C22⋊C4—442no—
335C22⋊C4—442no—
336C42—41no—
337C42—111no—
338C42—111no—
339C42—111no—
340C42—441no—
341C42—441no—
342C42—441no—
343C42D4×D1111yescharacteristic
344C16—22no—
345C16—222no—
346C11#3367211yescharacteristic, complemented, Sylow
347C23—111no—
348C23—442no—
349Q8—22no—
350Q8—41no—
351Q8—82no—
352Q8—222no—
353Q8—444no—
354Q8—441no—
355D4—442no—
356D4—442no—
357D4—882no—
358D4—884no—
359D4—882no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—111no—
364C2×C4—111no—
365C2×C4—111no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—444no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—884no—
374C2×C4—882no—
375C2×C4D8×D1111yescharacteristic
376C2×C4D8×D1111yescharacteristic
377C2×C4C2×D4×D1111yescharacteristic
378C8—21no—
379C8—221no—
380C8—221no—
381C8C2×#434311yescharacteristic
382C8#41×D1111yescharacteristic
383C22—112no—
384C22—221no—
385C22—221no—
386C22—882no—
387C22—882no—
388C22—882no—
389C22C2×D8×D1111yescharacteristic
390C4—21no—
391C4—42no—
392C4—82no—
393C4—81no—
394C4—221no—
395C4—221no—
396C4—221no—
397C4—442no—
398C4—881no—
399C4#1062253112yes—
400C4#1062315811yescharacteristic
401C4#1062330811yescharacteristic
402C2—222no—
403C2—1762no—
404C2#1307861811yescharacteristic
405C2D11×#50911yescharacteristic
406C2C2×#1062253111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2227C2
socleC22×C11C22×D8
prime radical#13079196C2
hypercenter#2227D11
hypocenterC11#33672
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

Complements

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

NH ≅ G/Ntype
2. C4×Q16×D11C2semidirect
3. #13070798C2semidirect
4. #13070765C2semidirect
5. #13070657C2semidirect
6. #13070656C2semidirect
7. #13070534C2semidirect
8. #13070483C2semidirect
9. #13070479C2semidirect
10. #13070418C2semidirect
11. C11×#2227C2semidirect
109. C11×Q16#41semidirect
135. Dic44#41semidirect
148. #2227D11semidirect
314. Q16#4343semidirect
346. C11#33672semidirect

Maximal subgroups

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

subgroupindex
#130791962
C4×Q16×D112
#130707982
#130707652
#130706572
#130706562
#130705342
#130704832
#130704792
#130704182
C11×#22272
#3367211