Finite Group Databasebeta

← #14908814

Subgroups — #14908814

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#13079190C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic, complemented
3#13070797C211yesmaximal, characteristic, complemented
4#13070794C211yesmaximal, characteristic, complemented
5#13070766C212yesmaximal, complemented
6#13070654C212yesmaximal, complemented
7#13070533C211yesmaximal, characteristic, complemented
8#13070483C212yesmaximal, complemented
9#13070481C212yesmaximal, complemented
10#13070416C211yesmaximal, characteristic, complemented
11C11×#2185C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×Q8×Dic11—21no—
14#10623127—21no—
15C2×C11×SD32C2212yes—
16C11×#466C2211yescharacteristic
17C2×#66899—21no—
18Q16×Dic11—21no—
19Q16×Dic11—21no—
20Q16×Dic11C2212yes—
21Q16×Dic11C2212yes—
22C2×#66892C2212yes—
23#10622764C2211yescharacteristic
24D8×Dic11C2211yescharacteristic
25#10622728C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622651—21no—
29#10622487C2211yescharacteristic
30#10622485C2211yescharacteristic
31#10622373—21no—
32#10622369—21no—
33C11×#358C2212yes—
34C11×C22⋊C16C2211yescharacteristic
35#10622202C2212yes—
36#10622200C2212yes—
37C22⋊(C11⋊C16)C2211yescharacteristic
38#10622147C2212yes—
39#10622142C2212yes—
40#10622140C2212yes—
41Dic11⋊C16C2212yes—
42#10622127C2212yes—
43C22×Q8×C11—21no—
44C2×#4341—41no—
45C2×C11×Q16—24no—
46C2×C11×Q16—21no—
47C2×C11×Q16C2312yes—
48C2×C11×D8C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×#121—21no—
51Q8×Dic11—22no—
52Q8×Dic11—22no—
53Q8×Dic11—41no—
54Q8×Dic11—41no—
55#66993—21no—
56#66992—41no—
57D4×Dic11—21no—
58C2×#4323—21no—
59#66983—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—41no—
62C2×C4×Dic11—41no—
63C2×C4×Dic11D411yescharacteristic
64C22×C11⋊C8D411yescharacteristic
65C2×D88C2311yescharacteristic
66#66946—21no—
67#66941—21no—
68#66938—41no—
69(C22⋊D11)⋊C4—41no—
70C11×SD32—24no—
71C2×C11×C16C2312yes—
72C11×#107C2311yescharacteristic
73C11×#102—21no—
74#66899—22no—
75#66899—22no—
76#66896—21no—
77#66892—24no—
78#66885—21no—
79#66882—21no—
80#66882C2311yescharacteristic
81#66882C2312yes—
82C8×Dic11D411yescharacteristic
83C8×Dic11D411yescharacteristic
84C8×Dic11C2311yescharacteristic
85C8×Dic11C2311yescharacteristic
86C2×C11⋊C16C2312yes—
87#66873—21no—
88#66871—21no—
89#33672—111nomaximal, Sylow
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—42no—
93C2×Q8×C11—41no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C2×C22⋊D11—41no—
99C2×C22⋊D11—41no—
100C2×C22⋊D11—41no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11D811yescharacteristic
104C22×Dic11D811yescharacteristic
105#4341—84no—
106C2×D44—21no—
107C2×C4×D11—41no—
108C2×Dic22—41no—
109C11×Q16—24no—
110C11×Q16—22no—
111C11×Q16#4114yescomplemented
112C11×D8—22no—
113C2×C8×C11—22no—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2411yescharacteristic
116C11×C4⋊C4—21no—
117C11×C22⋊C4—41no—
118C22⋊Dic11—41no—
119#4323—42no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—42no—
125C4⋊Dic11—42no—
126C4⋊Dic11—41no—
127Dic11⋊C4—41no—
128C4×Dic11—42no—
129C4×Dic11—42no—
130C4×Dic11D811yescharacteristic
131C4×Dic11D811yescharacteristic
132C4×Dic11C2×D411yescharacteristic
133C4×Dic11C2×D411yescharacteristic
134C2×C11⋊C8—41no—
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137D88—22no—
138C11×C16—22no—
139C11⋊C16—22no—
140#3169—111no—
141C2×C4×Q16—111no—
142#2232—111no—
143#2232—111no—
144#2227—112no—
145#2207—112no—
146#2185—111no—
147#2185D1111yescharacteristic, complemented
148#2175—112no—
149#2175—112no—
150#2163—111no—
151C23×C11—41no—
152C23×C11C2×D811yescharacteristic
153C22×D11—41no—
154Q8×C11—24no—
155Q8×C11—44no—
156Q8×C11—42no—
157D4×C11—41no—
158D4×C11—41no—
159D4×C11—82no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—44no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C22⋊D11—82no—
168C22⋊D11—82no—
169C22⋊D11—82no—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—82no—
175C2×Dic11—82no—
176C2×Dic11C2×D811yescharacteristic
177C2×Dic11C2×D811yescharacteristic
178C2×Dic11C2×D811yescharacteristic
179C2×Dic11C2×D811yescharacteristic
180D44—41no—
181D44—41no—
182C4×D11—82no—
183Dic22—82no—
184C8×C11—21no—
185C8×C11C2×#4112yes—
186C11⋊C8—21no—
187C11⋊C8—21no—
188C22×Q16C2×D1111yescharacteristic
189#532—221no—
190C2×C4×Q8—221no—
191C2×SD32—112no—
192C2×SD32C2×D1112yes—
193#500—111no—
194#493—111no—
195#486—221no—
196#466—111no—
197#466—221no—
198#466C2×D1111yescharacteristic
199C4×Q16—112no—
200C4×Q16—112no—
201C4×Q16—221no—
202C4×Q16—221no—
203C4×D8—111no—
204C4×D8—111no—
205C4×D8—221no—
206C2×#107—111no—
207C2×#103—221no—
208C2×C4×C8—111no—
209#366—112no—
210#366—112no—
211C4⋊C16—112no—
212#358—112no—
213#358C2×D1112yes—
214#357—112no—
215#357—112no—
216C22⋊C16—111no—
217C22⋊C16C2×D1111yescharacteristic
218#346—112no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11#50912yes—
225C22×C11C22×D811yescharacteristic
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C4×C11—21no—
230C4×C11—44no—
231C4×C11—81no—
232C4×C11#52511yescharacteristic
233C4×C11#57511yescharacteristic
234Dic11—21no—
235Dic11—21no—
236Dic11—21no—
237Dic11—81no—
238Dic11—82no—
239Dic11#51012yes—
240C2×#41—441no—
241C22×Q8—21no—
242C2×Q16—24no—
243C2×Q16—21no—
244C2×Q16C22×D1112yes—
245C2×D8—111no—
246C2×D8—221no—
247C2×D8C22×D1111yescharacteristic
248C22×C8—111no—
249C22×C8C22×D1111yescharacteristic
250C4⋊Q8—221no—
251#127—221no—
252#124—441no—
253#121—21no—
254#121—221no—
255#121—441no—
256C4×Q8—222no—
257C4×Q8—222no—
258C4×Q8—441no—
259C4×Q8—441no—
260C4×D4—221no—
261C4×D4—221no—
262C4×D4—441no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—441no—
265C2×C42—111no—
266C2×C42—441no—
267SD32—24no—
268SD32—224no—
269C2×C16—112no—
270C2×C16C22×D1112yes—
271#107—112no—
272#107—111no—
273#107—221no—
274#107—221no—
275#107C22×D1111yescharacteristic
276#103—222no—
277#103—222no—
278#102—21no—
279#102—221no—
280#102—221no—
281#102—221no—
282C4×C8—111no—
283C4×C8—111no—
284C4×C8—111no—
285C4×C8—111no—
286C2×C11—22no—
287C2×C11—161no—
288C2×C11#310011yescharacteristic
289C2×C11C2×#50911yescharacteristic
290C2×C11C2×#51011yescharacteristic
291D11—161no—
292#41—884no—
293C2×Q8—24no—
294C2×Q8—22no—
295C2×Q8—42no—
296C2×Q8—41no—
297C2×Q8—441no—
298C2×D4—21no—
299C2×D4—41no—
300C2×D4—221no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—441no—
304C22×C4—41no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4D4×D1111yescharacteristic
311Q16—24no—
312Q16—22no—
313Q16#434114yescomplemented
314D8—22no—
315D8—222no—
316D8—442no—
317C2×C8—22no—
318C2×C8—111no—
319C2×C8—111no—
320C2×C8—441no—
321C2×C8D4×D1111yescharacteristic
322C2×C8C23×D1111yescharacteristic
323C4⋊C4—21no—
324C4⋊C4—221no—
325C4⋊C4—222no—
326C4⋊C4—442no—
327C4⋊C4—442no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C22⋊C4—41no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C42—111no—
335C42—111no—
336C42—111no—
337C42—111no—
338C42—442no—
339C42—442no—
340C16—22no—
341C16—222no—
342C11#3367211yescharacteristic, complemented, Sylow
343C23—41no—
344C23—441no—
345C23D8×D1111yescharacteristic
346Q8—24no—
347Q8—44no—
348Q8—42no—
349Q8—882no—
350D4—41no—
351D4—41no—
352D4—82no—
353D4—441no—
354D4—441no—
355D4—882no—
356D4—882no—
357D4—882no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—44no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—111no—
364C2×C4—111no—
365C2×C4—111no—
366C2×C4—111no—
367C2×C4—222no—
368C2×C4—222no—
369C2×C4—442no—
370C2×C4—441no—
371C2×C4—882no—
372C2×C4—882no—
373C2×C4—882no—
374C2×C4D8×D1111yescharacteristic
375C2×C4C2×D4×D1111yescharacteristic
376C8—21no—
377C8—221no—
378C8—221no—
379C8C2×#434112yes—
380C22—21no—
381C22—21no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—881no—
386C22—881no—
387C22—881no—
388C22#1062252712yes—
389C22C2×D8×D1111yescharacteristic
390C4—21no—
391C4—44no—
392C4—81no—
393C4—112no—
394C4—221no—
395C4—221no—
396C4—221no—
397C4—881no—
398C4—882no—
399C4#1062311711yescharacteristic
400C4#1062330411yescharacteristic
401C2—22no—
402C2—161no—
403C2—1761no—
404C2#1307861111yescharacteristic
405C2C2×#1062252711yescharacteristic
406C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2185C2
socleC22×C11C22×D8
prime radical#13079190C2
hypercenter#2185D11
hypocenterC11#33672
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2185

Complements

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

NH ≅ G/Ntype
2. C2×Q16×Dic11C2semidirect
3. #13070797C2semidirect
4. #13070794C2semidirect
5. #13070766C2semidirect
6. #13070654C2semidirect
7. #13070533C2semidirect
8. #13070483C2semidirect
9. #13070481C2semidirect
10. #13070416C2semidirect
11. C11×#2185C2semidirect
111. C11×Q16#41semidirect
147. #2185D11semidirect
313. Q16#4341semidirect
342. C11#33672semidirect

Maximal subgroups

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

subgroupindex
#130791902
C2×Q16×Dic112
#130707972
#130707942
#130707662
#130706542
#130705332
#130704832
#130704812
#130704162
C11×#21852
#3367211