Finite Group Databasebeta

← #14908869

Subgroups — #14908869

Order 2816.

548 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
1#13079187C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic, complemented
3#13070816C211yesmaximal, characteristic, complemented
4#13070802C211yesmaximal, characteristic
5#13070778C212yesmaximal, complemented
6#13070680C212yesmaximal, complemented
7#13070533C211yesmaximal, characteristic
8#13070487C212yesmaximal, complemented
9#13070483C212yesmaximal, complemented
10#13070416C211yesmaximal, characteristic, complemented
11C11×#2188C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×Q8×Dic11—21no—
14#10623155—21no—
15C2×C11×Q32C2212yes—
16C11×#467C2211yescharacteristic
17C2×#66899—21no—
18#10622804C2211yescharacteristic
19Q16×Dic11—21no—
20Q16×Dic11—21no—
21Q16×Dic11C2212yes—
22Q16×Dic11C2212yes—
23Q16×Dic11C2211yescharacteristic
24C2×#66892C2212yes—
25#10622728C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622661—21no—
29#10622491C2211yescharacteristic
30#10622485C2211yescharacteristic
31#10622413—21no—
32#10622401—21no—
33C11×#358C2212yes—
34C11×C22⋊C16C2211yescharacteristic
35#10622202C2212yes—
36#10622202C2212yes—
37C22⋊(C11⋊C16)C2211yescharacteristic
38#10622147C2212yes—
39#10622143C2212yes—
40#10622140C2212yes—
41Dic11⋊C16C2212yes—
42#10622127C2212yes—
43C22×Q8×C11—21no—
44C2×C11×Q16—24no—
45C2×C11×Q16—21no—
46C2×C11×Q16C2311yescharacteristic
47C2×C11×Q16C2312yes—
48C22×C8×C11C2311yescharacteristic
49C11×C22⋊Q8—21no—
50#67000—21no—
51Q8×Dic11—22no—
52Q8×Dic11—22no—
53Q8×Dic11—21no—
54Q8×Dic11—41no—
55Q8×Dic11—41no—
56C2×#4325—21no—
57#66983—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—41no—
60C2×C4×Dic11—41no—
61C2×C4×Dic11D411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63C2×D88C2311yescharacteristic
64#66951—41no—
65#66946—21no—
66#66945—41no—
67#66943—21no—
68#66939—41no—
69(C22⋊D11)⋊C4—41no—
70C11×Q32—24no—
71C2×C11×C16C2312yes—
72C11×#107C2311yescharacteristic
73C11×#103—21no—
74#66899—22no—
75#66899—22no—
76#66899—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#66872—21no—
89#33677—111nomaximal, Sylow
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—21no—
93C2×Q8×C11—42no—
94C2×Q8×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C2×C22⋊D11—41no—
98C22×Dic11—41no—
99C22×Dic11D811yescharacteristic
100C22×Dic11D811yescharacteristic
101C2×D44—21no—
102C2×C4×D11—41no—
103C11×Q16—24no—
104C11×Q16—22no—
105C11×Q16—22no—
106C11×Q16#4114yes—
107C2×C8×C11—22no—
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2411yescharacteristic
110C11×C4⋊C4—21no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113#4325—42no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118C4⋊Dic11—21no—
119C4⋊Dic11—22no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—42no—
123C4⋊Dic11—42no—
124C4⋊Dic11—41no—
125Dic11⋊C4—41no—
126C4×Dic11—41no—
127C4×Dic11—42no—
128C4×Dic11—42no—
129C4×Dic11D811yescharacteristic
130C4×Dic11D811yescharacteristic
131C4×Dic11C2×D411yescharacteristic
132C4×Dic11C2×D411yescharacteristic
133C2×C11⋊C8—41no—
134C2×C11⋊C8C2×D411yescharacteristic
135C2×C11⋊C8C2×D411yescharacteristic
136D88—22no—
137C11×C16—22no—
138C11⋊C16—22no—
139#3168—111no—
140C2×C4×Q16—111no—
141#2236—111no—
142#2233—111no—
143#2229—112no—
144#2211—112no—
145#2188D1111yescharacteristic, complemented
146#2185—111no—
147#2176—112no—
148#2175—112no—
149#2163—111no—
150C23×C11C2×D811yescharacteristic
151C22×D11—41no—
152Q8×C11—24no—
153Q8×C11—44no—
154Q8×C11—42no—
155Q8×C11—41no—
156Q8×C11—41no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C22×D411yescharacteristic
165C22⋊D11—82no—
166C2×Dic11—22no—
167C2×Dic11—41no—
168C2×Dic11—42no—
169C2×Dic11—41no—
170C2×Dic11—82no—
171C2×Dic11C2×D811yescharacteristic
172C2×Dic11C2×D811yescharacteristic
173C2×Dic11C2×D811yescharacteristic
174C2×Dic11C2×D811yescharacteristic
175D44—41no—
176D44—41no—
177C4×D11—82no—
178C8×C11—21no—
179C8×C11C2×#4112yes—
180C11⋊C8—21no—
181C11⋊C8—21no—
182C22×Q16C2×D1111yescharacteristic
183#529—221no—
184C2×C4×Q8—221no—
185C2×Q32C2×D1112yes—
186C2×SD32—112no—
187#499—111no—
188#495—111no—
189#488—221no—
190#467C2×D1111yescharacteristic
191#466—111no—
192#465—221no—
193C4×Q16—111no—
194C4×Q16—112no—
195C4×Q16—112no—
196C4×Q16—221no—
197C4×Q16—221no—
198C4×SD16—221no—
199C4×D8—111no—
200C2×#107—111no—
201C2×#103—221no—
202C2×C4×C8—111no—
203#367—112no—
204#366—112no—
205C4⋊C16—112no—
206#358—112no—
207#358—112no—
208#358C2×D1112yes—
209#357—112no—
210C22⋊C16—111no—
211C22⋊C16C2×D1111yescharacteristic
212#346—112no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11#51012yes—
216C22×C11C22×D811yescharacteristic
217C2×D11—81no—
218C2×D11—81no—
219C2×D11—81no—
220C4×C11—21no—
221C4×C11—44no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11#52511yescharacteristic
225C4×C11#57511yescharacteristic
226Dic11—21no—
227Dic11—21no—
228Dic11—21no—
229Dic11—21no—
230Dic11—81no—
231Dic11—82no—
232C22×Q8—21no—
233C2×Q16—24no—
234C2×Q16—21no—
235C2×Q16C22×D1111yescharacteristic
236C2×Q16C22×D1112yes—
237C2×SD16—221no—
238C2×D8—111no—
239C22×C8—111no—
240C22×C8C22×D1111yescharacteristic
241#126—441no—
242#125—221no—
243#124—221no—
244#123—441no—
245C22⋊Q8—21no—
246#121—221no—
247C4×Q8—222no—
248C4×Q8—222no—
249C4×Q8—221no—
250C4×Q8—441no—
251C4×Q8—441no—
252C4×D4—221no—
253C4×D4—441no—
254#117—441no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—441no—
257C2×C42—111no—
258C2×C42—441no—
259Q32—24no—
260SD32—224no—
261C2×C16—112no—
262C2×C16C22×D1112yes—
263#107—112no—
264#107—111no—
265#107—221no—
266#107C22×D1111yescharacteristic
267#106—221no—
268#103—21no—
269#103—222no—
270#103—222no—
271#103—221no—
272#102—221no—
273#102—221no—
274C4×C8—111no—
275C4×C8—111no—
276C4×C8—111no—
277C4×C8—111no—
278C2×C11—22no—
279C2×C11#310011yescharacteristic
280C2×C11C2×#51011yescharacteristic
281C2×C11#341411yescharacteristic
282D11—161no—
283C2×Q8—24no—
284C2×Q8—22no—
285C2×Q8—21no—
286C2×Q8—42no—
287C2×Q8—41no—
288C2×D4—221no—
289C2×D4—441no—
290C22×C4—41no—
291C22×C4—111no—
292C22×C4—111no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4D4×D1111yescharacteristic
296Q16—24no—
297Q16—22no—
298Q16—22no—
299Q16#434114yes—
300SD16—442no—
301D8—222no—
302C2×C8—22no—
303C2×C8—111no—
304C2×C8—111no—
305C2×C8—441no—
306C2×C8D4×D1111yescharacteristic
307C2×C8C23×D1111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—221no—
311C4⋊C4—222no—
312C4⋊C4—442no—
313C4⋊C4—442no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C22⋊C4—41no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C22⋊C4—441no—
323C42—111no—
324C42—111no—
325C42—111no—
326C42—111no—
327C42—442no—
328C42—442no—
329C42—441no—
330C16—22no—
331C16—222no—
332C11#3367711yescharacteristic, complemented, Sylow
333C23—441no—
334C23D8×D1111yescharacteristic
335Q8—24no—
336Q8—44no—
337Q8—42no—
338Q8—41no—
339Q8—41no—
340D4—441no—
341D4—441no—
342D4—882no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—111no—
350C2×C4—111no—
351C2×C4—111no—
352C2×C4—111no—
353C2×C4—222no—
354C2×C4—441no—
355C2×C4—442no—
356C2×C4—441no—
357C2×C4—882no—
358C2×C4—882no—
359C2×C4D8×D1111yescharacteristic
360C2×C4C2×D4×D1111yescharacteristic
361C8—21no—
362C8—221no—
363C8—221no—
364C8C2×#434112yes—
365C22—21no—
366C22—21no—
367C22—881no—
368C22—881no—
369C22—881no—
370C22#1062253112yes—
371C22C2×D8×D1111yescharacteristic
372C4—21no—
373C4—44no—
374C4—81no—
375C4—81no—
376C4—221no—
377C4—221no—
378C4—221no—
379C4—221no—
380C4—881no—
381C4—882no—
382C4#1062311711yescharacteristic
383C4#1062330411yescharacteristic
384C2—22no—
385C2—1761no—
386C2#1307861111yescharacteristic
387C2C2×#1062253111yescharacteristic
388C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2188C2
socleC22×C11C22×D8
prime radical#10622728C22
hypercenter#2188D11
hypocenterC11#33677
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2188

Complements

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

NH ≅ G/Ntype
2. C2×Q16×Dic11C2semidirect
3. #13070816C2semidirect
5. #13070778C2semidirect
6. #13070680C2semidirect
8. #13070487C2semidirect
9. #13070483C2semidirect
10. #13070416C2semidirect
11. C11×#2188C2semidirect
145. #2188D11semidirect
332. C11#33677semidirect

Maximal subgroups

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

subgroupindex
#130791872
C2×Q16×Dic112
#130708162
#130708022
#130707782
#130706802
#130705332
#130704872
#130704832
#130704162
C11×#21882
#3367711