Finite Group Databasebeta

← #14644743

Subgroups — #14644743

Order 2816.

528 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071183C211yesmaximal, characteristic
2#13068471C211yesmaximal, characteristic
3C4⋊C8×Dic11C211yesmaximal, characteristic
4C2×#10622119C211yesmaximal, characteristic
5C2×#10622119C211yesmaximal, characteristic
6#13066499C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic
8C2×#66940C412yes—
9C2×#66922C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C11×#384C2211yescharacteristic
13C2×#66879—21no—
14C2×C8×Dic11—21no—
15C4⋊C4×Dic11—21no—
16C4⋊C4×Dic11—21no—
17#10622587C412yes—
18#10622586—21no—
19#10622586—21no—
20C42×Dic11C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23#10622188—21no—
24#10622188—21no—
25#10622119C414yescomplemented
26#10622119C414yescomplemented
27C22×Dic22C2×C412yes—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×Dic11⋊C4—22no—
37C2×C4×Dic11—22no—
38C2×C4×Dic11C2×C411yescharacteristic
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11D411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46#66940—44no—
47#66922—21no—
48#66922—21no—
49#66922C2×C412yes—
50#66922C2×C412yes—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8C2×C412yes—
54C11×C4⋊C8C2×C412yes—
55C11⋊#95—22no—
56C11⋊#95—22no—
57#66879—42no—
58C8×Dic11—42no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)C2×C412yes—
62C4⋊(C11⋊C8)C2×C412yes—
63#8235—111nomaximal, Sylow
64C22×C4×C11—22no—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—22no—
69C22×Dic11C22⋊C411yescharacteristic
70C22×Dic11C22⋊C411yescharacteristic
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C2×Dic22—22no—
74C2×Dic22—42no—
75C2×Dic22—42no—
76C2×Dic22C4214yes—
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C42×C11C22×C411yescharacteristic
89C42×C11C22×C411yescharacteristic
90C42×C11#4111yescharacteristic
91C42×C11#4111yescharacteristic
92C4⋊Dic11—22no—
93C4⋊Dic11—22no—
94C4⋊Dic11—22no—
95C4⋊Dic11—22no—
96Dic11⋊C4—44no—
97C4×Dic11—22no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—41no—
105C4×Dic11—44no—
106C4×Dic11SD1612yes—
107C4×Dic11Q1612yes—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C4×C4⋊Q8—111no—
115#1767—111no—
116C4×C4⋊C8—111no—
117C2×#333—111no—
118C2×#333—111no—
119#1296—111no—
120#1296D1111yescharacteristic
121C23×C11C2×C22⋊C411yescharacteristic
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11C2×C4211yescharacteristic
128C2×C4×C11#11711yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11C2×SD1611yescharacteristic
134C2×C4×C11C2×Q1611yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—24no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11#10012yes—
154C2×Dic11#10312yes—
155C2×Dic11#10312yes—
156Dic22—44no—
157Dic22—44no—
158C8×C11—42no—
159C8×C11—42no—
160C11⋊C8—42no—
161C11⋊C8—42no—
162C2×C4⋊Q8—111no—
163C2×C4×Q8—112no—
164C2×C4⋊C8—111no—
165C2×C4⋊C8—111no—
166C2×C4⋊C8C2×D1111yescharacteristic
167C2×C4⋊C8C2×D1111yescharacteristic
168C2×#97—221no—
169C2×C4×C8—221no—
170#391—112no—
171#389—221no—
172#389—221no—
173#384C2×D1111yescharacteristic
174C4×C4⋊C4—221no—
175C4×C4⋊C4—221no—
176C43—111no—
177#336—221no—
178#336—221no—
179#333—114no—
180#333—114no—
181C22×C11C4×C22⋊C411yescharacteristic
182C22×C11C2×#10011yescharacteristic
183C22×C11#41311yescharacteristic
184C22×C11C2×#10311yescharacteristic
185C22×C11#41611yescharacteristic
186C22×C11#41711yescharacteristic
187C22×C11#41911yescharacteristic
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—82no—
191C4×C11C4×SD1611yescharacteristic
192C4×C11C4×SD1611yescharacteristic
193C4×C11C4×Q1611yescharacteristic
194C4×C11C4×Q1611yescharacteristic
195C4×C11#44011yescharacteristic
196C4×C11#44011yescharacteristic
197C4×C11#44111yescharacteristic
198C4×C11#44111yescharacteristic
199Dic11—22no—
200Dic11—22no—
201Dic11—22no—
202Dic11—41no—
203Dic11—44no—
204C22×Q8—112no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—221no—
208C22×C8—221no—
209C4⋊Q8—112no—
210C4⋊Q8—112no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213C4×Q8—444no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—222no—
219C2×C4⋊C4C4×D1112yes—
220C2×C42—111no—
221C2×C42—111no—
222C2×C42—111no—
223C2×C42—111no—
224C2×C42—111no—
225C2×C42—111no—
226C2×C42—222no—
227C2×C42C22×D1111yescharacteristic
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—112no—
231C4⋊C8—112no—
232C4⋊C8—221no—
233C4⋊C8—221no—
234C4⋊C8C4×D1112yes—
235C4⋊C8C4×D1112yes—
236#97—442no—
237C4×C8—442no—
238#95—222no—
239#95—222no—
240C2×C11#154811yescharacteristic
241C2×C11#155011yescharacteristic
242C2×C11#155111yescharacteristic
243C2×C11#155411yescharacteristic
244C2×C11C4×#10011yescharacteristic
245C2×C11C4×#10311yescharacteristic
246C2×C11#176311yescharacteristic
247C2×Q8—114no—
248C2×Q8—222no—
249C2×Q8—442no—
250C2×Q8—442no—
251C22×C4—22no—
252C22×C4—111no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—222no—
257C22×C4C2×C4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—222no—
267C2×C8—222no—
268C2×C8—441no—
269C2×C8—441no—
270C2×C8—441no—
271C2×C8—441no—
272C4⋊C4—42no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C4⋊C4—444no—
282C42—112no—
283C42—112no—
284C42—222no—
285C42—221no—
286C42—221no—
287C42—221no—
288C42—221no—
289C42—221no—
290C42—221no—
291C42—441no—
292C42—444no—
293C42C2×C4×D1111yescharacteristic
294C42C2×C4×D1111yescharacteristic
295C42#434111yescharacteristic
296C42#434311yescharacteristic
297C11#823511yescharacteristic, complemented, Sylow
298C23C22⋊C4×D1111yescharacteristic
299Q8—444no—
300Q8—444no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—112no—
307C2×C4—112no—
308C2×C4—112no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—224no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4C42×D1111yescharacteristic
322C2×C4(C22⋊D11)⋊C411yescharacteristic
323C2×C4(C22⋊D11)⋊C411yescharacteristic
324C2×C4#6694511yescharacteristic
325C2×C4#6694611yescharacteristic
326C2×C4#6694611yescharacteristic
327C2×C4#6696411yescharacteristic
328C2×C4#6696511yescharacteristic
329C2×C4SD16×D1111yescharacteristic
330C2×C4#6696811yescharacteristic
331C2×C4#6696811yescharacteristic
332C2×C4#6696911yescharacteristic
333C2×C4Q16×D1111yescharacteristic
334C2×C4#6697111yescharacteristic
335C8—42no—
336C8—42no—
337C8—442no—
338C8—442no—
339C22#1062227911yescharacteristic
340C22D11×#10011yescharacteristic
341C22#1062236411yescharacteristic
342C22#1062238411yescharacteristic
343C22#1062238511yescharacteristic
344C22D11×#10311yescharacteristic
345C22#1062241511yescharacteristic
346C4—21no—
347C4—21no—
348C4—82no—
349C4—222no—
350C4—222no—
351C4—222no—
352C4—441no—
353C4—444no—
354C4#1062237011yescharacteristic
355C4#1062237111yescharacteristic
356C4#1062240211yescharacteristic
357C4#1062240311yescharacteristic
358C4#1062246511yescharacteristic
359C4#1062246611yescharacteristic
360C4#1062248611yescharacteristic
361C4#1062250211yescharacteristic
362C2#1306729511yescharacteristic
363C2#1306730511yescharacteristic
364C2#1306730811yescharacteristic
365C2#1306732311yescharacteristic
366C2#1306840711yescharacteristic
367C2#1306843511yescharacteristic
368C2#1306844511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1296D11
hypocenterC11#8235
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
25. #10622119C4semidirect
26. #10622119C4semidirect
297. C11#8235semidirect

Maximal subgroups

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

subgroupindex
#130711832
#130684712
C4⋊C8×Dic112
C2×#106221192
#130664992
C11×#12962
#823511