Finite Group Databasebeta

← #14652832

Subgroups — #14652832

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076974C211yesmaximal, characteristic
2#13068767C211yesmaximal, characteristic, complemented
3C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
4C2×#10622185C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6C2×#10622123C211yesmaximal, characteristic
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#67000—22no—
10C2×#66927C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×Dic11⋊C8—22no—
14C2×C8×Dic11—21no—
15#10622601—21no—
16#10622601—21no—
17#10622601C414yes—
18C42×Dic11C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C11×#332—22no—
22#10622188—21no—
23#10622185—22no—
24#10622123—22no—
25#10622123—22no—
26C22×Q8×C11—21no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44C2×C412yes—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C42×C11C2311yescharacteristic
39#67000—44no—
40#67000—44no—
41C2×(C2×D11)⋊C4—24no—
42C2×(C2×D11)⋊C4—24no—
43C2×C4×Dic11C2×C412yes—
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D412yes—
47C22×C11⋊C8—21no—
48C22×C11⋊C8—21no—
49#66927—21no—
50#66927—21no—
51#66927—21no—
52#66927—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8D412yes—
57Dic11⋊C8—44no—
58C8×Dic11—42no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)D412yes—
63#9698—111nomaximal, Sylow
64C23×D11—22no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11—42no—
68C2×Q8×C11—42no—
69C22×C4×C11—22no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11C22⋊C412yes—
74C22×Dic11C22⋊C412yes—
75C2×D44—22no—
76C2×D44—22no—
77C2×D44—44no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—42no—
83C2×D44—42no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×C8×C11—22no—
89C2×C8×C11—41no—
90C2×C8×C11—42no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101(C2×D11)⋊C4—48no—
102(C2×D11)⋊C4—48no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—42no—
108C4×Dic11D814yes—
109C4×Dic11SD1614yes—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—42no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#2858—111no—
116#1842—111no—
117C4×C4⋊C8—111no—
118C2×#332—111no—
119C2×#332D1111yescharacteristic, complemented
120C2×#331—111no—
121C2×#331—111no—
122C23×C11C2×C22⋊C411yescharacteristic
123C22×D11—42no—
124C22×D11—44no—
125C22×D11—44no—
126C22×D11—42no—
127C22×D11—42no—
128Q8×C11—82no—
129Q8×C11—81no—
130Q8×C11—81no—
131C2×C4×C11—22no—
132C2×C4×C11—42no—
133C2×C4×C11—44no—
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11C4×D411yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12411yescharacteristic
139C2×C4×C11#12711yescharacteristic
140C2×C4×C11C2×D812yes—
141C2×C4×C11C2×SD1612yes—
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11#13511yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×Dic11—22no—
147C2×Dic11—22no—
148C2×Dic11—22no—
149C2×Dic11—22no—
150C2×Dic11#10214yes—
151C2×Dic11#10214yes—
152D44—82no—
153D44—82no—
154D44—81no—
155D44—81no—
156D44—81no—
157D44—81no—
158D44—82no—
159D44—81no—
160D44—81no—
161C8×C11—42no—
162C8×C11—81no—
163C11⋊C8—42no—
164C11⋊C8—81no—
165C2×C4⋊Q8C2×D1111yescharacteristic
166C2×#127—111no—
167C2×#124—222no—
168C2×C4⋊C8—111no—
169C2×C4⋊C8—111no—
170C2×C4⋊C8—222no—
171C2×C4⋊C8C2×D1111yescharacteristic
172C2×C4⋊C8C2×D1111yescharacteristic
173C2×C4×C8—221no—
174#390—114no—
175#390—221no—
176#390—221no—
177C43—111no—
178#336—221no—
179#332—22no—
180#332—222no—
181#331—222no—
182#331—222no—
183C22×C11#39011yescharacteristic
184C22×C11#41312yes—
185C22×C11C2×#10212yes—
186C22×C11#41611yescharacteristic
187C22×C11#41711yescharacteristic
188C2×D11—84no—
189C2×D11—84no—
190C2×D11—82no—
191C2×D11—82no—
192C2×D11—82no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—82no—
196C4×C11#46311yescharacteristic
197C4×C11#46311yescharacteristic
198C4×C11#46411yescharacteristic
199C4×C11#46411yescharacteristic
200C4×C11#48612yes—
201C4×C11#49211yescharacteristic
202C4×C11#49311yescharacteristic
203Dic11—24no—
204Dic11—24no—
205C22×Q8—21no—
206C22×D4—112no—
207C22×D4—221no—
208C22×D4—221no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—221no—
212C22×C8—221no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217#127—221no—
218#127—221no—
219#127—221no—
220#127—221no—
221#124—444no—
222#124—444no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C4×D1112yes—
225C2×C22⋊C4—224no—
226C2×C22⋊C4—224no—
227C2×C42—112no—
228C2×C42—111no—
229C2×C42—111no—
230C2×C42—112no—
231C2×C42C22×D1111yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—112no—
236C4⋊C8—221no—
237C4⋊C8—221no—
238C4⋊C8—221no—
239C4⋊C8—444no—
240C4⋊C8C22⋊D1112yes—
241C4×C8—442no—
242C2×C11#154012yes—
243C2×C11#154712yes—
244C2×C11#195711yescharacteristic
245C2×C11#196711yescharacteristic
246C2×C11#198311yescharacteristic
247D11—162no—
248C24—222no—
249C2×Q8—41no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—41no—
253C2×D4—222no—
254C2×D4—222no—
255C2×D4—444no—
256C2×D4—441no—
257C2×D4—441no—
258C2×D4—442no—
259C2×D4—442no—
260C2×D4—441no—
261C2×D4—441no—
262C2×D4—441no—
263C2×D4—441no—
264C2×D4—441no—
265C2×D4—441no—
266C22×C4—22no—
267C22×C4—112no—
268C22×C4—112no—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4D4×D1111yescharacteristic
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—42no—
276C2×C8—41no—
277C2×C8—222no—
278C2×C8—441no—
279C2×C8—441no—
280C2×C8—442no—
281C2×C8—441no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C22⋊C4—448no—
287C22⋊C4—448no—
288C42—114no—
289C42—114no—
290C42—221no—
291C42—221no—
292C42—221no—
293C42—221no—
294C42—442no—
295C42#433911yescharacteristic
296C42D4×D1111yescharacteristic
297C42#434111yescharacteristic
298C42C2×C22⋊D1111yescharacteristic
299C11#969811yescharacteristic, complemented, Sylow
300C23—442no—
301C23—444no—
302C23—444no—
303C23—442no—
304C23—442no—
305C23C22⋊C4×D1111yescharacteristic
306Q8—81no—
307Q8—81no—
308Q8—82no—
309D4—882no—
310D4—882no—
311D4—881no—
312D4—881no—
313D4—881no—
314D4—881no—
315D4—882no—
316D4—881no—
317D4—881no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—114no—
322C2×C4—114no—
323C2×C4—222no—
324C2×C4—222no—
325C2×C4—222no—
326C2×C4—222no—
327C2×C4(C22⋊D11)⋊C411yescharacteristic
328C2×C4#6693711yescharacteristic
329C2×C4#6693811yescharacteristic
330C2×C4D8×D1112yes—
331C2×C4SD16×D1112yes—
332C2×C4#6696711yescharacteristic
333C2×C4#6696911yescharacteristic
334C2×C4#6697111yescharacteristic
335C2×C4#6697211yescharacteristic
336C2×C4C4×C22⋊D1111yescharacteristic
337C2×C4#6699211yescharacteristic
338C2×C4#6699311yescharacteristic
339C8—42no—
340C8—81no—
341C8—442no—
342C8—881no—
343C22—884no—
344C22—884no—
345C22—882no—
346C22—882no—
347C22—882no—
348C22#1062236412yes—
349C22D11×#10212yes—
350C22#1062241611yescharacteristic
351C22#1062241711yescharacteristic
352C22#1062257011yescharacteristic
353C4—21no—
354C4—21no—
355C4—82no—
356C4—224no—
357C4—224no—
358C4#1062237312yes—
359C4#1062241111yescharacteristic
360C4#1062243211yescharacteristic
361C4#1062276411yescharacteristic
362C4#1062277811yescharacteristic
363C4#1062278811yescharacteristic
364C4#1062279811yescharacteristic
365C2—1762no—
366C2#1306726412yes—
367C2#1306729212yes—
368C2#1306942011yescharacteristic
369C2#1306946411yescharacteristic
370C2#1306954511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenterC2×#332D11
hypocenterC11#9698
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #13068767C2semidirect
3. C4⋊C8×Dic11C2semidirect
4. C2×#10622185C2semidirect
7. C2×C11×#332C2semidirect
119. C2×#332D11semidirect
299. C11#9698semidirect

Maximal subgroups

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

subgroupindex
#130769742
#130687672
C4⋊C8×Dic112
C2×#106221852
C2×#106221232
C2×C11×#3322
#969811