Finite Group Databasebeta

← #14652814

Subgroups — #14652814

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077012C211yesmaximal, characteristic
2#13068767C211yesmaximal, characteristic
3C4⋊C8×Dic11C211yesmaximal, characteristic
4C2×#10622120C211yesmaximal, characteristic
5C2×#10622185C211yesmaximal, characteristic
6C2×#10622124C211yesmaximal, characteristic
7C2×C11×#332C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66997—21no—
10C2×#66997—21no—
11C2×#66922C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×Dic11⋊C8—22no—
15C2×C8×Dic11—21no—
16#10622589—22no—
17#10622589C414yes—
18C42×Dic11C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C11×#332—22no—
22#10622188—21no—
23#10622185—22no—
24#10622124—22no—
25#10622120—22no—
26C22×Q8×C11—21no—
27C22×Dic22—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C412yes—
36C2×C42×C11C2311yescharacteristic
37#66997—42no—
38#66997—42no—
39#66997—42no—
40#66997—42no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11C2×C412yes—
43C2×Dic11⋊C4—24no—
44C2×Dic11⋊C4—24no—
45C2×C4×Dic11C2×C412yes—
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×C4×Dic11D412yes—
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59Dic11⋊C8—44no—
60C8×Dic11—42no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)D412yes—
65#9694—111nomaximal, Sylow
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C22×C4×C11—22no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—22no—
77C22×Dic11C22⋊C412yes—
78C22×Dic11C22⋊C412yes—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C2×Dic22—41no—
84C2×Dic22—41no—
85C2×C8×C11—22no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—42no—
89C2×C8×C11—41no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97C42×C11#4111yescharacteristic
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102Dic11⋊C4—48no—
103Dic11⋊C4—48no—
104C4×Dic11—24no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11D812yes—
108C4×Dic11SD1612yes—
109C4×Dic11SD1614yes—
110C4×Dic11Q1614yes—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—41no—
116#2868—111no—
117#1842—111no—
118C4×C4⋊C8—111no—
119C2×#332—111no—
120C2×#332—111no—
121C2×#332—111no—
122C2×#332D1111yescharacteristic
123C23×C11C2×C22⋊C411yescharacteristic
124Q8×C11—81no—
125Q8×C11—81no—
126Q8×C11—81no—
127Q8×C11—81no—
128C2×C4×C11—22no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12411yescharacteristic
137C2×C4×C11#12711yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C2×C4×C11C2×SD1612yes—
141C2×C4×C11C2×Q1612yes—
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11#10114yes—
150C2×Dic11#10214yes—
151C2×Dic11#10314yes—
152C2×Dic11#10314yes—
153Dic22—81no—
154Dic22—81no—
155Dic22—81no—
156Dic22—81no—
157C8×C11—42no—
158C8×C11—81no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161C2×C4⋊Q8—111no—
162C2×C4⋊Q8—221no—
163C2×C4⋊Q8—221no—
164C2×C4⋊Q8C2×D1111yescharacteristic
165C2×C4⋊C8—111no—
166C2×C4⋊C8—111no—
167C2×C4⋊C8—222no—
168C2×C4⋊C8C2×D1111yescharacteristic
169C2×C4⋊C8C2×D1111yescharacteristic
170C2×C4×C8—221no—
171#384—114no—
172#384—222no—
173C43—111no—
174#336—221no—
175#332—22no—
176#332—222no—
177#332—222no—
178#332—222no—
179C22×C11#39011yescharacteristic
180C22×C11C2×#10112yes—
181C22×C11C2×#10211yescharacteristic
182C22×C11C2×#10312yes—
183C22×C11#41811yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—82no—
187C4×C11#45911yescharacteristic
188C4×C11#45911yescharacteristic
189C4×C11#46011yescharacteristic
190C4×C11#46011yescharacteristic
191C4×C11#48712yes—
192C4×C11#49211yescharacteristic
193C4×C11#49411yescharacteristic
194Dic11—24no—
195Dic11—82no—
196Dic11#33218yescomplemented
197C22×Q8—21no—
198C22×Q8—221no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—221no—
202C22×C8—221no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8—442no—
212C4⋊Q8—442no—
213C4⋊Q8—442no—
214C4⋊Q8—442no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—112no—
217C2×C4⋊C4—224no—
218C2×C4⋊C4—224no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4C4×D1112yes—
221C2×C42—111no—
222C2×C42—112no—
223C2×C42—112no—
224C2×C42—111no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—112no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232C4⋊C8—221no—
233C4⋊C8—444no—
234C4⋊C8C22⋊D1112yes—
235C4×C8—442no—
236C2×C11C2×#33212yes—
237C2×C11#154912yes—
238C2×C11#195611yescharacteristic
239C2×C11#196611yescharacteristic
240C2×C11#198211yescharacteristic
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—441no—
248C2×Q8—441no—
249C2×Q8—441no—
250C2×Q8—441no—
251C2×Q8—441no—
252C2×Q8—441no—
253C22×C4—22no—
254C22×C4—112no—
255C22×C4—112no—
256C22×C4—222no—
257C22×C4C2×C4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—42no—
264C2×C8—41no—
265C2×C8—222no—
266C2×C8—441no—
267C2×C8—441no—
268C2×C8—442no—
269C2×C8—441no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—222no—
275C4⋊C4—222no—
276C4⋊C4—448no—
277C4⋊C4—448no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C42—112no—
281C42—114no—
282C42—112no—
283C42—114no—
284C42—224no—
285C42—221no—
286C42—221no—
287C42#433911yescharacteristic
288C42D4×D1111yescharacteristic
289C42#434111yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C11#969411yescharacteristic, complemented, Sylow
292C23C22⋊C4×D1111yescharacteristic
293Q8—81no—
294Q8—81no—
295Q8—81no—
296Q8—81no—
297Q8—881no—
298Q8—881no—
299Q8—881no—
300Q8—881no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—114no—
306C2×C4—114no—
307C2×C4—114no—
308C2×C4—114no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—442no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4(C22⋊D11)⋊C411yescharacteristic
315C2×C4#6693711yescharacteristic
316C2×C4#6693811yescharacteristic
317C2×C4D8×D1111yescharacteristic
318C2×C4#6696411yescharacteristic
319C2×C4SD16×D1111yescharacteristic
320C2×C4SD16×D1112yes—
321C2×C4#6696711yescharacteristic
322C2×C4Q16×D1112yes—
323C2×C4C4×C22⋊D1111yescharacteristic
324C2×C4#6699211yescharacteristic
325C2×C4#6699311yescharacteristic
326C8—42no—
327C8—81no—
328C8—442no—
329C8—881no—
330C22D11×#10112yes—
331C22D11×#10211yescharacteristic
332C22#1062238311yescharacteristic
333C22D11×#10312yes—
334C22#1062257011yescharacteristic
335C4—21no—
336C4—21no—
337C4—82no—
338C4—118no—
339C4—224no—
340C4—882no—
341C4#1062237511yescharacteristic
342C4#1062239911yescharacteristic
343C4#1062240512yes—
344C4#1062276311yescharacteristic
345C4#1062277611yescharacteristic
346C4#1062278811yescharacteristic
347C4#1062279411yescharacteristic
348C2D11×#33212yes—
349C2#1306729912yes—
350C2#1306941611yescharacteristic
351C2#1306945811yescharacteristic
352C2#1306954111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#332D11
hypocenterC11#9694
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
196. Dic11#332semidirect
291. C11#9694semidirect

Maximal subgroups

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

subgroupindex
#130770122
#130687672
C4⋊C8×Dic112
C2×#106221202
C2×#106221852
C2×#106221242
C2×C11×#3322
#969411