Finite Group Databasebeta

← #14652888

Subgroups — #14652888

Order 2816.

590 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#13076974C211yesmaximal, characteristic
2#13068732C211yesmaximal, characteristic, complemented
3#13068471C211yesmaximal, 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×#66879—21no—
14#10622601—21no—
15#10622601—21no—
16#10622601C414yes—
17C42×Dic11C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#332—22no—
21#10622188—21no—
22#10622188—22no—
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×Dic11D412yes—
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
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—
57#66879—42no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)D412yes—
62#9710—111nomaximal, Sylow
63C23×D11—22no—
64C2×Q8×C11—41no—
65C2×Q8×C11—41no—
66C2×Q8×C11—42no—
67C2×Q8×C11—42no—
68C22×C4×C11—22no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11C22⋊C412yes—
73C22×Dic11C22⋊C412yes—
74C2×D44—22no—
75C2×D44—22no—
76C2×D44—44no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—42no—
84C2×D44—42no—
85C2×D44—41no—
86C2×D44—41no—
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C2×C8×C11—42no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11#4111yescharacteristic
99C42×C11#4111yescharacteristic
100(C2×D11)⋊C4—48no—
101(C2×D11)⋊C4—48no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—22no—
106C4×Dic11—22no—
107C4×Dic11—21no—
108C4×Dic11—42no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—42no—
114#2858—111no—
115#1831—111no—
116#1767—111no—
117C2×#332—111no—
118C2×#332D1111yescharacteristic, complemented
119C2×#331—111no—
120C2×#331—111no—
121C23×C11C2×C22⋊C411yescharacteristic
122C22×D11—42no—
123C22×D11—44no—
124C22×D11—42no—
125C22×D11—42no—
126C22×D11—44no—
127Q8×C11—82no—
128Q8×C11—81no—
129Q8×C11—81no—
130C2×C4×C11—22no—
131C2×C4×C11—42no—
132C2×C4×C11—44no—
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12411yescharacteristic
138C2×C4×C11#12711yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11#13511yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)12yes—
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)12yes—
144C2×C4×C11#13711yescharacteristic
145C2×Dic11—22no—
146C2×Dic11—22no—
147C2×Dic11—22no—
148C2×Dic11—22no—
149C2×Dic11—22no—
150C2×Dic11—22no—
151D44—82no—
152D44—82no—
153D44—81no—
154D44—81no—
155D44—81no—
156D44—81no—
157D44—82no—
158D44—81no—
159D44—81no—
160C8×C11—42no—
161C8×C11—81no—
162C11⋊C8—42no—
163C11⋊C8—81no—
164C2×C4⋊Q8C2×D1111yescharacteristic
165C2×#127—111no—
166C2×#124—222no—
167C2×C4⋊C8—111no—
168C2×C4⋊C8—111no—
169C2×C4⋊C8C2×D1111yescharacteristic
170C2×C4⋊C8C2×D1111yescharacteristic
171C2×#97—221no—
172#390—114no—
173#390—221no—
174#390—221no—
175C43—111no—
176#336—222no—
177#336—221no—
178#332—22no—
179#332—222no—
180#331—222no—
181#331—222no—
182C22×C11#39011yescharacteristic
183C22×C11#41312yes—
184C22×C11#41611yescharacteristic
185C22×C11#41711yescharacteristic
186C22×C11#41812yes—
187C2×D11—84no—
188C2×D11—84no—
189C2×D11—82no—
190C2×D11—82no—
191C2×D11—82no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—82no—
195C4×C11#46311yescharacteristic
196C4×C11#46311yescharacteristic
197C4×C11#46411yescharacteristic
198C4×C11#46411yescharacteristic
199C4×C11#49012yes—
200C4×C11#49611yescharacteristic
201C4×C11#49611yescharacteristic
202Dic11—42no—
203Dic11—42no—
204C22×Q8—21no—
205C22×D4—112no—
206C22×D4—221no—
207C22×D4—221no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—221no—
211C22×C8—221no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216#127—221no—
217#127—221no—
218#127—221no—
219#127—221no—
220#124—444no—
221#124—444no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C4×D1112yes—
224C2×C22⋊C4—224no—
225C2×C22⋊C4—224no—
226C2×C42—112no—
227C2×C42—111no—
228C2×C42—111no—
229C2×C42—112no—
230C2×C42C22×D1111yescharacteristic
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—112no—
235C4⋊C8—221no—
236C4⋊C8—221no—
237C4⋊C8—221no—
238C4⋊C8C22⋊D1112yes—
239#97—442no—
240C2×C11#155312yes—
241C2×C11#155712yes—
242C2×C11#196111yescharacteristic
243C2×C11#196711yescharacteristic
244C2×C11#198311yescharacteristic
245D11—162no—
246C24—222no—
247C2×Q8—41no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—41no—
251C2×D4—222no—
252C2×D4—222no—
253C2×D4—444no—
254C2×D4—441no—
255C2×D4—441no—
256C2×D4—442no—
257C2×D4—442no—
258C2×D4—441no—
259C2×D4—441no—
260C2×D4—441no—
261C2×D4—441no—
262C2×D4—441no—
263C2×D4—441no—
264C22×C4—22no—
265C22×C4—112no—
266C22×C4—112no—
267C22×C4C2×C4×D1111yescharacteristic
268C22×C4D4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—42no—
274C2×C8—41no—
275C2×C8—222no—
276C2×C8—441no—
277C2×C8—441no—
278C2×C8—442no—
279C2×C8—441no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C22⋊C4—448no—
285C22⋊C4—448no—
286C42—222no—
287C42—221no—
288C42—222no—
289C42—221no—
290C42—221no—
291C42—221no—
292C42—442no—
293C42#433911yescharacteristic
294C42D4×D1111yescharacteristic
295C42#434111yescharacteristic
296C42C2×C22⋊D1111yescharacteristic
297C11#971011yescharacteristic, complemented, Sylow
298C23—442no—
299C23—444no—
300C23—444no—
301C23—442no—
302C23—442no—
303C23C22⋊C4×D1111yescharacteristic
304Q8—81no—
305Q8—81no—
306Q8—82no—
307D4—882no—
308D4—882no—
309D4—881no—
310D4—881no—
311D4—881no—
312D4—881no—
313D4—882no—
314D4—881no—
315D4—881no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—44no—
319C2×C4—222no—
320C2×C4—222no—
321C2×C4—222no—
322C2×C4—222no—
323C2×C4—222no—
324C2×C4—222no—
325C2×C4(C22⋊D11)⋊C411yescharacteristic
326C2×C4#6693711yescharacteristic
327C2×C4#6693811yescharacteristic
328C2×C4#6696412yes—
329C2×C4#6696711yescharacteristic
330C2×C4#6696712yes—
331C2×C4#6696911yescharacteristic
332C2×C4#6697111yescharacteristic
333C2×C4#6697211yescharacteristic
334C2×C4C4×C22⋊D1111yescharacteristic
335C2×C4#6699211yescharacteristic
336C2×C4#6699311yescharacteristic
337C8—42no—
338C8—81no—
339C8—442no—
340C8—881no—
341C22—884no—
342C22—884no—
343C22—882no—
344C22—882no—
345C22—882no—
346C22#1062236412yes—
347C22#1062238312yes—
348C22#1062241611yescharacteristic
349C22#1062241711yescharacteristic
350C22#1062257011yescharacteristic
351C4—21no—
352C4—21no—
353C4—82no—
354C4—442no—
355C4—442no—
356C4#1062237712yes—
357C4#1062241111yescharacteristic
358C4#1062243211yescharacteristic
359C4#1062276711yescharacteristic
360C4#1062277811yescharacteristic
361C4#1062278911yescharacteristic
362C4#1062279811yescharacteristic
363C2—1762no—
364C2#1306732012yes—
365C2#1306733712yes—
366C2#1306943811yescharacteristic
367C2#1306946411yescharacteristic
368C2#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#9710
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. #13068732C2semidirect
3. #13068471C2semidirect
4. C2×#10622185C2semidirect
7. C2×C11×#332C2semidirect
118. C2×#332D11semidirect
297. C11#9710semidirect

Maximal subgroups

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

subgroupindex
#130769742
#130687322
#130684712
C2×#106221852
C2×#106221232
C2×C11×#3322
#971011