Finite Group Databasebeta

← #14649205

Subgroups — #14649205

Order 2816.

512 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622639C211yesmaximal, characteristic
2#13067011C211yesmaximal, characteristic, complemented
3#13067008C211yesmaximal, characteristic
4#13066936C211yesmaximal, characteristic
5#13066460C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#2982C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C22×#4325C411yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C8×Q8×C11—22no—
12C8×Q8×C11—22no—
13C11×#431—22no—
14C11×#431C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C2×#66899C411yescharacteristic
17#10622639—22no—
18#10622639—22no—
19C2×#66873C411yescharacteristic
20C2×#66871C411yescharacteristic
21#10622538C2211yescharacteristic
22#10622538C2211yescharacteristic
23C2×#66867C2211yescharacteristic
24Q8⋊(C11⋊C8)—22no—
25#10622106—22no—
26#10622097—22no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D44C2×C411yescharacteristic
29C22×C4×D11—21no—
30C4×Q8×C11—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11D412yes—
33C4×Q8×C11D412yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C42×C11—21no—
37C2×C42×C11C2311yescharacteristic
38C2×#4325—22no—
39C2×#4325—22no—
40C2×#4325C814yescomplemented
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C22×C11⋊C8C2×C411yescharacteristic
44C22×C11⋊C8C2×C411yescharacteristic
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48C4×D44—21no—
49C11×C4⋊C8—24no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8D412yes—
54C4×C8×C11—24no—
55C4×C8×C11—21no—
56C4×C8×C11D412yes—
57#66899—22no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66873—22no—
61#66871—22no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#66867—21no—
65#66867—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68#9090—111nomaximal, Sylow
69C23×D11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11C22⋊C412yes—
74C2×Q8×C11C2×C812yes—
75C2×Q8×C11M1612yes—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×Dic11—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44C2×C812yes—
88C2×C4×D11—41no—
89C2×C4×D11—41no—
90C2×C4×D11—82no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4C22⋊C412yes—
97C42×C11—22no—
98C42×C11—22no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103#4325—28no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8C2×C812yes—
116#2982D1111yescharacteristic, complemented
117C2×#440—111no—
118#1479—111no—
119#1478—111no—
120#1460—111no—
121#1281—111no—
122#1275—111no—
123C23×C11C4×D411yescharacteristic
124C22×D11—22no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—81no—
128C22×D11—81no—
129Q8×C11—22no—
130Q8×C11—22no—
131Q8×C11—22no—
132Q8×C11C22⋊C814yes—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—81no—
140C2×C4×C11C2×C22⋊C411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12311yescharacteristic
146C2×C4×C11C22×C811yescharacteristic
147C2×C4×C11C2×M1611yescharacteristic
148C2×C4×C11#13111yescharacteristic
149C2×C4×C11#13111yescharacteristic
150C2×Dic11—41no—
151C2×Dic11—81no—
152D44—22no—
153D44—22no—
154D44—41no—
155D44—41no—
156C4×D11—82no—
157C4×D11—82no—
158C8×C11—42no—
159C8×C11—42no—
160C11⋊C8—22no—
161C11⋊C8—41no—
162C11⋊C8—81no—
163C11⋊C8—81no—
164C22×SD16—111no—
165C2×C4×Q8C2×D1111yescharacteristic
166C2×C4×D4—111no—
167C8×Q8—22no—
168C8×Q8—22no—
169#440—222no—
170#440—222no—
171#431—22no—
172#431—111no—
173#431—111no—
174#431C2×D1111yescharacteristic
175#431C2×D1111yescharacteristic
176C2×#107—111no—
177C2×#103—111no—
178C2×#102—111no—
179C2×#97—111no—
180Q8⋊C8—222no—
181D4⋊C8—222no—
182#323—222no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11#38611yescharacteristic
186C22×C11C8×D411yescharacteristic
187C22×C11#43511yescharacteristic
188C2×D11—42no—
189C2×D11—82no—
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—82no—
193C4×C11—24no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—42no—
199C4×C11C2×C22⋊C811yescharacteristic
200C4×C11#40811yescharacteristic
201C4×C11C8×D411yescharacteristic
202C4×C11#43511yescharacteristic
203Dic11—81no—
204C22×Q8C4×D1111yescharacteristic
205C22×D4—111no—
206C23×C4—221no—
207C2×SD16—114no—
208C2×SD16—222no—
209C2×SD16—222no—
210C22×C8—111no—
211C22×C8—111no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8D4412yes—
215C4×Q8C22⋊D1112yes—
216C4×D4—221no—
217C4×D4—221no—
218C4×D4—221no—
219C4×D4—221no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4C4×D1111yescharacteristic
223C2×C22⋊C4—221no—
224C2×C42—21no—
225C2×C42C22×D1111yescharacteristic
226#107—222no—
227C4⋊C8—24no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232#103—222no—
233#102—222no—
234C22⋊C8—21no—
235C22⋊C8—221no—
236C22⋊C8—221no—
237C22⋊C8C22⋊D1112yes—
238#97—221no—
239#97—221no—
240C4×C8—24no—
241C4×C8—21no—
242C4×C8—221no—
243C4×C8—221no—
244C4×C8C22⋊D1112yes—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11#186911yescharacteristic
248C2×C11#190311yescharacteristic
249C2×C11#190511yescharacteristic
250D11—82no—
251C24—221no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8C8×D1112yes—
256C2×Q8#431312yes—
257C2×Q8(C2×D11)⋊C412yes—
258C2×D4—112no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—221no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—221no—
267C22×C4—441no—
268C22×C4—441no—
269C22×C4—882no—
270C22×C4C2×C4×D1111yescharacteristic
271C22×C4#433911yescharacteristic
272C22×C4C2×C22⋊D1111yescharacteristic
273SD16—228no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—112no—
277C2×C8—221no—
278C2×C8—221no—
279C2×C8—221no—
280C2×C8—221no—
281C2×C8—221no—
282C2×C8—441no—
283C2×C8—441no—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4(C2×D11)⋊C412yes—
290C22⋊C4—441no—
291C22⋊C4—441no—
292C42—22no—
293C42—22no—
294C42C2×D4411yescharacteristic
295C42#433911yescharacteristic
296C42C2×C22⋊D1111yescharacteristic
297C42C2×C22⋊D1111yescharacteristic
298C11#909011yescharacteristic, complemented, Sylow
299C23—222no—
300C23—441no—
301C23—441no—
302C23—881no—
303C23—881no—
304C23C4×C22⋊D1111yescharacteristic
305Q8—22no—
306Q8—22no—
307Q8—22no—
308Q8(C2×D11)⋊C814yes—
309D4—222no—
310D4—222no—
311D4—441no—
312D4—441no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—441no—
321C2×C4—882no—
322C2×C4—882no—
323C2×C4—881no—
324C2×C4C2×C8×D1111yescharacteristic
325C2×C4C2×#431311yescharacteristic
326C2×C4#6695411yescharacteristic
327C2×C4#6695411yescharacteristic
328C2×C4C2×(C2×D11)⋊C411yescharacteristic
329C2×C4C4×C22⋊D1111yescharacteristic
330C2×C4#6698211yescharacteristic
331C2×C4#6698311yescharacteristic
332C2×C4#6698311yescharacteristic
333C2×C4#6700611yescharacteristic
334C8—42no—
335C8—42no—
336C8—222no—
337C8—441no—
338C8—881no—
339C8—881no—
340C22—21no—
341C22—21no—
342C22—442no—
343C22—882no—
344C22—882no—
345C22—881no—
346C22—881no—
347C22C8×C22⋊D1111yescharacteristic
348C22#1062272411yescharacteristic
349C22#1062282611yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—24no—
355C4—42no—
356C4—881no—
357C4C2×(C2×D11)⋊C811yescharacteristic
358C4C8×C22⋊D1111yescharacteristic
359C4#1062272311yescharacteristic
360C4#1062272411yescharacteristic
361C2—21no—
362C2—21no—
363C2—882no—
364C2#1306890811yescharacteristic
365C2#1306909611yescharacteristic
366C2#1306911011yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#2982C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#2982D11
hypocenterC11#9090
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #13067011C2semidirect
5. #13066460C2semidirect
6. #13066446C2semidirect
7. C11×#2982C2semidirect
40. C2×#4325C8semidirect
116. #2982D11semidirect
298. C11#9090semidirect

Maximal subgroups

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

subgroupindex
C2×#106226392
#130670112
#130670082
#130669362
#130664602
#130664462
C11×#29822
#909011