Finite Group Databasebeta

← #14649458

Subgroups — #14649458

Order 2816.

612 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#13076968C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622124C212yesmaximal, complemented
4#13066500C212yesmaximal, complemented
5C2×C11×#423C211yesmaximal, characteristic
6C22×C11×M16—21no—
7C22×C42×C11C2211yescharacteristic
8C2×#66977—21no—
9C2×#66922C2211yescharacteristic
10C11×#423—24no—
11C2×C11×C4⋊C8—21no—
12C2×C11×C4⋊C8C2212yes—
13#10622825—21no—
14#10622825C412yes—
15C2×C22⋊(C11⋊C8)—21no—
16#10622548C2211yescharacteristic
17#10622542—21no—
18#10622541—21no—
19#10622541C412yes—
20C2×C4⋊(C11⋊C8)C2212yes—
21#10622162—21no—
22#10622124—24no—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22—21no—
27C2×C11×M16—24no—
28C2×C11×M16—42no—
29C2×C11×M16—42no—
30C22×C8×C11—22no—
31C2×C42×C11—22no—
32C2×C42×C11—22no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×C22⋊Dic11—22no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11C2×C412yes—
42C2×C4⋊Dic11C2×C412yes—
43#66977—44no—
44C2×Dic11⋊C4—22no—
45C22×C11⋊C8—22no—
46#66922—22no—
47#66922—22no—
48C11×C4⋊C8—24no—
49C11×C4⋊C8—22no—
50C11×C4⋊C8D414yes—
51C11⋊#95—22no—
52C11⋊#95—22no—
53C22⋊(C11⋊C8)—42no—
54C4⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—22no—
56#9137—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11SD1612yes—
73C22×C4×C11Q1612yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—22no—
78C22×Dic11—22no—
79C2×Dic22—42no—
80C2×Dic22—42no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C11×M16—48no—
84C2×C8×C11—24no—
85C2×C8×C11—42no—
86C2×C8×C11—42no—
87C42×C11—22no—
88C42×C11—21no—
89C42×C11—22no—
90C42×C11—21no—
91C42×C11C2×D412yes—
92C42×C11#4112yes—
93C22⋊Dic11—44no—
94C4⋊Dic11—24no—
95C4⋊Dic11—42no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—42no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101Dic11⋊C4—44no—
102C2×C11⋊C8—42no—
103C2×C11⋊C8—42no—
104C2×C11⋊C8—42no—
105C2×#423D1111yescharacteristic
106#2857—111no—
107#1797—111no—
108C2×#332—112no—
109#1296—112no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11#10312yes—
117C23×C11C2×C22⋊C411yescharacteristic
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—44no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11#10112yes—
135C2×C4×C11#10312yes—
136C2×C4×C11C4×D412yes—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12112yes—
139C2×C4×C11#12311yescharacteristic
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11C2×Q1611yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)12yes—
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153Dic22—82no—
154Dic22—82no—
155C8×C11—44no—
156C11⋊C8—82no—
157C22×M16—21no—
158C2×C4⋊Q8—111no—
159C2×C22⋊Q8—221no—
160C22×C42C2×D1111yescharacteristic
161#423—24no—
162C2×C4⋊C8—21no—
163C2×C4⋊C8—112no—
164C2×C4⋊C8C2×D1112yes—
165C2×C22⋊C8—221no—
166#391—221no—
167#389—112no—
168#389—221no—
169#384—111no—
170#380—112no—
171#380—221no—
172#336—221no—
173#332—224no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11#38611yescharacteristic
182C22×C11C2×#10111yescharacteristic
183C22×C11#41311yescharacteristic
184C22×C11C2×#10311yescharacteristic
185C22×C11#41711yescharacteristic
186C22×C11#41711yescharacteristic
187C22×C11#41811yescharacteristic
188C4×C11—22no—
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—41no—
192C4×C11#45011yescharacteristic
193C4×C11#45111yescharacteristic
194C4×C11#46812yes—
195C4×C11#46912yes—
196C4×C11#48311yescharacteristic
197C4×C11#48411yescharacteristic
198Dic11—82no—
199Dic11—82no—
200C22×Q8—221no—
201C23×C4C4×D1111yescharacteristic
202C23×C4D4411yescharacteristic
203C23×C4C22⋊D1111yescharacteristic
204C2×M16—24no—
205C2×M16—42no—
206C2×M16—42no—
207C22×C8—22no—
208C22×C8—222no—
209C4⋊Q8—222no—
210C4⋊Q8—222no—
211C22⋊Q8—444no—
212C2×C4⋊C4—112no—
213C2×C4⋊C4—112no—
214C2×C4⋊C4—222no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C22⋊C4—222no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42C4×D1111yescharacteristic
222C2×C42D4411yescharacteristic
223C2×C42C22⋊D1111yescharacteristic
224C2×C42C22×D1111yescharacteristic
225C4⋊C8—24no—
226C4⋊C8—22no—
227C4⋊C8—222no—
228C4⋊C8—222no—
229C4⋊C8C22⋊D1114yes—
230C22⋊C8—442no—
231#95—222no—
232#95—222no—
233C2×C11—42no—
234C2×C11#154911yescharacteristic
235C2×C11#155011yescharacteristic
236C2×C11#155711yescharacteristic
237C2×C11#156111yescharacteristic
238C2×C11#187211yescharacteristic
239C2×C11#189511yescharacteristic
240C2×C11#190111yescharacteristic
241C24(C2×D11)⋊C411yescharacteristic
242C2×Q8—442no—
243C2×Q8—441no—
244C2×Q8—441no—
245C2×Q8—442no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—41no—
257C22×C4—222no—
258C22×C4—222no—
259C22×C4(C2×D11)⋊C411yescharacteristic
260C22×C4(C2×D11)⋊C411yescharacteristic
261C22×C4(C2×D11)⋊C411yescharacteristic
262C22×C4#432412yes—
263C22×C4#432612yes—
264C22×C4C2×C4×D1111yescharacteristic
265C22×C4C2×D4411yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267M16—48no—
268C2×C8—24no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—442no—
272C2×C8—442no—
273C2×C8—442no—
274C4⋊C4—224no—
275C4⋊C4—442no—
276C4⋊C4—444no—
277C4⋊C4—442no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C22⋊C4—444no—
283C42—22no—
284C42—21no—
285C42—22no—
286C42—21no—
287C42#433912yes—
288C42C2×C22⋊D1112yes—
289C11#913711yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23#6687412yes—
297C23C2×(C2×D11)⋊C411yescharacteristic
298Q8—882no—
299Q8—882no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—44no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4#6687412yes—
323C2×C4#6688812yes—
324C2×C4#6696112yes—
325C2×C4#6696111yescharacteristic
326C2×C4#6696211yescharacteristic
327C2×C4C4×C22⋊D1112yes—
328C2×C4#6698211yescharacteristic
329C2×C4#6698312yes—
330C2×C4#6698511yescharacteristic
331C2×C4C2×#432411yescharacteristic
332C2×C4#6699511yescharacteristic
333C2×C4C2×#432611yescharacteristic
334C2×C4#6700611yescharacteristic
335C8—44no—
336C8—882no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22#1062257911yescharacteristic
345C22C2×#6687411yescharacteristic
346C22#1062274411yescharacteristic
347C22#1062274511yescharacteristic
348C22#1062274611yescharacteristic
349C22C2×#6688811yescharacteristic
350C22#1062282611yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—882no—
356C4—882no—
357C4#1062258311yescharacteristic
358C4#1062258411yescharacteristic
359C4#1062274712yes—
360C4#1062274812yes—
361C4#1062283111yescharacteristic
362C4#1062284111yescharacteristic
363C2—42no—
364C2#1306730211yescharacteristic
365C2#1306730711yescharacteristic
366C2#1306733611yescharacteristic
367C2#1306735311yescharacteristic
368C2#1306892311yescharacteristic
369C2#1306905411yescharacteristic
370C2#1306908411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#423C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#423D11
hypocenterC11#9137
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
3. C2×#10622124C2semidirect
4. #13066500C2semidirect
289. C11#9137semidirect

Maximal subgroups

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

subgroupindex
#130769682
#130685962
C2×#106221242
#130665002
C2×C11×#4232
#913711