Finite Group Databasebeta

← #14649408

Subgroups — #14649408

Order 2816.

644 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
1#13076968C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622119C212yesmaximal, complemented
4#13066500C212yesmaximal, complemented
5C22×C11×C4⋊C8C211yesmaximal, characteristic
6C23×C8×C11—21no—
7C22×C42×C11C2211yescharacteristic
8C2×#66977C412yes—
9C2×#66922C2211yescharacteristic
10C2×C11×C4⋊C8—21no—
11C2×C11×C4⋊C8—24no—
12C2×C11×C4⋊C8C2212yes—
13#10622825—21no—
14#10622825—21no—
15C2×C22⋊(C11⋊C8)—21no—
16#10622548C2211yescharacteristic
17#10622542C412yes—
18#10622541—21no—
19#10622541—21no—
20C2×C4⋊(C11⋊C8)C2212yes—
21#10622162—21no—
22#10622119—24no—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22C2×C412yes—
27C22×C8×C11—24no—
28C22×C8×C11—22no—
29C22×C8×C11—42no—
30C22×C8×C11—42no—
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⋊Dic11—21no—
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#9127—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—41no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11SD1612yes—
71C22×C4×C11SD1612yes—
72C22×C4×C11Q1612yes—
73C22×C4×C11Q1612yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—22no—
78C22×Dic11—22no—
79C2×Dic22—24no—
80C2×Dic22—42no—
81C2×Dic22—42no—
82C2×C8×C11—24no—
83C2×C8×C11—48no—
84C2×C8×C11—42no—
85C2×C8×C11—42no—
86C42×C11—22no—
87C42×C11—21no—
88C42×C11—22no—
89C42×C11—21no—
90C42×C11C2×D412yes—
91C42×C11#4112yes—
92C22⋊Dic11—44no—
93C4⋊Dic11—42no—
94C4⋊Dic11—41no—
95C4⋊Dic11—42no—
96C4⋊Dic11—41no—
97C4⋊Dic11—42no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100Dic11⋊C4—44no—
101C2×C11⋊C8—42no—
102C2×C11⋊C8—42no—
103C2×C11⋊C8—42no—
104C22×C4⋊C8D1111yescharacteristic
105#2857—111no—
106#1797—111no—
107C2×#333—112no—
108#1296—112no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11#10012yes—
114C23×C11#10312yes—
115C23×C11#10312yes—
116C23×C11C2×C22⋊C411yescharacteristic
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—24no—
126C2×C4×C11—24no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—44no—
133C2×C4×C11#10312yes—
134C2×C4×C11#10312yes—
135C2×C4×C11C4×D412yes—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12112yes—
138C2×C4×C11#12311yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11C2×Q1611yescharacteristic
142C2×C4×C11C2×Q1611yescharacteristic
143C2×C4×C11#13512yes—
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152Dic22—84no—
153C8×C11—44no—
154C11⋊C8—82no—
155C23×C8—21no—
156C2×C4⋊Q8—111no—
157C2×C22⋊Q8—112no—
158C22×C42C2×D1111yescharacteristic
159C2×C4⋊C8—21no—
160C2×C4⋊C8—24no—
161C2×C4⋊C8—112no—
162C2×C4⋊C8C2×D1112yes—
163C2×C22⋊C8—221no—
164#391—112no—
165#389—221no—
166#389—221no—
167#384—111no—
168#380—221no—
169#380—221no—
170#336—221no—
171#333—224no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11#33314yescomplemented
179C22×C11#38611yescharacteristic
180C22×C11C2×#10011yescharacteristic
181C22×C11#41311yescharacteristic
182C22×C11C2×#10311yescharacteristic
183C22×C11C2×#10311yescharacteristic
184C22×C11#41611yescharacteristic
185C22×C11#41711yescharacteristic
186C4×C11—22no—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—41no—
190C4×C11#45011yescharacteristic
191C4×C11#45111yescharacteristic
192C4×C11#46512yes—
193C4×C11#46712yes—
194C4×C11#48311yescharacteristic
195C4×C11#48411yescharacteristic
196Dic11—82no—
197Dic11—82no—
198C22×Q8—112no—
199C23×C4C4×D1111yescharacteristic
200C23×C4D4411yescharacteristic
201C23×C4C22⋊D1111yescharacteristic
202C22×C8—24no—
203C22×C8—22no—
204C22×C8—42no—
205C22×C8—42no—
206C22×C8—222no—
207C4⋊Q8—222no—
208C4⋊Q8—222no—
209C22⋊Q8—444no—
210C2×C4⋊C4—112no—
211C2×C4⋊C4—222no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C22⋊C4—222no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42C4×D1111yescharacteristic
220C2×C42D4411yescharacteristic
221C2×C42C22⋊D1111yescharacteristic
222C2×C42C22×D1111yescharacteristic
223C4⋊C8—24no—
224C4⋊C8—22no—
225C4⋊C8—222no—
226C4⋊C8—222no—
227C4⋊C8C22⋊D1114yes—
228C22⋊C8—442no—
229#95—222no—
230#95—222no—
231C2×C11—24no—
232C2×C11C2×#33311yescharacteristic
233C2×C11#154211yescharacteristic
234C2×C11#155011yescharacteristic
235C2×C11#155111yescharacteristic
236C2×C11#187211yescharacteristic
237C2×C11#189211yescharacteristic
238C2×C11#190011yescharacteristic
239C24(C2×D11)⋊C411yescharacteristic
240C2×Q8—224no—
241C2×Q8—442no—
242C2×Q8—442no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—222no—
253C22×C4—222no—
254C22×C4#431412yes—
255C22×C4Dic4412yes—
256C22×C4(C2×D11)⋊C411yescharacteristic
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4(C2×D11)⋊C411yescharacteristic
259C22×C4#432412yes—
260C22×C4#432612yes—
261C22×C4C2×C4×D1111yescharacteristic
262C22×C4C2×D4411yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264C2×C8—24no—
265C2×C8—48no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—442no—
269C2×C8—442no—
270C2×C8—442no—
271C4⋊C4—442no—
272C4⋊C4—444no—
273C4⋊C4—442no—
274C4⋊C4—441no—
275C4⋊C4—442no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C22⋊C4—444no—
280C42—22no—
281C42—21no—
282C42—22no—
283C42—21no—
284C42#433912yes—
285C42C2×C22⋊D1112yes—
286C11#912711yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23#6687412yes—
292C23#6688012yes—
293C23#6688712yes—
294C23C2×(C2×D11)⋊C411yescharacteristic
295Q8—884no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4#6687412yes—
319C2×C4#6688012yes—
320C2×C4C2×#431411yescharacteristic
321C2×C4#6695712yes—
322C2×C4C2×Dic4411yescharacteristic
323C2×C4C4×C22⋊D1112yes—
324C2×C4#6698211yescharacteristic
325C2×C4#6698312yes—
326C2×C4#6698511yescharacteristic
327C2×C4C2×#432411yescharacteristic
328C2×C4#6699511yescharacteristic
329C2×C4C2×#432611yescharacteristic
330C2×C4#6700611yescharacteristic
331C8—44no—
332C8—882no—
333C22—22no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22#1062211914yescomplemented
340C22#1062257911yescharacteristic
341C22C2×#6687411yescharacteristic
342C22C2×#6688011yescharacteristic
343C22#1062272611yescharacteristic
344C22C2×#6688711yescharacteristic
345C22#1062274511yescharacteristic
346C22#1062282611yescharacteristic
347C4—22no—
348C4—22no—
349C4—22no—
350C4—41no—
351C4—882no—
352C4—882no—
353C4#1062258311yescharacteristic
354C4#1062258411yescharacteristic
355C4#1062272712yes—
356C4#1062272912yes—
357C4#1062283111yescharacteristic
358C4#1062284111yescharacteristic
359C2—24no—
360C2C2×#1062211911yescharacteristic
361C2#1306727411yescharacteristic
362C2#1306730411yescharacteristic
363C2#1306730911yescharacteristic
364C2#1306892311yescharacteristic
365C2#1306903911yescharacteristic
366C2#1306907911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC22×C11×C4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC22×C4⋊C8D11
hypocenterC11#9127
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#10622119C2semidirect
4. #13066500C2semidirect
178. C22×C11#333semidirect
286. C11#9127semidirect
339. C22#10622119semidirect

Maximal subgroups

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

subgroupindex
#130769682
#130685962
C2×#106221192
#130665002
C22×C11×C4⋊C82
#912711