Finite Group Databasebeta

← #14664342

Subgroups — #14664342

Order 2816.

652 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 652 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073562C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic, complemented
3#13066612C214yesmaximal, complemented
4C4×C11×#99C211yesmaximal, characteristic, complemented
5C2×C4×D4×C11C2211yescharacteristic
6C2×#66993—21no—
7C2×#66983—21no—
8C2×#66983—21no—
9C2×#66927C411yescharacteristic, complemented
10C2×C11×#99—21no—
11C4×C11×C22⋊C4—21no—
12#10622820—21no—
13#10622601—21no—
14#10622573C412yescomplemented
15#10622573C2212yes—
16C4×C4⋊Dic11C411yescharacteristic, complemented
17C11×#342C2212yes—
18#10622166—21no—
19#10622163C2212yes—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C22×C22⋊D11—22no—
24C22×C22⋊D11—22no—
25C22×D44—21no—
26C22×D44—21no—
27C22×D44C2×C412yes—
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C42×C11—41no—
35C2×C42×C11C2×C411yescharacteristic
36#66993—44no—
37#66983—44no—
38#66983—44no—
39C2×(C2×D11)⋊C4—22no—
40C2×(C2×D11)⋊C4—22no—
41C2×C4⋊Dic11—21no—
42C2×C4×Dic11—21no—
43C2×#4318—41no—
44#66927—41no—
45#66927—41no—
46C11×#99—24no—
47C11×#95—41no—
48C11⋊#95C2×C412yes—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)—41no—
51#11776—111nomaximal, Sylow
52C24×C11C22⋊C411yescharacteristic
53C24×C11C2×D411yescharacteristic
54C23×D11—22no—
55C2×D4×C11—22no—
56C2×D4×C11—22no—
57C2×D4×C11—41no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C2×C22⋊D11—44no—
71C2×C22⋊D11—44no—
72C2×C22⋊D11—44no—
73C2×C22⋊D11—44no—
74C2×C22⋊D11—82no—
75C2×C22⋊D11—82no—
76C22×Dic11—22no—
77C2×D44—42no—
78C2×D44—42no—
79C2×D44—42no—
80C2×D44—42no—
81C2×D44—42no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—42no—
85C2×D44—82no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—24no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—42no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—82no—
94(C2×D11)⋊C4—44no—
95(C2×D11)⋊C4—44no—
96C4⋊Dic11—24no—
97C4×Dic11—42no—
98#4318—82no—
99C2×C11⋊C8—42no—
100#2541—111no—
101C4×#99D1111yescharacteristic, complemented
102#1465—111no—
103#1343—114no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11C2×C22⋊C411yescharacteristic
114C23×C11AGL(1,ℤ/8)12yes—
115C22×D11—42no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—42no—
119C22×D11—42no—
120C22×D11—42no—
121C22×D11—42no—
122D4×C11—44no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—22no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—44no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—82no—
138C2×C4×C11—82no—
139C2×C4×C11#9911yescharacteristic
140C2×C4×C11#9911yescharacteristic
141C2×C4×C11#10412yes—
142C22⋊D11—88no—
143C22⋊D11—88no—
144C2×Dic11—24no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147D44—82no—
148D44—84no—
149D44—84no—
150D44—82no—
151C11⋊C8—82no—
152C2×#127—111no—
153C2×#127—221no—
154C2×#121—221no—
155C2×#121—221no—
156C2×C4×D4C2×D1111yescharacteristic
157C2×#99—21no—
158#407—221no—
159#392—112no—
160#392—112no—
161#390—221no—
162C4×C4⋊C4—111no—
163C4×C22⋊C4—21no—
164#342C2×D1112yes—
165#324—221no—
166#323—112no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—42no—
171C22×C11—42no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11C2×#9911yescharacteristic
180C22×C11#41811yescharacteristic
181C22×C11C2×#10411yescharacteristic
182C2×D11—82no—
183C2×D11—82no—
184C2×D11—82no—
185C2×D11—82no—
186C2×D11—82no—
187C2×D11—82no—
188C2×D11—82no—
189C4×C11—21no—
190C4×C11—22no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—84no—
195C4×C11#35312yes—
196Dic11—44no—
197C22×D4—112no—
198C22×D4—222no—
199C22×D4—222no—
200C22×D4—221no—
201C22×D4—221no—
202C22×D4C22⋊D1111yescharacteristic
203C23×C4D4411yescharacteristic
204C23×C4C22⋊D1111yescharacteristic
205C2×M16—441no—
206#127—441no—
207#127—441no—
208#127—444no—
209#121—444no—
210#121—444no—
211C4×D4—41no—
212C4×D4—41no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4D4411yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—222no—
217C2×C22⋊C4—222no—
218C2×C22⋊C4C4×D1111yescharacteristic
219C2×C22⋊C4C22×D1111yescharacteristic
220C2×C42—41no—
221C2×C42—221no—
222C2×C42C4×D1111yescharacteristic
223#99—24no—
224C22⋊C8—222no—
225C22⋊C8—441no—
226#95—41no—
227#95—112no—
228C2×C11—21no—
229C2×C11—21no—
230C2×C11—42no—
231C2×C11—81no—
232C2×C11#150711yescharacteristic
233C2×C11#212211yescharacteristic
234C2×C11C2×#35311yescharacteristic
235D11—162no—
236C24—222no—
237C24(C2×D11)⋊C411yescharacteristic
238C24C2×C22⋊D1111yescharacteristic
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—41no—
242C2×D4—442no—
243C2×D4—442no—
244C2×D4—442no—
245C2×D4—442no—
246C2×D4—442no—
247C2×D4—444no—
248C2×D4—444no—
249C2×D4—444no—
250C2×D4—444no—
251C2×D4—442no—
252C2×D4—441no—
253C2×D4—441no—
254C2×D4—882no—
255C2×D4—882no—
256C2×D4—882no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—222no—
265C22×C4(C2×D11)⋊C411yescharacteristic
266C22×C4(C2×D11)⋊C411yescharacteristic
267C22×C4(C2×D11)⋊C411yescharacteristic
268C22×C4C2×C4×D1111yescharacteristic
269C22×C4C2×D4411yescharacteristic
270M16—882no—
271C2×C8—442no—
272C4⋊C4—41no—
273C4⋊C4—224no—
274C22⋊C4—24no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—42no—
278C22⋊C4—444no—
279C22⋊C4—444no—
280C42—21no—
281C42—21no—
282C42—82no—
283C42—442no—
284C11#1177611yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—442no—
295C23—442no—
296C23—442no—
297C23—442no—
298C23—442no—
299C23—442no—
300C23—442no—
301C23C2×(C2×D11)⋊C411yescharacteristic
302C23#6700212yes—
303D4—44no—
304D4—884no—
305D4—882no—
306D4—884no—
307D4—888no—
308D4—888no—
309D4—882no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—44no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—224no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4#6686912yes—
330C2×C4#6687011yescharacteristic
331C2×C4#6687011yescharacteristic
332C8—882no—
333C22—21no—
334C22—21no—
335C22—22no—
336C22—42no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22—882no—
346C22—882no—
347C22—882no—
348C22—882no—
349C22—882no—
350C22—882no—
351C22—882no—
352C22C2×#6686911yescharacteristic
353C22C2×#6687011yescharacteristic
354C22#1062261411yescharacteristic
355C4—22no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—84no—
361C4—444no—
362C4#1062211212yes—
363C2—21no—
364C2—21no—
365C2—42no—
366C2—81no—
367C2—1762no—
368C2#1306713111yescharacteristic
369C2#1307026511yescharacteristic
370C2C2×#1062211211yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radical#13073562C2
cosocleC2×C11×C22⋊C4C23
hypercenterC4×#99D11
hypocenterC11#11776
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #13066954C2semidirect
3. #13066612C2semidirect
4. C4×C11×#99C2semidirect
9. C2×#66927C4semidirect
14. #10622573C4semidirect
16. C4×C4⋊Dic11C4semidirect
101. C4×#99D11semidirect
284. C11#11776semidirect

Maximal subgroups

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

subgroupindex
#130735622
#130669542
#130666122
C4×C11×#992
#1177611