Finite Group Databasebeta

← #14663330

Subgroups — #14663330

Order 2816.

496 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 83 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#13073083C211yesmaximal, characteristic
2C2×#10622166C211yesmaximal, characteristic, complemented
3#13066561C212yesmaximal, complemented
4#13066547C212yesmaximal, complemented
5C11×#1463C211yesmaximal, characteristic, complemented
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66983C411yescharacteristic
8C2×#66982—21no—
9C2×#66982—21no—
10C11×#407—21no—
11C4×C22⋊Dic11C411yescharacteristic
12C2×C22⋊(C11⋊C8)—21no—
13#10622605—21no—
14#10622605—21no—
15#10622601C411yescharacteristic
16#10622601C2211yescharacteristic
17#10622589C411yescharacteristic
18#10622589C2211yescharacteristic
19C11×#324—21no—
20C11×#324C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×D44C2×C411yescharacteristic
28C2×C11×M16—41no—
29C2×C11×C4⋊C4—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36#66983—41no—
37#66983—41no—
38#66982—44no—
39#66982—44no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11C2×C411yescharacteristic
51C2×C4×Dic11C2×C411yescharacteristic
52C22×C11⋊C8—41no—
53C11×C22⋊C8—22no—
54C11×C22⋊C8—41no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11549—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C23×D11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—41no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C2×D44—22no—
85C2×D44—41no—
86C2×D44—41no—
87C11×M16—82no—
88C2×C8×C11—42no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C22⋊Dic11—24no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99C4⋊Dic11—41no—
100Dic11⋊C4—42no—
101Dic11⋊C4—42no—
102Dic11⋊C4—42no—
103Dic11⋊C4—42no—
104C4×Dic11—22no—
105C4×Dic11—41no—
106C2×C11⋊C8—42no—
107C2×C11⋊C8—82no—
108#2501—111no—
109#1463D1111yescharacteristic, complemented
110C2×#324—111no—
111#1325—112no—
112#1318—112no—
113C23×C11—22no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—41no—
117C23×C11#9911yescharacteristic
118C23×C11#9911yescharacteristic
119C23×C11C2×C22⋊C411yescharacteristic
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11#13112yes—
147C22⋊D11—82no—
148C22⋊D11—82no—
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158D44—82no—
159C8×C11—82no—
160C11⋊C8—82no—
161C2×#123—221no—
162C2×#123—221no—
163C2×#121—111no—
164C22×C4⋊C4C2×D1111yescharacteristic
165#407—21no—
166C2×C22⋊C8—221no—
167#399—221no—
168#399—221no—
169#390—111no—
170#390—111no—
171#384—111no—
172#384—111no—
173C4×C22⋊C4—111no—
174#324—21no—
175#324—112no—
176#324—221no—
177#324C2×D1112yes—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11#35312yes—
188C22×C11#40811yescharacteristic
189C22×C11C2×#9911yescharacteristic
190C22×C11#41311yescharacteristic
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C4×C11—22no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—41no—
204Dic11—42no—
205Dic11—42no—
206Dic11—81no—
207C22×D4—111no—
208C22×D4—221no—
209C23×C4C4×D1111yescharacteristic
210C23×C4D4411yescharacteristic
211C23×C4C22⋊D1111yescharacteristic
212C2×M16—41no—
213C22×C8—441no—
214#123—444no—
215#123—444no—
216#121—441no—
217#121—441no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4C4×D1111yescharacteristic
226C2×C4⋊C4D4411yescharacteristic
227C2×C4⋊C4C22⋊D1111yescharacteristic
228C2×C4⋊C4C22×D1111yescharacteristic
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C42—111no—
236C2×C42—111no—
237C22⋊C8—22no—
238C22⋊C8—41no—
239C22⋊C8—222no—
240C22⋊C8—441no—
241#95—221no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—22no—
245C2×C11—41no—
246C2×C11#146811yescharacteristic
247C2×C11C2×#35311yescharacteristic
248C2×C11#213311yescharacteristic
249D11—161no—
250C24—221no—
251C24(C2×D11)⋊C411yescharacteristic
252C2×D4—222no—
253C2×D4—441no—
254C2×D4—441no—
255C2×D4—442no—
256C2×D4—442no—
257C2×D4—441no—
258C2×D4—441no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—41no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4(C2×D11)⋊C411yescharacteristic
273C22×C4(C2×D11)⋊C411yescharacteristic
274C22×C4(C2×D11)⋊C411yescharacteristic
275C22×C4C2×C4×D1111yescharacteristic
276C22×C4C2×D4411yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278M16—82no—
279C2×C8—42no—
280C2×C8—442no—
281C2×C8—882no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—441no—
287C4⋊C4—442no—
288C4⋊C4—442no—
289C4⋊C4—442no—
290C4⋊C4—442no—
291C22⋊C4—224no—
292C22⋊C4—442no—
293C22⋊C4—442no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C22⋊C4—442no—
297C42—222no—
298C42—441no—
299C11#1154911yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—22no—
303C23—41no—
304C23—441no—
305C23—441no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23—441no—
311C23#6687011yescharacteristic
312C23#6687011yescharacteristic
313C23C2×(C2×D11)⋊C411yescharacteristic
314D4—882no—
315D4—882no—
316D4—882no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—222no—
337C2×C4—222no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4#6696012yes—
346C8—82no—
347C8—882no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—42no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22—881no—
364C22#1062211212yes—
365C22C2×#6687011yescharacteristic
366C22#1062274211yescharacteristic
367C22#1062274511yescharacteristic
368C4—22no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—442no—
375C4—442no—
376C4—881no—
377C2—21no—
378C2—21no—
379C2—22no—
380C2—41no—
381C2—1761no—
382C2#1306696511yescharacteristic
383C2C2×#1062211211yescharacteristic
384C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1463C2
socleC22×C11C2×#99
prime radicalC2×#66983C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1463D11
hypocenterC11#11549
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. C2×#10622166C2semidirect
3. #13066561C2semidirect
4. #13066547C2semidirect
5. C11×#1463C2semidirect
109. #1463D11semidirect
299. C11#11549semidirect

Maximal subgroups

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

subgroupindex
#130730832
C2×#106221662
#130665612
#130665472
C11×#14632
#1154911