Finite Group Databasebeta

← #14663386

Subgroups — #14663386

Order 2816.

748 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 748 conjugacy classes of subgroups — too many to draw. Only its 95 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#13066954C211yesmaximal, characteristic, complemented
2#13066937C211yesmaximal, characteristic, complemented
3#13066544C214yesmaximal, complemented
4C11×#2408C211yesmaximal, characteristic
5C23×D4×C11C411yescharacteristic
6C2×C11×#121—21no—
7C2×C11×#120C412yes—
8C2×C4×D4×C11C2211yescharacteristic
9C11×#394—21no—
10C11×#392—21no—
11C11×#390—21no—
12C11×#380C411yescharacteristic
13C11×#379C2212yes—
14#10622820—21no—
15#10622538—21no—
16#10622166—21no—
17#10622163—21no—
18#10622163C2212yes—
19#10622163C2212yes—
20C25×C11C2×C412yes—
21C22×D4×C11—22no—
22C22×D4×C11—21no—
23C22×D4×C11—21no—
24C22×D4×C11—41no—
25C22×D4×C11—41no—
26C22×D4×C11—44no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C11×#121—44no—
31C11×#120—44no—
32C4×D4×C11—41no—
33C4×D4×C11—41no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4C2×C412yes—
40C2×C11×C22⋊C4D411yescharacteristic
41C2×C11×C22⋊C4C2311yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×#4318—41no—
44C11×#95—21no—
45C22⋊(C11⋊C8)—22no—
46C22⋊(C11⋊C8)—22no—
47C22⋊(C11⋊C8)—41no—
48C4⋊(C11⋊C8)—41no—
49C4×C11⋊C8—41no—
50#11561—111nomaximal, Sylow
51C24×C11—22no—
52C24×C11—24no—
53C24×C11—42no—
54C24×C11—44no—
55C24×C11—42no—
56C24×C11—82no—
57C24×C11C22⋊C411yescharacteristic
58C24×C11C22×C411yescharacteristic
59C2×D4×C11—24no—
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—41no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C2×D4×C11—44no—
66C2×D4×C11—48no—
67C2×D4×C11—44no—
68C2×D4×C11—44no—
69C2×D4×C11—44no—
70C2×D4×C11—44no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—82no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—22no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C11×C4⋊C4—41no—
87C11×C4⋊C4—42no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—44no—
91C11×C22⋊C4—44no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—82no—
94C42×C11—21no—
95C42×C11—21no—
96#4318—82no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—42no—
99#2408D1111yescharacteristic
100#1465—111no—
101#1460—111no—
102#1316—114no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—24no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—42no—
114C23×C11—42no—
115C23×C11—42no—
116C23×C11—44no—
117C23×C11—44no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11—42no—
121C23×C11—84no—
122C23×C11—88no—
123C23×C11—88no—
124C23×C11—84no—
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11#13112yes—
127D4×C11—44no—
128D4×C11—44no—
129D4×C11—48no—
130D4×C11—44no—
131D4×C11—88no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—22no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—81no—
148C2×C4×C11#9911yescharacteristic
149C2×C4×C11#9911yescharacteristic
150C2×C4×C11#10012yes—
151C11⋊C8—82no—
152C11⋊C8—82no—
153C23×D4Dic1111yescharacteristic
154C2×#121—21no—
155C2×#120Dic1112yes—
156C2×C4×D4C2×D1111yescharacteristic
157#431—221no—
158#407—221no—
159#394—21no—
160#392—21no—
161#390—21no—
162#380Dic1111yescharacteristic
163#379C2×D1112yes—
164#324—221no—
165#323—112no—
166#323—112no—
167#323—221no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—22no—
171C22×C11—42no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11—44no—
175C22×C11—44no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—44no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—81no—
183C22×C11—82no—
184C22×C11—82no—
185C22×C11—88no—
186C22×C11—88no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11#40811yescharacteristic
190C22×C11C2×#9911yescharacteristic
191C22×C11C2×#10011yescharacteristic
192C4×C11—21no—
193C4×C11—22no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—82no—
198C4×C11AΣL(1,𝔽16)12yes—
199C25C2×Dic1112yes—
200C22×D4—22no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—41no—
204C22×D4—41no—
205C22×D4—44no—
206C22×D4C2×Dic1111yescharacteristic
207C23×C4C2×Dic1111yescharacteristic
208C23×C4C22⋊D1111yescharacteristic
209C2×M16—441no—
210#121—44no—
211#120—44no—
212C4×D4—41no—
213C4×D4—41no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C22⋊D1111yescharacteristic
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4C2×Dic1112yes—
220C2×C22⋊C4C22⋊D1111yescharacteristic
221C2×C22⋊C4C22×D1111yescharacteristic
222C2×C42C22⋊D1111yescharacteristic
223C4⋊C8—441no—
224C22⋊C8—222no—
225C22⋊C8—222no—
226C22⋊C8—441no—
227C4×C8—441no—
228#95—21no—
229C2×C11—21no—
230C2×C11—21no—
231C2×C11—42no—
232C2×C11—81no—
233C2×C11—84no—
234C2×C11#147111yescharacteristic
235C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
236C2×C11#212211yescharacteristic
237C24—22no—
238C24—24no—
239C24—42no—
240C24—44no—
241C24—42no—
242C24—82no—
243C24C22⋊Dic1111yescharacteristic
244C24C22×Dic1111yescharacteristic
245C2×D4—24no—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—41no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—44no—
252C2×D4—48no—
253C2×D4—44no—
254C2×D4—44no—
255C2×D4—44no—
256C2×D4—44no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—82no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4C22⋊Dic1111yescharacteristic
268C22×C4C22⋊Dic1111yescharacteristic
269C22×C4C22⋊Dic1111yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272M16—882no—
273C2×C8—442no—
274C2×C8—442no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—44no—
280C22⋊C4—44no—
281C22⋊C4—42no—
282C22⋊C4—82no—
283C42—21no—
284C42—21no—
285C11#1156111yescharacteristic, complemented, Sylow
286C23—21no—
287C23—21no—
288C23—24no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—42no—
297C23—42no—
298C23—42no—
299C23—44no—
300C23—44no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—84no—
305C23—88no—
306C23—88no—
307C23—84no—
308C23#6700112yes—
309C23C2×C22⋊Dic1111yescharacteristic
310D4—44no—
311D4—44no—
312D4—48no—
313D4—44no—
314D4—88no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4#6689712yes—
332C2×C4#6689811yescharacteristic
333C2×C4#6689811yescharacteristic
334C8—882no—
335C8—882no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—42no—
341C22—42no—
342C22—44no—
343C22—44no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—44no—
348C22—41no—
349C22—41no—
350C22—81no—
351C22—82no—
352C22—82no—
353C22—88no—
354C22—88no—
355C22—82no—
356C22—82no—
357C22C2×#6689711yescharacteristic
358C22C2×#6689811yescharacteristic
359C22#1062284711yescharacteristic
360C4—21no—
361C4—22no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—82no—
366C4#1062217412yes—
367C2—21no—
368C2—21no—
369C2—42no—
370C2—81no—
371C2—84no—
372C2#1306697611yescharacteristic
373C2C2×#1062217411yescharacteristic
374C2#1307026611yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
Fitting, prime radicalC11×#2408C2
socleC22×C11C2×#99
cosocleC2×C11×C22⋊C4C23
hypercenter#2408D11
hypocenterC11#11561
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. #13066954C2semidirect
2. #13066937C2semidirect
3. #13066544C2semidirect
285. C11#11561semidirect

Maximal subgroups

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

subgroupindex
#130669542
#130669372
#130665442
C11×#24082
#1156111