Finite Group Databasebeta

← #14649544

Subgroups — #14649544

Order 2816.

902 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#10622824C211yesmaximal, characteristic
2#13068526C211yesmaximal, characteristic
3C2×#10622176C212yesmaximal, complemented
4#13066494C212yesmaximal, complemented
5C11×#2848C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C2×C11×C22⋊Q8C412yescomplemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C22⋊Dic11—21no—
10C11×#385—21no—
11C11×#385—22no—
12C11×#380C412yescomplemented
13C11×#380C2211yescharacteristic
14C11×#379—21no—
15#10622824—24no—
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2212yes—
18C2×C22⋊(C11⋊C8)—22no—
19C2×C22⋊(C11⋊C8)C2212yes—
20#10622176—24no—
21C25×C11D411yescharacteristic
22C22×Q8×C11C2×C411yescharacteristic
23C23×C4×C11—22no—
24C23×C4×C11—22no—
25C23×C4×C11—44no—
26C23×C4×C11C2×C412yes—
27C23×C4×C11D412yes—
28C23×C4×C11D411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—22no—
31C11×C22⋊Q8—22no—
32C11×C22⋊Q8—22no—
33C11×C22⋊Q8—44no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C412yes—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C22⋊Dic11—24no—
43C2×C22⋊Dic11—44no—
44C22×C11⋊C8—22no—
45C11×#95—22no—
46C11×#95—21no—
47C11⋊#95—24no—
48C11⋊#95—22no—
49C11⋊#95D414yes—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—44no—
53#9154—111nomaximal, Sylow
54C24×C11—24no—
55C24×C11—21no—
56C24×C11—21no—
57C24×C11—22no—
58C24×C11—22no—
59C24×C11—42no—
60C24×C11C22⋊C412yes—
61C24×C11C2×D411yescharacteristic
62C2×Q8×C11—22no—
63C2×Q8×C11—42no—
64C22×C4×C11—24no—
65C22×C4×C11—24no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—21no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—48no—
78C22×C4×C11—48no—
79C22×C4×C11C22⋊C412yes—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D412yes—
83C22×C4×C11#4112yes—
84C22×Dic11—24no—
85C22×Dic11—44no—
86C22×Dic11—44no—
87C22×Dic11—42no—
88C22×Dic11—42no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—44no—
91C11×C4⋊C4—42no—
92C11×C4⋊C4—42no—
93C11×C22⋊C4—44no—
94C11×C22⋊C4—44no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—42no—
98C22⋊Dic11—48no—
99C2×C11⋊C8—44no—
100C2×C11⋊C8—42no—
101#2848D1111yescharacteristic
102C2×#381—111no—
103#1779—111no—
104C2×#328—112no—
105#1294—112no—
106C23×C11—22no—
107C23×C11—22no—
108C23×C11—24no—
109C23×C11—24no—
110C23×C11—22no—
111C23×C11—22no—
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—22no—
115C23×C11—22no—
116C23×C11—48no—
117C23×C11—48no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11—42no—
121C23×C11—42no—
122C23×C11#9914yes—
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11#12011yescharacteristic
125C23×C11#12311yescharacteristic
126C23×C11#13512yes—
127C23×C11#13712yes—
128Q8×C11—82no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—48no—
137C2×C4×C11—48no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11C4×D412yes—
148C2×C4×C11#12112yes—
149C2×Dic11—44no—
150C2×Dic11—44no—
151C2×Dic11—44no—
152C2×Dic11—84no—
153C2×Dic11—84no—
154C11⋊C8—82no—
155C24×C4C2×D1111yescharacteristic
156C2×C22⋊Q8Dic1112yescomplemented
157C2×C22⋊Q8C2×D1111yescharacteristic
158C22×C22⋊C4—221no—
159C2×C22⋊C8—112no—
160C2×C22⋊C8—222no—
161#385—21no—
162#385—22no—
163#381—224no—
164#380Dic1112yescomplemented
165#380C2×D1111yescharacteristic
166#379—21no—
167C2×#95—112no—
168C2×#95—221no—
169#328—224no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—24no—
175C22×C11—24no—
176C22×C11—24no—
177C22×C11—24no—
178C22×C11—24no—
179C22×C11—48no—
180C22×C11—48no—
181C22×C11—42no—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11—42no—
185C22×C11#38611yescharacteristic
186C22×C11C2×#9912yes—
187C22×C11#41611yescharacteristic
188C22×C11#41911yescharacteristic
189C22×C11#42112yes—
190C22×C11#45212yes—
191C22×C11#48512yes—
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—42no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—82no—
198Dic11—84no—
199C25C22⋊D1111yescharacteristic
200C22×Q8C2×Dic1111yescharacteristic
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—44no—
204C23×C4—222no—
205C23×C4C2×Dic1112yes—
206C23×C4C22⋊D1112yes—
207C23×C4C22⋊D1111yescharacteristic
208C23×C4C22×D1111yescharacteristic
209C22×C8—222no—
210C22⋊Q8—22no—
211C22⋊Q8—22no—
212C22⋊Q8—44no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×Dic1111yescharacteristic
216C2×C4⋊C4C2×Dic1112yes—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—224no—
222C2×C22⋊C4—444no—
223C22⋊C8—222no—
224C22⋊C8—222no—
225C22⋊C8—444no—
226#95—22no—
227#95—21no—
228#95—114no—
229#95—224no—
230#95—222no—
231C2×C11—22no—
232C2×C11—22no—
233C2×C11—44no—
234C2×C11#151112yes—
235C2×C11#151612yes—
236C2×C11#187311yescharacteristic
237C2×C11#189711yescharacteristic
238C2×C11#189811yescharacteristic
239C24—24no—
240C24—21no—
241C24—21no—
242C24—22no—
243C24—22no—
244C24—42no—
245C24C22⋊Dic1112yes—
246C24C2×C22⋊D1111yescharacteristic
247C2×Q8—22no—
248C2×Q8—42no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—48no—
263C22×C4—48no—
264C22×C4—224no—
265C22×C4—444no—
266C22×C4—444no—
267C22×C4—442no—
268C22×C4—442no—
269C22×C4C22⋊Dic1112yes—
270C22×C4D4×D1112yes—
271C22×C4#434112yes—
272C22×C4C22×Dic1111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274C2×C8—444no—
275C2×C8—442no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—44no—
279C4⋊C4—42no—
280C22⋊C4—44no—
281C22⋊C4—44no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—42no—
285C22⋊C4—448no—
286C11#915411yescharacteristic, complemented, Sylow
287C23—22no—
288C23—22no—
289C23—24no—
290C23—24no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—48no—
298C23—48no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—42no—
303C23#6689814yes—
304C23#6698811yescharacteristic
305C23#6699011yescharacteristic
306C23#6699512yes—
307C23#6700312yes—
308C23C2×C22⋊Dic1111yescharacteristic
309Q8—82no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—48no—
318C2×C4—48no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—444no—
329C2×C4—444no—
330C2×C4—444no—
331C2×C4—884no—
332C2×C4—884no—
333C2×C4D4×Dic1112yes—
334C2×C4#6699212yes—
335C8—882no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—24no—
341C22—24no—
342C22—24no—
343C22—24no—
344C22—24no—
345C22—48no—
346C22—48no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22#1062265812yes—
352C22#1062266012yes—
353C22C2×#6689812yes—
354C22#1062283311yescharacteristic
355C22#1062283811yescharacteristic
356C22#1062284611yescharacteristic
357C22#1062284912yes—
358C4—22no—
359C4—22no—
360C4—42no—
361C4—81no—
362C4—81no—
363C4—82no—
364C4—884no—
365C2—22no—
366C2—22no—
367C2—44no—
368C2#1306714912yes—
369C2#1306717212yes—
370C2#1306892911yescharacteristic
371C2#1306906511yescharacteristic
372C2#1306907011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2848C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenter#2848D11
hypocenterC11#9154
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2848

Complements

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

NH ≅ G/Ntype
3. C2×#10622176C2semidirect
4. #13066494C2semidirect
7. C2×C11×C22⋊Q8C4semidirect
12. C11×#380C4semidirect
156. C2×C22⋊Q8Dic11semidirect
164. #380Dic11semidirect
286. C11#9154semidirect

Maximal subgroups

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

subgroupindex
C2×#106228242
#130685262
C2×#106221762
#130664942
C11×#28482
#915411