Finite Group Databasebeta

← #14649529

Subgroups — #14649529

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622825C211yesmaximal, 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—
10C22×C4⋊Dic11—21no—
11C11×#385—21no—
12C11×#385—22no—
13C11×#380C412yescomplemented
14C11×#380C2211yescharacteristic
15C11×#379—21no—
16#10622825—24no—
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×C11D411yescharacteristic
28C23×C4×C11D412yes—
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—42no—
44C2×C22⋊Dic11—42no—
45C2×C4⋊Dic11—24no—
46C2×C4⋊Dic11—44no—
47C22×C11⋊C8—22no—
48C11×#95—22no—
49C11×#95—21no—
50C11⋊#95—22no—
51C11⋊#95D414yes—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54C22⋊(C11⋊C8)—44no—
55#9151—111nomaximal, Sylow
56C24×C11—21no—
57C24×C11—21no—
58C24×C11—21no—
59C24×C11—21no—
60C24×C11—42no—
61C24×C11—42no—
62C24×C11C22⋊C412yes—
63C24×C11SD1612yes—
64C24×C11Q1612yes—
65C24×C11C2×D411yescharacteristic
66C2×Q8×C11—22no—
67C2×Q8×C11—42no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—21no—
76C22×C4×C11—22no—
77C22×C4×C11—21no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11—48no—
82C22×C4×C11—48no—
83C22×C4×C11C22⋊C412yes—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D412yes—
87C22×C4×C11#4112yes—
88C22×Dic11—24no—
89C22×Dic11—44no—
90C22×Dic11—44no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—44no—
96C11×C4⋊C4—42no—
97C11×C22⋊C4—44no—
98C11×C22⋊C4—44no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C22⋊Dic11—48no—
104C4⋊Dic11—48no—
105C2×C11⋊C8—44no—
106C2×C11⋊C8—42no—
107#2848D1111yescharacteristic
108C2×#380—111no—
109#1779—111no—
110C2×#328—112no—
111#1294—112no—
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—22no—
115C23×C11—22no—
116C23×C11—22no—
117C23×C11—22no—
118C23×C11—22no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—44no—
125C23×C11—44no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—44no—
131C23×C11—44no—
132C23×C11#10314yes—
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11#12011yescharacteristic
135C23×C11#12311yescharacteristic
136C23×C11C2×SD1611yescharacteristic
137C23×C11C2×Q1611yescharacteristic
138C23×C11AGL(1,ℤ/8)11yescharacteristic
139C23×C11#13711yescharacteristic
140Q8×C11—82no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—48no—
150C2×C4×C11—48no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11#9914yes—
159C2×C4×C11C4×D412yes—
160C2×C4×C11#12112yes—
161C2×Dic11—44no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C2×Dic11—84no—
165C2×Dic11—84no—
166C11⋊C8—82no—
167C24×C4C2×D1111yescharacteristic
168C2×C22⋊Q8Dic1112yescomplemented
169C2×C22⋊Q8C2×D1111yescharacteristic
170C22×C4⋊C4—221no—
171C22×C22⋊C4—221no—
172C2×C22⋊C8—112no—
173C2×C22⋊C8—222no—
174#385—21no—
175#385—22no—
176#380—224no—
177#380Dic1112yescomplemented
178#380C2×D1111yescharacteristic
179#379—21no—
180C2×#95—112no—
181#328—224no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—24no—
191C22×C11—24no—
192C22×C11—24no—
193C22×C11—44no—
194C22×C11—44no—
195C22×C11—44no—
196C22×C11—44no—
197C22×C11—42no—
198C22×C11—42no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11#38611yescharacteristic
202C22×C11C2×#9912yes—
203C22×C11C2×#10311yescharacteristic
204C22×C11#41711yescharacteristic
205C22×C11#42112yes—
206C22×C11#45011yescharacteristic
207C22×C11#45111yescharacteristic
208C22×C11#48311yescharacteristic
209C22×C11#48411yescharacteristic
210C4×C11—24no—
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11—82no—
216Dic11—84no—
217C25C22⋊D1111yescharacteristic
218C22×Q8C2×Dic1111yescharacteristic
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—44no—
222C23×C4—222no—
223C23×C4C2×Dic1112yes—
224C23×C4C22⋊D1111yescharacteristic
225C23×C4C22⋊D1112yes—
226C23×C4C22×D1111yescharacteristic
227C22×C8—222no—
228C22⋊Q8—22no—
229C22⋊Q8—22no—
230C22⋊Q8—44no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—224no—
234C2×C4⋊C4—444no—
235C2×C4⋊C4C2×Dic1111yescharacteristic
236C2×C4⋊C4C2×Dic1112yes—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—224no—
242C2×C22⋊C4—442no—
243C2×C22⋊C4—442no—
244C22⋊C8—222no—
245C22⋊C8—222no—
246C22⋊C8—444no—
247#95—22no—
248#95—21no—
249#95—114no—
250#95—222no—
251C2×C11—21no—
252C2×C11—21no—
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—44no—
256C2×C11#151312yes—
257C2×C11#152012yes—
258C2×C11#187211yescharacteristic
259C2×C11#189711yescharacteristic
260C2×C11#189811yescharacteristic
261C24—21no—
262C24—21no—
263C24—21no—
264C24—21no—
265C24—42no—
266C24—42no—
267C24#432512yes—
268C24#432612yes—
269C24C22⋊Dic1112yes—
270C24C2×C22⋊D1111yescharacteristic
271C2×Q8—22no—
272C2×Q8—42no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—48no—
287C22×C4—48no—
288C22×C4—224no—
289C22×C4—444no—
290C22×C4—444no—
291C22×C4—442no—
292C22×C4—442no—
293C22×C4C22⋊Dic1112yes—
294C22×C4D4×D1112yes—
295C22×C4#434112yes—
296C22×C4C22×Dic1111yescharacteristic
297C22×C4C2×C22⋊D1111yescharacteristic
298C2×C8—444no—
299C2×C8—442no—
300C4⋊C4—22no—
301C4⋊C4—42no—
302C4⋊C4—44no—
303C4⋊C4—42no—
304C4⋊C4—448no—
305C22⋊C4—44no—
306C22⋊C4—44no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—448no—
312C11#915111yescharacteristic, complemented, Sylow
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—22no—
325C23—44no—
326C23—44no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23—42no—
331C23—44no—
332C23—44no—
333C23#6689914yes—
334C23#6698811yescharacteristic
335C23#6699011yescharacteristic
336C23C2×#432511yescharacteristic
337C23C2×#432611yescharacteristic
338C23#6700211yescharacteristic
339C23#6700411yescharacteristic
340C23C2×C22⋊Dic1111yescharacteristic
341Q8—82no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—48no—
351C2×C4—48no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—444no—
360C2×C4—444no—
361C2×C4—444no—
362C2×C4—884no—
363C2×C4—884no—
364C2×C4#6689814yes—
365C2×C4D4×Dic1112yes—
366C2×C4#6699212yes—
367C8—882no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—24no—
377C22—24no—
378C22—24no—
379C22—44no—
380C22—44no—
381C22—44no—
382C22—44no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22#1062265611yescharacteristic
388C22#1062265711yescharacteristic
389C22#1062265911yescharacteristic
390C22#1062266311yescharacteristic
391C22C2×#6689812yes—
392C22#1062283311yescharacteristic
393C22C2×#6689911yescharacteristic
394C22#1062284511yescharacteristic
395C22#1062284912yes—
396C4—22no—
397C4—24no—
398C4—22no—
399C4—81no—
400C4—81no—
401C4—82no—
402C4—884no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2—21no—
407C2—44no—
408C2#1306715912yes—
409C2#1306718812yes—
410C2#1306892411yescharacteristic
411C2#1306906511yescharacteristic
412C2#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#9151
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
13. C11×#380C4semidirect
168. C2×C22⋊Q8Dic11semidirect
177. #380Dic11semidirect
312. C11#9151semidirect

Maximal subgroups

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

subgroupindex
C2×#106228252
#130685262
C2×#106221762
#130664942
C11×#28482
#915111