Finite Group Databasebeta

← #14649492

Subgroups — #14649492

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076956C211yesmaximal, characteristic
2C2×#10622262C211yesmaximal, characteristic
3#13068682C211yesmaximal, characteristic
4C2×#10622105C211yesmaximal, characteristic
5C2×#10622090C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C2×#66977C2211yescharacteristic
9C22×Dic11⋊C4—21no—
10C22×C4×Dic11—21no—
11C22×C4×Dic11C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15C2×C11⋊#95C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622598C412yescomplemented
18#10622587C412yescomplemented
19#10622563—21no—
20#10622556—21no—
21#10622266—22no—
22#10622262—22no—
23#10622262—22no—
24#10622188—22no—
25#10622105—22no—
26#10622090—22no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—21no—
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C22×Dic22C2×C411yescharacteristic
33C22×C8×C11—21no—
34C2×C11×C4⋊C4C2×C412yes—
35C2×C11×C22⋊C4—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39#66977—21no—
40#66977—21no—
41#66977—21no—
42#66977—21no—
43C2×Dic11⋊C4—24no—
44C2×Dic11⋊C4—28no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11—21no—
48C2×C4×Dic11—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11—24no—
51C2×C4×Dic11—42no—
52C2×C4×Dic11—42no—
53C2×C4×Dic11C2×C412yes—
54C2×C4×Dic11D412yes—
55C22×C11⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95D412yes—
61C11⋊#95—21no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95D412yes—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#9144—111nomaximal, Sylow
69C24×C11C2×D411yescharacteristic
70C22×C4×C11—24no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×Dic11—24no—
84C22×Dic11—24no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—22no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—42no—
95C22×Dic11—41no—
96C22×Dic11—41no—
97C22×Dic11C22⋊C412yes—
98C22×Dic11C22⋊C412yes—
99C22×Dic11SD1612yes—
100C22×Dic11Q1612yes—
101C2×Dic22—21no—
102C2×Dic22—21no—
103C2×Dic22—42no—
104C2×C8×C11—42no—
105C2×C8×C11—41no—
106C11×C4⋊C4—42no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—44no—
114Dic11⋊C4—216no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117C4×Dic11—22no—
118C4×Dic11—22no—
119C4×Dic11—22no—
120C4×Dic11—22no—
121C4×Dic11—48no—
122C2×C11⋊C8—42no—
123C2×C11⋊C8—41no—
124#2855—111no—
125C2×C4×C4⋊C4—111no—
126#1817—111no—
127C2×#328—111no—
128C2×#328—111no—
129#1294—111no—
130#1294D1111yescharacteristic
131C23×C11—22no—
132C23×C11—22no—
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
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—24no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—44no—
149C2×C4×C11—44no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×Dic11—24no—
159C2×Dic11—24no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—22no—
167C2×Dic11—22no—
168C2×Dic11—24no—
169C2×Dic11—42no—
170C2×Dic11—44no—
171C2×Dic11—44no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11#10314yes—
178C2×Dic11#10414yes—
179Dic22—81no—
180Dic22—81no—
181C8×C11—81no—
182C11⋊C8—81no—
183C2×C22⋊Q8—111no—
184C22×C4⋊C4—221no—
185C22×C42—111no—
186C22×C42—221no—
187C2×C22⋊C8—111no—
188C2×C22⋊C8C2×D1111yescharacteristic
189#391—112no—
190#389—112no—
191#387—222no—
192#385—221no—
193#381—221no—
194#380C2×D1111yescharacteristic
195C4×C4⋊C4—222no—
196C4×C4⋊C4—222no—
197C2×#95—111no—
198C2×#95C2×D1111yescharacteristic
199#336—222no—
200#328—222no—
201#328—222no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11#38611yescharacteristic
211C22×C11#41012yes—
212C22×C11C2×#10311yescharacteristic
213C22×C11#41711yescharacteristic
214C22×C11C2×#10412yes—
215C22×C11#45011yescharacteristic
216C22×C11#45111yescharacteristic
217C22×C11#48311yescharacteristic
218C22×C11#48411yescharacteristic
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—44no—
224C4×C11—82no—
225Dic11—24no—
226Dic11—24no—
227Dic11—44no—
228Dic11—81no—
229Dic11—81no—
230C22×Q8—111no—
231C23×C4—21no—
232C23×C4—111no—
233C23×C4—111no—
234C23×C4—221no—
235C23×C4C22×D1111yescharacteristic
236C22×C8—21no—
237C22×C8—221no—
238C22⋊Q8—221no—
239C22⋊Q8—221no—
240C22⋊Q8—221no—
241C22⋊Q8—221no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—224no—
244C2×C4⋊C4—228no—
245C2×C4⋊C4—222no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4C4×D1112yes—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—221no—
250C2×C42—112no—
251C2×C42—112no—
252C2×C42—221no—
253C2×C42—221no—
254C2×C42—221no—
255C2×C42—221no—
256C2×C42—224no—
257C2×C42—442no—
258C2×C42—442no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—221no—
262C22⋊C8—221no—
263#95—21no—
264#95—21no—
265#95—112no—
266#95—222no—
267#95—222no—
268#95—222no—
269#95—221no—
270#95D4412yes—
271C2×C11—21no—
272C2×C11—21no—
273C2×C11—21no—
274C2×C11—21no—
275C2×C11#150312yes—
276C2×C11#150912yes—
277C2×C11#187211yescharacteristic
278C2×C11#189611yescharacteristic
279C2×C11#189911yescharacteristic
280C24D4×D1111yescharacteristic
281C2×Q8—221no—
282C2×Q8—221no—
283C2×Q8—442no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—112no—
292C22×C4—112no—
293C22×C4—112no—
294C22×C4—112no—
295C22×C4—224no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—224no—
303C22×C4—222no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—442no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4C2×C4×D1111yescharacteristic
310C22×C4C2×D4411yescharacteristic
311C22×C4#433911yescharacteristic
312C22×C4D4×D1111yescharacteristic
313C22×C4D4×D1111yescharacteristic
314C22×C4#434311yescharacteristic
315C2×C8—42no—
316C2×C8—41no—
317C2×C8—442no—
318C2×C8—441no—
319C4⋊C4—42no—
320C4⋊C4—2216no—
321C4⋊C4—221no—
322C4⋊C4—221no—
323C4⋊C4—444no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—441no—
329C22⋊C4—441no—
330C42—222no—
331C42—222no—
332C42—222no—
333C42—222no—
334C42—448no—
335C11#914411yescharacteristic, complemented, Sylow
336C23—22no—
337C23—22no—
338C23C22⋊C4×D1111yescharacteristic
339C23#6693511yescharacteristic
340C23#6694711yescharacteristic
341C23#6696411yescharacteristic
342C23SD16×D1111yescharacteristic
343C23#6696811yescharacteristic
344C23Q16×D1111yescharacteristic
345Q8—881no—
346Q8—881no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—114no—
362C2×C4—114no—
363C2×C4—224no—
364C2×C4—224no—
365C2×C4—222no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—224no—
374C2×C4—442no—
375C2×C4—444no—
376C2×C4—444no—
377C2×C4—442no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4C4×D4411yescharacteristic
383C2×C4#6693711yescharacteristic
384C2×C4#6694611yescharacteristic
385C2×C4#6694811yescharacteristic
386C8—81no—
387C8—881no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22#1062227811yescharacteristic
397C22#1062235312yes—
398C22#1062238411yescharacteristic
399C22#1062238911yescharacteristic
400C22D11×#10311yescharacteristic
401C22#1062242111yescharacteristic
402C22D11×#10412yes—
403C22#1062247511yescharacteristic
404C22#1062249711yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—44no—
410C4—82no—
411C4—224no—
412C4—224no—
413C4—444no—
414C4—881no—
415C4—881no—
416C2—21no—
417C2—21no—
418C2—21no—
419C2—21no—
420C2#1306711312yes—
421C2#1306713812yes—
422C2#1306892211yescharacteristic
423C2#1306905811yescharacteristic
424C2#1306907311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9144
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
17. #10622598C4semidirect
18. #10622587C4semidirect
335. C11#9144semidirect

Maximal subgroups

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

subgroupindex
#130769562
C2×#106222622
#130686822
C2×#106221052
C2×#106220902
#130664942
C11×#12942
#914411