Finite Group Databasebeta

← #14657203

Subgroups — #14657203

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073604C211yesmaximal, characteristic
2#13069576C211yesmaximal, characteristic
3#13068618C211yesmaximal, characteristic
4C2×#10622124C211yesmaximal, characteristic
5C2×#10622122C211yesmaximal, characteristic
6#13066457C211yesmaximal, characteristic
7C11×#1948C211yesmaximal, characteristic
8C2×#66922—21no—
9C2×#66922C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C2×C11×#106—21no—
12C2×C11×C4⋊C8C2211yescharacteristic
13C11×#384C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15#10622598—21no—
16#10622598—21no—
17C2×#66874—21no—
18#10622542—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622274—22no—
22C11×#340—21no—
23#10622167—22no—
24#10622167—21no—
25#10622124—22no—
26#10622122—22no—
27C22×Dic22—21no—
28C22×Dic22D411yescharacteristic
29C22×C8×C11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11—22no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11D411yescharacteristic
41C2×C4⋊Dic11D412yes—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46#66922—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922—42no—
51#66922—42no—
52C4×Dic22—21no—
53C4×Dic22—21no—
54C4×Dic22—21no—
55C4×Dic22—21no—
56C11×#106—42no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×#95—21no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62#66874—42no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4×C11⋊C8—21no—
66C4×C11⋊C8—21no—
67#10418—111nomaximal, Sylow
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—22no—
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×Dic22—21no—
80C2×Dic22—21no—
81C2×Dic22—21no—
82C2×Dic22—41no—
83C2×Dic22—41no—
84C2×Dic22—41no—
85C2×Dic22—41no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×Dic22SD1612yes—
89C2×C8×C11—22no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4SD1612yes—
100C11×C4⋊C4Q1612yes—
101C42×C11—41no—
102C42×C11—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105C42×C11#4111yescharacteristic
106C42×C11#4111yescharacteristic
107C4⋊Dic11—21no—
108C4⋊Dic11—22no—
109C4⋊Dic11—21no—
110C4⋊Dic11—22no—
111C4⋊Dic11—44no—
112C4⋊Dic11—44no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117C4×Dic11—41no—
118C4×Dic11—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125#2546—111no—
126#1990—111no—
127#1948D1111yescharacteristic
128#1803—111no—
129C2×#332—111no—
130C2×Q8⋊C8—111no—
131#1279—111no—
132C23×C11#12011yescharacteristic
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12311yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×C4×C11#12411yescharacteristic
150C2×C4×C11C2×SD1611yescharacteristic
151C2×C4×C11C2×SD1611yescharacteristic
152C2×C4×C11C2×Q1611yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C2×Dic11—22no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167Dic22—22no—
168Dic22—22no—
169Dic22—41no—
170Dic22—41no—
171Dic22—81no—
172Dic22—81no—
173Dic22—81no—
174Dic22—81no—
175C8×C11—42no—
176C11⋊C8—42no—
177C11⋊C8—81no—
178C2×C4⋊Q8—111no—
179C2×C4⋊Q8—221no—
180C2×C4×Q8—111no—
181C2×#106—21no—
182C2×C4⋊C8—111no—
183C2×C4⋊C8C2×D1111yescharacteristic
184C2×#103—221no—
185C2×C4×C8—111no—
186#398—222no—
187#391—221no—
188#389—221no—
189#389—221no—
190#384C2×D1111yescharacteristic
191C4×C4⋊C4C2×D1111yescharacteristic
192#340—21no—
193#340—221no—
194#340—222no—
195#332—222no—
196Q8⋊C8—222no—
197C22×C11#39411yescharacteristic
198C22×C11#44811yescharacteristic
199C22×C11#44911yescharacteristic
200C22×C11#45011yescharacteristic
201C22×C11#45111yescharacteristic
202C22×C11#45411yescharacteristic
203C22×C11#45611yescharacteristic
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—42no—
207C4×C11—42no—
208C4×C11—161no—
209C4×C11#46111yescharacteristic
210C4×C11#46211yescharacteristic
211C4×C11#46511yescharacteristic
212C4×C11#46911yescharacteristic
213C4×C11#48111yescharacteristic
214C4×C11#48211yescharacteristic
215C4×C11#48711yescharacteristic
216C4×C11#49111yescharacteristic
217Dic11—42no—
218Dic11—82no—
219Dic11—81no—
220C22×Q8—111no—
221C22×Q8—221no—
222C22×C8—21no—
223C22×C8—221no—
224C22×C8—221no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228C4⋊Q8—221no—
229C4⋊Q8—442no—
230C4⋊Q8—442no—
231C4×Q8—221no—
232C4×Q8—221no—
233C4×Q8—221no—
234C4×Q8—221no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—112no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4—222no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4C22⋊D1111yescharacteristic
245C2×C4⋊C4C22⋊D1111yescharacteristic
246C2×C42—21no—
247C2×C42—221no—
248C2×C42C22×D1111yescharacteristic
249#106—42no—
250C4⋊C8—21no—
251C4⋊C8—221no—
252C4⋊C8—221no—
253C4⋊C8D4412yes—
254#103—442no—
255C4×C8—221no—
256C4×C8—221no—
257#95—21no—
258#95—222no—
259#95—222no—
260C2×C11#162611yescharacteristic
261C2×C11#163711yescharacteristic
262C2×C11#164811yescharacteristic
263C2×C11#165111yescharacteristic
264C2×C11#203411yescharacteristic
265C2×C11#203811yescharacteristic
266C2×C11#204311yescharacteristic
267C2×Q8—112no—
268C2×Q8—221no—
269C2×Q8—221no—
270C2×Q8—221no—
271C2×Q8—221no—
272C2×Q8—221no—
273C2×Q8—441no—
274C2×Q8—441no—
275C2×Q8—441no—
276C2×Q8—441no—
277C2×Q8—441no—
278C2×Q8—441no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—222no—
285C22×C4D4×D1111yescharacteristic
286C22×C4D4×D1111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—222no—
292C2×C8—441no—
293C2×C8—441no—
294C2×C8—441no—
295C2×C8—441no—
296C2×C8—441no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—42no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—221no—
305C4⋊C4—222no—
306C4⋊C4—221no—
307C4⋊C4—222no—
308C4⋊C4—444no—
309C4⋊C4—444no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C4⋊C4#432412yes—
315C4⋊C4#432612yes—
316C42—41no—
317C42—41no—
318C42—441no—
319C42—441no—
320C42C2×D4411yescharacteristic
321C42#433911yescharacteristic
322C42#434311yescharacteristic
323C42#434311yescharacteristic
324C11#1041811yescharacteristic, complemented, Sylow
325C23#6699011yescharacteristic
326Q8—222no—
327Q8—222no—
328Q8—441no—
329Q8—441no—
330Q8—881no—
331Q8—881no—
332Q8—881no—
333Q8—881no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—222no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—442no—
354C2×C4#6694711yescharacteristic
355C2×C4#6694711yescharacteristic
356C2×C4#6694811yescharacteristic
357C2×C4#6694811yescharacteristic
358C2×C4SD16×D1111yescharacteristic
359C2×C4#6696711yescharacteristic
360C2×C4#6696711yescharacteristic
361C2×C4#6696911yescharacteristic
362C2×C4#6698311yescharacteristic
363C2×C4C2×#432411yescharacteristic
364C2×C4C2×#432611yescharacteristic
365C2×C4#6700011yescharacteristic
366C2×C4#6700411yescharacteristic
367C2×C4#6700411yescharacteristic
368C8—42no—
369C8—442no—
370C8—881no—
371C22#1062260411yescharacteristic
372C22#1062265311yescharacteristic
373C22#1062266311yescharacteristic
374C22#1062278211yescharacteristic
375C22#1062278511yescharacteristic
376C22#1062281411yescharacteristic
377C22#1062281811yescharacteristic
378C4—21no—
379C4—21no—
380C4—42no—
381C4—42no—
382C4—161no—
383C4—442no—
384C4—881no—
385C4—882no—
386C4#1062247611yescharacteristic
387C4#1062247711yescharacteristic
388C4#1062247811yescharacteristic
389C4#1062247911yescharacteristic
390C4#1062263211yescharacteristic
391C4#1062264411yescharacteristic
392C4#1062268211yescharacteristic
393C4#1062270611yescharacteristic
394C2#1306771111yescharacteristic
395C2#1306778011yescharacteristic
396C2#1306785711yescharacteristic
397C2#1306787711yescharacteristic
398C2#1306980711yescharacteristic
399C2#1306983511yescharacteristic
400C2#1306986211yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1948C2
socle, prime radicalC23×C11#120
hypercenter#1948D11
hypocenterC11#10418
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
324. C11#10418semidirect

Maximal subgroups

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

subgroupindex
#130736042
#130695762
#130686182
C2×#106221242
C2×#106221222
#130664572
C11×#19482
#1041811