Finite Group Databasebeta

← #14648028

Subgroups — #14648028

Order 2816.

498 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071528C211yesmaximal, characteristic
2#13069377C211yesmaximal, characteristic
3#13068618C211yesmaximal, characteristic
4C2×#10622094C211yesmaximal, characteristic
5#13066499C211yesmaximal, characteristic
6#13066456C211yesmaximal, characteristic
7C11×#1834C211yesmaximal, characteristic
8C2×#66940—21no—
9C2×C4×Dic22C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C11×#384C2211yescharacteristic
13#10622589—21no—
14C4⋊C4×Dic11—21no—
15#10622586—21no—
16#10622585—22no—
17C2×#66874—21no—
18C2×#66872—21no—
19C4×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C11×#340—22no—
23#10622167—21no—
24#10622167—21no—
25#10622094C414yescomplemented
26C22×Dic22D411yescharacteristic
27C22×C8×C11—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D412yes—
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—22no—
40C2×Dic11⋊C4—22no—
41C2×C4×Dic11—21no—
42C2×C4×Dic11—22no—
43C2×C4×Dic11—21no—
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46#66940—42no—
47#66940—42no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C4×Dic22C2×C412yes—
51C4×Dic22Q812yes—
52C4×C8×C11—21no—
53C4×C8×C11C2×C412yes—
54C11⋊#95—22no—
55C11⋊#95—21no—
56#66874—42no—
57#66872—42no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)C2×C412yes—
62#8896—111nomaximal, Sylow
63C22×C4×C11—22no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×Dic22—21no—
75C2×Dic22C4⋊C412yes—
76C2×Dic22SD1612yes—
77C2×Dic22SD1612yes—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—42no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C42×C11C22×C411yescharacteristic
92C42×C11C2×Q811yescharacteristic
93C42×C11#4111yescharacteristic
94C42×C11#4111yescharacteristic
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11C4⋊C412yes—
100C4⋊Dic11Q1612yes—
101Dic11⋊C4—22no—
102Dic11⋊C4—22no—
103Dic11⋊C4—44no—
104Dic11⋊C4—82no—
105C4×Dic11—22no—
106C4×Dic11—22no—
107C4×Dic11—44no—
108C4×Dic11—41no—
109C4×Dic11—41no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116Q8×C4⋊C4—111no—
117#1948—111no—
118#1834D1111yescharacteristic
119#1803—111no—
120C2×Q8⋊C8—111no—
121#1296—111no—
122#1279—111no—
123C23×C11#12011yescharacteristic
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11C2×C4⋊C411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11C22⋊Q811yescharacteristic
136C2×C4×C11C22⋊Q811yescharacteristic
137C2×C4×C11#12311yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C2×C4×C11C2×Q1611yescharacteristic
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11#13711yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×Dic11—22no—
147C2×Dic11—22no—
148C2×Dic11—22no—
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158Dic22—22no—
159Dic22—22no—
160Dic22—22no—
161Dic22#10614yescomplemented
162C8×C11—42no—
163C11⋊C8—42no—
164C11⋊C8—81no—
165C2×C4×Q8—111no—
166C2×C4×Q8—221no—
167C2×#106—221no—
168C2×C4⋊C8—111no—
169C2×C4⋊C8—111no—
170C2×#103—221no—
171C2×C4×C8C2×D1111yescharacteristic
172#389—221no—
173#389—222no—
174#384—221no—
175#384C2×D1111yescharacteristic
176#384C2×D1111yescharacteristic
177C4×C4⋊C4—111no—
178C4×C4⋊C4—221no—
179#340—22no—
180#340—221no—
181#340—221no—
182Q8⋊C8—114no—
183C22×C11#38511yescharacteristic
184C22×C11#44811yescharacteristic
185C22×C11#44911yescharacteristic
186C22×C11#45011yescharacteristic
187C22×C11#45111yescharacteristic
188C22×C11#45411yescharacteristic
189C22×C11#45511yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—82no—
193C4×C11—161no—
194C4×C11C2×#10611yescharacteristic
195C4×C11#42811yescharacteristic
196C4×C11C4×Q1611yescharacteristic
197C4×C11#44011yescharacteristic
198C4×C11#47711yescharacteristic
199C4×C11#47911yescharacteristic
200C4×C11#48111yescharacteristic
201C4×C11#48311yescharacteristic
202Dic11—24no—
203Dic11—42no—
204Dic11—42no—
205Dic11—81no—
206C22×Q8—111no—
207C22×C8—21no—
208C22×C8—221no—
209C22×C8—221no—
210C4×Q8—112no—
211C4×Q8—112no—
212C4×Q8—221no—
213C4×Q8—221no—
214C4×Q8—442no—
215C4×Q8—442no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—222no—
226C2×C4⋊C4—222no—
227C2×C4⋊C4C22⋊D1112yes—
228C2×C42—221no—
229C2×C42—222no—
230C2×C42—221no—
231C2×C42C22×D1111yescharacteristic
232#106—442no—
233C4⋊C8—112no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236C4⋊C8—221no—
237#103—442no—
238C4×C8—21no—
239C4×C8C4×D1112yes—
240#95—222no—
241#95—221no—
242C2×C11#162611yescharacteristic
243C2×C11#163711yescharacteristic
244C2×C11#164211yescharacteristic
245C2×C11#164511yescharacteristic
246C2×C11#185311yescharacteristic
247C2×C11#186011yescharacteristic
248C2×C11#186311yescharacteristic
249C2×Q8—112no—
250C2×Q8—112no—
251C2×Q8—112no—
252C2×Q8—221no—
253C2×Q8—221no—
254C2×Q8—221no—
255C22×C4—22no—
256C22×C4—41no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—222no—
268C2×C8—441no—
269C2×C8—441no—
270C2×C8—441no—
271C2×C8—441no—
272C2×C8—441no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—112no—
284C4⋊C4—112no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—222no—
288C4⋊C4—222no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—444no—
292C4⋊C4—882no—
293C42—222no—
294C42—222no—
295C42—444no—
296C42—441no—
297C42—441no—
298C42C2×C4×D1111yescharacteristic
299C42#433911yescharacteristic
300C42Q8×D1111yescharacteristic
301C42#434311yescharacteristic
302C11#889611yescharacteristic, complemented, Sylow
303C23#6699011yescharacteristic
304Q8—114no—
305Q8—222no—
306Q8—222no—
307Q8—222no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—222no—
317C2×C4—222no—
318C2×C4—222no—
319C2×C4—222no—
320C2×C4—222no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4C4⋊C4×D1111yescharacteristic
329C2×C4#6694611yescharacteristic
330C2×C4#6694711yescharacteristic
331C2×C4#6694911yescharacteristic
332C2×C4#6696411yescharacteristic
333C2×C4#6696511yescharacteristic
334C2×C4SD16×D1111yescharacteristic
335C2×C4SD16×D1111yescharacteristic
336C2×C4#6696711yescharacteristic
337C2×C4#6696811yescharacteristic
338C2×C4Q16×D1111yescharacteristic
339C2×C4#6697111yescharacteristic
340C2×C4C4×C22⋊D1111yescharacteristic
341C2×C4#6699911yescharacteristic
342C8—42no—
343C8—442no—
344C8—881no—
345C22#1062260211yescharacteristic
346C22#1062267411yescharacteristic
347C22#1062267511yescharacteristic
348C22#1062277111yescharacteristic
349C22#1062278211yescharacteristic
350C22#1062278311yescharacteristic
351C22#1062279911yescharacteristic
352C4—21no—
353C4—21no—
354C4—82no—
355C4—161no—
356C4—224no—
357C4—442no—
358C4—442no—
359C4—881no—
360C4D11×#10611yescharacteristic
361C4#1062247411yescharacteristic
362C4#1062247511yescharacteristic
363C4#1062247611yescharacteristic
364C4#1062248611yescharacteristic
365C4#1062248811yescharacteristic
366C4#1062249011yescharacteristic
367C4#1062250211yescharacteristic
368C2#1306770911yescharacteristic
369C2#1306777811yescharacteristic
370C2#1306781311yescharacteristic
371C2#1306783411yescharacteristic
372C2#1306880711yescharacteristic
373C2#1306884811yescharacteristic
374C2#1306886711yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1834C2
socle, prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1834D11
hypocenterC11#8896
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
25. #10622094C4semidirect
161. Dic22#106semidirect
302. C11#8896semidirect

Maximal subgroups

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

subgroupindex
#130715282
#130693772
#130686182
C2×#106220942
#130664992
#130664562
C11×#18342
#889611