Finite Group Databasebeta

← #14657376

Subgroups — #14657376

Order 2816.

440 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10622454C211yesmaximal, characteristic
2#13068605C211yesmaximal, characteristic
3#13067289C211yesmaximal, characteristic, complemented
4#13067287C211yesmaximal, characteristic, complemented
5#13067006C211yesmaximal, characteristic
6#13066513C211yesmaximal, characteristic, complemented
7C11×#1570C211yesmaximal, characteristic, complemented
8C22×#4314—21no—
9C2×C4×D44C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×#66887—21no—
15C2×#66880—21no—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622454—22no—
19#10622454—22no—
20C11×#334—22no—
21#10622192—21no—
22#10622124—22no—
23#10622121—22no—
24#10622120—22no—
25C22×D44D411yescharacteristic
26C22×C4×D11—21no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C22×C8×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C2×(C2×D11)⋊C4—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11D411yescharacteristic
35C2×#4318—21no—
36C2×#4314—24no—
37C2×#4314—42no—
38C2×#4314—42no—
39C4×D44—21no—
40C4×D44—21no—
41C4×D44—21no—
42C4×D44—21no—
43#66922—21no—
44#66922—21no—
45#66922—21no—
46#66922D412yes—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D412yes—
51C11×C4⋊C8D412yes—
52C11×C22⋊C8—21no—
53C4×C8×C11—21no—
54C22⋊(C11⋊C8)—21no—
55#66887—42no—
56#66880—24no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4×C11⋊C8—21no—
61#10445—111nomaximal, Sylow
62C23×D11—21no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C22×C4×C11#4111yescharacteristic
66C22×Dic11—21no—
67C22×Dic11—41no—
68C2×D44—21no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44SD1612yes—
74C2×C4×D11—41no—
75C2×C4×D11—41no—
76C2×C4×D11—82no—
77C2×Dic22—22no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C11×M16—41no—
84C11×M16—41no—
85C2×C8×C11—22no—
86C2×C8×C11—22no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11#4111yescharacteristic
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96C4⋊Dic11—21no—
97C4⋊Dic11—22no—
98C4⋊Dic11—21no—
99C4⋊Dic11—22no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106#4314—48no—
107C2×#461—111no—
108#1800—111no—
109#1570D1111yescharacteristic, complemented
110#1546—111no—
111#1546—111no—
112#1478—111no—
113#1301—111no—
114C23×C11#12311yescharacteristic
115C22×D11—22no—
116C22×D11—41no—
117C22×D11—41no—
118C22×D11—81no—
119C22×D11—81no—
120C2×C4×C11—22no—
121C2×C4×C11—41no—
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12311yescharacteristic
127C2×C4×C11#12411yescharacteristic
128C2×C4×C11C2×SD1611yescharacteristic
129C2×C4×C11#13511yescharacteristic
130C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×Dic11—42no—
133C2×Dic11—41no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137D44—22no—
138D44—22no—
139D44—41no—
140D44—41no—
141C4×D11—82no—
142C4×D11—82no—
143Dic22—42no—
144Dic22—42no—
145Dic22—81no—
146Dic22—81no—
147C8×C11—42no—
148C8×C11—42no—
149C8×C11—81no—
150C11⋊C8—81no—
151C11⋊C8—81no—
152C22×SD16—221no—
153C2×C4⋊Q8—111no—
154C2×C4×D4—111no—
155#461—222no—
156#461—222no—
157#431—111no—
158#431C2×D1111yescharacteristic
159#423—111no—
160#423C2×D1111yescharacteristic
161C2×C4⋊C8C2×D1111yescharacteristic
162C2×#103—221no—
163C2×#100—221no—
164#343—221no—
165#334—22no—
166#332—222no—
167#332—222no—
168D4⋊C8—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#39411yescharacteristic
172C22×C11#48111yescharacteristic
173C22×C11#48211yescharacteristic
174C2×D11—42no—
175C2×D11—82no—
176C2×D11—81no—
177C2×D11—81no—
178C2×D11—82no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11#44911yescharacteristic
183C4×C11#45011yescharacteristic
184C4×C11#46511yescharacteristic
185C4×C11#46911yescharacteristic
186C4×C11#47112yes—
187Dic11—82no—
188Dic11—81no—
189C22×Q8—221no—
190C22×D4—111no—
191C23×C4—221no—
192C2×SD16—224no—
193C2×SD16—442no—
194C2×SD16—442no—
195C2×M16—21no—
196C2×M16—221no—
197C22×C8—21no—
198C4⋊Q8—112no—
199C4⋊Q8—221no—
200C4⋊Q8—221no—
201C4⋊Q8—221no—
202C4×D4—221no—
203C4×D4—221no—
204C4×D4—221no—
205C4×D4—221no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C42C22×D1111yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—221no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C4⋊C8D4412yes—
218C4⋊C8C22⋊D1112yes—
219#103—224no—
220#100—442no—
221C22⋊C8—21no—
222C22⋊C8—221no—
223C4×C8—21no—
224C4×C8—221no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11#203411yescharacteristic
228C2×C11#204611yescharacteristic
229C2×C11#204911yescharacteristic
230D11—82no—
231C24—221no—
232C2×Q8—222no—
233C2×Q8—441no—
234C2×Q8—441no—
235C2×Q8—441no—
236C2×Q8—441no—
237C2×Q8—441no—
238C2×D4—112no—
239C2×D4—221no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4—221no—
244C22×C4—221no—
245C22×C4—441no—
246C22×C4—441no—
247C22×C4—441no—
248C22×C4—882no—
249C22×C4#433911yescharacteristic
250C22×C4D4×D1111yescharacteristic
251C22×C4#434311yescharacteristic
252SD16—448no—
253M16—41no—
254M16—41no—
255M16—441no—
256M16—441no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—441no—
263C2×C8—441no—
264C4⋊C4—222no—
265C4⋊C4—221no—
266C4⋊C4—222no—
267C4⋊C4—221no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C22⋊C4—441no—
271C22⋊C4—441no—
272C42C2×D4411yescharacteristic
273C42D4×D1111yescharacteristic
274C42#434311yescharacteristic
275C42C2×C22⋊D1111yescharacteristic
276C11#1044511yescharacteristic, complemented, Sylow
277C23—222no—
278C23—441no—
279C23—441no—
280C23—881no—
281C23—881no—
282C23#6694711yescharacteristic
283Q8—442no—
284Q8—442no—
285Q8—881no—
286Q8—881no—
287D4—222no—
288D4—222no—
289D4—441no—
290D4—441no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—441no—
294C2×C4—442no—
295C2×C4—882no—
296C2×C4—881no—
297C2×C4—881no—
298C2×C4—882no—
299C2×C4—881no—
300C2×C4#6694711yescharacteristic
301C2×C4#6694811yescharacteristic
302C2×C4#6694811yescharacteristic
303C2×C4SD16×D1111yescharacteristic
304C2×C4#6696711yescharacteristic
305C2×C4#6696711yescharacteristic
306C2×C4#6696911yescharacteristic
307C2×C4#6698311yescharacteristic
308C2×C4#6699011yescharacteristic
309C2×C4#6700011yescharacteristic
310C8—42no—
311C8—42no—
312C8—81no—
313C8—881no—
314C8—881no—
315C22—21no—
316C22—21no—
317C22—442no—
318C22—882no—
319C22—882no—
320C22—881no—
321C22—881no—
322C22#1062247611yescharacteristic
323C22#1062247911yescharacteristic
324C22#1062260411yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—881no—
329C4—882no—
330C4#1062247711yescharacteristic
331C4#1062247811yescharacteristic
332C4#1062275412yes—
333C4#1062278211yescharacteristic
334C4#1062278511yescharacteristic
335C2—21no—
336C2—21no—
337C2—882no—
338C2#1306980711yescharacteristic
339C2#1306987911yescharacteristic
340C2#1306989811yescharacteristic
subgroupG/H
centerC22#10622604
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1570C2
socleC22×C11#394
prime radicalC22×D44D4
hypercenter#1570D11
hypocenterC11#10445
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
3. #13067289C2semidirect
4. #13067287C2semidirect
6. #13066513C2semidirect
7. C11×#1570C2semidirect
109. #1570D11semidirect
276. C11#10445semidirect

Maximal subgroups

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

subgroupindex
C2×#106224542
#130686052
#130672892
#130672872
#130670062
#130665132
C11×#15702
#1044511