Finite Group Databasebeta

← #14657360

Subgroups — #14657360

Order 2816.

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

normal subgroups only

This group has 460 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×#10622640C211yesmaximal, characteristic
2#13067388C211yesmaximal, characteristic, complemented
3#13067285C211yesmaximal, characteristic
4#13067285C211yesmaximal, characteristic
5#13067011C211yesmaximal, characteristic, complemented
6#13066511C211yesmaximal, characteristic, complemented
7C11×#1801C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C22×#4325—21no—
10C2×#66927C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×#101—21no—
14#10622640—22no—
15#10622640—22no—
16C2×#66873—21no—
17#10622538C2211yescharacteristic
18#10622538C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#343—21no—
21Q8⋊(C11⋊C8)—22no—
22#10622123—22no—
23#10622123—22no—
24#10622118—22no—
25C22×Q8×C11D411yescharacteristic
26C22×D44—21no—
27C22×D44—21no—
28C22×D44—21no—
29C2×C11×M16—21no—
30C2×C11×M16—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×#4325—24no—
40C2×#4325—42no—
41C2×#4325—42no—
42C22×C11⋊C8—21no—
43#66927—21no—
44#66927—21no—
45#66927—21no—
46#66927D412yes—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×#101—42no—
52C22⋊(C11⋊C8)—21no—
53C22⋊(C11⋊C8)—21no—
54#66873—24no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)D412yes—
58C4⋊(C11⋊C8)D412yes—
59C4×C11⋊C8—21no—
60C4×C11⋊C8—21no—
61#10443—111nomaximal, Sylow
62C23×D11—41no—
63C2×Q8×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11SD1612yes—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C2×D44—22no—
75C2×D44—22no—
76C2×D44—22no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—82no—
85C2×D44—82no—
86C11×M16—41no—
87C11×M16—41no—
88C11×M16—41no—
89C11×M16—41no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C42×C11—41no—
97C42×C11—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102#4325—48no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×#460—111no—
109#1801D1111yescharacteristic, complemented
110#1570—111no—
111#1545—111no—
112#1545—111no—
113#1479—111no—
114#1301—111no—
115C23×C11#12311yescharacteristic
116C22×D11—42no—
117C22×D11—82no—
118C22×D11—82no—
119C22×D11—81no—
120C22×D11—81no—
121Q8×C11—22no—
122Q8×C11—22no—
123Q8×C11—41no—
124Q8×C11—41no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—81no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×C4×C11#12411yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142D44—42no—
143D44—42no—
144D44—82no—
145D44—82no—
146D44—82no—
147D44—81no—
148D44—81no—
149D44—82no—
150C8×C11—81no—
151C8×C11—81no—
152C11⋊C8—42no—
153C11⋊C8—42no—
154C11⋊C8—81no—
155C22×SD16—221no—
156C2×#127—111no—
157C2×C4×Q8C2×D1111yescharacteristic
158#460—222no—
159#460—222no—
160#431—111no—
161#431—111no—
162#423C2×D1111yescharacteristic
163#423C2×D1111yescharacteristic
164C2×C4⋊C8—111no—
165C2×#102—221no—
166C2×#101—21no—
167#343—21no—
168#334—222no—
169#331—222no—
170#331—222no—
171Q8⋊C8—222no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11#39411yescharacteristic
175C22×C11#48111yescharacteristic
176C22×C11#48211yescharacteristic
177C2×D11—82no—
178C2×D11—82no—
179C2×D11—82no—
180C2×D11—162no—
181C2×D11—162no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—42no—
186C4×C11—81no—
187C4×C11#44911yescharacteristic
188C4×C11#45011yescharacteristic
189C4×C11#46511yescharacteristic
190C4×C11#46911yescharacteristic
191C4×C11#47112yes—
192C22×Q8C22⋊D1111yescharacteristic
193C22×D4—221no—
194C22×D4—221no—
195C22×D4—221no—
196C2×SD16—224no—
197C2×SD16—442no—
198C2×SD16—442no—
199C2×M16—21no—
200C2×M16—21no—
201C22×C8—221no—
202#127—112no—
203#127—221no—
204#127—221no—
205#127—221no—
206C4×Q8—21no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4C22⋊D1111yescharacteristic
212C2×C42—21no—
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—112no—
219C4⋊C8—112no—
220C4⋊C8—221no—
221C4⋊C8—221no—
222#102—224no—
223#101—42no—
224C22⋊C8—221no—
225C22⋊C8—221no—
226C4×C8—221no—
227C4×C8—221no—
228C2×C11—21no—
229C2×C11—21no—
230C2×C11#203411yescharacteristic
231C2×C11#204611yescharacteristic
232C2×C11#204811yescharacteristic
233D11—162no—
234C24—441no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8#432512yes—
241C2×D4—222no—
242C2×D4—222no—
243C2×D4—222no—
244C2×D4—441no—
245C2×D4—441no—
246C2×D4—441no—
247C2×D4—441no—
248C2×D4—441no—
249C2×D4—441no—
250C2×D4—441no—
251C2×D4—882no—
252C2×D4—882no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4#433911yescharacteristic
256C22×C4#433911yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258SD16—448no—
259M16—41no—
260M16—41no—
261M16—41no—
262M16—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—222no—
266C2×C8—222no—
267C2×C8—441no—
268C2×C8—441no—
269C2×C8—441no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C42—41no—
275C42—41no—
276C42D4×D1111yescharacteristic
277C42D4×D1111yescharacteristic
278C42D4×D1111yescharacteristic
279C42#434111yescharacteristic
280C11#1044311yescharacteristic, complemented, Sylow
281C23—442no—
282C23—882no—
283C23—882no—
284C23—881no—
285C23—881no—
286C23#6698211yescharacteristic
287Q8—22no—
288Q8—22no—
289Q8—41no—
290Q8—41no—
291D4—442no—
292D4—442no—
293D4—882no—
294D4—882no—
295D4—882no—
296D4—882no—
297D4—881no—
298D4—881no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4#6693611yescharacteristic
307C2×C4#6693711yescharacteristic
308C2×C4#6693711yescharacteristic
309C2×C4#6693811yescharacteristic
310C2×C4#6698511yescharacteristic
311C2×C4#6699011yescharacteristic
312C2×C4#6699211yescharacteristic
313C2×C4C2×#432511yescharacteristic
314C2×C4#6700211yescharacteristic
315C2×C4#6700311yescharacteristic
316C8—81no—
317C8—81no—
318C8—442no—
319C8—442no—
320C8—881no—
321C22—21no—
322C22—21no—
323C22—882no—
324C22—882no—
325C22—882no—
326C22—1762no—
327C22—1762no—
328C22#1062257211yescharacteristic
329C22#1062258111yescharacteristic
330C22#1062261611yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—81no—
336C4#1062236712yes—
337C4#1062265011yescharacteristic
338C4#1062265211yescharacteristic
339C4#1062265911yescharacteristic
340C4#1062266111yescharacteristic
341C2—21no—
342C2—21no—
343C2—1762no—
344C2#1306980511yescharacteristic
345C2#1306987511yescharacteristic
346C2#1306988911yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1801C2
socleC22×C11#394
prime radicalC2×#66927C22
hypercenter#1801D11
hypocenterC11#10443
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. #13067388C2semidirect
5. #13067011C2semidirect
6. #13066511C2semidirect
7. C11×#1801C2semidirect
109. #1801D11semidirect
280. C11#10443semidirect

Maximal subgroups

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

subgroupindex
C2×#106226402
#130673882
#130672852
#130670112
#130665112
C11×#18012
#1044311