Finite Group Databasebeta

← #14650313

Subgroups — #14650313

Order 2816.

428 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077565C211yesmaximal, characteristic
2#13069461C211yesmaximal, characteristic
3#13067306C211yesmaximal, characteristic
4C2×#10622185C211yesmaximal, characteristic
5#13066512C211yesmaximal, characteristic
6#13066465C211yesmaximal, characteristic
7C11×#3229C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#498—21no—
11C11×#487—21no—
12C11×#483C414yes—
13C11×#475—22no—
14C11×#431C2211yescharacteristic
15C2×#66900—21no—
16C2×#66900—21no—
17#10622637—22no—
18#10622637—21no—
19Q8×C11⋊C8—21no—
20#10622612—21no—
21#10622610—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622185—21no—
27#10622185—21no—
28#10622185—21no—
29#10622184—21no—
30C22×Q8×C11—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8C2×C412yes—
40C4×Q8×C11—21no—
41C4×Q8×C11D412yes—
42C11×#117—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4C2×C412yes—
45C2×C42×C11C2311yescharacteristic
46C2×#4318—21no—
47C2×#4318D411yescharacteristic
48C2×#4318D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51C11×#106—24no—
52C11×C4⋊C8—21no—
53C11×#103—24no—
54C11×C22⋊C8C2×C412yes—
55C4×C8×C11—21no—
56#66900—42no—
57#66900—42no—
58C4⋊(C11⋊C8)—22no—
59C4⋊(C11⋊C8)—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D411yescharacteristic
66C4⋊(C11⋊C8)D411yescharacteristic
67#66867—22no—
68#66867—21no—
69C4×C11⋊C8—22no—
70C4×C11⋊C8—21no—
71#9272—111nomaximal, Sylow
72C2×Q8×C11—21no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11C22⋊C412yes—
80C22×C4×C11—22no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×C8×C11—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4C22⋊C412yes—
95C11×C22⋊C4—22no—
96C42×C11—22no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101#4318—21no—
102#4318—21no—
103#4318—21no—
104#4318—41no—
105#4318—41no—
106#4318SD1612yes—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—81no—
116#3229D1111yescharacteristic
117#2962—111no—
118#1966—111no—
119#1550—111no—
120C2×#332—111no—
121#1301—111no—
122#1283—111no—
123C23×C11C4×D411yescharacteristic
124Q8×C11—42no—
125Q8×C11—41no—
126Q8×C11—41no—
127Q8×C11—81no—
128Q8×C11—81no—
129Q8×C11—81no—
130Q8×C11—81no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11C2×C22⋊C411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×C4×C11C2×SD1611yescharacteristic
146C2×C4×C11#13511yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C8×C11—42no—
150C11⋊C8—22no—
151C11⋊C8—41no—
152C11⋊C8—41no—
153C11⋊C8—41no—
154C11⋊C8—81no—
155C11⋊C8—81no—
156#533C2×D1111yescharacteristic
157C2×C4⋊Q8C2×D1111yescharacteristic
158#498—21no—
159#487—21no—
160#483Dic1114yes—
161#475—22no—
162#446—221no—
163#446—222no—
164C8×Q8—221no—
165#431C2×D1111yescharacteristic
166#424—221no—
167#423—111no—
168C2×C4⋊C8—111no—
169C2×C4⋊C8—111no—
170C2×#101—221no—
171C2×#101—221no—
172#405—221no—
173C4×M16—111no—
174#333—221no—
175#332—221no—
176#332—221no—
177#332—221no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11#38611yescharacteristic
181C22×C11C4×SD1611yescharacteristic
182C22×C11#44011yescharacteristic
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—42no—
187C4×C11—42no—
188C4×C11—82no—
189C4×C11#44811yescharacteristic
190C4×C11#44911yescharacteristic
191C4×C11#46011yescharacteristic
192C4×C11#46411yescharacteristic
193C4×C11#47111yescharacteristic
194C4×C11#47311yescharacteristic
195C22×Q8—21no—
196C2×M16—111no—
197C2×M16—111no—
198C2×M16—221no—
199C22×C8—221no—
200C22×C8—221no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8C22⋊D1111yescharacteristic
206C4⋊Q8C22⋊D1111yescharacteristic
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8C2×Dic1112yes—
210C4×Q8—21no—
211C4×Q8C22⋊D1112yes—
212#117—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×Dic1112yes—
215C2×C42C22×D1111yescharacteristic
216#106—24no—
217C4⋊C8—21no—
218C4⋊C8—111no—
219C4⋊C8—111no—
220C4⋊C8—222no—
221C4⋊C8—222no—
222C4⋊C8—221no—
223C4⋊C8—221no—
224C4⋊C8—221no—
225C4⋊C8—221no—
226C4⋊C8—221no—
227#103—24no—
228#101—442no—
229#101—442no—
230C22⋊C8C2×Dic1112yes—
231#97—222no—
232#97—221no—
233C4×C8—21no—
234C4×C8—222no—
235C4×C8—221no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11#188011yescharacteristic
239C2×C11#190811yescharacteristic
240C2×C11#191511yescharacteristic
241C2×Q8—21no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8C22⋊Dic1112yes—
249C22×C4—22no—
250C22×C4D4×D1111yescharacteristic
251C22×C4#434111yescharacteristic
252C22×C4C22×Dic1111yescharacteristic
253M16—112no—
254M16—221no—
255M16—221no—
256M16—221no—
257M16—441no—
258M16—441no—
259C2×C8—22no—
260C2×C8—221no—
261C2×C8—221no—
262C2×C8—221no—
263C2×C8—221no—
264C2×C8—441no—
265C2×C8—441no—
266C2×C8—441no—
267C2×C8—441no—
268C2×C8—881no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4C22⋊Dic1112yes—
279C22⋊C4—22no—
280C42—22no—
281C42D4×D1111yescharacteristic
282C42#434111yescharacteristic
283C42C2×C22⋊D1111yescharacteristic
284C42C2×C22⋊D1111yescharacteristic
285C11#927211yescharacteristic, complemented, Sylow
286C23D4×Dic1111yescharacteristic
287Q8—42no—
288Q8—41no—
289Q8—41no—
290Q8—81no—
291Q8—81no—
292Q8—81no—
293Q8—81no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4SD16×D1111yescharacteristic
303C2×C4#6696711yescharacteristic
304C2×C4#6696811yescharacteristic
305C2×C4#6696911yescharacteristic
306C2×C4D4×Dic1111yescharacteristic
307C2×C4#6698811yescharacteristic
308C2×C4#6699011yescharacteristic
309C2×C4#6699211yescharacteristic
310C2×C4#6699211yescharacteristic
311C2×C4C2×C22⋊Dic1111yescharacteristic
312C8—42no—
313C8—222no—
314C8—441no—
315C8—441no—
316C8—441no—
317C8—881no—
318C8—881no—
319C22—21no—
320C22—21no—
321C22SD16×Dic1111yescharacteristic
322C22#1062277711yescharacteristic
323C22#1062283311yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—82no—
330C4#1062277611yescharacteristic
331C4#1062277911yescharacteristic
332C4#1062278311yescharacteristic
333C4#1062278511yescharacteristic
334C4#1062281611yescharacteristic
335C4#1062281711yescharacteristic
336C2—21no—
337C2—21no—
338C2#1306897311yescharacteristic
339C2#1306913311yescharacteristic
340C2#1306916911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3229C2
socleC22×C11#386
prime radicalC23×C11C4×D4
cosocleC2×C42×C11C23
hypercenter#3229D11
hypocenterC11#9272
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
285. C11#9272semidirect

Maximal subgroups

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

subgroupindex
#130775652
#130694612
#130673062
C2×#106221852
#130665122
#130664652
C11×#32292
#927211