Finite Group Databasebeta

← #14649795

Subgroups — #14649795

Order 2816.

524 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077178C211yesmaximal, characteristic
2#13074385C211yesmaximal, characteristic
3#13067289C211yesmaximal, characteristic, complemented
4#13067287C211yesmaximal, characteristic, complemented
5#13066928C211yesmaximal, characteristic
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×M16×D11—21no—
9C2×#66950—21no—
10C2×#66925C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#423C2211yescharacteristic
14C11×#382C2211yescharacteristic
15#10622731—21no—
16#10622587—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622452—22no—
20#10622452—22no—
21#10622287—21no—
22#10622287C412yes—
23#10622274—21no—
24#10622274C412yes—
25#10622124—22no—
26#10622120—22no—
27#10622107—21no—
28#10622106—21no—
29C22×C4×D11D411yescharacteristic
30C22×Dic22—21no—
31C2×C11×M16—21no—
32C2×C11×C4⋊C4—21no—
33C2×C42×C11C2311yescharacteristic
34C2×(C2×D11)⋊C4—22no—
35C2×(C2×D11)⋊C4C2×C411yescharacteristic
36C2×(C2×D11)⋊C4D411yescharacteristic
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—22no—
39C2×C4⋊Dic11C2×C412yes—
40C2×Dic11⋊C4C2×C411yescharacteristic
41C2×Dic11⋊C4D411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×#4318—21no—
44M16×D11—42no—
45M16×D11—42no—
46C2×#4313—22no—
47C2×C8×D11—22no—
48#66950—42no—
49#66950—42no—
50#66925—21no—
51#66925—21no—
52#66925—21no—
53#66925—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×C22⋊C8—21no—
62C4×C8×C11—21no—
63C11×#95—21no—
64C11×#95C2×C412yes—
65C11⋊#95—22no—
66C11⋊#95—22no—
67C22⋊(C11⋊C8)—21no—
68Dic11⋊C8—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72C4×C11⋊C8—21no—
73#9195—111nomaximal, Sylow
74C23×D11C22⋊C411yescharacteristic
75C22×C4×C11—22no—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—22no—
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11D812yes—
88C2×C4×D11SD1612yes—
89C2×Dic22—41no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C11×M16—41no—
96C11×M16—41no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11#4111yescharacteristic
104C42×C11#4111yescharacteristic
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—44no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—44no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115Dic11⋊C4—21no—
116Dic11⋊C4—21no—
117Dic11⋊C4—21no—
118Dic11⋊C4—21no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121#4318—41no—
122#4318—41no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125#4313—44no—
126C8×D11—44no—
127#2905—111no—
128#2621—111no—
129#1546—111no—
130#1546—111no—
131#1458—111no—
132#1286—111no—
133#1286D1111yescharacteristic, complemented
134C23×C11C2×C22⋊C411yescharacteristic
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11#10212yes—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12311yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11#13711yescharacteristic
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11#10212yes—
165C4×D11—22no—
166C4×D11—22no—
167C4×D11—22no—
168C4×D11—22no—
169Dic22—81no—
170Dic22—81no—
171Dic22—81no—
172Dic22—81no—
173C8×C11—42no—
174C8×C11—81no—
175C11⋊C8—42no—
176C11⋊C8—81no—
177C22×M16—221no—
178C2×C4⋊Q8—111no—
179C2×C22⋊Q8—221no—
180C2×#117—111no—
181#431—111no—
182#431C2×D1111yescharacteristic
183#424—222no—
184#424—222no—
185#423—111no—
186#423—221no—
187#423C2×D1111yescharacteristic
188#398—112no—
189#398—221no—
190#397—112no—
191#397—221no—
192#391—221no—
193#382C2×D1111yescharacteristic
194#332—222no—
195#332—222no—
196#324—221no—
197#323—221no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11#38611yescharacteristic
201C22×C11C2×#10211yescharacteristic
202C22×C11#41711yescharacteristic
203C2×D11—22no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—42no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—82no—
213C4×C11#44711yescharacteristic
214C4×C11#44811yescharacteristic
215C4×C11#48011yescharacteristic
216C4×C11#48111yescharacteristic
217Dic11—22no—
218Dic11—41no—
219Dic11—41no—
220Dic11—82no—
221C22×Q8—221no—
222C23×C4—111no—
223C2×M16—21no—
224C2×M16—222no—
225C2×M16—221no—
226C2×M16—442no—
227C2×M16—442no—
228C22×C8—222no—
229C4⋊Q8—221no—
230C4⋊Q8—221no—
231C4⋊Q8—221no—
232C4⋊Q8—221no—
233C22⋊Q8—442no—
234C22⋊Q8—442no—
235#117—221no—
236#117—221no—
237#117—221no—
238#117—221no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—112no—
243C2×C4⋊C4—222no—
244C2×C4⋊C4—221no—
245C2×C22⋊C4—111no—
246C2×C22⋊C4—111no—
247C2×C22⋊C4—222no—
248C2×C42—111no—
249C2×C42C22×D1111yescharacteristic
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—112no—
253C4⋊C8—224no—
254C4⋊C8—221no—
255C4⋊C8—221no—
256C4⋊C8D4412yes—
257C22⋊C8—21no—
258C22⋊C8—221no—
259C4×C8—21no—
260C4×C8—221no—
261#95—21no—
262#95—222no—
263#95—222no—
264#95C4×D1112yes—
265C2×C11—21no—
266C2×C11—21no—
267C2×C11#187411yescharacteristic
268C2×C11#190911yescharacteristic
269C2×C11#191511yescharacteristic
270D11—42no—
271C24—111no—
272C2×Q8—441no—
273C2×Q8—441no—
274C2×Q8—441no—
275C2×Q8—441no—
276C2×Q8—441no—
277C2×Q8—441no—
278C22×C4—22no—
279C22×C4—111no—
280C22×C4—112no—
281C22×C4—112no—
282C22×C4—111no—
283C22×C4—111no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—222no—
289C22×C4C2×C4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291C22×C4D4×D1111yescharacteristic
292M16—41no—
293M16—41no—
294M16—444no—
295M16—441no—
296M16—441no—
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—222no—
300C2×C8—444no—
301C2×C8—441no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—222no—
309C4⋊C4—222no—
310C4⋊C4—444no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C22⋊C4—221no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C22⋊C4—221no—
317C22⋊C4—444no—
318C42—221no—
319C42—221no—
320C42C2×D4411yescharacteristic
321C42#433911yescharacteristic
322C42D4×D1111yescharacteristic
323C42#434311yescharacteristic
324C11#919511yescharacteristic, complemented, Sylow
325C23—112no—
326C23—221no—
327C23—221no—
328C23—441no—
329C23—441no—
330C23C22⋊C4×D1111yescharacteristic
331Q8—881no—
332Q8—881no—
333Q8—881no—
334Q8—881no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—112no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—222no—
344C2×C4—222no—
345C2×C4—222no—
346C2×C4—222no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—442no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4C4×D4411yescharacteristic
355C2×C4#6693511yescharacteristic
356C2×C4#6693711yescharacteristic
357C2×C4#6694611yescharacteristic
358C2×C4#6694711yescharacteristic
359C2×C4#6694811yescharacteristic
360C2×C4D8×D1111yescharacteristic
361C2×C4SD16×D1111yescharacteristic
362C2×C4#6696711yescharacteristic
363C2×C4#6697111yescharacteristic
364C8—42no—
365C8—81no—
366C8—442no—
367C8—881no—
368C22—21no—
369C22—21no—
370C22—222no—
371C22—442no—
372C22—441no—
373C22—441no—
374C22—881no—
375C22#1062227811yescharacteristic
376C22D11×#10211yescharacteristic
377C22#1062241611yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—222no—
384C4—441no—
385C4—441no—
386C4—882no—
387C4#1062238611yescharacteristic
388C4#1062241911yescharacteristic
389C4#1062247611yescharacteristic
390C4#1062249511yescharacteristic
391C2—21no—
392C2—21no—
393C2—442no—
394C2#1306893211yescharacteristic
395C2#1306913711yescharacteristic
396C2#1306916711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#386
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#9195
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
3. #13067289C2semidirect
4. #13067287C2semidirect
6. #13066474C2semidirect
7. C11×#1286C2semidirect
133. #1286D11semidirect
324. C11#9195semidirect

Maximal subgroups

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

subgroupindex
#130771782
#130743852
#130672892
#130672872
#130669282
#130664742
C11×#12862
#919511