Finite Group Databasebeta

← #14649793

Subgroups — #14649793

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#13074383C211yesmaximal, characteristic
3#13067288C211yesmaximal, characteristic, complemented
4#13066928C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1546C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66999—21no—
10C2×M16×D11—21no—
11C2×#66925C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#423C2211yescharacteristic
14#10622843—21no—
15#10622731—21no—
16#10622606—21no—
17#10622606C412yes—
18#10622593—21no—
19#10622593C412yes—
20#10622549C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622452—22no—
24#10622452—22no—
25C11×#332—22no—
26#10622185—22no—
27#10622107—21no—
28#10622106—21no—
29C22×Q8×C11—21no—
30C22×C4×D11D411yescharacteristic
31C2×C11×M16—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C42×C11C2311yescharacteristic
39#66999—42no—
40#66999—42no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4C2×C411yescharacteristic
43C2×(C2×D11)⋊C4D411yescharacteristic
44C2×C4⋊Dic11—21no—
45C2×Dic11⋊C4—22no—
46C2×Dic11⋊C4C2×C411yescharacteristic
47C2×Dic11⋊C4D411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×#4318—21no—
50M16×D11—42no—
51M16×D11—42no—
52C2×#4313—22no—
53C2×C8×D11—22no—
54#66925—21no—
55#66925—21no—
56#66925—21no—
57#66925—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×C22⋊C8—21no—
62C4×C8×C11—21no—
63C11⋊#95—21no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C11⋊#95C2×C412yes—
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
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C22×C4×C11—22no—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—22no—
86C22×Dic11C22⋊C411yescharacteristic
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11D812yes—
94C2×C4×D11SD1612yes—
95C11×M16—41no—
96C11×M16—41no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C42×C11#4111yescharacteristic
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—21no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4—44no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116Dic11⋊C4—21no—
117Dic11⋊C4—21no—
118Dic11⋊C4—44no—
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#1546D1111yescharacteristic, complemented
131#1458—111no—
132#1286—111no—
133#1286—111no—
134C23×C11C2×C22⋊C411yescharacteristic
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11#10212yes—
140Q8×C11—81no—
141Q8×C11—81no—
142Q8×C11—81no—
143Q8×C11—81no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12311yescharacteristic
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11C2×SD1611yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11#13711yescharacteristic
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11#10212yes—
169C4×D11—22no—
170C4×D11—22no—
171C4×D11—22no—
172C4×D11—22no—
173C8×C11—42no—
174C8×C11—81no—
175C11⋊C8—42no—
176C11⋊C8—81no—
177C22×M16—221no—
178C2×C4⋊Q8C2×D1111yescharacteristic
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#382—111no—
194#332—22no—
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—21no—
222C23×C4—111no—
223C2×M16—21no—
224C2×M16—222no—
225C2×M16—221no—
226C2×M16—442no—
227C2×M16—442no—
228C22×C8—222no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
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—222no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4C4×D1112yes—
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⋊C8C22⋊D1112yes—
257C22⋊C8—21no—
258C22⋊C8—221no—
259C4×C8—21no—
260C4×C8—221no—
261#95—112no—
262#95—222no—
263#95—222no—
264#95—221no—
265C2×C11—21no—
266C2×C11—21no—
267C2×C11#187411yescharacteristic
268C2×C11#190911yescharacteristic
269C2×C11#191511yescharacteristic
270D11—42no—
271C24—111no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
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—22no—
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—221no—
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—
320C42#433911yescharacteristic
321C42D4×D1111yescharacteristic
322C42#434111yescharacteristic
323C42C2×C22⋊D1111yescharacteristic
324C11#919511yescharacteristic, complemented, Sylow
325C23—112no—
326C23—221no—
327C23—221no—
328C23—441no—
329C23—441no—
330C23C22⋊C4×D1111yescharacteristic
331Q8—81no—
332Q8—81no—
333Q8—81no—
334Q8—81no—
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×C4(C22⋊D11)⋊C411yescharacteristic
355C2×C4#6693611yescharacteristic
356C2×C4#6693711yescharacteristic
357C2×C4D8×D1111yescharacteristic
358C2×C4#6696411yescharacteristic
359C2×C4SD16×D1111yescharacteristic
360C2×C4#6696811yescharacteristic
361C2×C4C4×C22⋊D1111yescharacteristic
362C2×C4#6699011yescharacteristic
363C2×C4#6699111yescharacteristic
364C8—42no—
365C8—81no—
366C8—442no—
367C8—881no—
368C22—21no—
369C22—21no—
370C22—222no—
371C22—442no—
372C22—441no—
373C22—441no—
374C22—881no—
375C22D11×#10211yescharacteristic
376C22#1062238411yescharacteristic
377C22#1062256911yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—222no—
384C4—441no—
385C4—441no—
386C4—882no—
387C4#1062238711yescharacteristic
388C4#1062239011yescharacteristic
389C4#1062276911yescharacteristic
390C4#1062278311yescharacteristic
391C2—21no—
392C2—21no—
393C2—442no—
394C2#1306893011yescharacteristic
395C2#1306913511yescharacteristic
396C2#1306916511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#386
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1546D11
hypocenterC11#9195
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. #13067288C2semidirect
5. #13066476C2semidirect
6. #13066475C2semidirect
7. C11×#1546C2semidirect
130. #1546D11semidirect
324. C11#9195semidirect

Maximal subgroups

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

subgroupindex
#130771782
#130743832
#130672882
#130669282
#130664762
#130664752
C11×#15462
#919511