Finite Group Databasebeta

← #14657600

Subgroups — #14657600

Order 2816.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622454C211yesmaximal, characteristic
2#13069577C211yesmaximal, characteristic, complemented
3#13069410C211yesmaximal, characteristic
4#13068617C211yesmaximal, characteristic
5C2×#10622120C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#334C211yesmaximal, characteristic, complemented
8C22×#4314—21no—
9C2×C4×D44C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66885—21no—
15C2×(C2×D11)⋊C8—21no—
16C2×(C2×D11)⋊C8—21no—
17C2×#66880—21no—
18#10622548C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20#10622454—22no—
21#10622454—22no—
22C11×#334—22no—
23#10622189—21no—
24#10622189—21no—
25#10622189—21no—
26#10622120—22no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C22×C8×C11D411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C22×C11⋊C8—21no—
43C2×#4314—24no—
44C2×#4314—42no—
45C2×#4314—42no—
46C4×D44—21no—
47C4×D44—21no—
48C4×D44—21no—
49C4×D44—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922D412yes—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D412yes—
58C4×C8×C11—21no—
59C4×C8×C11—21no—
60#66885—42no—
61(C2×D11)⋊C8—42no—
62(C2×D11)⋊C8—42no—
63#66880—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#10477—111nomaximal, Sylow
67C23×D11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—41no—
73C22×Dic11—41no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44SD1612yes—
80C2×C4×D11—41no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×Dic22—22no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×C8×C11—22no—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—21no—
97C2×C8×C11—21no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11SD1612yescomplemented
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110C4⋊Dic11—21no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11—21no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—81no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124#4314—48no—
125C2×#461—111no—
126#1990—111no—
127#1954—111no—
128#1802—111no—
129C2×#334D1111yescharacteristic, complemented
130C2×#332—111no—
131#1296—111no—
132C23×C11#12111yescharacteristic
133C22×D11—22no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12311yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11#12411yescharacteristic
148C2×C4×C11C2×SD1611yescharacteristic
149C2×C4×C11C2×SD1611yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×Dic11—42no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—81no—
161C2×Dic11—81no—
162C2×Dic11—81no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165D44—22no—
166D44—22no—
167D44—41no—
168D44—41no—
169C4×D11—81no—
170C4×D11—81no—
171C4×D11—81no—
172C4×D11—81no—
173Dic22—42no—
174Dic22—42no—
175Dic22—81no—
176Dic22—81no—
177C8×C11—22no—
178C8×C11—42no—
179C8×C11—41no—
180C8×C11—81no—
181C11⋊C8—81no—
182C22×SD16—221no—
183C2×C4⋊Q8—111no—
184C2×C4×D4—111no—
185#461—222no—
186#461—222no—
187C2×C4⋊C8—111no—
188C2×C4⋊C8C2×D1111yescharacteristic
189C2×C4⋊C8C2×D1111yescharacteristic
190C2×#103—221no—
191C2×#102—221no—
192C2×C22⋊C8—221no—
193C2×C22⋊C8—221no—
194C2×C4×C8C2×D1111yescharacteristic
195#384—111no—
196#340—221no—
197#340—221no—
198#340—221no—
199#334—22no—
200#332—222no—
201C22×C11#39411yescharacteristic
202C22×C11#46111yescharacteristic
203C22×C11#46311yescharacteristic
204C22×C11#46511yescharacteristic
205C22×C11#46911yescharacteristic
206C22×C11#47111yescharacteristic
207C22×C11#47311yescharacteristic
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—42no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11#44911yescharacteristic
218C4×C11#45011yescharacteristic
219C4×C11#46011yescharacteristic
220C4×C11#46411yescharacteristic
221C4×C11#46511yescharacteristic
222C4×C11#46811yescharacteristic
223C4×C11#48111yescharacteristic
224C4×C11#48211yescharacteristic
225Dic11—81no—
226Dic11—82no—
227Dic11—161no—
228C22×Q8—221no—
229C22×D4—111no—
230C23×C4—221no—
231C2×SD16—224no—
232C2×SD16—442no—
233C2×SD16—442no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—221no—
237C22×C8D4411yescharacteristic
238C22×C8D4411yescharacteristic
239C4⋊Q8—112no—
240C4⋊Q8—221no—
241C4⋊Q8—221no—
242C4⋊Q8—221no—
243C4×D4—221no—
244C4×D4—221no—
245C4×D4—221no—
246C4×D4—221no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C42C22×D1111yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8C22⋊D1112yes—
261#103—224no—
262#102—442no—
263C22⋊C8—442no—
264C22⋊C8—442no—
265C4×C8—21no—
266C4×C8—21no—
267C2×C11#167111yescharacteristic
268C2×C11#167911yescharacteristic
269C2×C11#169311yescharacteristic
270C2×C11#170111yescharacteristic
271C2×C11#203411yescharacteristic
272C2×C11#205211yescharacteristic
273C2×C11#205511yescharacteristic
274D11—82no—
275C24—221no—
276C2×Q8—222no—
277C2×Q8—441no—
278C2×Q8—441no—
279C2×Q8—441no—
280C2×Q8—441no—
281C2×Q8—441no—
282C2×D4—112no—
283C2×D4—221no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C22×C4—221no—
289C22×C4—441no—
290C22×C4—441no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4—441no—
297C22×C4C2×D4411yescharacteristic
298C22×C4D4×D1111yescharacteristic
299C22×C4#434311yescharacteristic
300SD16—448no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—441no—
313C2×C8—441no—
314C2×C8—441no—
315C2×C8#431412yescomplemented
316C4⋊C4—221no—
317C4⋊C4—222no—
318C4⋊C4—222no—
319C4⋊C4—221no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C4⋊C4—881no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C42#433911yescharacteristic
330C42D4×D1111yescharacteristic
331C42#434311yescharacteristic
332C42C2×C22⋊D1111yescharacteristic
333C11#1047711yescharacteristic, complemented, Sylow
334C23—222no—
335C23—441no—
336C23—441no—
337C23—441no—
338C23—441no—
339C23—441no—
340C23—441no—
341C23#6694811yescharacteristic
342Q8—442no—
343Q8—442no—
344Q8—881no—
345Q8—881no—
346D4—222no—
347D4—222no—
348D4—441no—
349D4—441no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—441no—
353C2×C4—442no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—881no—
357C2×C4—881no—
358C2×C4—881no—
359C2×C4—881no—
360C2×C4—881no—
361C2×C4—881no—
362C2×C4—881no—
363C2×C4—881no—
364C2×C4—881no—
365C2×C4#6694711yescharacteristic
366C2×C4#6694711yescharacteristic
367C2×C4#6694811yescharacteristic
368C2×C4C2×#431411yescharacteristic
369C2×C4#6695711yescharacteristic
370C2×C4#6696111yescharacteristic
371C2×C4#6696211yescharacteristic
372C2×C4SD16×D1111yescharacteristic
373C2×C4#6696711yescharacteristic
374C2×C4#6696711yescharacteristic
375C2×C4#6696911yescharacteristic
376C2×C4#6698311yescharacteristic
377C2×C4#6699011yescharacteristic
378C2×C4#6700011yescharacteristic
379C8—22no—
380C8—41no—
381C8—42no—
382C8—81no—
383C8—881no—
384C22—442no—
385C22—442no—
386C22—442no—
387C22—881no—
388C22—881no—
389C22—881no—
390C22—881no—
391C22#1062245411yescharacteristic
392C22#1062245711yescharacteristic
393C22#1062247711yescharacteristic
394C22#1062247811yescharacteristic
395C22#1062250911yescharacteristic
396C22#1062251111yescharacteristic
397C22#1062260411yescharacteristic
398C4—21no—
399C4—21no—
400C4—881no—
401C4—882no—
402C4—1761no—
403C4#1062245811yescharacteristic
404C4#1062246111yescharacteristic
405C4#1062247611yescharacteristic
406C4#1062247911yescharacteristic
407C4#1062272711yescharacteristic
408C4#1062274711yescharacteristic
409C4#1062278211yescharacteristic
410C4#1062278511yescharacteristic
411C2—882no—
412C2#1306799211yescharacteristic
413C2#1306804011yescharacteristic
414C2#1306813011yescharacteristic
415C2#1306817811yescharacteristic
416C2#1306980711yescharacteristic
417C2#1306991711yescharacteristic
418C2#1306993411yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#334C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#334D11
hypocenterC11#10477
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #13069577C2semidirect
5. C2×#10622120C2semidirect
6. #13066500C2semidirect
7. C2×C11×#334C2semidirect
103. C2×C8×C11SD16semidirect
129. C2×#334D11semidirect
315. C2×C8#4314semidirect
333. C11#10477semidirect

Maximal subgroups

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

subgroupindex
C2×#106224542
#130695772
#130694102
#130686172
C2×#106221202
#130665002
C2×C11×#3342
#1047711