Finite Group Databasebeta

← #14670713

Subgroups — #14670713

Order 2816.

582 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622770C211yesmaximal, characteristic
2C2×#10622493C211yesmaximal, characteristic, complemented
3C2×#10622200C211yesmaximal, characteristic, complemented
4C2×(C2×D11)⋊C16C211yesmaximal, characteristic, complemented
5#13066708C211yesmaximal, characteristic, complemented
6#13066707C211yesmaximal, characteristic, complemented
7C2×C11×#357C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×#66991—21no—
10C22×C8×D11C2211yescharacteristic
11C2×#66945—21no—
12C22×C11×C16C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14C2×#66896—21no—
15#10622770—22no—
16#10622770C414yescomplemented
17C2×#66882C2211yescharacteristic
18C2×#66882C2211yescharacteristic
19C22×C11⋊C16C2211yescharacteristic
20C2×#66872—21no—
21#10622493—22no—
22#10622493—22no—
23C11×#357—22no—
24#10622200—22no—
25(C2×D11)⋊C16—22no—
26C22×D4×C11—21no—
27C22×C22⋊D11—41no—
28C22×C4×D11D411yescharacteristic
29C2×C11×D8—21no—
30C2×C11×D8—21no—
31C2×C11×D8—21no—
32C2×C11×D8—21no—
33C2×C11×D8—21no—
34C2×C11×D8C2×C412yes—
35C22×C8×C11C2311yescharacteristic
36C2×C11×C4⋊C4—21no—
37C2×C22⋊Dic11—41no—
38#66991—24no—
39#66991—42no—
40C2×(C2×D11)⋊C4—41no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4×Dic11—41no—
44C22×C11⋊C8D411yescharacteristic
45C2×C8×D11—21no—
46C2×C8×D11—21no—
47C2×C8×D11—21no—
48C2×C8×D11—21no—
49C2×C8×D11C2×C412yes—
50C2×C8×D11D412yes—
51#66945—24no—
52#66945—42no—
53C2×C11×C16—21no—
54C2×C11×C16—21no—
55C2×C11×C16—21no—
56C11×#107—21no—
57C11×#107D412yescomplemented
58#66896—24no—
59#66882—21no—
60#66882—21no—
61#66882C2×C412yes—
62#66882D412yescomplemented
63C2×C11⋊C16—21no—
64C2×C11⋊C16—21no—
65C2×C11⋊C16—21no—
66#66872—24no—
67#12992—111nomaximal, Sylow
68C24×C11—41no—
69C23×D11D811yescharacteristic
70C2×D4×C11—22no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—44no—
79C2×C22⋊D11—82no—
80C2×C22⋊D11—82no—
81C22×Dic11—41no—
82C22×Dic11—41no—
83C22×Dic11D811yescharacteristic
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11C22⋊C412yes—
89C2×C4×D11SD1612yes—
90C11×D8—22no—
91C11×D8—22no—
92C11×D8—41no—
93C11×D8—41no—
94C2×C8×C11C22×C411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C11×C4⋊C4—22no—
101C11×C4⋊C4—41no—
102C22⋊Dic11—44no—
103(C2×D11)⋊C4—44no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4×Dic11—44no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8C22⋊C412yes—
112C8×D11—22no—
113C8×D11—22no—
114C8×D11—22no—
115C8×D11—22no—
116C11×C16—41no—
117C11⋊C16—41no—
118C2×#466—111no—
119C2×#427—111no—
120C2×#357—111no—
121C2×#357D1111yescharacteristic, complemented
122C2×C22⋊C16—111no—
123#1380—111no—
124#1380—111no—
125C23×C11—42no—
126C23×C11—81no—
127C23×C11—81no—
128C23×C11—81no—
129C23×C11—81no—
130C23×C11—81no—
131C23×C11—81no—
132C23×C11C2×D811yescharacteristic
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—21no—
139C22×D11#10212yes—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—81no—
143D4×C11—81no—
144C2×C4×C11—42no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11C2×C22⋊C411yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×C4×C11C2×SD1611yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11#13711yescharacteristic
153C22⋊D11—88no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—81no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161C2×Dic11—81no—
162C2×Dic11#10212yes—
163C4×D11—22no—
164C4×D11—22no—
165C4×D11—22no—
166C4×D11—22no—
167C8×C11C4×D411yescharacteristic
168C8×C11C4×D411yescharacteristic
169C8×C11#12111yescharacteristic
170C8×C11#12111yescharacteristic
171C11⋊C8—22no—
172C22×D8C2×D1111yescharacteristic
173C23×C8—111no—
174C2×#121—221no—
175C2×#117—221no—
176C22×C16—111no—
177C22×C16C2×D1111yescharacteristic
178#466—114no—
179#466—222no—
180#427—222no—
181#427—222no—
182C2×#107—111no—
183C2×#107—111no—
184C2×#107C2×D1111yescharacteristic
185C2×#106—221no—
186C2×#102—221no—
187#357—22no—
188#357—222no—
189C22⋊C16—222no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11—82no—
193C22×C11—161no—
194C22×C11—161no—
195C22×C11—161no—
196C22×C11—161no—
197C22×C11C2×#10211yescharacteristic
198C22×C11#44711yescharacteristic
199C22×C11#48011yescharacteristic
200C22×C11#50811yescharacteristic
201C22×C11#50811yescharacteristic
202C22×C11#50911yescharacteristic
203C22×C11#50911yescharacteristic
204C2×D11—22no—
205C2×D11—22no—
206C2×D11—22no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—41no—
211C4×C11—82no—
212C4×C11#38611yescharacteristic
213C4×C11#41711yescharacteristic
214C4×C11#44811yescharacteristic
215C4×C11#48111yescharacteristic
216Dic11—22no—
217Dic11—82no—
218Dic11—82no—
219C22×D4—21no—
220C22×D4—441no—
221C23×C4—111no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8C4×D1112yes—
228C22×C8—111no—
229C22×C8—112no—
230C22×C8—112no—
231C22×C8—221no—
232C22×C8—221no—
233C22×C8—221no—
234C22×C8—221no—
235C22×C8C22×D1111yescharacteristic
236#121—224no—
237#121—442no—
238#117—224no—
239#117—442no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C22⋊C4—441no—
244C2×C22⋊C4—441no—
245C2×C42—441no—
246C2×C16—21no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—221no—
250C2×C16—221no—
251C2×C16—221no—
252#107—21no—
253#107—112no—
254#107—112no—
255#107—221no—
256#107—221no—
257#107C22⋊D1112yescomplemented
258#106—224no—
259#102—224no—
260C2×C11—162no—
261C2×C11#187411yescharacteristic
262C2×C11#213811yescharacteristic
263C2×C11#214011yescharacteristic
264C2×C11#218611yescharacteristic
265C2×C11#218611yescharacteristic
266C2×C11#223411yescharacteristic
267C2×C11#223411yescharacteristic
268D11—42no—
269C24—41no—
270C24—111no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—444no—
278C2×D4—882no—
279C2×D4—882no—
280C22×C4—41no—
281C22×C4—111no—
282C22×C4—112no—
283C22×C4—112no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—441no—
289C22×C4—441no—
290C22×C4D4×D1111yescharacteristic
291D8—22no—
292D8—22no—
293D8—41no—
294D8—41no—
295C2×C8—112no—
296C2×C8—221no—
297C2×C8—221no—
298C2×C8—222no—
299C2×C8—222no—
300C2×C8—222no—
301C2×C8—222no—
302C2×C8C2×C4×D1111yescharacteristic
303C2×C8#433911yescharacteristic
304C2×C8D4×D1111yescharacteristic
305C2×C8D4×D1111yescharacteristic
306C2×C8#434111yescharacteristic
307C2×C8C2×C22⋊D1111yescharacteristic
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—222no—
311C4⋊C4—222no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C22⋊C4—444no—
315C22⋊C4—444no—
316C42—444no—
317C16—41no—
318C16—441no—
319C11#1299211yescharacteristic, complemented, Sylow
320C23—42no—
321C23—81no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—112no—
328C23—221no—
329C23—221no—
330C23—221no—
331C23—221no—
332C23—221no—
333C23—221no—
334C23D8×D1111yescharacteristic
335D4—42no—
336D4—42no—
337D4—81no—
338D4—81no—
339D4—888no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—112no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—222no—
347C2×C4—222no—
348C2×C4—222no—
349C2×C4—222no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—881no—
353C2×C4—881no—
354C2×C4—881no—
355C2×C4—881no—
356C2×C4C22⋊C4×D1111yescharacteristic
357C2×C4#6693611yescharacteristic
358C2×C4#6696411yescharacteristic
359C2×C4SD16×D1111yescharacteristic
360C2×C4#6696811yescharacteristic
361C2×C4#6699011yescharacteristic
362C8—222no—
363C8(C22⋊D11)⋊C411yescharacteristic
364C8#6693711yescharacteristic
365C8C4×C22⋊D1111yescharacteristic
366C8#6699111yescharacteristic
367C22—82no—
368C22—82no—
369C22—82no—
370C22—161no—
371C22—161no—
372C22—161no—
373C22—161no—
374C22—222no—
375C22—222no—
376C22—222no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22—441no—
381C22D11×#10211yescharacteristic
382C22#1062238711yescharacteristic
383C22#1062252411yescharacteristic
384C22#1062252511yescharacteristic
385C22#1062252711yescharacteristic
386C22#1062252911yescharacteristic
387C22#1062276911yescharacteristic
388C4—82no—
389C4—222no—
390C4—882no—
391C4—882no—
392C4#1062238411yescharacteristic
393C4#1062239011yescharacteristic
394C4#1062256911yescharacteristic
395C4#1062278311yescharacteristic
396C2—162no—
397C2—442no—
398C2#1306893011yescharacteristic
399C2#1307032011yescharacteristic
400C2#1307033011yescharacteristic
401C2#1307053611yescharacteristic
402C2#1307053811yescharacteristic
403C2#1307080511yescharacteristic
404C2#1307080611yescharacteristic
subgroupG/H
centerC23D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#357C2
socleC23×C11C2×D8
prime radicalC2×#10622770C2
cosocleC22×C8×C11C23
hypercenterC2×#357D11
hypocenterC11#12992
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#10622493C2semidirect
3. C2×#10622200C2semidirect
4. C2×(C2×D11)⋊C16C2semidirect
5. #13066708C2semidirect
6. #13066707C2semidirect
7. C2×C11×#357C2semidirect
16. #10622770C4semidirect
57. C11×#107D4semidirect
62. #66882D4semidirect
121. C2×#357D11semidirect
257. #107C22⋊D11semidirect
319. C11#12992semidirect

Maximal subgroups

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

subgroupindex
C2×#106227702
C2×#106224932
C2×#106222002
C2×(C2×D11)⋊C162
#130667082
#130667072
C2×C11×#3572
#1299211