Finite Group Databasebeta

← #14649550

Subgroups — #14649550

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076942C211yesmaximal, characteristic
2C2×#10622263C211yesmaximal, characteristic, complemented
3#13068682C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic
5#13066496C211yesmaximal, characteristic, complemented
6#13066495C211yesmaximal, characteristic, complemented
7C2×C11×#327C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×#66988—21no—
10C22×Dic11⋊C4—21no—
11C22×C4×Dic11C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14#10622834C412yescomplemented
15#10622833—21no—
16#10622825C2211yescharacteristic
17C2×C11⋊#95—21no—
18C2×C11⋊#95C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20#10622586C412yescomplemented
21#10622557—22no—
22#10622263—22no—
23#10622263—22no—
24C11×#327—22no—
25#10622188—22no—
26#10622175—22no—
27C22×D4×C11—21no—
28C22×D4×C11C2×C411yescharacteristic
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C23×Dic11D411yescharacteristic
34C22×C8×C11—21no—
35C11×#121—21no—
36C11×#121—21no—
37C11×#121—21no—
38C11×#121—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—22no—
43C2×C22⋊Dic11—22no—
44#66988—42no—
45#66988—42no—
46C2×C4⋊Dic11C2×C412yes—
47C2×Dic11⋊C4—24no—
48C2×Dic11⋊C4—22no—
49C2×Dic11⋊C4—42no—
50C2×Dic11⋊C4—42no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11—21no—
53C2×C4×Dic11—21no—
54C2×C4×Dic11—21no—
55C2×C4×Dic11C2×C412yes—
56C2×C4×Dic11D412yes—
57C22×C11⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61C11×#95D412yes—
62C11⋊#95—24no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—22no—
66C11⋊#95D412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#9156—111nomaximal, Sylow
70C24×C11—21no—
71C24×C11C2×D411yescharacteristic
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—42no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—42no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—22no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—22no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C22×Dic11—42no—
105C22×Dic11—41no—
106C22×Dic11—41no—
107C22×Dic11C22⋊C412yes—
108C22×Dic11C22⋊C412yes—
109C22×Dic11D812yes—
110C22×Dic11SD1612yes—
111C2×C8×C11—42no—
112C2×C8×C11—41no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C22⋊Dic11—44no—
118C22⋊Dic11—44no—
119C22⋊Dic11—41no—
120C22⋊Dic11—41no—
121C4⋊Dic11—42no—
122Dic11⋊C4—48no—
123Dic11⋊C4—44no—
124C4×Dic11—22no—
125C4×Dic11—22no—
126C4×Dic11—22no—
127C4×Dic11—22no—
128C2×C11⋊C8—42no—
129C2×C11⋊C8—41no—
130#2854—111no—
131C2×#382—111no—
132#1817—111no—
133C2×#327—111no—
134C2×#327D1111yescharacteristic
135#1294—111no—
136#1294—111no—
137C23×C11—22no—
138C23×C11—22no—
139C23×C11—41no—
140C23×C11—42no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11C2×C22⋊C411yescharacteristic
145C23×C11#12011yescharacteristic
146C23×C11#12311yescharacteristic
147C23×C11C2×D811yescharacteristic
148C23×C11C2×SD1611yescharacteristic
149C23×C11AGL(1,ℤ/8)11yescharacteristic
150C23×C11#13711yescharacteristic
151D4×C11—81no—
152D4×C11—81no—
153D4×C11—81no—
154D4×C11—81no—
155D4×C11—81no—
156D4×C11—81no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—82no—
170C2×C4×C11—82no—
171C2×C4×C11C4×D411yescharacteristic
172C2×C4×C11C4×D411yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—82no—
193C2×Dic11—82no—
194C2×Dic11#10214yes—
195C8×C11—81no—
196C11⋊C8—81no—
197C2×#123—221no—
198C2×#121C2×D1111yescharacteristic
199C22×C4⋊C4—221no—
200C22×C42—111no—
201C2×C22⋊C8—111no—
202C2×C22⋊C8C2×D1111yescharacteristic
203#390—112no—
204#389—112no—
205#388—222no—
206#386—221no—
207#382—222no—
208#382—222no—
209#380—111no—
210C2×#95—111no—
211C2×#95—221no—
212C2×#95C2×D1111yescharacteristic
213#336—222no—
214#327—22no—
215#327—222no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—22no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—82no—
228C22×C11—82no—
229C22×C11#38611yescharacteristic
230C22×C11#41012yes—
231C22×C11C2×#10211yescharacteristic
232C22×C11#41711yescharacteristic
233C22×C11#42112yes—
234C22×C11#44711yescharacteristic
235C22×C11#44811yescharacteristic
236C22×C11#48011yescharacteristic
237C22×C11#48111yescharacteristic
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—82no—
243C4×C11—81no—
244Dic11—24no—
245Dic11—42no—
246Dic11—82no—
247Dic11—82no—
248C22×D4—21no—
249C22×D4C4×D1111yescharacteristic
250C23×C4—21no—
251C23×C4—111no—
252C23×C4—111no—
253C23×C4—221no—
254C23×C4C22×D1111yescharacteristic
255C22×C8—21no—
256C22×C8—221no—
257#123—442no—
258#123—442no—
259#121—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4—224no—
266C2×C4⋊C4—442no—
267C2×C4⋊C4—442no—
268C2×C4⋊C4C4×D1111yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—221no—
273C2×C42—112no—
274C2×C42—112no—
275C2×C42—221no—
276C2×C42—221no—
277C2×C42—221no—
278C2×C42—221no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—221no—
282C22⋊C8—221no—
283#95—21no—
284#95—112no—
285#95—222no—
286#95—224no—
287#95—221no—
288#95—221no—
289#95C22⋊D1112yes—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—161no—
295C2×C11#151212yes—
296C2×C11#151712yes—
297C2×C11#187411yescharacteristic
298C2×C11#189711yescharacteristic
299C2×C11#189911yescharacteristic
300C24—21no—
301C24D4×D1111yescharacteristic
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—42no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—112no—
319C22×C4—112no—
320C22×C4—112no—
321C22×C4—112no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—222no—
329C22×C4—222no—
330C22×C4—442no—
331C22×C4—442no—
332C22×C4—442no—
333C22×C4—441no—
334C22×C4—441no—
335C22×C4C2×C4×D1111yescharacteristic
336C22×C4#433911yescharacteristic
337C22×C4D4×D1111yescharacteristic
338C22×C4D4×D1111yescharacteristic
339C22×C4#434111yescharacteristic
340C22×C4C2×C22⋊D1111yescharacteristic
341C2×C8—42no—
342C2×C8—41no—
343C2×C8—442no—
344C2×C8—441no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—442no—
348C4⋊C4—444no—
349C4⋊C4—448no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—444no—
353C22⋊C4—444no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C42—222no—
357C42—222no—
358C42—222no—
359C42—222no—
360C11#915611yescharacteristic, complemented, Sylow
361C23—22no—
362C23—22no—
363C23—41no—
364C23—42no—
365C23—41no—
366C23—41no—
367C23—42no—
368C23C22⋊C4×D1111yescharacteristic
369C23#6693611yescharacteristic
370C23D8×D1111yescharacteristic
371C23#6696411yescharacteristic
372C23SD16×D1111yescharacteristic
373C23#6696811yescharacteristic
374C23#6699011yescharacteristic
375D4—81no—
376D4—81no—
377D4—81no—
378D4—81no—
379D4—81no—
380D4—81no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—114no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—222no—
402C2×C4—222no—
403C2×C4—222no—
404C2×C4—222no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—882no—
414C2×C4—882no—
415C2×C4(C22⋊D11)⋊C411yescharacteristic
416C2×C4#6693711yescharacteristic
417C2×C4C4×C22⋊D1111yescharacteristic
418C2×C4#6699111yescharacteristic
419C8—81no—
420C8—881no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—82no—
433C22—82no—
434C22#1062235312yes—
435C22D11×#10211yescharacteristic
436C22#1062238411yescharacteristic
437C22#1062238711yescharacteristic
438C22#1062239011yescharacteristic
439C22#1062243412yes—
440C22#1062256911yescharacteristic
441C22#1062276911yescharacteristic
442C22#1062278311yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—82no—
448C4—81no—
449C4—224no—
450C4—442no—
451C4—882no—
452C4—882no—
453C2—21no—
454C2—21no—
455C2—21no—
456C2—21no—
457C2—161no—
458C2#1306715112yes—
459C2#1306717412yes—
460C2#1306893011yescharacteristic
461C2#1306906111yescharacteristic
462C2#1306907111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#327C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenterC2×#327D11
hypocenterC11#9156
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#10622263C2semidirect
3. #13068682C2semidirect
5. #13066496C2semidirect
6. #13066495C2semidirect
14. #10622834C4semidirect
20. #10622586C4semidirect
360. C11#9156semidirect

Maximal subgroups

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

subgroupindex
#130769422
C2×#106222632
#130686822
C2×#106221752
#130664962
#130664952
C2×C11×#3272
#915611