Finite Group Databasebeta

← #14649555

Subgroups — #14649555

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076942C211yesmaximal, characteristic
2C2×#10622264C211yesmaximal, 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×C4×Dic11C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C2×C11×#95C2211yescharacteristic
13#10622834C412yescomplemented
14#10622833—21no—
15#10622825C2211yescharacteristic
16C2×C11⋊#95—21no—
17C2×C11⋊#95—21no—
18C2×C11⋊#95C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20#10622586C412yescomplemented
21#10622557—22no—
22#10622264—22no—
23#10622264—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—22no—
48C2×C4×Dic11—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11C2×C412yes—
53C2×C4×Dic11D412yes—
54C22×C11⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×#95—21no—
58C11×#95D412yes—
59C11⋊#95—24no—
60C11⋊#95—24no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—22no—
64C11⋊#95D412yes—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#9157—111nomaximal, Sylow
68C24×C11—21no—
69C24×C11C2×D411yescharacteristic
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—42no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—42no—
82C22×C4×C11—42no—
83C22×C4×C11—42no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×Dic11—22no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—22no—
96C22×Dic11—21no—
97C22×Dic11—21no—
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—
109C2×C8×C11—42no—
110C2×C8×C11—41no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C22⋊Dic11—44no—
116C22⋊Dic11—44no—
117C22⋊Dic11—41no—
118C22⋊Dic11—41no—
119C4⋊Dic11—42no—
120Dic11⋊C4—44no—
121C4×Dic11—22no—
122C4×Dic11—22no—
123C4×Dic11—22no—
124C4×Dic11—22no—
125C2×C11⋊C8—42no—
126C2×C11⋊C8—41no—
127#2854—111no—
128C2×#383—111no—
129#1817—111no—
130C2×#327—111no—
131C2×#327D1111yescharacteristic
132#1294—111no—
133#1294—111no—
134C23×C11—22no—
135C23×C11—22no—
136C23×C11—41no—
137C23×C11—42no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—42no—
141C23×C11C2×C22⋊C411yescharacteristic
142C23×C11#12011yescharacteristic
143C23×C11#12311yescharacteristic
144C23×C11#13511yescharacteristic
145C23×C11#13511yescharacteristic
146C23×C11AGL(1,ℤ/8)11yescharacteristic
147C23×C11AGL(1,ℤ/8)11yescharacteristic
148D4×C11—81no—
149D4×C11—81no—
150D4×C11—81no—
151D4×C11—81no—
152D4×C11—81no—
153D4×C11—81no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—82no—
167C2×C4×C11—82no—
168C2×C4×C11C4×D411yescharacteristic
169C2×C4×C11C4×D411yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—82no—
191C2×Dic11—82no—
192C8×C11—81no—
193C11⋊C8—81no—
194C2×#123—221no—
195C2×#121C2×D1111yescharacteristic
196C22×C42—111no—
197C2×C22⋊C8—111no—
198C2×C22⋊C8C2×D1111yescharacteristic
199#390—112no—
200#389—112no—
201#388—222no—
202#386—221no—
203#383—222no—
204#383—222no—
205#380—111no—
206C2×#95—111no—
207C2×#95—221no—
208C2×#95—221no—
209C2×#95C2×D1111yescharacteristic
210#336—222no—
211#327—22no—
212#327—222no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—82no—
225C22×C11—82no—
226C22×C11#38611yescharacteristic
227C22×C11#41012yes—
228C22×C11#41611yescharacteristic
229C22×C11#41811yescharacteristic
230C22×C11#42112yes—
231C22×C11#44911yescharacteristic
232C22×C11#44911yescharacteristic
233C22×C11#48211yescharacteristic
234C22×C11#48211yescharacteristic
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—82no—
240C4×C11—81no—
241Dic11—42no—
242Dic11—42no—
243Dic11—82no—
244Dic11—82no—
245C22×D4—21no—
246C22×D4C4×D1111yescharacteristic
247C23×C4—21no—
248C23×C4—111no—
249C23×C4—111no—
250C23×C4—221no—
251C23×C4C22×D1111yescharacteristic
252C22×C8—21no—
253C22×C8—221no—
254#123—442no—
255#123—442no—
256#121—21no—
257#121—21no—
258#121—21no—
259#121—21no—
260C2×C4⋊C4—112no—
261C2×C4⋊C4—222no—
262C2×C4⋊C4C4×D1111yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—222no—
265C2×C22⋊C4—222no—
266C2×C22⋊C4—221no—
267C2×C42—112no—
268C2×C42—112no—
269C2×C42—221no—
270C2×C42—221no—
271C2×C42—221no—
272C2×C42—221no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277#95—21no—
278#95—112no—
279#95—222no—
280#95—224no—
281#95—224no—
282#95—221no—
283#95—221no—
284#95C22⋊D1112yes—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—161no—
290C2×C11#151412yes—
291C2×C11#152112yes—
292C2×C11#187511yescharacteristic
293C2×C11#189711yescharacteristic
294C2×C11#189911yescharacteristic
295C24—21no—
296C24D4×D1111yescharacteristic
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—112no—
314C22×C4—112no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—222no—
324C22×C4—222no—
325C22×C4—442no—
326C22×C4—442no—
327C22×C4—442no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4C2×C4×D1111yescharacteristic
331C22×C4#433911yescharacteristic
332C22×C4D4×D1111yescharacteristic
333C22×C4D4×D1111yescharacteristic
334C22×C4#434111yescharacteristic
335C22×C4C2×C22⋊D1111yescharacteristic
336C2×C8—42no—
337C2×C8—41no—
338C2×C8—442no—
339C2×C8—441no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—442no—
343C4⋊C4—444no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—444no—
347C22⋊C4—444no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C42—222no—
351C42—222no—
352C42—222no—
353C42—222no—
354C11#915711yescharacteristic, complemented, Sylow
355C23—22no—
356C23—22no—
357C23—41no—
358C23—42no—
359C23—41no—
360C23—41no—
361C23—42no—
362C23C22⋊C4×D1111yescharacteristic
363C23#6693611yescharacteristic
364C23#6696411yescharacteristic
365C23#6696511yescharacteristic
366C23#6696711yescharacteristic
367C23#6696911yescharacteristic
368C23#6699011yescharacteristic
369D4—81no—
370D4—81no—
371D4—81no—
372D4—81no—
373D4—81no—
374D4—81no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4—882no—
408C2×C4—882no—
409C2×C4(C22⋊D11)⋊C411yescharacteristic
410C2×C4#6693711yescharacteristic
411C2×C4C4×C22⋊D1111yescharacteristic
412C2×C4#6699111yescharacteristic
413C8—81no—
414C8—881no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—82no—
427C22—82no—
428C22#1062235312yes—
429C22#1062238311yescharacteristic
430C22#1062238511yescharacteristic
431C22#1062239211yescharacteristic
432C22#1062239711yescharacteristic
433C22#1062243412yes—
434C22#1062256911yescharacteristic
435C22#1062277111yescharacteristic
436C22#1062278511yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—81no—
443C4—442no—
444C4—442no—
445C4—882no—
446C4—882no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—161no—
452C2#1306716112yes—
453C2#1306719012yes—
454C2#1306893511yescharacteristic
455C2#1306906111yescharacteristic
456C2#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#9157
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×#10622264C2semidirect
3. #13068682C2semidirect
5. #13066496C2semidirect
6. #13066495C2semidirect
13. #10622834C4semidirect
20. #10622586C4semidirect
354. C11#9157semidirect

Maximal subgroups

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

subgroupindex
#130769422
C2×#106222642
#130686822
C2×#106221752
#130664962
#130664952
C2×C11×#3272
#915711