Finite Group Databasebeta

← #14646465

Subgroups — #14646465

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66946C211yesmaximal, characteristic
2#13068732C211yesmaximal, characteristic, complemented
3C4×Dic11⋊C8C211yesmaximal, characteristic, complemented
4C2×#10622097C211yesmaximal, characteristic
5C2×#10622121C211yesmaximal, characteristic
6#13066457C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C2×#66946C411yescharacteristic
9C2×#66946C411yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C2×C42×D11—21no—
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15C2×Dic11⋊C8—21no—
16C4⋊C4×Dic11C411yescharacteristic
17C4⋊C4×Dic11C411yescharacteristic
18C4×(C2×D11)⋊C4—21no—
19C42×Dic11C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622279—21no—
23#10622279—21no—
24#10622188—21no—
25#10622188—21no—
26#10622188—21no—
27#10622121—22no—
28#10622097—22no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11—21no—
31C22×C4×D11—21no—
32C22×C4×D11—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11C2×C411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C2×C4×Dic11D411yescharacteristic
51C22×C11⋊C8—21no—
52C22×C11⋊C8—21no—
53#66946—22no—
54#66946—22no—
55#66946—22no—
56#66946C814yescomplemented
57C4×D44—21no—
58C4×D44—21no—
59C4×D44D412yes—
60C4×D44Q812yes—
61C42×D11—42no—
62C42×D11—42no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C4×C8×C11—21no—
66C4×C8×C11—21no—
67C11×#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70Dic11⋊C8—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4×C11⋊C8—21no—
74C4×C11⋊C8—21no—
75#8565—111nomaximal, Sylow
76C23×D11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44C4⋊C412yes—
91C2×D44C2×C812yes—
92C2×D44M1612yes—
93C2×C4×D11—24no—
94C2×C4×D11—24no—
95C2×C4×D11—22no—
96C2×C4×D11—22no—
97C2×C4×D11—42no—
98C2×C4×D11—42no—
99C2×C4×D11—42no—
100C2×C4×D11—42no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4C2×C812yes—
114C11×C4⋊C4M1612yes—
115C42×C11—41no—
116C42×C11—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×Q811yescharacteristic
119C42×C11#4111yescharacteristic
120C42×C11#4111yescharacteristic
121(C2×D11)⋊C4—24no—
122(C2×D11)⋊C4—24no—
123(C2×D11)⋊C4—22no—
124(C2×D11)⋊C4—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11C4⋊C412yes—
127C4×Dic11—22no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131C4×Dic11—21no—
132C4×Dic11—21no—
133C4×Dic11—21no—
134C4×Dic11—41no—
135C4×Dic11—42no—
136C4×Dic11—42no—
137C4×Dic11C2×C812yes—
138C4×Dic11M1612yes—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—41no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C42×D4—111no—
146#1831—111no—
147C4×C4⋊C8—111no—
148C2×D4⋊C8—111no—
149C2×D4⋊C8—111no—
150#1279—111no—
151#1279D1111yescharacteristic, complemented
152C23×C11C2×C22⋊C411yescharacteristic
153C22×D11—22no—
154C22×D11—22no—
155C22×D11—22no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11C2×C4⋊C411yescharacteristic
169C2×C4×C11#11711yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11C22⋊Q811yescharacteristic
173C2×C4×C11C22⋊Q811yescharacteristic
174C2×C4×C11C22×C811yescharacteristic
175C2×C4×C11C2×M1611yescharacteristic
176C2×C4×C11C2×M1611yescharacteristic
177C2×C4×C11C2×M1611yescharacteristic
178C2×C4×C11#13511yescharacteristic
179C2×C4×C11#13511yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—22no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11C22⋊C812yes—
195C2×Dic11C22⋊C812yes—
196C2×Dic11#10412yes—
197D44—22no—
198D44—22no—
199D44—22no—
200D44C4⋊C814yescomplemented
201C4×D11—48no—
202C4×D11—48no—
203C4×D11—42no—
204C4×D11—42no—
205C4×D11—42no—
206C4×D11—42no—
207C8×C11—42no—
208C8×C11—81no—
209C11⋊C8—42no—
210C11⋊C8—81no—
211C2×C4×D4—111no—
212C2×C4×D4—111no—
213C2×C4×D4—111no—
214C22×C42—221no—
215C2×C4⋊C8—111no—
216C2×C4⋊C8—221no—
217C2×C4⋊C8C2×D1111yescharacteristic
218C2×C4×C8—111no—
219C2×C4×C8C2×D1111yescharacteristic
220C4×C4⋊C4—111no—
221C4×C4⋊C4—111no—
222C4×C4⋊C4C2×D1111yescharacteristic
223C4×C22⋊C4—221no—
224C4×C22⋊C4—221no—
225C4×C22⋊C4—221no—
226C43—111no—
227#336—221no—
228#336—221no—
229#336—221no—
230D4⋊C8—222no—
231D4⋊C8—222no—
232C22×C11#38011yescharacteristic
233C22×C11C2×C22⋊C811yescharacteristic
234C22×C11#40711yescharacteristic
235C22×C11#41611yescharacteristic
236C22×C11#41811yescharacteristic
237C22×C11C2×#10411yescharacteristic
238C22×C11#42111yescharacteristic
239C2×D11—24no—
240C2×D11—42no—
241C2×D11—42no—
242C2×D11—42no—
243C2×D11—42no—
244C2×D11—42no—
245C2×D11—42no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—42no—
249C4×C11—42no—
250C4×C11C2×C4⋊C811yescharacteristic
251C4×C11#42311yescharacteristic
252C4×C11#43111yescharacteristic
253C4×C11#43211yescharacteristic
254C4×C11#46311yescharacteristic
255C4×C11#46311yescharacteristic
256C4×C11#47811yescharacteristic
257C4×C11#47811yescharacteristic
258Dic11—22no—
259Dic11—22no—
260Dic11—22no—
261Dic11—42no—
262Dic11—41no—
263C22×D4—111no—
264C23×C4—221no—
265C23×C4—221no—
266C23×C4—221no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—221no—
270C22×C8—221no—
271C4×D4—114no—
272C4×D4—112no—
273C4×D4—112no—
274C4×D4—222no—
275C4×D4—222no—
276C4×D4—222no—
277C4×D4—221no—
278C4×D4—221no—
279C2×C4⋊C4—111no—
280C2×C4⋊C4C4×D1111yescharacteristic
281C2×C4⋊C4C4×D1111yescharacteristic
282C2×C22⋊C4—221no—
283C2×C22⋊C4—221no—
284C2×C22⋊C4—221no—
285C2×C42—21no—
286C2×C42—111no—
287C2×C42—111no—
288C2×C42—111no—
289C2×C42—111no—
290C2×C42—111no—
291C2×C42—111no—
292C2×C42—221no—
293C2×C42—221no—
294C2×C42—442no—
295C2×C42—442no—
296C2×C42C22×D1111yescharacteristic
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—224no—
300C4⋊C8—221no—
301C4⋊C8—221no—
302C4×C8—21no—
303C4×C8—21no—
304C4×C8—221no—
305C4×C8—221no—
306#95—21no—
307#95—221no—
308#95—221no—
309C2×C11#147611yescharacteristic
310C2×C11#147811yescharacteristic
311C2×C11#148811yescharacteristic
312C2×C11#149011yescharacteristic
313C2×C11#179711yescharacteristic
314C2×C11#180411yescharacteristic
315C2×C11#180611yescharacteristic
316D11—44no—
317C24—221no—
318C2×D4—112no—
319C2×D4—112no—
320C2×D4—112no—
321C2×D4—221no—
322C2×D4—221no—
323C2×D4—221no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—111no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—224no—
331C22×C4—224no—
332C22×C4—221no—
333C22×C4—222no—
334C22×C4—222no—
335C22×C4—442no—
336C22×C4—442no—
337C22×C4—442no—
338C22×C4—442no—
339C22×C4—441no—
340C22×C4—441no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4C2×C4×D1111yescharacteristic
344C22×C4D4×D1111yescharacteristic
345C22×C4D4×D1111yescharacteristic
346C2×C8—22no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—222no—
353C2×C8—441no—
354C2×C8—441no—
355C2×C8—441no—
356C2×C8—441no—
357C2×C8—441no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—112no—
361C4⋊C4—221no—
362C4⋊C4C8×D1112yes—
363C4⋊C4#431312yes—
364C22⋊C4—224no—
365C22⋊C4—224no—
366C22⋊C4—222no—
367C22⋊C4—222no—
368C42—41no—
369C42—41no—
370C42—112no—
371C42—112no—
372C42—222no—
373C42—221no—
374C42—221no—
375C42—221no—
376C42—221no—
377C42—221no—
378C42—221no—
379C42—441no—
380C42—442no—
381C42—442no—
382C42#433911yescharacteristic
383C42#433911yescharacteristic
384C42D4×D1111yescharacteristic
385C42Q8×D1111yescharacteristic
386C11#856511yescharacteristic, complemented, Sylow
387C23—222no—
388C23—222no—
389C23—222no—
390C23—441no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23C22⋊C4×D1111yescharacteristic
395D4—114no—
396D4—222no—
397D4—222no—
398D4—222no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—112no—
408C2×C4—112no—
409C2×C4—112no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—222no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—448no—
421C2×C4—448no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4#6692511yescharacteristic
429C2×C4#6693711yescharacteristic
430C2×C4#6693711yescharacteristic
431C2×C4C4⋊C4×D1111yescharacteristic
432C2×C4#6694911yescharacteristic
433C2×C4#6694911yescharacteristic
434C2×C4C2×C8×D1111yescharacteristic
435C2×C4C2×#431311yescharacteristic
436C2×C4M16×D1111yescharacteristic
437C2×C4M16×D1111yescharacteristic
438C2×C4#6696411yescharacteristic
439C2×C4#6696711yescharacteristic
440C2×C4#6696911yescharacteristic
441C2×C4#6697211yescharacteristic
442C8—42no—
443C8—81no—
444C8—442no—
445C8—881no—
446C22—224no—
447C22—442no—
448C22—442no—
449C22—442no—
450C22—442no—
451C22—442no—
452C22—442no—
453C22#1062228011yescharacteristic
454C22D11×C22⋊C811yescharacteristic
455C22#1062233911yescharacteristic
456C22#1062238311yescharacteristic
457C22#1062241711yescharacteristic
458C22D11×#10411yescharacteristic
459C22#1062243411yescharacteristic
460C4—21no—
461C4—21no—
462C4—42no—
463C4—42no—
464C4—222no—
465C4—222no—
466C4—222no—
467C4—441no—
468C4—442no—
469C4#1062229811yescharacteristic
470C4#1062231811yescharacteristic
471C4#1062240011yescharacteristic
472C4#1062243211yescharacteristic
473C4D11×C4⋊C811yescharacteristic
474C4#1062245011yescharacteristic
475C4#1062248411yescharacteristic
476C4#1062250411yescharacteristic
477C2—444no—
478C2#1306699711yescharacteristic
479C2#1306700511yescharacteristic
480C2#1306704911yescharacteristic
481C2#1306705711yescharacteristic
482C2#1306859511yescharacteristic
483C2#1306862511yescharacteristic
484C2#1306863511yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1279D11
hypocenterC11#8565
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #13068732C2semidirect
3. C4×Dic11⋊C8C2semidirect
6. #13066457C2semidirect
7. C11×#1279C2semidirect
56. #66946C8semidirect
151. #1279D11semidirect
200. D44C4⋊C8semidirect
386. C11#8565semidirect

Maximal subgroups

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

subgroupindex
C4×#669462
#130687322
C4×Dic11⋊C82
C2×#106220972
C2×#106221212
#130664572
C11×#12792
#856511