Finite Group Databasebeta

← #14645441

Subgroups — #14645441

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068702C212yesmaximal, complemented
2#13068604C211yesmaximal, characteristic, complemented
3#13067184C212yesmaximal, complemented
4#13066934C211yesmaximal, characteristic, complemented
5C2×C11×#547C211yesmaximal, characteristic
6C22×C11×#41—21no—
7C11×#547—24no—
8C11×#547—24no—
9C2×C11×C4⋊Q8C411yescharacteristic, complemented
10C2×C11×#123—21no—
11C2×C11×#123—21no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×#121C411yescharacteristic, complemented
14C2×C11×#121C2211yescharacteristic
15C2×C4×D4×C11C411yescharacteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C22×C11×C4⋊C4C411yescharacteristic, complemented
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66898—21no—
20#10622825C2212yes—
21C2×C22⋊(C11⋊C8)C2212yes—
22#10622175—24no—
23#10622167—24no—
24#10622166—21no—
25#10622164—21no—
26#10622163—21no—
27C2×C11×#41—28no—
28C2×C11×#41—44no—
29C2×C11×#41—42no—
30C2×C11×#41—42no—
31C22×Q8×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11C2×C411yescharacteristic
35C22×D4×C11D411yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11—21no—
38C23×C4×C11—21no—
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8—22no—
43C11×#123—28no—
44C11×#123—28no—
45C11×C22⋊Q8—28no—
46C11×#121—22no—
47C11×#121—22no—
48C11×#121—22no—
49C11×#121D414yes—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4D414yes—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4D411yescharacteristic
69C2×C11×C22⋊C4D411yescharacteristic
70C2×C42×C11C2×C411yescharacteristic
71C2×C22⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C22×C11⋊C8—22no—
74#66898—42no—
75C11⋊#95—22no—
76C22⋊(C11⋊C8)—22no—
77C22⋊(C11⋊C8)—22no—
78#8376—111nomaximal, Sylow
79C24×C11—21no—
80C24×C11C22⋊C411yescharacteristic
81C24×C11C2×D411yescharacteristic
82C11×#41—416no—
83C11×#41—416no—
84C2×Q8×C11—24no—
85C2×Q8×C11—42no—
86C2×Q8×C11—42no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—24no—
90C2×D4×C11—24no—
91C2×D4×C11—21no—
92C2×D4×C11—42no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—42no—
98C2×D4×C11C22⋊C412yes—
99C2×D4×C11D812yes—
100C2×D4×C11SD1612yes—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—24no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—41no—
115C22×C4×C11—41no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11C22⋊C411yescharacteristic
119C22×C4×C11C22⋊C411yescharacteristic
120C22×C4×C11C22⋊C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×Dic11—42no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4C22⋊C412yes—
134C11×C4⋊C4C22⋊C412yes—
135C11×C4⋊C4C22⋊C412yes—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—22no—
141C42×C11—21no—
142C42×C11—21no—
143C22⋊Dic11—42no—
144C22⋊Dic11—42no—
145C4⋊Dic11—44no—
146C2×C11⋊C8—44no—
147C2×C11⋊C8—42no—
148C2×#547D1111yescharacteristic
149#1823—112no—
150#1799—111no—
151#1519—112no—
152#1459—111no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—22no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11#10212yes—
165C23×C11C2×C22⋊C411yescharacteristic
166C23×C11#12012yes—
167C23×C11C2×D811yescharacteristic
168C23×C11C2×SD1611yescharacteristic
169C23×C11AGL(1,ℤ/8)12yes—
170Q8×C11—48no—
171D4×C11—24no—
172D4×C11—24no—
173D4×C11—42no—
174D4×C11—48no—
175D4×C11—44no—
176D4×C11—44no—
177D4×C11—42no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—24no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—48no—
191C2×C4×C11—48no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—44no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11#10212yes—
204C2×C4×C11C2×C22⋊C411yescharacteristic
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11#12012yes—
207C2×Dic11—82no—
208C2×Dic11—82no—
209C2×Dic11—82no—
210C11⋊C8—82no—
211C22×#41—21no—
212#547—24no—
213#547—24no—
214C2×C4⋊Q8Dic1111yescharacteristic, complemented
215C2×#123—21no—
216C2×#123—21no—
217C2×C22⋊Q8—21no—
218C2×#121Dic1111yescharacteristic, complemented
219C2×#121C2×D1111yescharacteristic
220C2×C4×D4Dic1111yescharacteristic, complemented
221C2×C4×D4C2×D1111yescharacteristic
222C22×C4⋊C4Dic1111yescharacteristic, complemented
223C22×C4⋊C4C2×D1111yescharacteristic
224C2×#99—221no—
225C2×C22⋊C8—112no—
226#380—112no—
227#342—221no—
228#340—224no—
229#327—224no—
230#324—221no—
231#323—221no—
232C22×C11—21no—
233C22×C11—22no—
234C22×C11—21no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11#37911yescharacteristic
250C22×C11C2×#10211yescharacteristic
251C22×C11#41811yescharacteristic
252C22×C11#44712yes—
253C22×C11#45012yes—
254C4×C11—21no—
255C4×C11—22no—
256C4×C11—22no—
257C4×C11—41no—
258C4×C11—41no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11#41012yes—
263Dic11—162no—
264C2×#41—28no—
265C2×#41—44no—
266C2×#41—42no—
267C2×#41—42no—
268C22×Q8—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4C2×Dic1111yescharacteristic
272C22×D4C22⋊D1111yescharacteristic
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4C2×Dic1111yescharacteristic
277C23×C4C22×D1111yescharacteristic
278C22×C8—222no—
279C4⋊Q8—22no—
280C4⋊Q8—22no—
281#123—28no—
282#123—28no—
283C22⋊Q8—28no—
284#121—22no—
285#121—22no—
286#121—22no—
287#121C22⋊D1114yes—
288C4×D4—22no—
289C4×D4—22no—
290C4×D4—22no—
291C4×D4—22no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4C2×Dic1111yescharacteristic
300C2×C4⋊C4C2×Dic1111yescharacteristic
301C2×C4⋊C4C2×Dic1111yescharacteristic
302C2×C4⋊C4C22⋊D1111yescharacteristic
303C2×C4⋊C4C22⋊D1114yes—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4C22⋊D1111yescharacteristic
309C2×C22⋊C4C22⋊D1111yescharacteristic
310C2×C42C2×Dic1111yescharacteristic
311#99—442no—
312C22⋊C8—222no—
313C22⋊C8—222no—
314#95—222no—
315C2×C11—22no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11—22no—
319C2×C11—42no—
320C2×C11—82no—
321C2×C11#178211yescharacteristic
322C2×C11#178611yescharacteristic
323C2×C11#179611yescharacteristic
324C24—21no—
325C24C22⋊Dic1111yescharacteristic
326C24C2×C22⋊D1111yescharacteristic
327#41—416no—
328#41—416no—
329C2×Q8—24no—
330C2×Q8—42no—
331C2×Q8—42no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—21no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—41no—
341C2×D4—42no—
342C2×D4—41no—
343C2×D4#432312yes—
344C2×D4#432412yes—
345C2×D4C22⋊Dic1112yes—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—24no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—41no—
360C22×C4—42no—
361C22×C4—41no—
362C22×C4—42no—
363C22×C4—442no—
364C22×C4C22⋊Dic1111yescharacteristic
365C22×C4C22⋊Dic1111yescharacteristic
366C22×C4C22⋊Dic1111yescharacteristic
367C22×C4C22×Dic1111yescharacteristic
368C22×C4C2×C22⋊D1112yes—
369C22×C4C2×C22⋊D1112yes—
370C22×C4C2×C22⋊D1111yescharacteristic
371C2×C8—444no—
372C2×C8—442no—
373C4⋊C4—24no—
374C4⋊C4—24no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—24no—
379C4⋊C4—22no—
380C4⋊C4—444no—
381C4⋊C4C22⋊Dic1112yes—
382C4⋊C4C22⋊Dic1112yes—
383C4⋊C4C22⋊Dic1112yes—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—22no—
387C22⋊C4—24no—
388C22⋊C4—22no—
389C22⋊C4—442no—
390C22⋊C4—442no—
391C42—21no—
392C42—21no—
393C11#837611yescharacteristic, complemented, Sylow
394C23—21no—
395C23—21no—
396C23—22no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—42no—
402C23—42no—
403C23—41no—
404C23—41no—
405C23#6689612yes—
406C23C2×#432311yescharacteristic
407C23#6698512yes—
408C23C2×#432411yescharacteristic
409C23C2×C22⋊Dic1111yescharacteristic
410C23#6700612yes—
411Q8—48no—
412D4—24no—
413D4—24no—
414D4—42no—
415D4—48no—
416D4—44no—
417D4—44no—
418D4—42no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—48no—
432C2×C4—48no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—882no—
445C2×C4—882no—
446C2×C4—882no—
447C2×C4#6689612yes—
448C2×C4C2×C22⋊Dic1111yescharacteristic
449C2×C4C2×C22⋊Dic1111yescharacteristic
450C2×C4#6700612yes—
451C8—882no—
452C22—21no—
453C22—22no—
454C22—21no—
455C22—22no—
456C22—22no—
457C22—41no—
458C22—42no—
459C22—41no—
460C22—42no—
461C22—42no—
462C22—41no—
463C22—41no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—82no—
468C22—82no—
469C22C2×#6689611yescharacteristic
470C22#1062282811yescharacteristic
471C22#1062283012yes—
472C22#1062283112yes—
473C22#1062286011yescharacteristic
474C4—22no—
475C4—22no—
476C4—21no—
477C4—42no—
478C4—42no—
479C4—42no—
480C4—41no—
481C4—41no—
482C4—1762no—
483C4#1062285312yes—
484C2—22no—
485C2—21no—
486C2—21no—
487C2—22no—
488C2—42no—
489C2—82no—
490C2#1306853411yescharacteristic
491C2#1306854711yescharacteristic
492C2#1306859111yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC2×C11×#547C2
socleC22×C11#379
cosocleC23×C4×C11C23
hypercenterC2×#547D11
hypocenterC11#8376
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13068702C2semidirect
2. #13068604C2semidirect
3. #13067184C2semidirect
4. #13066934C2semidirect
9. C2×C11×C4⋊Q8C4semidirect
13. C2×C11×#121C4semidirect
15. C2×C4×D4×C11C4semidirect
17. C22×C11×C4⋊C4C4semidirect
214. C2×C4⋊Q8Dic11semidirect
218. C2×#121Dic11semidirect
220. C2×C4×D4Dic11semidirect
222. C22×C4⋊C4Dic11semidirect
393. C11#8376semidirect

Maximal subgroups

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

subgroupindex
#130687022
#130686042
#130671842
#130669342
C2×C11×#5472
#837611