Finite Group Databasebeta

← #14645581

Subgroups — #14645581

Order 2816.

1148 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068934C212yesmaximal, complemented
2C2×#10622175C212yesmaximal, complemented
3C2×#10622166C211yesmaximal, characteristic, complemented
4#13066869C211yesmaximal, characteristic, complemented
5C2×C11×#537C211yesmaximal, characteristic
6C22×C11×#41—21no—
7C11×#537—24no—
8C11×#537—22no—
9C11×#537C414yescomplemented
10C2×C11×C22⋊Q8—22no—
11C2×C11×#121—22no—
12C2×C11×#121—21no—
13C2×C11×#121C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C2×#66896—22no—
17C2×C11⋊#95—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2212yes—
21#10622175—24no—
22#10622167—22no—
23#10622166—22no—
24C2×C11×#41—24no—
25C2×C11×#41—24no—
26C2×C11×#41—42no—
27C2×C11×#41—42no—
28C2×C11×#41—42no—
29C2×C11×#41—42no—
30C22×Q8×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—22no—
33C22×D4×C11—21no—
34C22×D4×C11D412yes—
35C23×C4×C11—22no—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11—21no—
40C23×Dic11—21no—
41C11×C22⋊Q8—28no—
42C11×C22⋊Q8—28no—
43C11×#121—24no—
44C11×#121—28no—
45C11×#121—28no—
46C11×#121—24no—
47C11×#121—22no—
48C11×#121—22no—
49C11×#121C2×C414yes—
50C11×#121D414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2×C412yes—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—42no—
61C22×C11⋊C8—22no—
62#66896—44no—
63C11⋊#95—22no—
64C11⋊#95—42no—
65C11⋊#95—42no—
66C22⋊(C11⋊C8)—22no—
67C22⋊(C11⋊C8)—22no—
68#8404—111nomaximal, Sylow
69C24×C11—22no—
70C24×C11C2×D411yescharacteristic
71C11×#41—48no—
72C11×#41—48no—
73C11×#41—48no—
74C11×#41—48no—
75C2×Q8×C11—24no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
78C2×D4×C11—24no—
79C2×D4×C11—24no—
80C2×D4×C11—24no—
81C2×D4×C11—24no—
82C2×D4×C11—22no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C2×D4×C11—42no—
90C2×D4×C11—42no—
91C2×D4×C11—81no—
92C2×D4×C11—81no—
93C2×D4×C11C22⋊C414yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—28no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—44no—
105C22×C4×C11—44no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11C22⋊C412yes—
109C22×C4×C11C22⋊C412yes—
110C22×C4×C11D812yes—
111C22×C4×C11SD1612yes—
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126C22×Dic11—41no—
127C22×Dic11—41no—
128C22×Dic11—41no—
129C22×Dic11—41no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4C22⋊C414yes—
135C11×C22⋊C4—28no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138C4⋊Dic11—24no—
139C4⋊Dic11—42no—
140C2×C11⋊C8—42no—
141C2×C11⋊C8—42no—
142C2×C11⋊C8—42no—
143C2×#537D1111yescharacteristic
144#1874—112no—
145C2×#327—112no—
146C2×#324—111no—
147#1441—111no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—24no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11C2×C22⋊C411yescharacteristic
160C23×C11#12011yescharacteristic
161C23×C11#12011yescharacteristic
162C23×C11C2×D811yescharacteristic
163C23×C11C2×SD1611yescharacteristic
164C23×C11AGL(1,ℤ/8)11yescharacteristic
165C23×C11AGL(1,ℤ/8)11yescharacteristic
166Q8×C11—48no—
167D4×C11—44no—
168D4×C11—48no—
169D4×C11—44no—
170D4×C11—44no—
171D4×C11—44no—
172D4×C11—44no—
173D4×C11—82no—
174D4×C11—84no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—416no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—81no—
195C2×C4×C11#10214yescomplemented
196C2×C4×C11C2×C22⋊C412yes—
197C2×C4×C11#12012yes—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—81no—
205C2×Dic11—81no—
206C2×Dic11—81no—
207C2×Dic11—81no—
208C2×Dic11—81no—
209C2×Dic11—81no—
210C2×Dic11—81no—
211C2×Dic11—81no—
212C11⋊C8—82no—
213C22×#41—21no—
214#537—24no—
215#537—22no—
216#537Dic1114yescomplemented
217C2×C22⋊Q8—22no—
218C2×#121—22no—
219C2×#121—21no—
220C2×#121C2×D1112yes—
221C22×C4⋊C4—111no—
222C22×C4⋊C4C2×D1111yescharacteristic
223C2×#102—222no—
224C2×C22⋊C8—112no—
225C2×#95—111no—
226C2×#95—221no—
227C2×#95—221no—
228#340—222no—
229#327—224no—
230#324—222no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—44no—
244C22×C11—44no—
245C22×C11—44no—
246C22×C11—82no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11#37911yescharacteristic
251C22×C11C2×#10211yescharacteristic
252C22×C11#41811yescharacteristic
253C22×C11#44711yescharacteristic
254C22×C11#44711yescharacteristic
255C22×C11#45011yescharacteristic
256C22×C11#45011yescharacteristic
257C22×C11#45411yescharacteristic
258C22×C11#45611yescharacteristic
259C22×C11B(4,𝔽2)11yescharacteristic
260C22×C11#45811yescharacteristic
261C4×C11—24no—
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—44no—
265C4×C11—42no—
266Dic11—82no—
267Dic11—82no—
268C2×#41—24no—
269C2×#41—24no—
270C2×#41—42no—
271C2×#41—42no—
272C2×#41—42no—
273C2×#41—42no—
274C22×Q8—21no—
275C22×D4—21no—
276C22×D4—22no—
277C22×D4—21no—
278C22×D4C22⋊D1112yes—
279C23×C4—22no—
280C23×C4—221no—
281C23×C4—221no—
282C23×C4C22⋊D1111yescharacteristic
283C23×C4C22⋊D1111yescharacteristic
284C23×C4C22×D1111yescharacteristic
285C22×C8—222no—
286C22⋊Q8—28no—
287C22⋊Q8—28no—
288#121—24no—
289#121—28no—
290#121—28no—
291#121—24no—
292#121—22no—
293#121—22no—
294#121C2×Dic1114yes—
295#121C22⋊D1114yes—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4—442no—
301C2×C4⋊C4C2×Dic1112yes—
302C2×C4⋊C4C22⋊D1112yes—
303C2×C4⋊C4C22⋊D1112yes—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306#102—444no—
307C22⋊C8—222no—
308C22⋊C8—222no—
309#95—222no—
310#95—442no—
311#95—442no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—84no—
317C2×C11#159811yescharacteristic
318C2×C11#160411yescharacteristic
319C2×C11#161011yescharacteristic
320C2×C11#161611yescharacteristic
321C2×C11#178611yescharacteristic
322C2×C11#179011yescharacteristic
323C2×C11#179311yescharacteristic
324C24—22no—
325C24C2×C22⋊D1111yescharacteristic
326#41—48no—
327#41—48no—
328#41—48no—
329#41—48no—
330C2×Q8—24no—
331C2×Q8—42no—
332C2×Q8—42no—
333C2×D4—24no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—22no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—42no—
343C2×D4—42no—
344C2×D4—42no—
345C2×D4—42no—
346C2×D4—81no—
347C2×D4—81no—
348C2×D4C22⋊Dic1114yes—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—28no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—44no—
360C22×C4—44no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4—441no—
368C22×C4—441no—
369C22×C4—441no—
370C22×C4—441no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4—441no—
376C22×C4—441no—
377C22×C4#432312yes—
378C22×C4#432412yes—
379C22×C4C22⋊Dic1112yes—
380C22×C4C22⋊Dic1112yes—
381C22×C4C22×Dic1111yescharacteristic
382C22×C4C2×C22⋊D1112yes—
383C22×C4C2×C22⋊D1112yes—
384C22×C4C2×C22⋊D1111yescharacteristic
385C2×C8—442no—
386C2×C8—442no—
387C2×C8—442no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—22no—
392C4⋊C4—224no—
393C4⋊C4—442no—
394C4⋊C4C22⋊Dic1114yes—
395C22⋊C4—28no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C11#840411yescharacteristic, complemented, Sylow
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—24no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23C2×#432311yescharacteristic
411C23#6698511yescharacteristic
412C23#6698511yescharacteristic
413C23C2×#432411yescharacteristic
414C23C2×C22⋊Dic1111yescharacteristic
415C23#6700611yescharacteristic
416C23#6700611yescharacteristic
417Q8—48no—
418D4—44no—
419D4—48no—
420D4—44no—
421D4—44no—
422D4—44no—
423D4—44no—
424D4—82no—
425D4—84no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—416no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—81no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—881no—
453C2×C4—881no—
454C2×C4—881no—
455C2×C4—881no—
456C2×C4—881no—
457C2×C4—881no—
458C2×C4—881no—
459C2×C4—881no—
460C2×C4#6689614yescomplemented
461C2×C4C2×C22⋊Dic1112yes—
462C2×C4#6700612yes—
463C8—882no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—82no—
483C22C2×#6689611yescharacteristic
484C22#1062282811yescharacteristic
485C22#1062283011yescharacteristic
486C22#1062283011yescharacteristic
487C22#1062283111yescharacteristic
488C22#1062283111yescharacteristic
489C22#1062285611yescharacteristic
490C22#1062285711yescharacteristic
491C22#1062285811yescharacteristic
492C22#1062285911yescharacteristic
493C22#1062286011yescharacteristic
494C4—24no—
495C4—22no—
496C4—22no—
497C4—44no—
498C4—42no—
499C4—882no—
500C4—882no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—84no—
506C2#1306755111yescharacteristic
507C2#1306758511yescharacteristic
508C2#1306761911yescharacteristic
509C2#1306765311yescharacteristic
510C2#1306854711yescharacteristic
511C2#1306856411yescharacteristic
512C2#1306857511yescharacteristic
subgroupG/H
centerC23#67006
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC2×C11×#537C2
socleC23×C11#120
cosocleC23×C4×C11C23
hypercenterC2×#537D11
hypocenterC11#8404
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #13068934C2semidirect
2. C2×#10622175C2semidirect
3. C2×#10622166C2semidirect
4. #13066869C2semidirect
9. C11×#537C4semidirect
195. C2×C4×C11#102semidirect
216. #537Dic11semidirect
398. C11#8404semidirect
460. C2×C4#66896semidirect

Maximal subgroups

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

subgroupindex
#130689342
C2×#106221752
C2×#106221662
#130668692
C2×C11×#5372
#840411