Finite Group Databasebeta

← #14853501

Subgroups — #14853501

Order 2816.

878 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
1#13076975C211yesmaximal, characteristic, complemented
2#127×Dic11C211yesmaximal, characteristic
3#13070180C211yesmaximal, characteristic, complemented
4#13070179C211yesmaximal, characteristic, complemented
5#13069847C211yesmaximal, characteristic
6#13069315C212yesmaximal, complemented
7#13069310C212yesmaximal, complemented
8#13068614C212yesmaximal, complemented
9#13068614C212yesmaximal, complemented
10#13068468C211yesmaximal, characteristic, complemented
11C11×#2041C211yesmaximal, characteristic
12C2×C11×#127C2211yescharacteristic
13C2×D4×Dic11—21no—
14C2×D4×Dic11—21no—
15C2×D4×Dic11C2212yes—
16C2×#66942—21no—
17C2×C11×#102C2212yes—
18C2×C11×#102C2212yes—
19C11×#389C2211yescharacteristic
20#10622834—21no—
21#10622834—21no—
22#10622834C2212yes—
23C2×#66896C2212yes—
24C2×#66896C2212yes—
25C2×#66879C2212yes—
26C2×Dic11⋊C8C2212yes—
27#10622598C2211yescharacteristic
28#10622589C2211yescharacteristic
29#10622589C2211yescharacteristic
30#10622586C2211yescharacteristic
31#10622585—21no—
32#10622548C2211yescharacteristic
33C42×Dic11C2211yescharacteristic
34#10622541C2211yescharacteristic
35#10622263—21no—
36#10622260—21no—
37C11×#336C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2211yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C23×Dic11—22no—
47C22×C8×C11C2312yes—
48C11×#127—24no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56D4×Dic11—24no—
57D4×Dic11—24no—
58D4×Dic11—44no—
59D4×Dic11—44no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—21no—
72C2×C4×Dic11D411yescharacteristic
73C2×C4×Dic11D411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C22×C11⋊C8C2312yes—
79#66942—44no—
80C11×#102—24no—
81C11×#102—42no—
82C11×#95—21no—
83#66896—24no—
84#66896—42no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88#66879—42no—
89Dic11⋊C8—24no—
90#29130—111nomaximal, Sylow
91C24×C11—22no—
92C2×D4×C11—24no—
93C2×D4×C11—24no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—42no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11—42no—
103C2×D4×C11#4114yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11—44no—
113C22×Dic11—44no—
114C22×Dic11—44no—
115C22×Dic11C2×D411yescharacteristic
116C22×Dic11C2×D411yescharacteristic
117C22×Dic11C2×D411yescharacteristic
118C22×Dic11C2×D411yescharacteristic
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—42no—
126C42×C11—22no—
127C22⋊Dic11—44no—
128C22⋊Dic11—44no—
129C22⋊Dic11—44no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135C4⋊Dic11—42no—
136C4⋊Dic11—42no—
137C4⋊Dic11—42no—
138Dic11⋊C4—42no—
139Dic11⋊C4—42no—
140Dic11⋊C4—42no—
141Dic11⋊C4—42no—
142Dic11⋊C4—42no—
143Dic11⋊C4—42no—
144C4×Dic11—22no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C4×Dic11—21no—
149C4×Dic11—21no—
150C4×Dic11#4114yes—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154#2859—111no—
155C4×#127—111no—
156#2100—111no—
157#2100—111no—
158#2041—111no—
159#2041D1111yescharacteristic
160#1936—112no—
161#1936—112no—
162#1802—112no—
163#1802—112no—
164#1767—111no—
165C23×C11—24no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11C22×D411yescharacteristic
173D4×C11—24no—
174D4×C11—24no—
175D4×C11—48no—
176D4×C11—48no—
177D4×C11—42no—
178D4×C11—42no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11AGL(1,ℤ/8)12yes—
190C2×C4×C11#13712yes—
191C2×C4×C11C2×#4112yes—
192C2×C4×C11C2×#4112yes—
193C2×C4×C11H(5,𝔽2)11yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—88no—
213C2×Dic11#12412yes—
214C2×Dic11#12412yes—
215C2×Dic11AGL(1,ℤ/8)12yes—
216C2×Dic11AGL(1,ℤ/8)12yes—
217C8×C11—42no—
218C11⋊C8—42no—
219C2×#127C2×D1111yescharacteristic
220C2×#125—221no—
221C2×C4×D4—112no—
222C2×C4×D4—221no—
223C2×C4×D4—221no—
224C2×C4⋊C8—112no—
225C2×#102—112no—
226C2×#102—112no—
227C2×#102C2×D1112yes—
228C2×#102C2×D1112yes—
229C2×#97—112no—
230#390—112no—
231#390—221no—
232#390—221no—
233#389—111no—
234#389—111no—
235#389—111no—
236#389—221no—
237#389—221no—
238#389C2×D1111yescharacteristic
239#384—111no—
240#384—111no—
241#384—111no—
242#382—221no—
243C43—111no—
244#340—112no—
245#340—112no—
246#340—112no—
247#340—112no—
248#336—111no—
249#336C2×D1111yescharacteristic
250C22×C11—44no—
251C22×C11—44no—
252C22×C11—44no—
253C22×C11—82no—
254C22×C11—82no—
255C22×C11—82no—
256C22×C11—82no—
257C22×C11#52511yescharacteristic
258C22×C11C2×#12411yescharacteristic
259C22×C11#53711yescharacteristic
260C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C11C2×#13711yescharacteristic
264C4×C11—22no—
265C4×C11—22no—
266C4×C11—81no—
267C4×C11—81no—
268C4×C11#55212yes—
269C4×C11#55312yes—
270Dic11—22no—
271Dic11—41no—
272Dic11—41no—
273Dic11—81no—
274Dic11—82no—
275Dic11—81no—
276Dic11#49014yes—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4C22×D1112yes—
280C23×C4—222no—
281C22×C8—112no—
282C22×C8C22×D1112yes—
283#127—24no—
284#125—444no—
285C4×D4—224no—
286C4×D4—224no—
287C4×D4—444no—
288C4×D4—444no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—221no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4C22×D1111yescharacteristic
303C2×C4⋊C4C22×D1111yescharacteristic
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C22⋊C4—222no—
307C2×C42—111no—
308C2×C42—111no—
309C2×C42—111no—
310C2×C42—111no—
311C2×C42—111no—
312C2×C42—111no—
313C2×C42C22×D1111yescharacteristic
314C4⋊C8—224no—
315#102—24no—
316#102—42no—
317#102—224no—
318#102—442no—
319#97—442no—
320#95—21no—
321#95—221no—
322#95—221no—
323#95—221no—
324C2×C11—84no—
325C2×C11#256211yescharacteristic
326C2×C11#310911yescharacteristic
327C2×C11#311011yescharacteristic
328C2×C11C2×#49011yescharacteristic
329C2×C11#314111yescharacteristic
330C2×C11#325311yescharacteristic
331C2×C11#325411yescharacteristic
332C24—22no—
333C2×D4—24no—
334C2×D4—24no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—42no—
343C2×D4—42no—
344C2×D4#434114yes—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—111no—
348C22×C4—111no—
349C22×C4—111no—
350C22×C4—111no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—222no—
354C22×C4—444no—
355C22×C4—444no—
356C22×C4—444no—
357C22×C4D4×D1111yescharacteristic
358C22×C4D4×D1111yescharacteristic
359C22×C4C23×D1111yescharacteristic
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8—222no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—42no—
370C4⋊C4—222no—
371C4⋊C4—221no—
372C4⋊C4—222no—
373C4⋊C4—222no—
374C4⋊C4—221no—
375C4⋊C4—442no—
376C4⋊C4—442no—
377C4⋊C4—442no—
378C4⋊C4—442no—
379C4⋊C4—442no—
380C4⋊C4—442no—
381C4⋊C4—442no—
382C4⋊C4—442no—
383C4⋊C4—442no—
384C22⋊C4—444no—
385C22⋊C4—444no—
386C22⋊C4—444no—
387C42—22no—
388C42—114no—
389C42—222no—
390C42—222no—
391C42—222no—
392C42—222no—
393C42—221no—
394C42—221no—
395C11#2913011yescharacteristic, complemented, Sylow
396C23—24no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23C2×D4×D1111yescharacteristic
404D4—24no—
405D4—24no—
406D4—48no—
407D4—48no—
408D4—42no—
409D4—42no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—112no—
421C2×C4—112no—
422C2×C4—112no—
423C2×C4—112no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—442no—
441C2×C4—888no—
442C2×C4#6696412yes—
443C2×C4#6696812yes—
444C2×C4C2×#434112yes—
445C2×C4#6703711yescharacteristic
446C2×C4#41×D1112yes—
447C2×C4#6704311yescharacteristic
448C8—42no—
449C8—442no—
450C22—44no—
451C22—44no—
452C22—44no—
453C22—82no—
454C22—82no—
455C22—82no—
456C22—82no—
457C22#1062311711yescharacteristic
458C22#1062313911yescharacteristic
459C22D11×#12411yescharacteristic
460C22C2×#6696411yescharacteristic
461C22C2×#6696811yescharacteristic
462C22D11×AGL(1,ℤ/8)11yescharacteristic
463C22D11×AGL(1,ℤ/8)11yescharacteristic
464C4—22no—
465C4—22no—
466C4—81no—
467C4—81no—
468C4—114no—
469C4—222no—
470C4—441no—
471C4—441no—
472C4—882no—
473C4—881no—
474C4—881no—
475C4#1062313212yes—
476C4#1062318112yes—
477C2—84no—
478C2#1307377611yescharacteristic
479C2#1307870211yescharacteristic
480C2#1307871011yescharacteristic
481C2D11×#49011yescharacteristic
482C2#1307900611yescharacteristic
483C2#1307999511yescharacteristic
484C2#1308000111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2041C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2041D11
hypocenterC11#29130
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2041

Complements

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

NH ≅ G/Ntype
1. #13076975C2semidirect
3. #13070180C2semidirect
4. #13070179C2semidirect
6. #13069315C2semidirect
7. #13069310C2semidirect
8. #13068614C2semidirect
9. #13068614C2semidirect
10. #13068468C2semidirect
395. C11#29130semidirect

Maximal subgroups

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

subgroupindex
#130769752
#127×Dic112
#130701802
#130701792
#130698472
#130693152
#130693102
#130686142
#130684682
C11×#20412
#2913011