Finite Group Databasebeta

← #14814837

Subgroups — #14814837

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622658C212yesmaximal, complemented
2#13071565C211yesmaximal, characteristic
3#13069816C212yesmaximal, complemented
4#13069809C212yesmaximal, complemented
5#13069540C211yesmaximal, characteristic, complemented
6#13069419C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic
8#13069379C211yesmaximal, characteristic, complemented
9#13068929C212yesmaximal, complemented
10C4×#66871C211yesmaximal, characteristic, complemented
11C11×#2542C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C22⋊Q8C2212yes—
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66979C2212yes—
17C11×#399—22no—
18C11×#390—21no—
19C11×#384—21no—
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66899C2212yes—
22C2×#66899C2212yes—
23C2×#66899C2212yes—
24C2×#66899C2212yes—
25#10622834—21no—
26#10622825C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622658—28no—
30C4⋊C4×Dic11—21no—
31C2×#66872C2212yes—
32C2×#66871C2211yescharacteristic
33C2×#66871C2211yescharacteristic
34#10622564—22no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×Q8×C11C2312yes—
43C22×D4×C11D411yescharacteristic
44C23×C4×C11C2312yes—
45C11×C4⋊Q8—22no—
46C11×C4⋊Q8—22no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—42no—
50C11×C22⋊Q8—42no—
51C4×D4×C11—22no—
52C4×D4×C11—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4D412yes—
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67#66979—24no—
68#66979—42no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4×Dic11—21no—
75C2×C4×Dic11—22no—
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2312yes—
78C22×C11⋊C8C2311yescharacteristic
79C11×#95—21no—
80#66899—24no—
81#66899—24no—
82#66899—42no—
83#66899—42no—
84C11⋊#95—21no—
85C11⋊#95—22no—
86C22⋊(C11⋊C8)—24no—
87C22⋊(C11⋊C8)—42no—
88#66872—24no—
89#66871—22no—
90#66871D414yescomplemented
91C4⋊(C11⋊C8)—22no—
92C4×C11⋊C8—22no—
93#26231—111nomaximal, Sylow
94C24×C11C2×D412yes—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—44no—
124C11×C4⋊C4—44no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4C2×D412yes—
128C11×C4⋊C4#4112yes—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—44no—
131C11×C22⋊C4—44no—
132C42×C11—42no—
133C42×C11#4112yes—
134C42×C11#4112yes—
135C22⋊Dic11—44no—
136C22⋊Dic11—82no—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—22no—
142C4⋊Dic11—42no—
143C4⋊Dic11—81no—
144C4⋊Dic11C2×D412yes—
145C4×Dic11—44no—
146C4×Dic11—42no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8C2×D412yes—
156C2×#485—112no—
157#2542D1111yescharacteristic
158#2354—111no—
159#2036—112no—
160#2035—112no—
161#1981—111no—
162#1956—111no—
163#1954—111no—
164#1948—111no—
165#1873—112no—
166C4×#107—111no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11C22×D411yescharacteristic
175Q8×C11—42no—
176Q8×C11—42no—
177Q8×C11—42no—
178Q8×C11—42no—
179D4×C11—44no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11#12312yes—
199C2×C4×C11#12312yes—
200C2×C4×C11#13512yes—
201C2×C4×C11#13712yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11H(5,𝔽2)11yescharacteristic
207C2×C4×C11H(5,𝔽2)11yescharacteristic
208C2×Dic11—22no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—41no—
217C11⋊C8—22no—
218C11⋊C8—41no—
219C11⋊C8—42no—
220C2×C4⋊Q8C2×D1111yescharacteristic
221C2×C22⋊Q8C2×D1112yes—
222C2×C22⋊Q8C2×D1112yes—
223C2×C4×D4C2×D1111yescharacteristic
224C2×#117—112no—
225#485—228no—
226C2×#107—111no—
227C2×#107—111no—
228C2×#106—112no—
229C2×C4⋊C8—111no—
230C2×#103—112no—
231C2×#103—112no—
232C2×#103—112no—
233C2×#103—112no—
234C2×C22⋊C8—112no—
235C2×C22⋊C8—112no—
236C2×C4×C8—111no—
237#399—22no—
238#390—21no—
239#390—221no—
240#388—222no—
241#384—21no—
242#384—111no—
243#380—112no—
244C4×C4⋊C4—111no—
245C4×C4⋊C4—221no—
246C4×C4⋊C4C2×D1111yescharacteristic
247#340—111no—
248#340—112no—
249#340—111no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11C2×#12311yescharacteristic
258C22×C11D4211yescharacteristic
259C22×C11#54611yescharacteristic
260C22×C11C2×#13511yescharacteristic
261C22×C11C2×#13711yescharacteristic
262C22×C11#57711yescharacteristic
263C22×C11#57811yescharacteristic
264C4×C11—22no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—82no—
269C4×C11#48514yescomplemented
270C4×C11#53211yescharacteristic
271C4×C11#54011yescharacteristic
272C4×C11#55011yescharacteristic
273C4×C11#55911yescharacteristic
274Dic11—42no—
275Dic11—82no—
276Dic11—81no—
277C22×Q8C22×D1112yes—
278C22×D4C22⋊D1111yescharacteristic
279C23×C4C22×D1112yes—
280C22×C8—111no—
281C22×C8—111no—
282C22×C8—112no—
283C4⋊Q8—22no—
284C4⋊Q8—22no—
285C22⋊Q8—24no—
286C22⋊Q8—24no—
287C22⋊Q8—42no—
288C22⋊Q8—42no—
289C4×D4—22no—
290C4×D4—22no—
291#117—224no—
292#117—442no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—112no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4C22⋊D1111yescharacteristic
303C2×C4⋊C4C22×D1111yescharacteristic
304C2×C4⋊C4C22×D1111yescharacteristic
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4C22⋊D1112yes—
310C2×C42—21no—
311C2×C42—222no—
312C2×C42—221no—
313C2×C42C22×D1111yescharacteristic
314#107—114no—
315#107—222no—
316#106—224no—
317C4⋊C8—222no—
318#103—224no—
319#103—224no—
320#103—442no—
321#103—442no—
322C22⋊C8—224no—
323C22⋊C8—442no—
324C4×C8—222no—
325#95—21no—
326#95—221no—
327#95—222no—
328C2×C11—82no—
329C2×C11#244511yescharacteristic
330C2×C11C2×#48511yescharacteristic
331C2×C11#309711yescharacteristic
332C2×C11#327811yescharacteristic
333C2×C11#328311yescharacteristic
334C2×C11#330311yescharacteristic
335C2×C11#332811yescharacteristic
336C24C2×C22⋊D1112yes—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—222no—
358C22×C4C2×C22⋊D1112yes—
359C22×C4C2×C22⋊D1111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361C22×C4C23×D1111yescharacteristic
362C2×C8—112no—
363C2×C8—221no—
364C2×C8—221no—
365C2×C8—222no—
366C2×C8—221no—
367C2×C8—222no—
368C2×C8—221no—
369C2×C8—222no—
370C2×C8—221no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—44no—
375C4⋊C4—44no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4—112no—
379C4⋊C4—221no—
380C4⋊C4—222no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—222no—
384C4⋊C4—442no—
385C4⋊C4—881no—
386C4⋊C4D4×D1112yes—
387C4⋊C4#434112yes—
388C22⋊C4—24no—
389C22⋊C4—44no—
390C22⋊C4—44no—
391C22⋊C4—444no—
392C22⋊C4—882no—
393C42—42no—
394C42—444no—
395C42—442no—
396C42#434112yes—
397C42#434112yes—
398C11#2623111yescharacteristic, complemented, Sylow
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23C22×C22⋊D1111yescharacteristic
407Q8—42no—
408Q8—42no—
409Q8—42no—
410Q8—42no—
411D4—44no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—222no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—442no—
434C2×C4—441no—
435C2×C4—442no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—442no—
439C2×C4#6698812yes—
440C2×C4#6698812yes—
441C2×C4#6699512yes—
442C2×C4#6700312yes—
443C2×C4C2×D4×D1111yescharacteristic
444C2×C4C2×#434111yescharacteristic
445C2×C4C2×#434111yescharacteristic
446C2×C4C2×#434111yescharacteristic
447C2×C4#6703711yescharacteristic
448C2×C4#6703711yescharacteristic
449C8—222no—
450C8—442no—
451C8—441no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22C2×#6698811yescharacteristic
460C22D4×C22⋊D1111yescharacteristic
461C22#1062333711yescharacteristic
462C22C2×#6699511yescharacteristic
463C22C2×#6700311yescharacteristic
464C22#1062336811yescharacteristic
465C22#1062336911yescharacteristic
466C4—22no—
467C4—42no—
468C4—42no—
469C4—42no—
470C4—82no—
471C4—442no—
472C4—882no—
473C4—881no—
474C4#1062265814yescomplemented
475C4#1062324411yescharacteristic
476C4#1062324711yescharacteristic
477C4#1062324911yescharacteristic
478C4#1062325011yescharacteristic
479C2—82no—
480C2#1307237711yescharacteristic
481C2C2×#1062265811yescharacteristic
482C2#1307857911yescharacteristic
483C2#1308027811yescharacteristic
484C2#1308033411yescharacteristic
485C2#1308054411yescharacteristic
486C2#1308089911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2542C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2542D11
hypocenterC11#26231
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. C2×#10622658C2semidirect
3. #13069816C2semidirect
4. #13069809C2semidirect
5. #13069540C2semidirect
6. #13069419C2semidirect
8. #13069379C2semidirect
9. #13068929C2semidirect
10. C4×#66871C2semidirect
90. #66871D4semidirect
269. C4×C11#485semidirect
398. C11#26231semidirect
474. C4#10622658semidirect

Maximal subgroups

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

subgroupindex
C2×#106226582
#130715652
#130698162
#130698092
#130695402
#130694192
#130694112
#130693792
#130689292
C4×#668712
C11×#25422
#2623111