Finite Group Databasebeta

← #14805624

Subgroups — #14805624

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622443C211yesmaximal, characteristic, complemented
2#13073825C211yesmaximal, characteristic, complemented
3#13073538C211yesmaximal, characteristic
4#13070115C212yesmaximal, complemented
5#13069988C212yesmaximal
6#13069578C211yesmaximal, characteristic, complemented
7#13069380C211yesmaximal, characteristic, complemented
8#13069342C212yesmaximal, complemented
9#13069296C212yesmaximal
10C4×#66896C211yesmaximal, characteristic
11C2×C11×#476C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66977—21no—
15C2×C4×Dic22C2211yescharacteristic
16C11×#476—24no—
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102C2212yes—
20#10622842—22no—
21#10622834C2212yes—
22C2×#66896C2211yescharacteristic
23C2×#66896C2211yescharacteristic
24#10622825—21no—
25C2×#66881C2212yes—
26C2×Dic11⋊C8C2212yes—
27C2×C8×Dic11C2212yes—
28#10622589—21no—
29#10622587—21no—
30#10622586C2212yes—
31#10622586C2212yes—
32#10622586C2212yes—
33#10622561—22no—
34#10622548C2211yescharacteristic
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622443—24no—
38#10622189C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22D411yescharacteristic
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11D411yescharacteristic
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65#66977—44no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4D412yes—
70C2×C4×Dic11—21no—
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C4×Dic22—22no—
75C4×Dic22—22no—
76C11×#106—24no—
77C11×C4⋊C8D414yes—
78C11×#102—24no—
79#66896—22no—
80#66896Q814yescomplemented
81C11⋊#95—21no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85#66881—24no—
86Dic11⋊C8—24no—
87C8×Dic11—24no—
88C4×C11⋊C8—22no—
89#25470—111nomaximal, Sylow
90C24×C11—21no—
91C2×Q8×C11—42no—
92C2×Q8×C11—81no—
93C2×Q8×C11—81no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11C2×Q812yes—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—22no—
111C22×Dic11C2×D412yes—
112C22×Dic11C2×D412yes—
113C2×Dic22—22no—
114C2×Dic22—22no—
115C2×Dic22SD1614yes—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11C2×D414yes—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—42no—
124C11×C22⋊C4—42no—
125C42×C11C2×D412yes—
126C42×C11#4112yes—
127C22⋊Dic11—44no—
128C22⋊Dic11—82no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—22no—
134C4⋊Dic11—42no—
135C4⋊Dic11—81no—
136C4⋊Dic11C2×Q812yes—
137C4⋊Dic11#4112yes—
138Dic11⋊C4—24no—
139Dic11⋊C4—44no—
140Dic11⋊C4—82no—
141Dic11⋊C4—82no—
142C4×Dic11—22no—
143C4×Dic11—22no—
144C4×Dic11—42no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8C2×Q812yes—
151C2×#476D1111yescharacteristic
152C2×C8×Q8—111no—
153#2567—111no—
154#2538—111no—
155#2088—112no—
156#2065—112no—
157#1990—111no—
158#1948—111no—
159#1941—112no—
160#1934—112no—
161C4×#102—111no—
162C23×C11—22no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11C22×D411yescharacteristic
170Q8×C11—84no—
171D4×C11—22no—
172D4×C11—22no—
173D4×C11—41no—
174D4×C11—41no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—84no—
184C2×C4×C11#12112yes—
185C2×C4×C11#12112yes—
186C2×C4×C11C2×SD1612yes—
187C2×C4×C11#13512yes—
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×Q811yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C112−1+411yescharacteristic
193C2×C4×C112−1+411yescharacteristic
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11C2×SD1614yes—
209Dic22—28no—
210C8×C11—24no—
211C11⋊C8—22no—
212C11⋊C8—41no—
213C2×C4⋊Q8C2×D1111yescharacteristic
214C2×C22⋊Q8—221no—
215C2×C4×Q8—111no—
216C2×C4×D4C2×D1111yescharacteristic
217#476—24no—
218C8×Q8—224no—
219C2×#106—112no—
220C2×#106C2×D1112yes—
221C2×C4⋊C8—112no—
222C2×C4⋊C8C2×D1111yescharacteristic
223C2×#102—111no—
224C2×#102—111no—
225C2×#102C2×D1112yes—
226C2×C4×C8—112no—
227C2×C4×C8—111no—
228#396—222no—
229#395—222no—
230#391—221no—
231#390—112no—
232#389—112no—
233#389—112no—
234#389—112no—
235#384—111no—
236#384—221no—
237#380—221no—
238C4×C4⋊C4—111no—
239#340—112no—
240#340—112no—
241#340—111no—
242#340—112no—
243#340—111no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11C2×#12111yescharacteristic
252C22×C11#54811yescharacteristic
253C22×C11D4×Q811yescharacteristic
254C22×C11C22×SD1611yescharacteristic
255C22×C11C2×#13511yescharacteristic
256C22×C11#57611yescharacteristic
257C22×C11#57711yescharacteristic
258C4×C11—22no—
259C4×C11—81no—
260C4×C11—82no—
261C4×C11#46514yes—
262C4×C11#53311yescharacteristic
263C4×C11#54111yescharacteristic
264C4×C11#54711yescharacteristic
265C4×C11D4×Q811yescharacteristic
266Dic11—24no—
267Dic11—42no—
268Dic11—42no—
269Dic11—42no—
270Dic11—82no—
271C22×Q8—21no—
272C22×Q8—111no—
273C22×D4C22×D1111yescharacteristic
274C23×C4—21no—
275C22×C8—111no—
276C22×C8—111no—
277C22×C8C22×D1112yes—
278C4⋊Q8—22no—
279C4⋊Q8—22no—
280C22⋊Q8—444no—
281C4×Q8—222no—
282C4×Q8—222no—
283C4×D4—22no—
284C4×D4—22no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4C22×D1111yescharacteristic
297C2×C4⋊C4C22×D1112yes—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—222no—
301C2×C42—112no—
302C2×C42—221no—
303C2×C42C22×D1111yescharacteristic
304#106—24no—
305#106—224no—
306C4⋊C8—224no—
307C4⋊C8C22⋊D1114yes—
308#102—24no—
309#102—114no—
310#102—222no—
311C4×C8—224no—
312C4×C8—222no—
313#95—222no—
314#95—222no—
315#95—222no—
316#95—221no—
317C2×C11—82no—
318C2×C11#242911yescharacteristic
319C2×C11C2×#46511yescharacteristic
320C2×C11#306211yescharacteristic
321C2×C11#336011yescharacteristic
322C2×C11#336211yescharacteristic
323C2×C11Q8×SD1611yescharacteristic
324C2×C11#338011yescharacteristic
325C24—21no—
326C2×Q8—42no—
327C2×Q8—81no—
328C2×Q8—81no—
329C2×Q8—114no—
330C2×Q8—222no—
331C2×Q8—222no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4Q8×D1112yes—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—112no—
344C22×C4—112no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—222no—
348C22×C4D4×D1111yescharacteristic
349C22×C4D4×D1111yescharacteristic
350C22×C4C23×D1111yescharacteristic
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—112no—
354C2×C8—221no—
355C2×C8—221no—
356C2×C8—221no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8C2×C22⋊D1114yes—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—42no—
365C4⋊C4—112no—
366C4⋊C4—112no—
367C4⋊C4—224no—
368C4⋊C4—222no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4—444no—
374C4⋊C4—442no—
375C4⋊C4—881no—
376C4⋊C4—882no—
377C4⋊C4—882no—
378C22⋊C4—42no—
379C22⋊C4—444no—
380C22⋊C4—882no—
381C42—222no—
382C42—222no—
383C42—442no—
384C42#434112yes—
385C42C2×C22⋊D1112yes—
386C11#2547011yescharacteristic, complemented, Sylow
387C23—22no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23C2×D4×D1111yescharacteristic
395Q8—84no—
396Q8—228no—
397D4—22no—
398D4—22no—
399D4—41no—
400D4—41no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—84no—
410C2×C4—114no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4SD16×D1112yes—
426C2×C4#6696912yes—
427C2×C4#6699112yes—
428C2×C4#6699112yes—
429C2×C4C2×#434111yescharacteristic
430C2×C4C2×Q8×D1111yescharacteristic
431C2×C4#6704011yescharacteristic
432C2×C4#41×D1111yescharacteristic
433C2×C4#6704311yescharacteristic
434C2×C4C22×C22⋊D1111yescharacteristic
435C8—24no—
436C8—222no—
437C8—441no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22#1062316311yescharacteristic
446C22#1062316411yescharacteristic
447C22C2×SD16×D1111yescharacteristic
448C22C2×#6696911yescharacteristic
449C22#1062330511yescharacteristic
450C22#1062330611yescharacteristic
451C22C2×#6699111yescharacteristic
452C4—22no—
453C4—82no—
454C4—81no—
455C4—224no—
456C4—442no—
457C4—442no—
458C4—442no—
459C4—882no—
460C4#1062278414yes—
461C4#1062315311yescharacteristic
462C4#1062315611yescharacteristic
463C4Q8×C22⋊D1111yescharacteristic
464C4#1062335511yescharacteristic
465C2—82no—
466C2#1307221111yescharacteristic
467C2C2×#1062278411yescharacteristic
468C2#1307829011yescharacteristic
469C2#1308126411yescharacteristic
470C2#1308128611yescharacteristic
471C2#1308147111yescharacteristic
472C2#1308148211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#476D11
hypocenterC11#25470
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10622443C2semidirect
2. #13073825C2semidirect
4. #13070115C2semidirect
6. #13069578C2semidirect
7. #13069380C2semidirect
8. #13069342C2semidirect
80. #66896Q8semidirect
386. C11#25470semidirect

Maximal subgroups

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

subgroupindex
C2×#106224432
#130738252
#130735382
#130701152
#130699882
#130695782
#130693802
#130693422
#130692962
C4×#668962
C2×C11×#4762
#2547011