Finite Group Databasebeta

← #14805630

Subgroups — #14805630

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×#10622621C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13073821C211yesmaximal, characteristic, complemented
4#13070117C212yesmaximal, complemented
5#13069990C212yesmaximal
6#13069576C211yesmaximal, characteristic, complemented
7#13069377C211yesmaximal, characteristic, complemented
8#13069341C212yesmaximal, complemented
9#13069302C212yesmaximal
10C4×#66896C211yesmaximal, characteristic
11C11×#2538C211yesmaximal, characteristic
12C2×C11×C22⋊Q8—21no—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C11×#396—22no—
17C11×#390C2212yes—
18C11×#389C2212yes—
19C11×#384C2211yescharacteristic
20C11×#380—21no—
21#10622843—21no—
22C2×#66896C2212yes—
23C2×#66896C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25Q8×C11⋊C8—24no—
26#10622621—24no—
27#10622592—22no—
28#10622589—21no—
29C2×#66872C2212yes—
30C2×#66872C2212yes—
31C4×C4⋊Dic11C2211yescharacteristic
32#10622541C2212yes—
33#10622541C2212yes—
34C2×C4⋊(C11⋊C8)C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37C2×C4×C11⋊C8C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42#10622167C2212yes—
43C22×Q8×C11D411yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22—21no—
47C11×C22⋊Q8—44no—
48C4×Q8×C11—22no—
49C4×Q8×C11—22no—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11—21no—
71C22×C11⋊C8C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73C22×C11⋊C8C2311yescharacteristic
74#66922—22no—
75#66922—22no—
76C11×#95—22no—
77#66896—22no—
78#66896—24no—
79#66896Q814yescomplemented
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—21no—
83#66872—24no—
84#66872—24no—
85C4⋊(C11⋊C8)—24no—
86C4⋊(C11⋊C8)D414yes—
87C4×C11⋊C8—22no—
88C4×C11⋊C8—24no—
89#25470—111nomaximal, Sylow
90C24×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11SD1614yes—
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×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C2×Dic22—42no—
114C2×Dic22—81no—
115C2×Dic22—81no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4—44no—
124C11×C4⋊C4—81no—
125C11×C22⋊C4—42no—
126C11×C22⋊C4—44no—
127C11×C22⋊C4—82no—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11C2×D412yes—
131C42×C11#4112yes—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—42no—
137C4⋊Dic11C2×Q812yes—
138C4⋊Dic11#4112yes—
139Dic11⋊C4—82no—
140Dic11⋊C4—82no—
141C4×Dic11—42no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8C2×D414yes—
150C2×C11⋊C8C2×Q812yes—
151C2×#476—111no—
152C2×C8×Q8—111no—
153#2567—111no—
154#2538D1111yescharacteristic
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—28no—
171D4×C11—22no—
172D4×C11—22no—
173D4×C11—41no—
174D4×C11—41no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—84no—
189C2×C4×C11#12112yes—
190C2×C4×C11#12112yes—
191C2×C4×C11C2×SD1614yes—
192C2×C4×C11C2×SD1612yes—
193C2×C4×C11#13512yes—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×Q811yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×C4×C112−1+411yescharacteristic
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209Dic22—84no—
210C11⋊C8—24no—
211C11⋊C8—22no—
212C11⋊C8—41no—
213C2×C4⋊Q8—111no—
214C2×C22⋊Q8—21no—
215C2×C4×Q8C2×D1111yescharacteristic
216C2×C4×D4C2×D1111yescharacteristic
217#476—224no—
218C8×Q8—224no—
219C2×#106—112no—
220C2×#106—112no—
221C2×C4⋊C8—111no—
222C2×C4⋊C8—112no—
223C2×#102—111no—
224C2×#102—111no—
225C2×#102—112no—
226C2×C4×C8—112no—
227C2×C4×C8—111no—
228#396—22no—
229#395—222no—
230#391—221no—
231#390C2×D1112yes—
232#389—112no—
233#389—112no—
234#389C2×D1112yes—
235#384—221no—
236#384C2×D1111yescharacteristic
237#380—21no—
238C4×C4⋊C4—111no—
239#340—112no—
240#340—111no—
241#340—112no—
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—24no—
259C4×C11—22no—
260C4×C11—42no—
261C4×C11—82no—
262C4×C11—81no—
263C4×C11#46514yes—
264C4×C11#53311yescharacteristic
265C4×C11#54111yescharacteristic
266C4×C11#54711yescharacteristic
267C4×C11D4×Q811yescharacteristic
268Dic11—42no—
269Dic11—42no—
270Dic11—82no—
271C22×Q8—221no—
272C22×Q8C22⋊D1111yescharacteristic
273C22×D4C22×D1111yescharacteristic
274C23×C4—21no—
275C22×C8—111no—
276C22×C8—112no—
277C22×C8—111no—
278C4⋊Q8—222no—
279C4⋊Q8—222no—
280C22⋊Q8—44no—
281C4×Q8—22no—
282C4×Q8—22no—
283C4×D4—22no—
284C4×D4—22no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4C22⋊D1111yescharacteristic
295C2×C4⋊C4C22⋊D1112yes—
296C2×C4⋊C4C22×D1111yescharacteristic
297C2×C4⋊C4C22×D1112yes—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C42—221no—
302C2×C42C22×D1112yes—
303C2×C42C22×D1111yescharacteristic
304#106—224no—
305#106—224no—
306C4⋊C8—114no—
307C4⋊C8—224no—
308#102—114no—
309#102—222no—
310#102—224no—
311C4×C8—224no—
312C4×C8—222no—
313#95—22no—
314#95—221no—
315#95—222no—
316#95—222no—
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—22no—
327C2×Q8—22no—
328C2×Q8—442no—
329C2×Q8—881no—
330C2×Q8—881no—
331C2×Q8#432414yes—
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—221no—
344C22×C4—221no—
345C22×C4—222no—
346C22×C4C2×C22⋊D1112yes—
347C22×C4C2×C22⋊D1112yes—
348C22×C4C2×C22⋊D1111yescharacteristic
349C22×C4C2×C22⋊D1111yescharacteristic
350C22×C4C23×D1111yescharacteristic
351C2×C8—114no—
352C2×C8—112no—
353C2×C8—221no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8—221no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8—221no—
360C4⋊C4—24no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—42no—
367C4⋊C4—44no—
368C4⋊C4—81no—
369C4⋊C4—112no—
370C4⋊C4—112no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—222no—
374C4⋊C4—222no—
375C4⋊C4—442no—
376C4⋊C4—882no—
377C4⋊C4—882no—
378C22⋊C4—44no—
379C22⋊C4—42no—
380C22⋊C4—82no—
381C42—22no—
382C42—22no—
383C42—442no—
384C42D4×D1112yes—
385C42#434112yes—
386C11#2547011yescharacteristic, complemented, Sylow
387C23—22no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23C22×C22⋊D1111yescharacteristic
395Q8—28no—
396Q8—884no—
397D4—22no—
398D4—22no—
399D4—41no—
400D4—41no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—84no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4C2×#432414yes—
425C2×C4C2×#432412yes—
426C2×C4#6699212yes—
427C2×C4#6699212yes—
428C2×C4#6700312yes—
429C2×C4C2×D4×D1111yescharacteristic
430C2×C4C2×#434111yescharacteristic
431C2×C4C2×Q8×D1111yescharacteristic
432C2×C4#6704011yescharacteristic
433C2×C4#41×D1111yescharacteristic
434C2×C4#6704311yescharacteristic
435C8—224no—
436C8—222no—
437C8—441no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22C22×#432411yescharacteristic
446C22C2×#6699211yescharacteristic
447C22Q8×C22⋊D1111yescharacteristic
448C22C2×#6700311yescharacteristic
449C22#1062336211yescharacteristic
450C22#1062336611yescharacteristic
451C22#1062336811yescharacteristic
452C4—22no—
453C4—24no—
454C4—42no—
455C4—81no—
456C4—82no—
457C4—442no—
458C4—442no—
459C4—882no—
460C4#1062265414yes—
461C4#1062315311yescharacteristic
462C4#1062315611yescharacteristic
463C4#1062316211yescharacteristic
464C4#1062316311yescharacteristic
465C2—82no—
466C2#1307221711yescharacteristic
467C2C2×#1062265411yescharacteristic
468C2#1307829811yescharacteristic
469C2#1308126111yescharacteristic
470C2#1308128311yescharacteristic
471C2Q8×#432411yescharacteristic
472C2#1308147911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2538C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2538D11
hypocenterC11#25470
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
3. #13073821C2semidirect
4. #13070117C2semidirect
6. #13069576C2semidirect
7. #13069377C2semidirect
8. #13069341C2semidirect
79. #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×#106226212
C2×Q8×C11⋊C82
#130738212
#130701172
#130699902
#130695762
#130693772
#130693412
#130693022
C4×#668962
C11×#25382
#2547011