Finite Group Databasebeta

← #14657313

Subgroups — #14657313

Order 2816.

530 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073534C211yesmaximal, characteristic
2#13068743C211yesmaximal, characteristic, complemented
3#13068613C211yesmaximal, characteristic
4C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic, complemented
7C11×#1803C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66999—21no—
10C2×C4×D44C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×#103—21no—
13C11×#384C2211yescharacteristic
14#10622607—22no—
15#10622600—21no—
16C2×#66873—21no—
17#10622552—21no—
18#10622548C2211yescharacteristic
19#10622541—21no—
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22C11×#340—21no—
23Q8⋊(C11⋊C8)—22no—
24#10622167—21no—
25#10622167—22no—
26#10622121—22no—
27C22×Q8×C11D411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×C8×C11—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42#66999—42no—
43#66999—42no—
44C2×(C2×D11)⋊C4—22no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—22no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D411yescharacteristic
50C2×C4⋊Dic11D412yes—
51C2×Dic11⋊C4—22no—
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54C4×D44—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×#103—42no—
61C11⋊#95—22no—
62#66873—42no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4×C11⋊C8—21no—
66C4×C11⋊C8D412yes—
67#10436—111nomaximal, Sylow
68C23×D11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11SD1612yes—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—22no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44Q1612yes—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11#4111yescharacteristic
113(C2×D11)⋊C4—44no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—82no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—42no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124Dic11⋊C4—44no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131#2538—111no—
132#1834—111no—
133#1803D1111yescharacteristic, complemented
134#1802—111no—
135C2×Q8⋊C8—111no—
136C2×D4⋊C8—111no—
137#1296—111no—
138C23×C11#12011yescharacteristic
139C22×D11—22no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146Q8×C11—22no—
147Q8×C11—22no—
148Q8×C11—41no—
149Q8×C11—41no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12311yescharacteristic
165C2×C4×C11#12311yescharacteristic
166C2×C4×C11#12411yescharacteristic
167C2×C4×C11C2×SD1611yescharacteristic
168C2×C4×C11C2×Q1611yescharacteristic
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11#13711yescharacteristic
175C2×Dic11—41no—
176C2×Dic11—42no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181D44—22no—
182D44—22no—
183D44—41no—
184D44—41no—
185C4×D11—81no—
186C4×D11—81no—
187C4×D11—81no—
188C4×D11—81no—
189C8×C11—81no—
190C11⋊C8—42no—
191C11⋊C8—81no—
192C2×C22⋊Q8—221no—
193C2×C4×Q8C2×D1111yescharacteristic
194C2×C4×D4—111no—
195C2×C4⋊C8—111no—
196C2×C4⋊C8C2×D1111yescharacteristic
197C2×#103—21no—
198C2×#102—221no—
199C2×C4×C8—111no—
200#396—222no—
201#390—221no—
202#389—221no—
203#384—111no—
204#384C2×D1111yescharacteristic
205#380—221no—
206#340—21no—
207#340—221no—
208#340—222no—
209Q8⋊C8—222no—
210D4⋊C8—222no—
211C22×C11#39411yescharacteristic
212C22×C11#44911yescharacteristic
213C22×C11#44911yescharacteristic
214C22×C11#45011yescharacteristic
215C22×C11#45111yescharacteristic
216C22×C11#45411yescharacteristic
217C22×C11#45511yescharacteristic
218C2×D11—42no—
219C2×D11—42no—
220C2×D11—42no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—42no—
228C4×C11—81no—
229C4×C11—161no—
230C4×C11#46511yescharacteristic
231C4×C11#46711yescharacteristic
232C4×C11#46811yescharacteristic
233C4×C11#46911yescharacteristic
234C4×C11#48111yescharacteristic
235C4×C11#48211yescharacteristic
236C4×C11#48411yescharacteristic
237C4×C11#48511yescharacteristic
238Dic11—82no—
239Dic11—81no—
240C22×Q8C22⋊D1111yescharacteristic
241C22×D4—111no—
242C23×C4—221no—
243C22×C8—21no—
244C22×C8—221no—
245C22×C8—221no—
246C22⋊Q8—442no—
247C22⋊Q8—442no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×D4—221no—
253C4×D4—221no—
254C4×D4—221no—
255C4×D4—221no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—112no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4C22⋊D1111yescharacteristic
266C2×C22⋊C4—222no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—222no—
269C2×C42—21no—
270C2×C42C22×D1111yescharacteristic
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—221no—
274C4⋊C8—221no—
275#103—42no—
276#102—442no—
277C4×C8—112no—
278C4×C8—221no—
279#95—222no—
280C2×C11#162811yescharacteristic
281C2×C11#163711yescharacteristic
282C2×C11#164211yescharacteristic
283C2×C11#164411yescharacteristic
284C2×C11#203411yescharacteristic
285C2×C11#203611yescharacteristic
286C2×C11#204011yescharacteristic
287D11—82no—
288C24—221no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8#432512yes—
295C2×D4—112no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—221no—
299C2×D4—221no—
300C2×D4—221no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—221no—
305C22×C4—222no—
306C22×C4—441no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4D4×D1111yescharacteristic
313C22×C4D4×D1111yescharacteristic
314C22×C4C2×C22⋊D1111yescharacteristic
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—222no—
319C2×C8—441no—
320C2×C8—441no—
321C2×C8—441no—
322C2×C8—441no—
323C2×C8—441no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4—442no—
336C4⋊C4—444no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C22⋊C4—444no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—882no—
345C42—41no—
346C42—41no—
347C42#433911yescharacteristic
348C42#433911yescharacteristic
349C42D4×D1111yescharacteristic
350C42#434111yescharacteristic
351C11#1043611yescharacteristic, complemented, Sylow
352C23—222no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23—441no—
357C23—441no—
358C23—441no—
359C23#6699011yescharacteristic
360Q8—22no—
361Q8—22no—
362Q8—41no—
363Q8—41no—
364D4—222no—
365D4—222no—
366D4—441no—
367D4—441no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—442no—
384C2×C4—441no—
385C2×C4—881no—
386C2×C4—881no—
387C2×C4—881no—
388C2×C4—881no—
389C2×C4#6693611yescharacteristic
390C2×C4#6693711yescharacteristic
391C2×C4#6693711yescharacteristic
392C2×C4#6693811yescharacteristic
393C2×C4#6696711yescharacteristic
394C2×C4#6696911yescharacteristic
395C2×C4Q16×D1111yescharacteristic
396C2×C4#6697111yescharacteristic
397C2×C4#6698211yescharacteristic
398C2×C4#6698511yescharacteristic
399C2×C4#6699211yescharacteristic
400C2×C4C2×#432511yescharacteristic
401C2×C4#6700211yescharacteristic
402C2×C4#6700311yescharacteristic
403C8—81no—
404C8—442no—
405C8—881no—
406C22—442no—
407C22—442no—
408C22—442no—
409C22—881no—
410C22—881no—
411C22—881no—
412C22—881no—
413C22#1062257211yescharacteristic
414C22#1062265011yescharacteristic
415C22#1062265911yescharacteristic
416C22#1062278511yescharacteristic
417C22#1062279911yescharacteristic
418C22#1062281411yescharacteristic
419C22#1062281511yescharacteristic
420C4—21no—
421C4—21no—
422C4—42no—
423C4—81no—
424C4—161no—
425C4—882no—
426C4—881no—
427C4#1062242211yescharacteristic
428C4#1062242511yescharacteristic
429C4#1062242611yescharacteristic
430C4#1062242811yescharacteristic
431C4#1062258111yescharacteristic
432C4#1062261611yescharacteristic
433C4#1062265211yescharacteristic
434C4#1062266111yescharacteristic
435C2—882no—
436C2#1306772511yescharacteristic
437C2#1306777911yescharacteristic
438C2#1306781511yescharacteristic
439C2#1306782811yescharacteristic
440C2#1306980511yescharacteristic
441C2#1306981711yescharacteristic
442C2#1306984311yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1803C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1803D11
hypocenterC11#10436
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. #13068743C2semidirect
4. C2×Q8⋊(C11⋊C8)C2semidirect
6. #13066500C2semidirect
7. C11×#1803C2semidirect
133. #1803D11semidirect
351. C11#10436semidirect

Maximal subgroups

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

subgroupindex
#130735342
#130687432
#130686132
C2×Q8⋊(C11⋊C8)2
C2×#106221212
#130665002
C11×#18032
#1043611