Finite Group Databasebeta

← #14808326

Subgroups — #14808326

Order 2816.

1298 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623257C211yesmaximal, characteristic
2C2×#10622697C211yesmaximal, characteristic, complemented
3#13073790C211yesmaximal, characteristic, complemented
4#13069807C214yesmaximal, complemented
5#13069569C211yesmaximal, characteristic, complemented
6#13069410C211yesmaximal, characteristic, complemented
7#13068807C214yesmaximal, complemented
8C4×#66885C211yesmaximal, characteristic, complemented
9C2×C11×#498C211yesmaximal, characteristic, complemented
10C22×#4343—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999—21no—
14#10623257—24no—
15#10623257—24no—
16C2×#66948C2212yes—
17C2×#66947—22no—
18C2×C4⋊C4×D11C2212yes—
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C11×#498—24no—
22C2×C11×#106C2214yes—
23C2×C4×C8×C11C2211yescharacteristic
24#10622844—22no—
25C2×#66885C2212yes—
26C2×(C2×D11)⋊C8C2214yes—
27#10622697—24no—
28#10622601—21no—
29#10622600C2214yes—
30#10622590—21no—
31C2×#66873C2212yes—
32C2×#66872C2212yes—
33C4×C4⋊Dic11C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622189C2212yes—
36#10622167C2214yes—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C2×#4343—28no—
40C2×#4343—44no—
41C2×#4343—44no—
42C22×D44—22no—
43C22×D44D411yescharacteristic
44C22×D44C2311yescharacteristic
45C22×C4×D11—22no—
46C22×C4×D11—21no—
47C22×C4×D11C2312yes—
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8D414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11C2311yescharacteristic
58#66999—28no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4D412yes—
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—21no—
68C22×C11⋊C8C2312yes—
69#66948—24no—
70#66948—24no—
71#66947—216no—
72C4⋊C4×D11—24no—
73C4⋊C4×D11—24no—
74C4×D44—22no—
75C4×D44—22no—
76C4×D44—22no—
77C4×D44D414yes—
78C11×#106—28no—
79C4×C8×C11—22no—
80C11⋊#95—21no—
81C11⋊#95—24no—
82#66885—24no—
83(C2×D11)⋊C8—28no—
84#66873—24no—
85#66872—24no—
86C4⋊(C11⋊C8)—22no—
87#25699—111nomaximal, Sylow
88C23×D11—21no—
89C23×D11C2×D412yes—
90C2×Q8×C11—24no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C2×Q8×C11—42no—
94C2×Q8×C11—82no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—22no—
102C22×Dic11C2×D412yes—
103#4343—432no—
104C2×D44—28no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44—21no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—44no—
111C2×D44—44no—
112C2×D44SD1614yes—
113C2×D44C2×D412yes—
114C2×C4×D11—28no—
115C2×C4×D11—24no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—24no—
119C2×C4×D11—24no—
120C2×C4×D11—44no—
121C2×C4×D11—44no—
122C2×C4×D11—42no—
123C2×C4×D11—42no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11#4114yescomplemented
127C11×C4⋊C4—24no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—42no—
132C11×C4⋊C4C2×D414yes—
133C42×C11C2×D412yes—
134C42×C11C2×D412yes—
135(C2×D11)⋊C4—28no—
136(C2×D11)⋊C4—24no—
137(C2×D11)⋊C4—24no—
138(C2×D11)⋊C4—84no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11C2×D412yes—
144Dic11⋊C4—28no—
145C4×Dic11—42no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—24no—
148C2×#547—111no—
149C2×#498D1111yescharacteristic, complemented
150C2×#476—111no—
151#2563—111no—
152#2034—114no—
153#1988—111no—
154#1954—111no—
155#1853—114no—
156C4×#102—111no—
157C23×C11C22×D411yescharacteristic
158C22×D11—22no—
159C22×D11—24no—
160C22×D11—22no—
161C22×D11—24no—
162C22×D11—22no—
163C22×D11—42no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—42no—
167C22×D11C2×SD1614yes—
168Q8×C11—48no—
169Q8×C11—84no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—44no—
176C2×C4×C11#12012yes—
177C2×C4×C11#12012yes—
178C2×C4×C11C2×SD1612yes—
179C2×C4×C11AGL(1,ℤ/8)12yes—
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C2×#4112yes—
183C2×C4×C112−1+412yes—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—24no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192D44—22no—
193D44—22no—
194D44—28no—
195D44—416no—
196D44—42no—
197C4×D11—416no—
198C4×D11—42no—
199C4×D11—42no—
200C4×D11—44no—
201C4×D11—48no—
202C8×C11—24no—
203C11⋊C8—42no—
204C22×#41—221no—
205#547—224no—
206#547—224no—
207C2×C4⋊Q8C2×D1111yescharacteristic
208C2×C4⋊Q8C2×D1111yescharacteristic
209C2×#123—222no—
210C2×C22⋊Q8—221no—
211C2×#121—112no—
212C2×C4×D4—111no—
213C2×C4×D4—111no—
214C22×C4⋊C4—112no—
215#498—24no—
216#476—224no—
217C2×#106—112no—
218C2×#106C2×D1114yes—
219C2×C4⋊C8—111no—
220C2×#102—112no—
221C2×#102—112no—
222C2×C22⋊C8—114no—
223C2×C4×C8C2×D1111yescharacteristic
224#393—222no—
225#390—221no—
226#382—221no—
227#380—114no—
228C4×C4⋊C4—111no—
229#340—112no—
230#340—114no—
231C22×C11C2×#12011yescharacteristic
232C22×C11#54712yes—
233C22×C11C22×SD1611yescharacteristic
234C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
235C22×C11#57712yes—
236C2×D11—28no—
237C2×D11—24no—
238C2×D11—44no—
239C2×D11—42no—
240C2×D11—42no—
241C2×D11—42no—
242C2×D11—42no—
243C2×D11—42no—
244C2×D11—82no—
245C2×D11—82no—
246C4×C11—22no—
247C4×C11—44no—
248C4×C11—82no—
249C4×C11#45014yes—
250C4×C11#53211yescharacteristic
251C4×C11#53611yescharacteristic
252C4×C11#54812yes—
253Dic11—42no—
254Dic11—42no—
255Dic11—82no—
256C2×#41—228no—
257C2×#41—444no—
258C2×#41—444no—
259C22×Q8—21no—
260C22×Q8—21no—
261C22×D4—111no—
262C22×D4—111no—
263C22×D4—222no—
264C23×C4—112no—
265C23×C4—222no—
266C23×C4—221no—
267C22×C8—112no—
268C22×C8C22×D1112yes—
269C4⋊Q8—22no—
270C4⋊Q8—22no—
271C4⋊Q8—22no—
272C4⋊Q8C22⋊D1114yes—
273#123—2216no—
274C22⋊Q8—228no—
275#121—224no—
276#121—224no—
277C4×D4—114no—
278C4×D4—222no—
279C4×D4—222no—
280C4×D4—222no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—224no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—224no—
289C2×C4⋊C4C22×D1112yes—
290C2×C4⋊C4C22×D1112yes—
291C2×C22⋊C4—112no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—224no—
295C2×C42—221no—
296C2×C42C22×D1111yescharacteristic
297#106—28no—
298#106—224no—
299C4⋊C8—222no—
300#102—224no—
301#102—224no—
302C22⋊C8—228no—
303C4×C8—22no—
304#95—224no—
305#95—221no—
306C2×C11#243211yescharacteristic
307C2×C11C2×#45011yescharacteristic
308C2×C11#301011yescharacteristic
309C2×C11#333512yes—
310C2×C11#335412yes—
311D11—44no—
312D11—82no—
313C24—112no—
314C24—221no—
315#41—4432no—
316C2×Q8—24no—
317C2×Q8—42no—
318C2×Q8—42no—
319C2×Q8—42no—
320C2×Q8—82no—
321C2×D4—114no—
322C2×D4—112no—
323C2×D4—228no—
324C2×D4—222no—
325C2×D4—222no—
326C2×D4—222no—
327C2×D4—222no—
328C2×D4—221no—
329C2×D4—444no—
330C2×D4—444no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—112no—
334C22×C4—228no—
335C22×C4—221no—
336C22×C4—224no—
337C22×C4—222no—
338C22×C4—224no—
339C22×C4—224no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—444no—
343C22×C4—444no—
344C22×C4—442no—
345C22×C4—442no—
346C22×C4D4×D1111yescharacteristic
347C22×C4D4×D1111yescharacteristic
348C22×C4C23×D1111yescharacteristic
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—222no—
352C2×C8—224no—
353C2×C8#434314yescomplemented
354C4⋊C4—24no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—42no—
359C4⋊C4—112no—
360C4⋊C4—228no—
361C4⋊C4—222no—
362C4⋊C4—221no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4C2×C22⋊D1114yes—
366C22⋊C4—228no—
367C22⋊C4—224no—
368C22⋊C4—224no—
369C22⋊C4—884no—
370C42—442no—
371C42D4×D1112yes—
372C42C2×C22⋊D1112yes—
373C11#2569911yescharacteristic, complemented, Sylow
374C23—114no—
375C23—224no—
376C23—222no—
377C23—224no—
378C23—222no—
379C23—222no—
380C23—442no—
381C23—441no—
382C23—441no—
383C23—442no—
384C23C2×D4×D1111yescharacteristic
385Q8—48no—
386Q8—84no—
387D4—222no—
388D4—222no—
389D4—228no—
390D4—4416no—
391D4—442no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—44no—
397C2×C4—42no—
398C2×C4—224no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—4416no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—448no—
407C2×C4—444no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4SD16×D1112yes—
412C2×C4#6696712yes—
413C2×C4#6699012yes—
414C2×C4#6699012yes—
415C2×C4C2×D4×D1111yescharacteristic
416C2×C4C2×#434312yes—
417C2×C4#6704012yes—
418C2×C4C22×C22⋊D1111yescharacteristic
419C8—24no—
420C8—442no—
421C22—224no—
422C22—228no—
423C22—442no—
424C22—444no—
425C22—442no—
426C22—442no—
427C22—442no—
428C22—442no—
429C22—882no—
430C22—882no—
431C22#1062325712yes—
432C22C2×SD16×D1111yescharacteristic
433C22C2×#6696711yescharacteristic
434C22#1062329312yes—
435C22C2×#6699011yescharacteristic
436C4—22no—
437C4—44no—
438C4—82no—
439C4—442no—
440C4—442no—
441C4—882no—
442C4#1062278214yes—
443C4#1062325511yescharacteristic
444C4#1062325611yescharacteristic
445C4#1062334812yes—
446C2—444no—
447C2—882no—
448C2#1307224111yescharacteristic
449C2C2×#1062278211yescharacteristic
450C2#1307789811yescharacteristic
451C2#1308097212yes—
452C2#1308121012yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#498C2
socleC23×C11C22×D4
prime radicalC2×#10623257C2
hypercenterC2×#498D11
hypocenterC11#25699
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
2. C2×#10622697C2semidirect
3. #13073790C2semidirect
4. #13069807C2semidirect
5. #13069569C2semidirect
6. #13069410C2semidirect
7. #13068807C2semidirect
8. C4×#66885C2semidirect
9. C2×C11×#498C2semidirect
126. C2×C8×C11#41semidirect
149. C2×#498D11semidirect
353. C2×C8#4343semidirect
373. C11#25699semidirect

Maximal subgroups

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

subgroupindex
C2×#106232572
C2×#106226972
#130737902
#130698072
#130695692
#130694102
#130688072
C4×#668852
C2×C11×#4982
#2569911