Finite Group Databasebeta

← #14811912

Subgroups — #14811912

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073652C211yesmaximal, characteristic, complemented
2#13071565C211yesmaximal, characteristic
3#13070002C212yesmaximal
4#13069760C212yesmaximal
5#13069572C212yesmaximal, complemented
6#13069375C211yesmaximal, characteristic, complemented
7#13069332C211yesmaximal, characteristic, complemented
8#13069207C212yesmaximal, complemented
9#13068743C211yesmaximal, characteristic, complemented
10C4×#66896C211yesmaximal, characteristic
11C11×#1802C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66979—21no—
14C2×#66943C2212yes—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#102C2212yes—
17C11×#384C2211yescharacteristic
18#10622834C2212yes—
19C2×#66896C2211yescharacteristic
20C2×#66896C2211yescharacteristic
21#10622825—21no—
22C2×#66882C2212yes—
23C2×Dic11⋊C8C2212yes—
24#10622598—21no—
25#10622597—22no—
26#10622589—21no—
27C4⋊C4×Dic11C2212yes—
28#10622586C2212yes—
29#10622564—22no—
30#10622548C2211yescharacteristic
31C4×C4⋊Dic11C2211yescharacteristic
32C4×C4⋊Dic11C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34C11×#340C2212yes—
35#10622189C2212yes—
36#10622188C2212yes—
37#10622167C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2211yescharacteristic
40#10622167C2212yes—
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11—21no—
43C22×C8×C11C2312yes—
44C4×D4×C11—22no—
45C4×D4×C11Q814yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—22no—
54#66979—44no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11D411yescharacteristic
59C2×C4⋊Dic11D411yescharacteristic
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11C2312yes—
68C22×C11⋊C8C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70#66943—24no—
71#66943—42no—
72C11×C4⋊C8—22no—
73C11×#102—42no—
74#66896—22no—
75#66896—22no—
76C11⋊#95—21no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95D412yes—
80#66882—24no—
81Dic11⋊C8—42no—
82C4×C11⋊C8—22no—
83#26025—111nomaximal, Sylow
84C24×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11C2×Q812yes—
91C22×C4×C11—21no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—22no—
102C22×Dic11C2×D412yes—
103C22×Dic11C2×D412yes—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—81no—
112C11×C4⋊C4C2×Q812yes—
113C11×C22⋊C4—24no—
114C42×C11C2×Q812yes—
115C42×C11#4112yes—
116C22⋊Dic11—44no—
117C22⋊Dic11—82no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—44no—
125C4⋊Dic11—42no—
126C4⋊Dic11—81no—
127C4⋊Dic11#4112yes—
128C4⋊Dic11#4112yes—
129Dic11⋊C4—44no—
130Dic11⋊C4—82no—
131C4×Dic11—22no—
132C4×Dic11—22no—
133C4×Dic11—44no—
134C4×Dic11—42no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141#2552—111no—
142#2354—111no—
143#2067—112no—
144#2025—112no—
145#1989—112no—
146#1947—111no—
147#1939—111no—
148#1921—112no—
149#1834—111no—
150#1802D1111yescharacteristic
151C4×#102—111no—
152C23×C11—22no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11C22×D411yescharacteristic
160D4×C11—22no—
161D4×C11—22no—
162D4×C11—41no—
163D4×C11—41no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—48no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11C22⋊Q812yes—
174C2×C4×C11C22⋊Q812yes—
175C2×C4×C11#13512yes—
176C2×C4×C11AGL(1,ℤ/8)12yes—
177C2×C4×C11C22×Q811yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C2×C4×C11C2×#4111yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11H(5,𝔽2)11yescharacteristic
182C2×C4×C112−1+411yescharacteristic
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C8×C11—42no—
199C11⋊C8—41no—
200C11⋊C8—41no—
201C2×#125—112no—
202C2×C4×D4C2×D1111yescharacteristic
203C2×#117—221no—
204C2×#107—112no—
205C2×C4⋊C8—112no—
206C2×C4⋊C8C2×D1111yescharacteristic
207C2×#102—111no—
208C2×#102—111no—
209C2×#102C2×D1112yes—
210C2×C4×C8—111no—
211#398—222no—
212#390—112no—
213#389—112no—
214#389—221no—
215#388—222no—
216#384—111no—
217#384—221no—
218#384C2×D1111yescharacteristic
219#380—221no—
220C4×C4⋊C4—111no—
221C4×C4⋊C4—112no—
222C4×C4⋊C4—111no—
223#340—112no—
224#340—112no—
225#340—112no—
226#340—111no—
227#340—111no—
228#340C2×D1112yes—
229#336—112no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11C2×C22⋊Q811yescharacteristic
238C22×C11#54611yescharacteristic
239C22×C11#54811yescharacteristic
240C22×C11C2×#13511yescharacteristic
241C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
242C22×C11#57611yescharacteristic
243C22×C11#57811yescharacteristic
244C4×C11—22no—
245C4×C11—42no—
246C4×C11—82no—
247C4×C11#47814yes—
248C4×C11#53311yescharacteristic
249C4×C11#54411yescharacteristic
250C4×C11#55511yescharacteristic
251C4×C11#55611yescharacteristic
252Dic11—42no—
253Dic11—42no—
254Dic11—42no—
255Dic11—42no—
256Dic11—82no—
257C22×D4C22×D1111yescharacteristic
258C23×C4—21no—
259C22×C8—111no—
260C22×C8—111no—
261C22×C8C22×D1112yes—
262#125—224no—
263#125—442no—
264C4×D4—22no—
265C4×D4Dic2214yes—
266#117—444no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—111no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—221no—
279C2×C4⋊C4C22×D1112yes—
280C2×C4⋊C4C22×D1111yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—222no—
283C2×C22⋊C4—222no—
284C2×C42—112no—
285C2×C42—222no—
286C2×C42—221no—
287C2×C42C22×D1111yescharacteristic
288#107—224no—
289C4⋊C8—22no—
290C4⋊C8—442no—
291#102—42no—
292#102—222no—
293#102—222no—
294C4×C8—222no—
295#95—112no—
296#95—222no—
297#95—222no—
298#95—221no—
299C2×C11—82no—
300C2×C11#243911yescharacteristic
301C2×C11C2×#47811yescharacteristic
302C2×C11#308311yescharacteristic
303C2×C11#330511yescharacteristic
304C2×C11#333011yescharacteristic
305C2×C11#336411yescharacteristic
306C2×C11#336611yescharacteristic
307C24—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4C2×Dic2212yes—
314C22×C4—21no—
315C22×C4—24no—
316C22×C4—22no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—112no—
320C22×C4—112no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—222no—
324C22×C4D4×D1111yescharacteristic
325C22×C4D4×D1111yescharacteristic
326C22×C4C23×D1111yescharacteristic
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—221no—
331C2×C8—221no—
332C2×C8—221no—
333C2×C8—221no—
334C2×C8—221no—
335C2×C8—221no—
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—42no—
340C4⋊C4—81no—
341C4⋊C4—112no—
342C4⋊C4—112no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—222no—
348C4⋊C4—222no—
349C4⋊C4—444no—
350C4⋊C4—444no—
351C4⋊C4—442no—
352C4⋊C4—881no—
353C4⋊C4—882no—
354C4⋊C4C2×Dic2212yes—
355C22⋊C4—24no—
356C22⋊C4—444no—
357C22⋊C4—882no—
358C42—222no—
359C42—222no—
360C42—444no—
361C42—442no—
362C42C2×Dic2212yes—
363C42#434112yes—
364C11#2602511yescharacteristic, complemented, Sylow
365C23—22no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23C2×D4×D1111yescharacteristic
373D4—22no—
374D4—22no—
375D4—41no—
376D4—41no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—48no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4#6693112yes—
402C2×C4#6693112yes—
403C2×C4#6696512yes—
404C2×C4#6696712yes—
405C2×C4C22×Dic2211yescharacteristic
406C2×C4C2×#434111yescharacteristic
407C2×C4#6703711yescharacteristic
408C2×C4#6704011yescharacteristic
409C2×C4#41×D1111yescharacteristic
410C2×C4#41×D1111yescharacteristic
411C8—42no—
412C8—441no—
413C8—441no—
414C22—42no—
415C22—42no—
416C22—42no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22C2×#6693111yescharacteristic
422C22#1062314311yescharacteristic
423C22#1062316411yescharacteristic
424C22C2×#6696511yescharacteristic
425C22C2×#6696711yescharacteristic
426C22#1062330511yescharacteristic
427C22#1062331011yescharacteristic
428C4—22no—
429C4—42no—
430C4—82no—
431C4—442no—
432C4—442no—
433C4—442no—
434C4—442no—
435C4—882no—
436C4#1062237914yes—
437C4#1062303111yescharacteristic
438C4#1062304811yescharacteristic
439C4#1062314711yescharacteristic
440C4#1062317211yescharacteristic
441C2—82no—
442C2#1307230811yescharacteristic
443C2C2×#1062237911yescharacteristic
444C2#1307847111yescharacteristic
445C2#1308056911yescharacteristic
446C2#1308092411yescharacteristic
447C2#1308130011yescharacteristic
448C2#1308132211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1802D11
hypocenterC11#26025
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
1. #13073652C2semidirect
5. #13069572C2semidirect
6. #13069375C2semidirect
7. #13069332C2semidirect
8. #13069207C2semidirect
9. #13068743C2semidirect
364. C11#26025semidirect

Maximal subgroups

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

subgroupindex
#130736522
#130715652
#130700022
#130697602
#130695722
#130693752
#130693322
#130692072
#130687432
C4×#668962
C11×#18022
#2602511