Finite Group Databasebeta

← #14811857

Subgroups — #14811857

Order 2816.

786 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073645C211yesmaximal, characteristic, complemented
2#13071565C211yesmaximal, characteristic
3#13070002C212yesmaximal
4#13069750C212yesmaximal
5#13069566C212yesmaximal, complemented
6#13069375C211yesmaximal, characteristic, complemented
7#13069332C211yesmaximal, characteristic, complemented
8#13069186C212yesmaximal, complemented
9#13068743C211yesmaximal, characteristic, complemented
10C4×#66896C211yesmaximal, characteristic
11C11×#1802C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66979—21no—
14C2×#66941—21no—
15C2×#66941C2212yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#102C2212yes—
18C11×#384C2211yescharacteristic
19#10622834C2212yes—
20C2×#66896C2211yescharacteristic
21C2×#66896C2211yescharacteristic
22#10622825—21no—
23C2×#66882C2212yes—
24C2×Dic11⋊C8C2212yes—
25#10622592—22no—
26C4⋊C4×Dic11C2212yes—
27#10622586—21no—
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×Dic22—22no—
44C22×C8×C11C2312yes—
45C4×D4×C11—22no—
46C4×D4×C11Q814yescomplemented
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55#66979—44no—
56C2×C4⋊Dic11—21no—
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#66941—24no—
71#66941—42no—
72#66941—44no—
73C11×C4⋊C8—22no—
74C11×#102—42no—
75#66896—22no—
76#66896—22no—
77C11⋊#95—21no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95D412yes—
81#66882—24no—
82Dic11⋊C8—42no—
83C4×C11⋊C8—22no—
84#26020—111nomaximal, Sylow
85C24×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11C2×Q812yes—
92C22×C4×C11—21no—
93C22×C4×C11—24no—
94C22×C4×C11—22no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—22no—
103C22×Dic11C2×D412yes—
104C22×Dic11C2×D412yes—
105C2×Dic22—44no—
106C2×Dic22—44no—
107C2×Dic22—82no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4—81no—
116C11×C4⋊C4C2×Q812yes—
117C11×C22⋊C4—24no—
118C42×C11C2×Q812yes—
119C42×C11#4112yes—
120C22⋊Dic11—44no—
121C22⋊Dic11—82no—
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—42no—
128C4⋊Dic11—81no—
129C4⋊Dic11D814yes—
130C4⋊Dic11#4112yes—
131C4⋊Dic11#4112yes—
132Dic11⋊C4—44no—
133Dic11⋊C4—44no—
134C4×Dic11—22no—
135C4×Dic11—22no—
136C4×Dic11—44no—
137C4×Dic11—42no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144#2551—111no—
145#2354—111no—
146#2067—112no—
147#2023—112no—
148#1988—112no—
149#1947—111no—
150#1939—111no—
151#1918—112no—
152#1834—111no—
153#1802D1111yescharacteristic
154C4×#102—111no—
155C23×C11—22no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11C22×D411yescharacteristic
163D4×C11—22no—
164D4×C11—22no—
165D4×C11—41no—
166D4×C11—41no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—48no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11C22⋊Q812yes—
177C2×C4×C11C22⋊Q812yes—
178C2×C4×C11C2×D812yes—
179C2×C4×C11#13712yes—
180C2×C4×C11C22×Q811yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×C4×C11H(5,𝔽2)11yescharacteristic
185C2×C4×C112−1+411yescharacteristic
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11C2×D814yes—
201Dic22—88no—
202C8×C11—42no—
203C11⋊C8—41no—
204C11⋊C8—41no—
205C2×C4⋊Q8—112no—
206C2×C4⋊Q8—221no—
207C2×C4×D4C2×D1111yescharacteristic
208C2×#117—221no—
209C2×#107—112no—
210C2×C4⋊C8—112no—
211C2×C4⋊C8C2×D1111yescharacteristic
212C2×#102—111no—
213C2×#102—111no—
214C2×#102C2×D1112yes—
215C2×C4×C8—111no—
216#395—222no—
217#390—112no—
218#389—112no—
219#389—221no—
220#388—222no—
221#384—111no—
222#384C2×D1111yescharacteristic
223#380—221no—
224C4×C4⋊C4—111no—
225C4×C4⋊C4—112no—
226C4×C4⋊C4—111no—
227#340—112no—
228#340—112no—
229#340—112no—
230#340—111no—
231#340—111no—
232#340C2×D1112yes—
233#336—112no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11C2×C22⋊Q811yescharacteristic
242C22×C11#54611yescharacteristic
243C22×C11#54811yescharacteristic
244C22×C11C22×D811yescharacteristic
245C22×C11C2×#13711yescharacteristic
246C22×C11#57711yescharacteristic
247C22×C11#57711yescharacteristic
248C4×C11—22no—
249C4×C11—42no—
250C4×C11—82no—
251C4×C11#47414yes—
252C4×C11#53311yescharacteristic
253C4×C11#54411yescharacteristic
254C4×C11#55511yescharacteristic
255C4×C11#55611yescharacteristic
256Dic11—24no—
257Dic11—42no—
258Dic11—42no—
259Dic11—42no—
260Dic11—82no—
261C22×Q8—222no—
262C22×D4C22×D1111yescharacteristic
263C23×C4—21no—
264C22×C8—111no—
265C22×C8—111no—
266C22×C8C22×D1112yes—
267C4⋊Q8—224no—
268C4⋊Q8—442no—
269C4⋊Q8—444no—
270C4×D4—22no—
271C4×D4Dic2214yescomplemented
272#117—444no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4—111no—
279C2×C4⋊C4—112no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4C22×D1112yes—
285C2×C4⋊C4C22×D1111yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—222no—
288C2×C22⋊C4—222no—
289C2×C42—112no—
290C2×C42—222no—
291C2×C42—221no—
292C2×C42C22×D1111yescharacteristic
293#107—224no—
294C4⋊C8—22no—
295C4⋊C8—442no—
296#102—42no—
297#102—222no—
298#102—222no—
299C4×C8—222no—
300#95—112no—
301#95—222no—
302#95—222no—
303#95—221no—
304C2×C11—82no—
305C2×C11#243911yescharacteristic
306C2×C11C2×#47411yescharacteristic
307C2×C11#308411yescharacteristic
308C2×C11#329411yescharacteristic
309C2×C11#332911yescharacteristic
310C2×C11#335811yescharacteristic
311C2×C11#336911yescharacteristic
312C24—21no—
313C2×Q8—444no—
314C2×Q8—444no—
315C2×Q8—882no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4C2×Dic2212yes—
322C22×C4—21no—
323C22×C4—24no—
324C22×C4—22no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—112no—
328C22×C4—112no—
329C22×C4—221no—
330C22×C4—221no—
331C22×C4—222no—
332C22×C4D4×D1111yescharacteristic
333C22×C4D4×D1111yescharacteristic
334C22×C4C23×D1111yescharacteristic
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—221no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8—221no—
343C2×C8—221no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—42no—
348C4⋊C4—81no—
349C4⋊C4—114no—
350C4⋊C4—112no—
351C4⋊C4—112no—
352C4⋊C4—222no—
353C4⋊C4—221no—
354C4⋊C4—221no—
355C4⋊C4—222no—
356C4⋊C4—222no—
357C4⋊C4—444no—
358C4⋊C4—444no—
359C4⋊C4—442no—
360C4⋊C4—881no—
361C4⋊C4C2×Dic2212yes—
362C22⋊C4—24no—
363C22⋊C4—444no—
364C22⋊C4—882no—
365C42—222no—
366C42—222no—
367C42—444no—
368C42—442no—
369C42C2×Dic2212yes—
370C42#434112yes—
371C11#2602011yescharacteristic, complemented, Sylow
372C23—22no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23C2×D4×D1111yescharacteristic
380Q8—888no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—48no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—114no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—222no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4#6693112yes—
410C2×C4#6693112yes—
411C2×C4D8×D1112yes—
412C2×C4#6696812yes—
413C2×C4C22×Dic2211yescharacteristic
414C2×C4C2×#434111yescharacteristic
415C2×C4#6703711yescharacteristic
416C2×C4#6704011yescharacteristic
417C2×C4#41×D1111yescharacteristic
418C2×C4#41×D1111yescharacteristic
419C8—42no—
420C8—441no—
421C8—441no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22C2×#6693111yescharacteristic
430C22#1062314311yescharacteristic
431C22#1062316411yescharacteristic
432C22C2×D8×D1111yescharacteristic
433C22C2×#6696811yescharacteristic
434C22#1062330611yescharacteristic
435C22#1062330911yescharacteristic
436C4—22no—
437C4—42no—
438C4—82no—
439C4—224no—
440C4—442no—
441C4—442no—
442C4—442no—
443C4—882no—
444C4#1062237214yes—
445C4#1062303111yescharacteristic
446C4#1062304811yescharacteristic
447C4#1062314711yescharacteristic
448C4#1062317211yescharacteristic
449C2—82no—
450C2#1307230811yescharacteristic
451C2C2×#1062237211yescharacteristic
452C2#1307848211yescharacteristic
453C2#1308043211yescharacteristic
454C2#1308091311yescharacteristic
455C2#1308125011yescharacteristic
456C2#1308135511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1802D11
hypocenterC11#26020
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. #13073645C2semidirect
5. #13069566C2semidirect
6. #13069375C2semidirect
7. #13069332C2semidirect
8. #13069186C2semidirect
9. #13068743C2semidirect
46. C4×D4×C11Q8semidirect
271. C4×D4Dic22semidirect
371. C11#26020semidirect

Maximal subgroups

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

subgroupindex
#130736452
#130715652
#130700022
#130697502
#130695662
#130693752
#130693322
#130691862
#130687432
C4×#668962
C11×#18022
#2602011