Finite Group Databasebeta

← #14798868

Subgroups — #14798868

Order 2816.

642 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
1#13077417C211yesmaximal, characteristic, complemented
2#13070069C212yesmaximal, complemented
3#13069919C212yesmaximal, complemented
4#13069515C211yesmaximal, characteristic, complemented
5#13069367C211yesmaximal, characteristic, complemented
6#13069119C212yesmaximal, complemented
7#13068741C211yesmaximal, characteristic, complemented
8#13068721C212yesmaximal, complemented
9#13068662C211yesmaximal, characteristic, complemented
10#13068458C211yesmaximal, characteristic, complemented
11C11×#3067C211yesmaximal, characteristic
12C11×#575C2212yes—
13C2×C11×#135C2211yescharacteristic
14C2×C11×#131C2211yescharacteristic
15#41×Dic11C2212yes—
16C11×#473—21no—
17C11×#472—21no—
18C11×#471—22no—
19C2×C11×#108C2211yescharacteristic
20C11×#413C2212yes—
21#10622853C2212yes—
22#10622853C2212yes—
23#10622849C2212yes—
24C2×#66901C2211yescharacteristic
25#10622846C2211yescharacteristic
26#10622846C2212yes—
27#10622797—21no—
28#10622777—22no—
29#10622765—21no—
30#10622732C2212yes—
31#10622719C2211yescharacteristic
32#10622719C2211yescharacteristic
33#10622714C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35#10622197C2212yes—
36#10622196C2211yescharacteristic
37#10622195C2212yes—
38#10622195C2212yes—
39#10622193C2212yes—
40#10622193C2211yescharacteristic
41C2×C11×#41C2312yes—
42C2×C11×#41C2311yescharacteristic
43C11×#137—22no—
44C11×#137—22no—
45C11×AGL(1,ℤ/8)—22no—
46C11×AGL(1,ℤ/8)—22no—
47C11×#135—21no—
48C11×#135—21no—
49C11×#135—21no—
50C11×#135—21no—
51C11×#135—42no—
52C2×C11×Q16D411yescharacteristic
53C2×C11×SD16D412yes—
54C2×C11×D8D411yescharacteristic
55C11×#131—21no—
56C11×#131—21no—
57C11×#131—21no—
58C11×#131—21no—
59C2×C11×M16—21no—
60C2×C11×M16C2312yes—
61C2×C11×M16C2311yescharacteristic
62C22×C8×C11—21no—
63C22×C8×C11C2311yescharacteristic
64Q8×Dic11—22no—
65D4×Dic11—22no—
66D4×Dic11—42no—
67#66979—22no—
68#66979C2312yes—
69#66979C2312yes—
70#66979C2311yescharacteristic
71C2×C4×Dic11—22no—
72C2×C4×Dic11C2311yescharacteristic
73C2×#4318C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C11×#108—21no—
76C11×#108—21no—
77C11×#101—22no—
78C11×#100—22no—
79#66901—22no—
80#66901—42no—
81#66899—22no—
82#66899—21no—
83#66898—42no—
84#66898—42no—
85#66896—22no—
86#66896—21no—
87#66882—21no—
88#66882—21no—
89#66881—21no—
90#66881—21no—
91#66879—21no—
92#66879—21no—
93#66879—21no—
94Dic11⋊C8—42no—
95C8×Dic11—21no—
96#24986—111nomaximal, Sylow
97C11×#41—21no—
98C11×#41—21no—
99C11×#41—21no—
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—21no—
105C2×Q8×C11C2×D412yes—
106C2×Q8×C11#4111yescharacteristic
107C2×D4×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11C2×D412yes—
110C2×D4×C11#4111yescharacteristic
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—21no—
115C22×Dic11—42no—
116C11×Q16—21no—
117C11×Q16—21no—
118C11×Q16—42no—
119C11×SD16—22no—
120C11×SD16—22no—
121C11×SD16—42no—
122C11×SD16—42no—
123C11×D8—21no—
124C11×D8—21no—
125C11×D8—42no—
126C11×M16—21no—
127C11×M16—22no—
128C11×M16—21no—
129C11×M16—22no—
130C11×M16—41no—
131C11×M16—41no—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11—41no—
135C2×C8×C11—41no—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11#4111yescharacteristic
139C2×C8×C11#4111yescharacteristic
140C2×C8×C11#4111yescharacteristic
141C2×C8×C11#4111yescharacteristic
142C22⋊Dic11—22no—
143C22⋊Dic11—21no—
144C22⋊Dic11—22no—
145C22⋊Dic11—42no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11—42no—
150C4×Dic11—21no—
151C4×Dic11—21no—
152C4×Dic11—22no—
153C4×Dic11—22no—
154C4×Dic11—42no—
155C4×Dic11#4112yes—
156#4318—21no—
157#4318—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162#3067D1111yescharacteristic
163#2943—111no—
164#2080—112no—
165#2053—112no—
166#1976—111no—
167#1946—111no—
168#1906—112no—
169#1833—111no—
170#1827—112no—
171#1812—111no—
172#1765—111no—
173C23×C11—22no—
174C23×C11—21no—
175C23×C11H(5,𝔽2)11yescharacteristic
176Q8×C11—22no—
177Q8×C11—21no—
178Q8×C11—21no—
179Q8×C11—22no—
180D4×C11—22no—
181D4×C11—21no—
182D4×C11—21no—
183D4×C11—22no—
184D4×C11—41no—
185D4×C11—42no—
186D4×C11—41no—
187D4×C11—42no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11H(5,𝔽2)11yescharacteristic
200C2×Dic11—22no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11—81no—
205C2×Dic11—84no—
206C8×C11—41no—
207C8×C11—42no—
208C8×C11#12311yescharacteristic
209C8×C11#12311yescharacteristic
210C8×C11#12311yescharacteristic
211C8×C11#12311yescharacteristic
212C11⋊C8—41no—
213C11⋊C8—41no—
214#575C2×D1112yes—
215C2×#135C2×D1111yescharacteristic
216C2×#131C2×D1111yescharacteristic
217C4×#41—112no—
218#473—21no—
219#472—21no—
220#471—22no—
221#442—221no—
222#441—221no—
223#440—222no—
224C2×#108C2×D1111yescharacteristic
225#427—111no—
226#427—111no—
227#424—112no—
228#421—112no—
229C2×#104—111no—
230#416—111no—
231#416—112no—
232#413C2×D1112yes—
233#410—112no—
234#410—112no—
235#405—111no—
236C2×#97—111no—
237#344—112no—
238#341—111no—
239#339—111no—
240#339—112no—
241H(3,ℤ/4)—112no—
242H(3,ℤ/4)—112no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—42no—
246C22×C11—81no—
247C22×C11—82no—
248C22×C11#54011yescharacteristic
249C22×C11#54611yescharacteristic
250C22×C11#55311yescharacteristic
251C4×C11—42no—
252C4×C11—41no—
253C4×C11C2×#12311yescharacteristic
254C4×C11#52911yescharacteristic
255C4×C11#54611yescharacteristic
256C4×C11#55511yescharacteristic
257Dic11—42no—
258Dic11—82no—
259Dic11—81no—
260Dic11—82no—
261C2×#41C22×D1111yescharacteristic
262C2×#41C22×D1112yes—
263#137—22no—
264#137—22no—
265AGL(1,ℤ/8)—22no—
266AGL(1,ℤ/8)—22no—
267#135—21no—
268#135—21no—
269#135—21no—
270#135—21no—
271#135—42no—
272C2×Q16C22⋊D1111yescharacteristic
273C2×SD16C22⋊D1112yes—
274C2×D8C22⋊D1111yescharacteristic
275#131—21no—
276#131—21no—
277#131—21no—
278#131—21no—
279C2×M16—21no—
280C2×M16—111no—
281C2×M16C22×D1111yescharacteristic
282C2×M16C22×D1112yes—
283C22×C8—21no—
284C22×C8—111no—
285C22×C8C22×D1111yescharacteristic
286C4×Q8—222no—
287C4×D4—222no—
288C4×D4—442no—
289#117—112no—
290#117—111no—
291#117—112no—
292#117—222no—
293C2×C42—111no—
294C2×C42—222no—
295#108—21no—
296#108—21no—
297#107—221no—
298#107—221no—
299#106—221no—
300#106—221no—
301C4⋊C8—442no—
302#104—222no—
303#104—442no—
304#103—221no—
305#103—222no—
306#102—221no—
307#102—222no—
308#101—22no—
309#100—22no—
310#99—442no—
311#99—442no—
312#97—221no—
313#97—221no—
314#97—221no—
315C4×C8—221no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11—21no—
319C2×C11—81no—
320C2×C11—82no—
321C2×C11#242011yescharacteristic
322#41—21no—
323#41—22no—
324#41—22no—
325#41—22no—
326#41—22no—
327#41—21no—
328#41—21no—
329#41—21no—
330C2×Q8#434111yescharacteristic
331C2×Q8C2×C22⋊D1112yes—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4#434111yescharacteristic
335C2×D4C2×C22⋊D1112yes—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—221no—
339C22×C4—442no—
340C22×C4C23×D1111yescharacteristic
341Q16—21no—
342Q16—21no—
343Q16—42no—
344SD16—22no—
345SD16—22no—
346SD16—42no—
347SD16—42no—
348D8—21no—
349D8—21no—
350D8—42no—
351M16—21no—
352M16—22no—
353M16—21no—
354M16—22no—
355M16—41no—
356M16—41no—
357M16—221no—
358M16—221no—
359C2×C8—21no—
360C2×C8—22no—
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—221no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8#434111yescharacteristic
368C2×C8#434111yescharacteristic
369C2×C8#434111yescharacteristic
370C2×C8#434111yescharacteristic
371C2×C8C2×C22⋊D1111yescharacteristic
372C2×C8C2×C22⋊D1111yescharacteristic
373C4⋊C4—221no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4—442no—
377C22⋊C4—221no—
378C22⋊C4—222no—
379C22⋊C4—222no—
380C22⋊C4—442no—
381C42—112no—
382C42—221no—
383C42—221no—
384C42—222no—
385C42—222no—
386C42—442no—
387C11#2498611yescharacteristic, complemented, Sylow
388C23—22no—
389C23—21no—
390C23#6704211yescharacteristic
391Q8—22no—
392Q8—21no—
393Q8—22no—
394Q8—21no—
395D4—22no—
396D4—21no—
397D4—22no—
398D4—21no—
399D4—41no—
400D4—42no—
401D4—41no—
402D4—42no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—222no—
410C2×C4—442no—
411C2×C4—441no—
412C2×C4—442no—
413C2×C4—881no—
414C2×C4—884no—
415C2×C4C2×#434111yescharacteristic
416C2×C4C2×#434111yescharacteristic
417C2×C4C2×#434111yescharacteristic
418C2×C4#6703711yescharacteristic
419C2×C4#41×D1111yescharacteristic
420C2×C4C22×C22⋊D1111yescharacteristic
421C8—41no—
422C8—42no—
423C8—441no—
424C8—441no—
425C8#6698811yescharacteristic
426C8#6698811yescharacteristic
427C8#6698811yescharacteristic
428C8#6698811yescharacteristic
429C22—41no—
430C22—41no—
431C22—42no—
432C22—82no—
433C22—81no—
434C22#1062314911yescharacteristic
435C22#1062315011yescharacteristic
436C22#1062336011yescharacteristic
437C4—42no—
438C4—41no—
439C4—442no—
440C4—882no—
441C4—882no—
442C4—881no—
443C4#1062313111yescharacteristic
444C4#1062314711yescharacteristic
445C4C2×#6698811yescharacteristic
446C4#1062333711yescharacteristic
447C2—21no—
448C2—21no—
449C2—21no—
450C2—82no—
451C2—81no—
452C2#1307210411yescharacteristic
subgroupG/H
centerC4#10623147
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3067C2
socleC2×C11#2420
hypercenter#3067D11
hypocenterC11#24986
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. #13077417C2semidirect
2. #13070069C2semidirect
3. #13069919C2semidirect
4. #13069515C2semidirect
5. #13069367C2semidirect
6. #13069119C2semidirect
7. #13068741C2semidirect
8. #13068721C2semidirect
9. #13068662C2semidirect
10. #13068458C2semidirect
387. C11#24986semidirect

Maximal subgroups

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

subgroupindex
#130774172
#130700692
#130699192
#130695152
#130693672
#130691192
#130687412
#130687212
#130686622
#130684582
C11×#30672
#2498611