Finite Group Databasebeta

← #14798892

Subgroups — #14798892

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622773C211yesmaximal, characteristic
2#13070077C212yesmaximal, complemented
3#13069887C212yesmaximal, complemented
4#13069527C211yesmaximal, characteristic, complemented
5#13069406C211yesmaximal, characteristic, complemented
6#13069103C212yesmaximal, complemented
7#13068739C211yesmaximal, characteristic, complemented
8#13068727C212yesmaximal, complemented
9#13068667C211yesmaximal, characteristic, complemented
10#13068417C211yesmaximal, characteristic, complemented
11C11×#2948C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C11×#518C2212yes—
14C2×#66985C2212yes—
15C2×#66954C2211yescharacteristic
16C11×#442—22no—
17C4×C11×D8—22no—
18C11×#427C2211yescharacteristic
19C11×#418C2212yes—
20C11×#405C2211yescharacteristic
21C2×#66897C2212yes—
22C2×#66897C2212yes—
23#10622828C2212yes—
24#10622773—22no—
25#10622773—22no—
26#10622745C2211yescharacteristic
27#10622737C2212yes—
28C2×#66883C2211yescharacteristic
29C2×#66883C2211yescharacteristic
30#10622714C2211yescharacteristic
31#10622619C2211yescharacteristic
32#10622618C2212yes—
33#10622197C2211yescharacteristic
34#10622171C2212yes—
35#10622171C2212yes—
36#10622171C2212yes—
37#10622171C2211yescharacteristic
38#10622169C2212yes—
39C22×D4×C11C2312yes—
40C2×#4339C2311yescharacteristic
41C2×C11×D8—21no—
42C2×C11×D8—21no—
43C2×C11×D8—21no—
44C2×C11×D8—21no—
45C2×C11×D8D412yes—
46C2×C11×D8D412yes—
47C2×C11×M16C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C4×D4×C11—24no—
50C4×D4×C11—42no—
51C11×#117C2312yes—
52C11×#117C2311yescharacteristic
53C2×C11×C22⋊C4—24no—
54C2×#4324—22no—
55#66985—24no—
56#66985—42no—
57C2×#4323—22no—
58#66979C2311yescharacteristic
59C2×#4318C2312yes—
60C2×#4318C2312yes—
61C2×#4318C2311yescharacteristic
62C2×#4318C2311yescharacteristic
63#66954—21no—
64#66954—21no—
65#66954—21no—
66#66954—21no—
67C2×#4313—21no—
68C2×C8×D11—21no—
69C11×#107—21no—
70C11×#106—21no—
71C11×#102—24no—
72C11×#97—21no—
73C4×C8×C11—21no—
74#66897—24no—
75#66897—42no—
76#66896—42no—
77#66888—21no—
78#66887—21no—
79#66886—42no—
80#66883—21no—
81#66883—21no—
82#66883—21no—
83#66883—21no—
84#66879—21no—
85C8×Dic11—21no—
86#66870—22no—
87#66869—42no—
88#24988—111nomaximal, Sylow
89C24×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11C2×D414yes—
96C22×C4×C11—44no—
97C22×C4×C11C2411yescharacteristic
98C2×C22⋊D11—21no—
99#4339—21no—
100#4339—21no—
101#4339—21no—
102#4339—21no—
103C2×D44#4111yescharacteristic
104C2×C4×D11—21no—
105C2×Dic22#4111yescharacteristic
106C11×D8—22no—
107C11×D8—22no—
108C11×D8—22no—
109C11×D8—22no—
110C11×M16—21no—
111C11×M16—21no—
112C2×C8×C11—21no—
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11#4111yescharacteristic
116C2×C8×C11#4111yescharacteristic
117C2×C8×C11#4111yescharacteristic
118C2×C8×C11#4111yescharacteristic
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C22⋊C4—22no—
122C11×C22⋊C4—44no—
123C11×C22⋊C4#4112yes—
124C42×C11—21no—
125C42×C11—22no—
126C22⋊Dic11—21no—
127#4324—44no—
128#4323—44no—
129C4⋊Dic11—21no—
130C4×Dic11—21no—
131#4318—22no—
132#4318—21no—
133#4318—22no—
134#4318—21no—
135#4318—21no—
136#4318—22no—
137#4318—22no—
138#4318—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143#4313—41no—
144#4313—41no—
145C8×D11—41no—
146C8×D11—41no—
147C2×#472—111no—
148#2948D1111yescharacteristic, complemented
149#2081—112no—
150#2048—112no—
151#1978—111no—
152#1953—111no—
153#1904—112no—
154#1833—111no—
155#1829—112no—
156#1814—111no—
157#1757—111no—
158C23×C11—24no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—162no—
162C23×C11C2×#4111yescharacteristic
163C22×D11—21no—
164D4×C11—24no—
165D4×C11—24no—
166D4×C11—42no—
167D4×C11—42no—
168C2×C4×C11—22no—
169C2×C4×C11—42no—
170C2×C4×C11—164no—
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C2×#4111yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C2×C4×C11H(5,𝔽2)11yescharacteristic
176C2×C4×C11H(5,𝔽2)11yescharacteristic
177C22⋊D11—41no—
178C22⋊D11—41no—
179C2×Dic11—21no—
180C2×Dic11—41no—
181D44—21no—
182D44—21no—
183C4×D11—41no—
184C4×D11—41no—
185Dic22—21no—
186Dic22—21no—
187C8×C11—41no—
188C8×C11#12311yescharacteristic
189C8×C11#12311yescharacteristic
190C8×C11#12311yescharacteristic
191C8×C11#12311yescharacteristic
192C11⋊C8—41no—
193C11⋊C8—42no—
194C11⋊C8—42no—
195C11⋊C8—41no—
196C2×AGL(1,ℤ/8)—112no—
197C22×D8C2×D1111yescharacteristic
198C2×#131—111no—
199#518C2×D1112yes—
200#472—222no—
201#472—222no—
202#442—22no—
203C4×D8—22no—
204#430—112no—
205C2×#108—111no—
206C2×#108—111no—
207#427C2×D1111yescharacteristic
208#421—112no—
209#418—112no—
210#418C2×D1112yes—
211#413—111no—
212C2×#100—112no—
213C2×#100—112no—
214#410—111no—
215#405—111no—
216#405C2×D1111yescharacteristic
217#344—111no—
218#344—112no—
219#344—112no—
220#344—111no—
221#344—112no—
222H(3,ℤ/4)—112no—
223C22×C11—41no—
224C22×C11—44no—
225C22×C11—84no—
226C22×C11—162no—
227C22×C11—162no—
228C22×C11#52911yescharacteristic
229C22×C11#54611yescharacteristic
230C22×C11#55511yescharacteristic
231C2×D11—41no—
232C2×D11—81no—
233C4×C11—42no—
234C4×C11—82no—
235C4×C11C2×#12311yescharacteristic
236C4×C11#54011yescharacteristic
237C4×C11#54611yescharacteristic
238C4×C11#55311yescharacteristic
239Dic11—41no—
240Dic11—81no—
241C2×#41—111no—
242C22×D4C22×D1112yes—
243AGL(1,ℤ/8)—224no—
244AGL(1,ℤ/8)—442no—
245C2×SD16—222no—
246C2×D8—21no—
247C2×D8—21no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—222no—
251C2×D8C22⋊D1112yes—
252C2×D8C22⋊D1112yes—
253#131—221no—
254#131—221no—
255#131—221no—
256#131—221no—
257C2×M16—111no—
258C2×M16—112no—
259C2×M16—111no—
260C2×M16—112no—
261C2×M16—221no—
262C2×M16C22×D1111yescharacteristic
263C22×C8—221no—
264C22×C8C22×D1111yescharacteristic
265C4×D4—24no—
266C4×D4—42no—
267#117—111no—
268#117C22×D1112yes—
269#117C22×D1111yescharacteristic
270C2×C22⋊C4—24no—
271#108—221no—
272#108—221no—
273#108—221no—
274#108—221no—
275#108—442no—
276#107—21no—
277#106—21no—
278#104—442no—
279#102—24no—
280#102—442no—
281#101—221no—
282#100—221no—
283#100—224no—
284#100—442no—
285#99—222no—
286#97—21no—
287#97—221no—
288C4×C8—21no—
289C4×C8—221no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—21no—
293C2×C11—84no—
294C2×C11#242011yescharacteristic
295D11—81no—
296C24—22no—
297#41—221no—
298#41—221no—
299#41—221no—
300#41—221no—
301C2×Q8—111no—
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—111no—
308C2×D4—221no—
309C2×D4C2×C22⋊D1114yes—
310C22×C4—44no—
311C22×C4—221no—
312C22×C4C23×D1111yescharacteristic
313SD16—444no—
314D8—22no—
315D8—22no—
316D8—22no—
317D8—22no—
318D8—444no—
319M16—21no—
320M16—21no—
321M16—222no—
322M16—221no—
323M16—221no—
324M16—222no—
325M16—221no—
326M16—222no—
327M16—221no—
328M16—222no—
329M16—441no—
330M16—441no—
331C2×C8—21no—
332C2×C8—221no—
333C2×C8—221no—
334C2×C8—222no—
335C2×C8—222no—
336C2×C8—441no—
337C2×C8—441no—
338C2×C8#433911yescharacteristic
339C2×C8#433911yescharacteristic
340C2×C8#433911yescharacteristic
341C2×C8#433911yescharacteristic
342C2×C8C2×C22⋊D1111yescharacteristic
343C2×C8C2×C22⋊D1111yescharacteristic
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—221no—
347C22⋊C4—22no—
348C22⋊C4—44no—
349C22⋊C4—221no—
350C22⋊C4#434112yes—
351C42—21no—
352C42—22no—
353C42—221no—
354C11#2498811yescharacteristic, complemented, Sylow
355C23—24no—
356C23—42no—
357C23—42no—
358C23—162no—
359C23—221no—
360C23C2×#434111yescharacteristic
361Q8—221no—
362Q8—221no—
363D4—24no—
364D4—24no—
365D4—42no—
366D4—42no—
367D4—221no—
368D4—221no—
369D4—441no—
370D4—441no—
371C2×C4—22no—
372C2×C4—42no—
373C2×C4—164no—
374C2×C4—221no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4C2×#433911yescharacteristic
379C2×C4C2×#433911yescharacteristic
380C2×C4#6703711yescharacteristic
381C2×C4#41×D1111yescharacteristic
382C2×C4#6704211yescharacteristic
383C2×C4C22×C22⋊D1111yescharacteristic
384C8—41no—
385C8—441no—
386C8—441no—
387C8—442no—
388C8—442no—
389C8#6698211yescharacteristic
390C8#6698211yescharacteristic
391C8#6698211yescharacteristic
392C8#6698211yescharacteristic
393C22—41no—
394C22—44no—
395C22—84no—
396C22—162no—
397C22—162no—
398C22—441no—
399C22—881no—
400C22#1062308811yescharacteristic
401C22#1062309411yescharacteristic
402C22#1062333711yescharacteristic
403C4—42no—
404C4—82no—
405C4—441no—
406C4—881no—
407C4#1062308911yescharacteristic
408C4#1062309311yescharacteristic
409C4C2×#6698211yescharacteristic
410C4#1062336011yescharacteristic
411C2—21no—
412C2—21no—
413C2—21no—
414C2—84no—
415C2—881no—
416C2#1307210211yescharacteristic
subgroupG/H
centerC2#13072102
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2948C2
socleC2×C11#2420
prime radicalC2×#10622773C2
hypercenter#2948D11
hypocenterC11#24988
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2948

Complements

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

NH ≅ G/Ntype
2. #13070077C2semidirect
3. #13069887C2semidirect
4. #13069527C2semidirect
5. #13069406C2semidirect
6. #13069103C2semidirect
7. #13068739C2semidirect
8. #13068727C2semidirect
9. #13068667C2semidirect
10. #13068417C2semidirect
11. C11×#2948C2semidirect
148. #2948D11semidirect
354. C11#24988semidirect

Maximal subgroups

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

subgroupindex
C2×#106227732
#130700772
#130698872
#130695272
#130694062
#130691032
#130687392
#130687272
#130686672
#130684172
C11×#29482
#2498811