Finite Group Databasebeta

← #14798894

Subgroups — #14798894

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
1#13077468C211yesmaximal, characteristic, complemented
2#13070076C212yesmaximal, complemented
3#13069886C212yesmaximal, complemented
4#13069527C211yesmaximal, characteristic, complemented
5#13069404C211yesmaximal, characteristic, complemented
6#13069105C212yesmaximal, complemented
7#13068741C211yesmaximal, characteristic, complemented
8#13068725C212yesmaximal, complemented
9#13068670C211yesmaximal, characteristic, complemented
10#13068416C211yesmaximal, characteristic, complemented
11C2×C11×#472C211yesmaximal, characteristic
12C2×C11×AGL(1,ℤ/8)C2212yes—
13C22×C11×D8C2211yescharacteristic
14C2×C11×#131C2211yescharacteristic
15#10623329C2212yes—
16C11×#472—22no—
17C11×#472—22no—
18C2×C11×#108C2211yescharacteristic
19C2×C11×#100C2212yes—
20#10622853C2211yescharacteristic
21#10622850C2211yescharacteristic
22#10622849C2212yes—
23C2×#66897C2212yes—
24#10622828C2212yes—
25#10622828C2212yes—
26#10622765—22no—
27D8×Dic11—22no—
28#10622737C2212yes—
29C2×#66883C2211yescharacteristic
30#10622719C2211yescharacteristic
31#10622714C2211yescharacteristic
32#10622714C2211yescharacteristic
33#10622197C2212yes—
34#10622197C2212yes—
35#10622195C2212yes—
36#10622194C2212yes—
37#10622194C2211yescharacteristic
38#10622194C2211yescharacteristic
39C2×C11×#41C2311yescharacteristic
40C22×D4×C11C2312yes—
41C11×AGL(1,ℤ/8)—24no—
42C11×AGL(1,ℤ/8)—42no—
43C2×C11×SD16—22no—
44C2×C11×D8—22no—
45C2×C11×D8—21no—
46C2×C11×D8—21no—
47C2×C11×D8—21no—
48C2×C11×D8—21no—
49C2×C11×D8D412yes—
50C2×C11×D8D412yes—
51C11×#131—21no—
52C11×#131—21no—
53C11×#131—21no—
54C11×#131—21no—
55C2×C11×M16—21no—
56C2×C11×M16C2312yes—
57C2×C11×M16C2311yescharacteristic
58C22×C8×C11—21no—
59C22×C8×C11C2311yescharacteristic
60C2×C22⋊Dic11—24no—
61D4×Dic11—24no—
62D4×Dic11—42no—
63#66979C2312yes—
64#66979C2311yescharacteristic
65#66979C2311yescharacteristic
66C2×#4318C2312yes—
67C2×#4318C2311yescharacteristic
68C2×#4318C2311yescharacteristic
69C11×#108—21no—
70C11×#108—21no—
71C11×#100—24no—
72#66901—42no—
73#66900—21no—
74#66898—22no—
75#66897—21no—
76#66897—42no—
77#66896—24no—
78#66896—42no—
79#66886—42no—
80#66883—21no—
81#66883—21no—
82#66882—21no—
83#66881—21no—
84#66879—21no—
85#66879—21no—
86C8×Dic11—21no—
87C8×Dic11—21no—
88#24988—111nomaximal, Sylow
89C24×C11—22no—
90C11×#41—21no—
91C11×#41—21no—
92C11×#41—21no—
93C11×#41—21no—
94C2×Q8×C11#4111yescharacteristic
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11C2×D414yes—
102C2×D4×C11#4111yescharacteristic
103C22×C4×C11—21no—
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—44no—
106C11×SD16—44no—
107C11×D8—22no—
108C11×D8—22no—
109C11×D8—22no—
110C11×D8—22no—
111C11×D8—44no—
112C11×M16—21no—
113C11×M16—22no—
114C11×M16—21no—
115C11×M16—22no—
116C11×M16—41no—
117C11×M16—41no—
118C2×C8×C11—21no—
119C2×C8×C11—22no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11#4111yescharacteristic
125C2×C8×C11#4111yescharacteristic
126C2×C8×C11#4111yescharacteristic
127C2×C8×C11#4111yescharacteristic
128C22⋊Dic11—21no—
129C22⋊Dic11—22no—
130C22⋊Dic11—44no—
131C22⋊Dic11#4112yes—
132C4⋊Dic11—22no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135C4×Dic11—21no—
136C4×Dic11—21no—
137C4×Dic11—22no—
138#4318—22no—
139#4318—21no—
140#4318—21no—
141#4318—21no—
142#4318—21no—
143#4318—22no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—22no—
147C2×#472D1111yescharacteristic
148#2948—111no—
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—21no—
159C23×C11—24no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—162no—
163C23×C11C2×#4111yescharacteristic
164Q8×C11—21no—
165Q8×C11—21no—
166D4×C11—24no—
167D4×C11—21no—
168D4×C11—24no—
169D4×C11—21no—
170D4×C11—41no—
171D4×C11—41no—
172D4×C11—42no—
173D4×C11—42no—
174C2×C4×C11—21no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C2×C4×C11C2×#4111yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11H(5,𝔽2)11yescharacteristic
182C2×C4×C11H(5,𝔽2)11yescharacteristic
183C2×Dic11—22no—
184C2×Dic11—42no—
185C2×Dic11—41no—
186C2×Dic11—164no—
187C8×C11—41no—
188C8×C11—42no—
189C8×C11#12311yescharacteristic
190C8×C11#12311yescharacteristic
191C8×C11#12311yescharacteristic
192C8×C11#12311yescharacteristic
193C11⋊C8—42no—
194C11⋊C8—41no—
195C11⋊C8—41no—
196C2×AGL(1,ℤ/8)C2×D1112yes—
197C22×D8C2×D1111yescharacteristic
198C2×#131C2×D1111yescharacteristic
199#518—112no—
200#472—22no—
201#472—22no—
202#442—222no—
203C4×D8—222no—
204#430—112no—
205C2×#108—111no—
206C2×#108C2×D1111yescharacteristic
207#427—111no—
208#421—112no—
209#418—112no—
210#418—112no—
211#413—111no—
212C2×#100—112no—
213C2×#100C2×D1112yes—
214#410—111no—
215#405—111no—
216#405—111no—
217#344—112no—
218#344—112no—
219#344—111no—
220#344—111no—
221#344—112no—
222H(3,ℤ/4)—112no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—44no—
226C22×C11—81no—
227C22×C11—84no—
228C22×C11—162no—
229C22×C11—162no—
230C22×C11#52911yescharacteristic
231C22×C11#54611yescharacteristic
232C22×C11#55511yescharacteristic
233C4×C11—41no—
234C4×C11C2×#12311yescharacteristic
235C4×C11#54011yescharacteristic
236C4×C11#54611yescharacteristic
237C4×C11#55311yescharacteristic
238Dic11—42no—
239Dic11—81no—
240Dic11—82no—
241C2×#41C22×D1111yescharacteristic
242C22×D4C22×D1112yes—
243AGL(1,ℤ/8)—24no—
244AGL(1,ℤ/8)—42no—
245C2×SD16—22no—
246C2×D8—22no—
247C2×D8—21no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—21no—
251C2×D8C22⋊D1112yes—
252C2×D8C22⋊D1112yes—
253#131—21no—
254#131—21no—
255#131—21no—
256#131—21no—
257C2×M16—21no—
258C2×M16—111no—
259C2×M16—112no—
260C2×M16—111no—
261C2×M16C22×D1111yescharacteristic
262C2×M16C22×D1112yes—
263C22×C8—21no—
264C22×C8C22×D1111yescharacteristic
265C4×D4—224no—
266C4×D4—442no—
267#117—111no—
268#117—112no—
269#117—111no—
270C2×C22⋊C4—224no—
271#108—21no—
272#108—21no—
273#108—221no—
274#108—221no—
275#108—442no—
276#107—221no—
277#106—221no—
278#104—442no—
279#102—224no—
280#102—442no—
281#101—221no—
282#100—24no—
283#100—221no—
284#100—442no—
285#99—222no—
286#97—221no—
287#97—221no—
288C4×C8—221no—
289C4×C8—221no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—21no—
293C2×C11—81no—
294C2×C11—84no—
295C2×C11#242011yescharacteristic
296C24—22no—
297#41—21no—
298#41—21no—
299#41—21no—
300#41—21no—
301C2×Q8#434111yescharacteristic
302C2×D4—21no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4#434111yescharacteristic
309C2×D4C2×C22⋊D1114yes—
310C22×C4—21no—
311C22×C4—444no—
312C22×C4C23×D1111yescharacteristic
313SD16—44no—
314D8—22no—
315D8—22no—
316D8—22no—
317D8—22no—
318D8—44no—
319M16—21no—
320M16—22no—
321M16—21no—
322M16—22no—
323M16—41no—
324M16—41no—
325M16—221no—
326M16—221no—
327M16—222no—
328M16—221no—
329M16—221no—
330M16—222no—
331C2×C8—21no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—221no—
336C2×C8—222no—
337C2×C8—221no—
338C2×C8#434111yescharacteristic
339C2×C8#434111yescharacteristic
340C2×C8#434111yescharacteristic
341C2×C8#434111yescharacteristic
342C2×C8C2×C22⋊D1111yescharacteristic
343C2×C8C2×C22⋊D1111yescharacteristic
344C4⋊C4—221no—
345C4⋊C4—221no—
346C4⋊C4—222no—
347C22⋊C4—112no—
348C22⋊C4—221no—
349C22⋊C4—222no—
350C22⋊C4—444no—
351C42—221no—
352C42—221no—
353C42—222no—
354C11#2498811yescharacteristic, complemented, Sylow
355C23—24no—
356C23—21no—
357C23—42no—
358C23—42no—
359C23—162no—
360C23#41×D1111yescharacteristic
361Q8—21no—
362Q8—21no—
363D4—24no—
364D4—21no—
365D4—24no—
366D4—21no—
367D4—41no—
368D4—41no—
369D4—42no—
370D4—42no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—222no—
375C2×C4—442no—
376C2×C4—441no—
377C2×C4—1764no—
378C2×C4C2×#434111yescharacteristic
379C2×C4C2×#434111yescharacteristic
380C2×C4C2×#434111yescharacteristic
381C2×C4#6703711yescharacteristic
382C2×C4#6704211yescharacteristic
383C2×C4C22×C22⋊D1111yescharacteristic
384C8—41no—
385C8—42no—
386C8—441no—
387C8—441no—
388C8—442no—
389C8#6698811yescharacteristic
390C8#6698811yescharacteristic
391C8#6698811yescharacteristic
392C8#6698811yescharacteristic
393C22—41no—
394C22—41no—
395C22—44no—
396C22—84no—
397C22—81no—
398C22—162no—
399C22—162no—
400C22#1062313111yescharacteristic
401C22#1062314711yescharacteristic
402C22#1062336011yescharacteristic
403C4—41no—
404C4—442no—
405C4—882no—
406C4—881no—
407C4#1062314911yescharacteristic
408C4#1062315011yescharacteristic
409C4C2×#6698811yescharacteristic
410C4#1062333711yescharacteristic
411C2—21no—
412C2—21no—
413C2—21no—
414C2—84no—
415C2—81no—
416C2#1307210411yescharacteristic
subgroupG/H
centerC2#13072104
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#472C2
socleC2×C11#2420
hypercenterC2×#472D11
hypocenterC11#24988
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. #13077468C2semidirect
2. #13070076C2semidirect
3. #13069886C2semidirect
4. #13069527C2semidirect
5. #13069404C2semidirect
6. #13069105C2semidirect
7. #13068741C2semidirect
8. #13068725C2semidirect
9. #13068670C2semidirect
10. #13068416C2semidirect
354. C11#24988semidirect

Maximal subgroups

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

subgroupindex
#130774682
#130700762
#130698862
#130695272
#130694042
#130691052
#130687412
#130687252
#130686702
#130684162
C2×C11×#4722
#2498811