Finite Group Databasebeta

← #14909531

Subgroups — #14909531

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078195C211yesmaximal, characteristic
2C2×#10622500C211yesmaximal, characteristic, complemented
3#13070826C212yesmaximal, complemented
4#13070813C211yesmaximal, characteristic, complemented
5#13070711C212yesmaximal, complemented
6#13070708C212yesmaximal, complemented
7#13070557C212yesmaximal, complemented
8#13070552C211yesmaximal, characteristic, complemented
9#13070532C211yesmaximal, characteristic, complemented
10D11×C22⋊C16C211yesmaximal, characteristic, complemented
11C11×#2232C211yesmaximal, characteristic, complemented
12C2×#66965C2211yescharacteristic
13C22×Dic44C2211yescharacteristic
14C22×C8×D11C2211yescharacteristic
15#10623137—21no—
16C2×#66950—21no—
17C11×#466C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622770C2211yescharacteristic
20C2×#66891C2212yescomplemented
21#10622729C2211yescharacteristic
22#10622654—21no—
23C2×#66874—21no—
24C2×Dic88C2212yescomplemented
25C2×C16×D11C2212yes—
26#10622500—21no—
27#10622500—21no—
28#10622500C2211yescharacteristic
29#10622500C2212yes—
30#10622500C2212yes—
31#10622493C2211yescharacteristic
32#10622391—21no—
33#10622385—21no—
34C11×#366C2212yescomplemented
35C11×#357C2212yescomplemented
36C11×C22⋊C16C2211yescharacteristic
37C22⋊(C11⋊C16)C2211yescharacteristic
38(C2×D11)⋊C16C2212yes—
39#10622141C2212yescomplemented
40#10622130C2212yescomplemented
41#10622130C2212yescomplemented
42#10622128C2212yescomplemented
43C2×#4341—21no—
44C22×C4×D11D411yescharacteristic
45C22×Dic22—21no—
46C2×C11×D8C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×#121—21no—
49C2×C11×C4⋊C4—21no—
50#66991—21no—
51#66990—41no—
52D4×Dic11—41no—
53C2×#4324—21no—
54C2×(C2×D11)⋊C4—41no—
55C2×C4⋊Dic11—41no—
56#66977—21no—
57C22×C11⋊C8D411yescharacteristic
58#66965—42no—
59C2×Dic44—21no—
60C2×Dic44—42no—
61C2×Dic44C2311yescharacteristic
62C2×Dic44C2312yes—
63C2×C8×D11—42no—
64C2×C8×D11D411yescharacteristic
65C2×C8×D11D411yescharacteristic
66C2×C8×D11C2311yescharacteristic
67C2×C8×D11C2311yescharacteristic
68#66950—22no—
69#66950—22no—
70#66950—21no—
71#66950—41no—
72#66950—41no—
73#66945—21no—
74#66936—41no—
75(C22⋊D11)⋊C4—41no—
76C2×C11×C16C2312yes—
77C11×#107—21no—
78C11×#107C2311yescharacteristic
79C11×#107C2312yes—
80C11×#102—21no—
81#66896—21no—
82#66891—42no—
83#66882C2311yescharacteristic
84#66880—21no—
85C2×C11⋊C16C2312yes—
86#66874—22no—
87#66874—22no—
88#66874—21no—
89#66872—21no—
90Dic88—42no—
91C16×D11—42no—
92#33756—111nomaximal, Sylow
93C23×D11D811yescharacteristic
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C2×C22⋊D11—41no—
99C2×C22⋊D11—41no—
100C22×Dic11—41no—
101C22×Dic11—41no—
102C22×Dic11D811yescharacteristic
103#4341—42no—
104#4341—42no—
105C2×C4×D11—41no—
106C2×C4×D11—41no—
107C2×C4×D11D811yescharacteristic
108C2×C4×D11D811yescharacteristic
109C2×C4×D11C2×D411yescharacteristic
110C2×C4×D11C2×D411yescharacteristic
111C2×Dic22—22no—
112C2×Dic22—21no—
113C2×Dic22—42no—
114C2×Dic22—42no—
115C2×Dic22—41no—
116C11×D8—22no—
117C2×C8×C11—22no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2411yescharacteristic
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—41no—
123C11×C22⋊C4—41no—
124C22⋊Dic11—41no—
125C22⋊Dic11—41no—
126#4324—42no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—42no—
130(C2×D11)⋊C4—42no—
131C4⋊Dic11—21no—
132C4⋊Dic11—41no—
133C4⋊Dic11—42no—
134C4⋊Dic11—42no—
135Dic11⋊C4—41no—
136C4×Dic11—41no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8C2×D411yescharacteristic
139C2×C11⋊C8C2×D411yescharacteristic
140Dic44—22no—
141Dic44—22no—
142Dic44—22no—
143Dic44—42no—
144C8×D11—22no—
145C8×D11—22no—
146C8×D11—41no—
147C8×D11—41no—
148C11×C16—22no—
149C11⋊C16—22no—
150#3050—111no—
151C2×#467—111no—
152#2237—112no—
153#2235—111no—
154#2232D1111yescharacteristic, complemented
155#2217—112no—
156#2216—112no—
157#2189—112no—
158#2188—111no—
159#2185—111no—
160C2×C22⋊C16—111no—
161C23×C11—41no—
162C23×C11C2×D811yescharacteristic
163C22×D11—22no—
164C22×D11—22no—
165C22×D11—41no—
166C22×D11C2×D811yescharacteristic
167C22×D11C2×D811yescharacteristic
168D4×C11—41no—
169D4×C11—41no—
170D4×C11—82no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—82no—
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C22⋊D11—82no—
179C22⋊D11—82no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184C2×Dic11—82no—
185C2×Dic11—82no—
186C2×Dic11C2×D811yescharacteristic
187C2×Dic11C2×D811yescharacteristic
188C4×D11—21no—
189C4×D11—21no—
190C4×D11—21no—
191C4×D11—21no—
192C4×D11—41no—
193C4×D11—41no—
194Dic22—42no—
195Dic22—41no—
196Dic22—42no—
197Dic22—41no—
198Dic22—82no—
199C8×C11—21no—
200C8×C11H(5,𝔽2)12yes—
201C11⋊C8—21no—
202C11⋊C8—21no—
203C2×#135—111no—
204C22×Q16—111no—
205C23×C8—111no—
206#525—221no—
207C2×C22⋊Q8—221no—
208C2×Q32—112no—
209C2×SD32—112no—
210C22×C16—112no—
211#467—111no—
212#467—112no—
213#467—111no—
214#467—112no—
215#467—221no—
216#467—221no—
217#466—111no—
218#466C2×D1111yescharacteristic
219#465—221no—
220#465—221no—
221#427—111no—
222C2×#107C2×D1111yescharacteristic
223#416—221no—
224C2×#103—221no—
225#367—112no—
226#366C2×D1112yescomplemented
227#358—112no—
228#358—112no—
229#358—112no—
230#357C2×D1112yescomplemented
231C22⋊C16—111no—
232C22⋊C16—112no—
233C22⋊C16C2×D1111yescharacteristic
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11#50812yes—
240C22×C11C22×D811yescharacteristic
241C2×D11—21no—
242C2×D11—21no—
243C2×D11—21no—
244C2×D11—21no—
245C2×D11—21no—
246C2×D11—44no—
247C2×D11#51012yes—
248C4×C11—21no—
249C4×C11—82no—
250C4×C11—81no—
251C4×C11#53411yescharacteristic
252C4×C11#57511yescharacteristic
253Dic11—21no—
254Dic11—21no—
255Dic11—81no—
256Dic11—82no—
257Dic11—81no—
258C2×#41—221no—
259C22×Q8—221no—
260C23×C4—111no—
261#135—442no—
262C2×Q16—112no—
263C2×Q16—111no—
264C2×Q16—221no—
265C2×Q16—442no—
266C2×SD16—221no—
267C2×D8C22×D1111yescharacteristic
268C22×C8—111no—
269C22×C8—111no—
270C22×C8—111no—
271C22×C8—111no—
272C22×C8—111no—
273C22×C8—442no—
274C22×C8C22×D1111yescharacteristic
275#123—441no—
276C22⋊Q8—222no—
277C22⋊Q8—222no—
278C22⋊Q8—221no—
279C22⋊Q8—221no—
280C22⋊Q8—441no—
281C22⋊Q8—441no—
282#121—21no—
283#121—221no—
284#120—441no—
285C4×D4—441no—
286C4×D4—441no—
287#117—221no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—441no—
290C2×C22⋊C4—441no—
291Q32—442no—
292SD32—442no—
293C2×C16—112no—
294C2×C16—442no—
295C2×C16C22×D1112yes—
296#107—21no—
297#107—111no—
298#107C22×D1112yes—
299#107C22×D1111yescharacteristic
300#106—221no—
301#103—222no—
302#103—222no—
303#103—221no—
304#103—221no—
305#102—21no—
306#102—221no—
307C2×C11—22no—
308C2×C11—161no—
309C2×C11#318611yescharacteristic
310C2×C11C2×#50811yescharacteristic
311C2×C11C2×#51011yescharacteristic
312D11—22no—
313D11—41no—
314C24—111no—
315#41—442no—
316#41—442no—
317C2×Q8—221no—
318C2×Q8—222no—
319C2×Q8—442no—
320C2×Q8—442no—
321C2×Q8—441no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—441no—
325C2×D4—441no—
326C22×C4—41no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—111no—
332C22×C4—441no—
333C22×C4—441no—
334C22×C4—441no—
335C22×C4—441no—
336C22×C4D4×D1111yescharacteristic
337Q16—222no—
338Q16—222no—
339Q16—222no—
340Q16—442no—
341SD16—442no—
342D8—22no—
343C2×C8—22no—
344C2×C8—111no—
345C2×C8—111no—
346C2×C8—222no—
347C2×C8—222no—
348C2×C8—441no—
349C2×C8—441no—
350C2×C8—441no—
351C2×C8D4×D1111yescharacteristic
352C2×C8C23×D1111yescharacteristic
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4—41no—
356C4⋊C4—221no—
357C4⋊C4—442no—
358C4⋊C4—442no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C22⋊C4—41no—
362C22⋊C4—442no—
363C22⋊C4—442no—
364C22⋊C4—441no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C42—441no—
369C16—22no—
370C16—222no—
371C11#3375611yescharacteristic, complemented, Sylow
372C23—41no—
373C23—111no—
374C23—111no—
375C23—222no—
376C23—222no—
377C23—441no—
378C23D8×D1111yescharacteristic
379Q8—442no—
380Q8—441no—
381Q8—441no—
382Q8—442no—
383Q8—882no—
384D4—41no—
385D4—41no—
386D4—82no—
387D4—882no—
388D4—882no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—82no—
394C2×C4—111no—
395C2×C4—111no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—442no—
406C2×C4—882no—
407C2×C4—882no—
408C2×C4D8×D1111yescharacteristic
409C2×C4C2×D4×D1111yescharacteristic
410C8—21no—
411C8—221no—
412C8—221no—
413C8#6704212yes—
414C22—21no—
415C22—21no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—112no—
420C22—221no—
421C22—221no—
422C22—221no—
423C22—221no—
424C22—221no—
425C22—444no—
426C22#1062252512yes—
427C22C2×D8×D1111yescharacteristic
428C4—21no—
429C4—82no—
430C4—81no—
431C4—221no—
432C4—221no—
433C4—881no—
434C4—882no—
435C4—881no—
436C4#1062318411yescharacteristic
437C4#1062330811yescharacteristic
438C2—22no—
439C2—161no—
440C2—222no—
441C2—441no—
442C2#1307936611yescharacteristic
443C2C2×#1062252511yescharacteristic
444C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2232C2
socleC22×C11C22×D8
prime radical#13078195C2
hypercenter#2232D11
hypocenterC11#33756
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
2. C2×#10622500C2semidirect
3. #13070826C2semidirect
4. #13070813C2semidirect
5. #13070711C2semidirect
6. #13070708C2semidirect
7. #13070557C2semidirect
8. #13070552C2semidirect
9. #13070532C2semidirect
10. D11×C22⋊C16C2semidirect
11. C11×#2232C2semidirect
20. C2×#66891C22semidirect
24. C2×Dic88C22semidirect
34. C11×#366C22semidirect
35. C11×#357C22semidirect
39. #10622141C22semidirect
40. #10622130C22semidirect
41. #10622130C22semidirect
42. #10622128C22semidirect
154. #2232D11semidirect
226. #366C2×D11semidirect
230. #357C2×D11semidirect
371. C11#33756semidirect

Maximal subgroups

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

subgroupindex
#130781952
C2×#106225002
#130708262
#130708132
#130707112
#130707082
#130705572
#130705522
#130705322
D11×C22⋊C162
C11×#22322
#3375611